Download Measurement of cardiac output during exercise in patients with

.
Measurement of cardiac output
during exercise in patients
with chronic heart failure
Validation study
MSc Thesis
B.T.H.M. Sleutjes
BMTE07.21, August 2007
Committee:
Prof.dr.ir. F.N. van de Vosse
Prof.dr.ir. P.F.F. Wijn
Ir. C.H.L. Peters
Drs. H.M.C. Kemps
Dr. G. Schep
Máxima Medical Centre, Veldhoven
Clinical Physics / Sports Medicine
Eindhoven University of Technology
Faculty of Biomedical Engineering
1
Contents
Abstract
4
Samenvatting
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1 Introduction
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2 Clinical background
2.1 Chronic heart failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Clinical relevance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3 Physiological background
3.1 The heart . . . . . . . . .
3.2 The cardiac cycle . . . . .
3.3 The cardiovascular system
3.4 Cardiac output . . . . . .
3.4.1 Exercise . . . . . .
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4 Measurement of cardiac output
4.1 Fick method . . . . . . . . . . . . . . . . .
4.2 Indicator dilution methods . . . . . . . . .
4.2.1 Lithium dilution . . . . . . . . . .
4.3 Impedance cardiography . . . . . . . . . .
4.3.1 Theory of impedance cardiography
4.3.2 Theory of Physioflow . . . . . . . .
4.3.3 Discussion . . . . . . . . . . . . . .
4.4 Pulse Contour Analysis . . . . . . . . . .
4.4.1 The three element model . . . . .
4.4.2 Theory of PulseCO system . . . .
4.4.3 Discussion . . . . . . . . . . . . . .
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5 Data processing
5.1 Characteristics of equipment
5.2 Outlier detection . . . . . . .
5.3 Re-sampling the data . . . . .
5.4 Synchronizing the data . . . .
5.5 Averaging the data . . . . . .
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6 Materials and Methods
6.1 Methodology . . . . . . . . . . .
6.1.1 Exercise protocol . . . . .
6.1.2 The continuous and direct
6.1.3 Lithium dilution . . . . .
6.1.4 Impedance cardiography .
6.1.5 Pulse contour analysis . .
6.1.6 Statistical analysis . . . .
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Fick method
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7 The reliability of continuous measurement of mixed venous oxygen saturation during exercise in patients with chronic heart failure1
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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8 Results
8.1 Measurements at rest . . . . . . . . . . . . .
8.2 Measurements at steady state exercise test .
8.2.1 Cardiac output . . . . . . . . . . . .
8.2.2 Tracking changes of stroke volume .
8.3 Measurements during maximal exercise . . .
8.3.1 Cardiac output . . . . . . . . . . . .
8.3.2 Tracking changes of stroke volume .
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9 Discussion
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10 Conclusion
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11 Recommendations
11.1 Clinical applications . . . . . . . . . .
11.2 Technical applications . . . . . . . . .
11.3 Modeling of the human arterial system
11.4 Discussion . . . . . . . . . . . . . . . .
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Acknowledgement
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12 Appendix
12.1 Modeling of the human arterial system .
12.2 Theory of arterial system . . . . . . . .
12.3 End segments . . . . . . . . . . . . . . .
12.4 The parameters used as input of model .
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Bibliography
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Concept for publication to European Journal of Applied Physiology
3
Abstract
In patients with chronic heart failure (CHF), the measurement of cardiac output can be useful for clinical purposes like measuring effects of therapeutic interventions and assessment
of prognosis. The direct Fick (dFick) method is considered as the gold standard for the
measurement of cardiac output, but is highly invasive and therefore difficult to use routinely
in clinical settings. Recently two new devices have been developed, which are less-invasive
and have the potential to be used clinically for the measurement of cardiac output. These
two methods are Physioflow, which is based on impedance cardiography and is completely
non-invasive and PulseCO, which is based on pulse contour analysis and makes use of a
peripheral arterial catheter. Because both devices have not been validated during exercise in
patients with CHF the goal of this study is to compare the performance of these two new
devices with the Fick method at rest and during exercise. Further, this study evaluated the
reliability of a fiberoptic pulmonary artery catheter for measuring SvO2 during exercise for
continuous Fick (cFick) cardiac output.
Ten patients with stable CHF (NYHA class II-III) performed steady state exercise tests at
workload corresponding with 30% and 80% of the ventilatory threshold and consequently a
symptom limited incremental exercise test. In this study it was shown that the fiberoptic
pulmonary catheter was feasible and reliable of measuring SvO2 during exercise in patients
with CHF. Because of this result cFick cardiac output was used as reference method during
exercise for the validation of cardiac output by Physioflow and PulseCO. In rest dFick cardiac
output was used as reference method.
At rest, lithium dilution cardiac output (LiDCO) was used as calibration for PulseCO and
showed clinical acceptable agreement with dFick cardiac output. Physioflow showed an overestimation of cardiac output with dFick, due to the incorrect calibration. In steady state
exercise and the incremental exercise PulseCO showed clinical acceptable agreement with
cFick cardiac output and Physioflow showed an overestimation of cardiac output. The results
were also analyzed by investigating the possibility of both methods in changes of stroke volume. PulseCO showed clinical acceptable results compared with cFick in tracking changes.
Physioflow showed wider limits of agreement compared with PulseCO and cFick. The larger
limits of agreement in both methods for cardiac output and tracking changes of stroke volume
in maximal exercise could be due to the decreased accuracy of cFick cardiac output. At the
end a model is described, which could be used for further development in the estimation of
cardiac output.
4
Samenvatting
Bij patiënten met chronisch hartfalen kan het meten van het hartminuutvolume bruikbaar
zijn voor klinische doeleinden, zoals het meten van therapeutische interventies en vaststellen
van prognoses. De directe Fick (dFick) methode wordt gezien als de betrouwbaarste methode
voor het meten van hartminuutvolume, maar het is erg invasief en daarom erg moeilijk om
routinematig te gebruiken in klinische omgeving. Onlangs zijn er twee methodes ontwikkeld,
die minder invasief zijn en de mogelijkheid hebben om klinisch te worden gebruikt voor het
meten van hartminuutvolume. Deze twee methodes zijn Physioflow, gebaseerd op impedantie
cardiografie en is volledig non-invasief en PulseCO, gebaseerd op puls contour analyse en
maakt gebruik van een perifere arteria radialis catheter. Omdat beide methodes nog niet
gevalideerd zijn tijdens inspanning bij patiënten met chronisch hartfalen is het doel van deze
studie om het hartminuutvolume van deze methodes te vergelijken met de Fick methode
tijdens rust en inspanning. Verder wordt in deze studie ook de betrouwbaarheid van een
fiberoptische arteria pulmonalis catheter onderzocht voor het meten van gemengd veneuze
zuurstof saturatie tijdens inspanning voor het meten van continue Fick (cFick) hartminuutvolume.
Tien patiënten met chronisch hartfalen (NYHA klasse II-III) hebben een submaximale inspanningstest uitgevoerd op een vermogen dat overeenkomt met 30% en 80% van de ventilatoire drempel gevolgd door een maximale inspanningstest. In deze studie is aangetoond
dat de fiberoptische arteria pulmonalis catheter betrouwbaar is voor het meten van gemengd
veneuze zuurstof saturatie. Vanwege dit resultaat wordt cFick hartminuutvolume gebruikt
tijdens inspanning voor het valideren van het hartminuutvolume van Physioflow en PulseCO.
In rust wordt dFick als validatie methode gebruikt.
In rust is lithium dilutie hartminuutvolume (LiDCO) gebruikt voor kalibratie van PulseCO en
toonde klinisch acceptabele overeenkomst met dFick hartminuutvolume. Physioflow toonde
een overschatting van het hartminuutvolume vergeleken met dFick, vanwege de incorrecte
kalibratie. In de submaximale en maximale inspanningstest toonde PulseCO klinisch
acceptabele overeenkomst met cFick hartminuutvolume en Physioflow een overschatting van
het hartminuutvolume. De resultaten werden ook geanalyseerd in het volgen van veranderingen van slagvolume. PulseCO toonde klinisch acceptabele resultaten voor veranderingen
van slagvolume vergeleken met cFick. Physioflow toonde minder nauwkeurige resultaten
vergeleken met PulseCO en cFick. De grotere onnauwkeurigheid van beide methodes voor
hartminuutvolume en veranderingen van slagvolume tijdens de maximale inspanning kunnen veroorzaakt zijn door de mindere nauwkeurigheid van cFick hartminuutvolume. Op het
einde van de studie is een model beschreven, die gebruikt kan worden voor het schatten van
hartminuutvolume en wat gebruikt kan worden voor verdere ontwikkelingen.
5
Chapter 1
Introduction
In the Netherlands the number of patients with chronic heart failure (CHF) is about 200.000,
which is 1%-2% of the population. [1] Chronic heart failure can be defined as a decreased
function of the heart as a pump and can have several pathophysiological causes. In normal
conditions a balance consist between the amount of blood that is pumped by the heart and
the need for oxygen, nutrients or excess carbon dioxide and other catabolites in tissues.
This balance enables tissues to regulate their supply of blood flow by vasoconstriction or
vasodilatation of the vascular bed. The principal symptoms of chronic heart failure are
fatigue, shortness of breathing during light exercise and fluid retention and often result in
decreased exercise capacity. [2]
Once the diagnosis of chronic heart has been established, patients in stable condition
should be encouraged to carry out some physical activity and leisure time activities that do
not induce symptoms, to prevent muscle de-conditioning. [3] In exercise tests in patients with
chronic heart failure exercise tolerance is decreased, due to limitations in muscle metabolism
and a reduction of cardiac output response to exercise. [3, 4, 5] Therefore the measurement of
cardiac output during exercise can give more information about the relative contribution of
the central and peripheral factors to the decreased exercise performance in the CHF patients.
In addition, the measurement of cardiac output during exercise can be useful for clinical
purposes like measuring effects of therapeutic interventions. The most reliable method for
the measurement of cardiac output is the direct Fick method and directly derived from this
method, the indicator dilution methods. An important drawback of the direct Fick method is
the need for inserting a pulmonary artery catheter, which is complicated and invasive. Several
other less-invasive or even non-invasive techniques are available, like indicator dilution methods, re-breathing methods, radio nuclide methods and Doppler echocardiography. However,
all of these techniques have their specific limitations during exercise.
- Indicator dilution based methods using a peripheral arterial catheter give reliable values
in rest, but during exercise indicator dilution curves are distorted due to peripheral
vasoconstriction in parts of the body that are not involved during exercise. [6]
- The reliability of Doppler echocardiography is difficult to perform and is limited by the
need of a highly skilled operator. [7]
- Methods based on measurements with lung perfusion can give errors in resting conditions
and in patients with pulmonary abnormalities. Also, patients with decreased exercise
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tolerance are not always able to perform a precise breathing manoeuvre, required for
the assessment of cardiac output. [8]
- Radio nuclide methods can only be used in steady-state conditions and therefore can
not be used in a maximal exercise test. [7] Also the subjects are exposured to radiation
and because the exercise is performed in sitting or upright position this method is not
suitable for accurate measurement of cardiac output.
Recently two new devices have been developed, which have the potential to be used clinically
for the measurement of cardiac output. These two methods are Physioflow, which is based
on impedance cardiography and is completely non-invasive and PulseCO, which is based on
pulse contour analysis. Impedance cardiography uses the principle that changes in electrical impedance reflect changes in blood volume. Pulse contour analysis uses the shape of
the arterial blood pressure waveform for the calculation of the cardiac output. The performance of these two methods has already been tested frequently and gives promising results.
[9, 10, 11, 12, 13, 14, 15, 16] However, none of the mentioned devices have been validated
during exercise in patients with CHF. The goal of this study is to compare the performance
of these two new devices with the Fick method during submaximal and maximal exercise.
The Fick method is considered as the golden standard.
Before the validation of both methods are discussed in this report, first the clinical background (chapter 2), the physiological background (chapter 3) and the technical background
of those techniques used for the measurement of cardiac output are discussed (chapter 4). In
the second part the data processing steps, and the materials and methods of this study are
explained (chapter 5, 6), followed by the results of the validation study. (chapter 7 and 8)
The last part contains the discussion and conclusion (chapter 9 and 10) and recommendations
for further research divided into a clinical part and technical part. (chapter 11)
7
Chapter 2
Clinical background
To gain more insight in the background of this study and its clinical relevance some information is required about the clinical management of chronic heart failure. The clinical
management consists of diagnosis and treatment of patients with chronic heart failure. In the
next section a short overview will be given of the treatment of chronic heart failure in clinical
environment.
2.1
Chronic heart failure
Chronic heart failure is a complex syndrome that results from any structural or functional
cardiac disorder that result in a decreased ability of the heart to function as a pump. As a
result of decreased pumping of the heart, tissue can not sufficiently be supplied with oxygen
and nutrients anymore when demand increases during, for example, physical activity. The
major symptoms that originate from a reduced pump function are dyspnoea, exercise intolerance and fluid retention. The body attempts to increase the blood flow in the vascular bed
by retaining fluid. This fluid retention can cause lung oedeem or peripheral oedeem.
The aetiology of chronic heart failure can originate from many factors. A few examples are
myocardial infarction, ischemic cardiomyopathy and hypertrophy of the heart muscle, valve
insufficiency, valve stenosis and arrhythmia. All these factors, eventually results in the inability of the heart to function as a pump at an appropriate level for the bodies requirements.
To classify the severity of heart failure the New York Heart Association (NYHA) classification is in widespread use. In this classification heart failure is divided in four classes:
- Class I: No limitations, during ordinary activity there are no symptoms
- Class II: Slight limitations of physical activity, Comfortable with rest or with mild
exertion.
- Class III: Marked limitations of physical activity, Comfortable only at rest and symptoms occur even in mild activity.
- Class IV: Unable to carry out any physical activity without discomfort, even at rest
symptoms occur patients who should be at complete rest, confined to bed or chair.
Therapeutic approaches to chronic heart failure are multiple and can grossly be divided
in three groups: non-pharmacological therapy, pharmacological therapy and the last group
consists of mechanical devices and surgery. Therapeutic interventions commonly consist of a
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combination of above therapeutic approaches. First, in the non-pharmacological management
general advice will be given where patients should pay attention to in daily life, like weight
control, dietary measures, non-smoking etc. For patients with chronic heart failure in stable
condition, another important non-pharmacological management is the encouragement of performing physical activity. By performing exercise training programmes patients can increase
their physical capacity by about 15% − 25%. Secondly, in pharmacological therapy medicines
and drug agents are prescribed. Because the aetiology of heart failure is very diverse, several
kinds of medicines exist. Examples are Angiotensin-converting enzyme (ACE) inhibitors.
These are primarily used for the treatment of hypertension. Usually ACE inhibitors are used
in combination with diuretics to reduce fluid retentions Another example are β-blockers, also
used for treating hypertension, or after myocardial infarction or cardiac arrhythmia. Third,
mechanical devices or surgical intervention as a therapy for patients with chronic heart failure is an option. Dependent on the underlying aetiology revascularization can be performed
when there is a ischaemic origin. In patients with severe left ventricular dysfunction mitral
valve surgery can lead to symptomatic improvement. When a patient is in the end-stage of
treatment of heart failure and no alternative forms of treatment exist heart transplantation
can be considered. An example of the use of devices in chronic heart failure patients, which
have discoordinated ventricular contraction due to intraventricular conduction disturbances,
is resynchronization therapy using bi-ventricular pacing. Another mechanical device, which
is used, is the implantable cardioverter defibrillator (ICD). An ICD is effective in treating
recurrence of arrhythmia either by antitachycardia pacing or cardioversion defibrillation.
2.2
Clinical relevance
This project focuses on patients with stable chronic heart failure. These patients are often
included in heart revalidation programs. In these programs they are encouraged to carry out
physical activity to prevent declining of the condition of the muscles. The exercise intolerance
in patients with chronic heart failure has its origin from the reduced pump function of the
heart and limitation of the metabolism of the peripheral skeletal muscles. Measuring the
course of the cardiac output during exercise can contribute to a better understanding of the
contribution of the central and peripheral factors. This information can result in a better
patient specific treatment of chronic heart failure. Also the measurement of cardiac output
has been proven useful for defining the quality of life and to indicate the need for heart transplantation. In addition, measurement of cardiac output is expected to give more information
for the indication for other therapeutic interventions, like valve surgery, biventricular pacing
or physical training. Furthermore, cardiac output can be a valuable tool for the effects of
these therapeutic interventions. From this it may be clear that research on cardiac output
can provide a lot of additional information, that can be very useful in clinical practice.
9
Chapter 3
Physiological background
In this chapter the basic principles of the underlying physiology of this study will be explained. First, the physiology of the heart will be discussed, followed by the cardiovascular
system and the mechanism that control the cardiovascular system. In addition regulation of
cardiac output, which is part of the cardiovascular regulation will be discussed.
3.1
The heart
The heart is enclosed in a double-walled sac, which is called the pericardium. The pericardium
protects the heart, anchors it to the surrounding structure an prevents overfilling of the heart
with blood. The heart wall consists of three layers. The outer wall is called the epicardium,
the middle layer the myocardium and the inner layer, the endocardium. The pericardium is
often infiltrated with fat, especially in older people. The myocardium is the thickest of the
three layers and is the layer that actually contracts. The endocardium consist of a white sheet
of endothelium resting on a connective tissue layer and covers the connective tissue skeleton
of the valves.
The heart functions as a pump and can be divided in four chambers, the left atrium, the left
ventricle, right atrium and right ventricle, see figure 3.1. The left atrium and the left ventricle
are separated by the mitral valve. From the left ventricle the blood flows into the circulatory
system through the aortic valve into the aorta. The blood enters the right atrium through
three veins. The superior vena cava returns blood from above the diaphragm, second the
inferior vena cava returns blood from below the diaphragm and the last returning blood flow
is from the coronary veins of the heart. The right atrium and right ventricle are separated
by the tricuspid valve. The blood enters the pulmonary artery through the pulmonary valve.
Then the blood flows to the right lung and left lung through the right pulmonary artery and
left pulmonary artery.
10
Figure 3.1: The anatomy of the heart. Modified from [17].
3.2
The cardiac cycle
The cardiac cycle can be divided in four phases: the diastolic phase, the isovolumic contraction
phase, the ejection phase and the isovolumic relaxation phase, see figure 3.2. In the first part
of the diastolic phase when the mitral valve is opened the ventricle is filled with blood. In the
last part of the diastolic phase an action potential is generated by the sinus node, located in
the right atrium and causes an additional filling of the left atrium. The action potential will
travel rapidly through both atria and through the A-V bundle and the conducting system and
causes the initiation of the contraction of the ventricles. The ventricular pressure will increase
and causes the mitral valve closure and marks the beginning of the isovolumic contraction
phase. In this phase the ventricular volume remains constant, but the ventricular pressure
increases. When the ventricular pressure rises above the pressure in the aorta, the aortic valve
will open and the ejection phase begins. During the ejection phase, the aortic and ventricular
pressure increase to its maximum and then decreases, at the point where the ventricular
pressure is less then the aortic pressure, a slightly aortic back flow occurs which results in
the closure of the aortic valve. This marks the beginning of the isovolumic relaxation phase.
In this phase the ventricular volume remains constant and the pressure of the ventricle will
decrease. As soon as the ventricular pressure drops below the atrial pressure, the mitral valve
will open and the cardiac cycle begins again.
11
Figure 3.2: The cardiac cycle with the four different phases, diastolic d, isovolumic contraction
ic, ejection e, and isovolumic relaxation ir and the time course of left ventricular pressure, plv ,
aortic pressure pao , left atrial pressure pla and left ventricular volume Vlv . Typical volumes of
left ventricle at two time points are the end-diastolic volume EDV and end-systolic volume
ESV . Modified from [18]
3.3
The cardiovascular system
The function of the circulation, which consist of the heart and the blood vessels, is to supply
the tissues in the body with oxygen and nutrients and to transport waste products away. The
regulation of the circulation to satisfy the oxygen demands through the body is controlled
by the autonomic nervous system. The autonomic nerves system can be divided in the
sympathetic nervous system and the parasympathetic nervous system. The sympathetic
nervous system is activated in stressful, emotional situations or by physical activity and the
parasympathetic nervous system is more active in rest, and for example stimulates the organs
for digesting food. When sympathetic stimulation excites the blood flow to a particular
organ, often parasympathetic stimulation inhibits it. That is, the two systems occasionally
act reciprocally to each other. However, the blood flow to most organs is mainly controlled
by one of the two systems. For the control of blood flow, the effect of the two systems on
arterial pressure, on the blood vessels, and on the heart are most significant. Blood pressure
is regulated by means of the baroreceptor reflex. The baroreceptor reflex is the most powerful
tool in the control of systemic arterial pressure. Baroreceptors are lying in the walls of the
carotid sinus and the aortic arch. As soon as the blood pressure falls and the baroreceptors are
less stimulated, the sympathetic nervous system is activated and the parasympathetic activity
is decreased. As a consequence, heart rate and cardiac contractility increase and the small
arteries and large arterioles are constricted. This way the arterial blood pressure is regulated
towards steady state again. Most blood vessels are constricted by sympathetic stimulation.
Sympathetic constriction of the small arteries and the large arterioles increases the resistance
12
and therefore reduces the blood flow through the vessels. Sympathetic stimulation of the
veins decreases the volume of these vessels and therefore translocates the blood into the heart.
Parasympathetic stimulation has little or no effect on blood vessels. It merely dilates vessels
in certain restricted areas, such as in the blush area of the face. The heart is controlled
by both systems. Sympathetic stimulation increases the heart rate and enhances cardiac
contractility. Parasympathetic stimulation causes mainly the opposite effects, it decreases the
heart rate and also slightly decreases contractility. In short, sympathetic activity increases
the effectiveness of the heart as a pump whereas parasympathetic stimulation decreases the
pumping capability of the heart.
3.4
Cardiac output
Cardiac output is the amount of blood that is pumped by the heart into the aorta each
minute. It equals the product of heart rate and stroke volume. With a heart rate at rest of 70
beats/min and a stroke volume of 70ml the heart pumps about 4.9L/min and this amount
can increase to about four to seven times during heavy exercise.
Stroke volume (SV ) represents the difference between volume of blood in the ventricle at the
end of the diastolic phase, the end-diastolic volume (EDV ) and the volume of blood that
remains in the ventricle after its contraction, the end-systolic volume (ESV ):
SV [ml] = EDV [ml] − ESV [ml]
(3.1)
The pumping ability of the heart depends on contractility, preload, afterload and heart rate.
The most important factors that affect the SV by causing changes in EDV or ESV are the
contractility, the force of contraction of the cardiac muscle cells, preload, which is the degree
of stretch of the cardiac muscle cells before contraction and the afterload, the pressure that
must be overcome for the ventricles to eject blood from the heart. Afterload influences stroke
volume by affecting the velocity of contraction. The intact heart can increase its contractility
with the help of the Frank-Starling mechanism. The Frank-Starling mechanism means the
intrinsic ability of the heart to adapt to changing loads of inflowing blood. The heart pumps
all the blood that comes to it into the aorta without allowing excessive damming of blood in
the veins. If the amount of blood returning to the heart is increased (larger EDV ), causing the
preload to increase, the cardiac muscle is stretched more and, in turn, contracts with increased
force. The increased force of contraction is probably caused by the fact that the contractile
proteins become more sensitive for calcium when they are stretched. Also the contractility can
be increased by extrinsic control by the sympathetic nervous system activity. The contractility
increase caused by the activation of the sympathetic nervous system is independent of the
stretch of the cardiac muscle fiber and the EDV . The sympathetic stimulation is responsible
for the increases in heart rate. In contrast the parasympathetic nervous system reduces the
heart rate. The factors that are involved in the regulation of the cardiac output are shown in
figure 3.3.
3.4.1
Exercise
During exercise three major effects occur that are essential for the circulatory system, to
supply the markedly increased blood flow required by the the muscles. These three effect are
13
Figure 3.3: Schematic view of the factors that play an important role in the regulation of the
cardiac output.
the activation of the sympathetic nervous system, the increased arterial blood pressure and
the increase in cardiac output. When starting with exercise, the activation of the sympathetic
nervous system results in: First, the stimulation to increase heart rate, cardiac contraction
and simultaneously attenuation of parasympathetic activity. Secondly, the contraction of
the arterioles of the peripheral circulation, except the arterioles to the active muscles, which
are vasodilated by local vasodilator effects in the muscle itself. Only the blood supply to the
coronary and cerebral system remains unchanged, because the heart and brain are as essential
as the skeletal muscles. And at last, the muscle walls of the veins and other large veins are
contracted , increasing the mean systolic filling pressure, resulting in the increase of venous
return. In addition, the increased sympathetic activity results in the increase of the arterial
blood pressure, caused by the three circulatory effects mentioned above. The sympathetic
stimulation of the heart almost entirely causes the increase in cardiac output by the increase
in the heart rate and the cardiac contractility. All the physiological effect occurring during
exercise causes the cardiac output to increase in proportion to the degree of exercise.
14
Chapter 4
Measurement of cardiac output
The direct Fick method and the indicator dilution method are considered to be the gold
standard for the measurement of cardiac output. [8] However both methods are invasive and
difficult to perform in clinical settings routinely and therefore other less-invasive methods
has been developed to overcome the problems occurring in the gold standard methods. In
this chapter, first, the gold standard methods will be discussed, followed by the new cardiac
output methods, that will be validated in this study.
4.1
Fick method
The cardiac output can be calculated by using the Fick principle. The Fick principle is based
on the uptake of oxygen by blood as it flows through the lungs. It is assumed that all oxygen
molecules in the pulmonary vein has its origin from the blood in the pulmonary artery or
from the oxygen transported from the lung to the blood. The oxygen that enters the blood is
reflected by the difference in oxygen content between the pulmonary vein and the pulmonary
artery, assuming that no oxygen is consumed by the tissues between the pulmonary artery
and vein. Because the entire output of the right heart passes through the lungs, assuming
that there are no shunts across the pulmonary system, the blood flow through the lungs is
equivalent to cardiac output. This can be written as [19]:
FO2 = CO CaO2 − CO CvO2 so CO =
FO2
[CaO2 − CvO2 ]
(4.1)
with FO2 the oxygen flow from lung to blood in mlO2 /min, CO the cardiac output in L/min
and CvO2 and CaO2 the oxygen contents of vein and artery in mlO2 /L. In figure 4.1 an
example of the Fick method is shown.
Because it is impossible to measure the rate at which oxygen is taken up by the capillaries,
the rate of oxygen uptake must be measured at the mouth. Then FO2 is often expressed as
V O2 . The error introduced by measuring oxygen at the mouth is unimportant if the period of
measurement is much longer than the time of a single breath. [21] The V O2 can be measured
by making use of spirometry. The values of CvO2 and CaO2 can be determined indirectly by
taking blood samples at the appropriate location. Because the concentrations fluctuate due
to the pulsations caused by respiration and circulation the values has to be averaged for a
sufficient time. The arterial oxygen content of blood can be sampled at any convenient location in the large arteries, since oxygen transfer to the tissues only take place in the capillaries.
15
Figure 4.1: The Fick method to determine the cardiac output. If the oxygen consumption is
200ml/min and the difference in oxygen content between the right side of the heart and the
left side of the heart is 40ml/L, then the amount of blood flowing through the lungs has to be
5L/min. Modified from [20].
In contrast, the venous oxygen content in blood can very significant between measuring sites,
because it depends on how much oxygen the organs have extracted. Only where the different
oxygen contents from the veins merge, like the right atrium, right ventricle or pulmonary
artery, the so called mixed venous oxygen content, can be measured. The oxygen in the
blood is primarily bounded to hemoglobin as oxyhemoglobin. The O2 carrying capacity of
mL O2
hemoglobin Hb is 1.34 gram
Hb .
The oxygen content of the blood can then be calculated by:
CaO2 = Hb 1.34 SaO2 10−2 + 0.031PaO2
(4.2)
CvO2 = Hb 1.34 SvO2 10−2 + 0.031PvO2
(4.3)
with Hb the concentration of hemoglobin in blood in gram/L. SaO2 and SvO2 are the oxygen saturation of blood in %. The oxygen saturation at the arterial site, SaO2 can also be
measured continuously with a pulse oximeter. The mixed venous oxygen saturation, SvO2 ,
can be measured continuously with a pulmonary artery catheter. PaO2 and PvO2 represents
the partial pressure of oxygen at the arterial and venous site in mmHg and 0.031 is the
mLO2
solubility coefficient of oxygen in blood in LmmHg
. For the continuously measurement of the
cardiac output the partial oxygen pressures are often ignored, because it has only a small
contribution.
16
4.2
Indicator dilution methods
The indicator dilution method is very similar to the Fick method, but instead of the measurement of oxygen, the concentration of an indicator is measured. In indicator dilution methods
a bolus of an indicator is brought into the blood stream and the concentration of the indicator
is measured downstream. There are many indicators like chemicals, inert gases, radioactive
isotopes, dyes and heat. [19] The indicator dilution method is based on the following theory.
If the concentration of a small known bolus that is uniformly dispersed in an unknown volume
V is determined, and the volume of the injected indicator is known, then the unknown volume
can be determined too [22]:
dV (t)
φ(t) =
(4.4)
dt
where φ(t) and V (t) are the instantaneous flow and volume of the carrier. Then the next
expression counts too:
dm
c(t) =
(4.5)
dV
with m and c(t) the mass of the tracer and its concentration at time t. Then the following
equation can be derived:
1 dm
dV (t)
=
(4.6)
φ(t) =
dt
c(t) dt
Because only the averaged flow determines how much indicator is transported, and not the
fluctuations of the flow the previous equation can be rewritten into [19, 22]:
Z ∞
Z ∞
m
(4.7)
m=
φ(t)c(t)dt = CO
c(t)dt − − > CO = R ∞
0
0
0 c(t)dt
The instantaneous flow φ(t) can be expressed as the cardiac output CO and put out of
the integral. Before the concentration decreases to zero, some of the indicator has already
circulated and passes the measurement site for the second time, this is also called recirculation,
see figure 4.2 Because of this phenomena an extrapolation is necessary for the calculation of
Figure 4.2: Examples of two indicator dilution curves with recirculation at the end and the
area filled with color is the area under the extrapolated curve. Modified from [20]
the area of the curve without circulation.
17
The basic assumption of indicator dilution techniques for the injection of a bolus are that the
blood flow is constant during the measurement, there is no loss of the indicator, the mixing
of the indicator is uniform and the rapid injection can be modeled as an impulse.
4.2.1
Lithium dilution
An example of an dye as indicator dilution is Lithium Chloride. Ones lithium is injected
it will be detected by a sensor, which consist of a lithium-selective electrode. The lithium
electrode is attached to the arterial line via a three-way tap, which, when is open, allows blood
flow through the sensor by a peristaltic pump. The electrode contains a membrane, which
is selective permeable to lithium. Because in the absence of lithium, the baseline voltage is
determined by the sodium concentration a correction is done for plasma sodium concentration.
The voltage across the membrane is related to the plasma lithium concentration by the Nernst
equation [22]:
RT ln(Cout )
E=
(4.8)
zF ln(Cin )
where Cout and Cin are the lithium concentration across the membrane, E is called the N ernst
potential in V olt, R is the ideal gas constant 8.31J/mol−1 Kelvin−1 , T the temperature in
Kelvin, F the constant of Faraday, 96.5104 C/mol and z the valence of the ion, in this case
1, Li+ . Equation 4.8 shows that the voltage has a logarithmical relation with the lithium
concentration. When the lithium indicator dilution curve has been measured, the area under
the extrapolated curve and the cardiac output is calculated by modifying equation 4.7 for
lithium dilution [23]:
CO =
60 LiCl
(area under curve) (1 − P CV )
(4.9)
with CO in L/min. The mass in equation 4.7 is replaced by the LiCl dosis in mmol.
The area under curve is the integral of the primary curve in mM s. P CV is the Packed Cell
Volume, which is estimated at Hb/34 with Hb in g/dL. [24]
18
4.3
Impedance cardiography
For the last 40 years impedance cardiography has been studied as a technique for the determination of several cardiac output. This method gained interest because it is non-invasive and
simple to perform. It was Kubicek et al [25] who first proposed to calculate the stroke volume
by the method, called thoracic electrical bioimpedance. The principle is shown in figure 4.3.
There are two pair of electrodes. The I-electrodes are current conducting electrodes and the
P-electrodes are potential measuring electrodes. The P-electrodes are placed at the base of
the neck and around the thorax at the level of the xiphoid point. The I-electrodes are placed
at least 3 cm above/below the P-electrodes. [26] The thoracic impedance is then, measured by
passing an alternating current in the frequency range of 20 − 100kHz longitudinal through the
thorax by the I-electrodes and the P-electrodes by measuring the potential difference caused
by the current. This potential difference divided by the current gives the thoracic impedance.
Figure 4.3: The place of the conducted current electrodes (I-electrodes) in the neck just
above the potential measuring electrodes (P-electrodes) and the I-electrodes just below the
P-electrodes at the level of the xiphoid. Modified from [27]
The impedance signal
The thoracic impedance consists of three components. The largest component, the baseline
impedance Z0 , is the electrical impedance of the total thoracic mass, which include the different tissues, fluid and air. The second component corresponds with the changes due to
respiration, Zr (t). The third component is related to the changes caused by the cardiac cycle,
Zc (t). This gives the next equation [27]:
Z(t) = Z0 + Zr (t)Zc (t)
(4.10)
The values of Z0 is about 25Ω for healthy men. The changes of the impedance signal induced
by respiration is about 1Ω. The third and smallest variation due to the cardiac cycle in the
impedance signal is approximately 0.1Ω to 0.2Ω. The contribution to the changes in the
thoracic impedance signal, especially the cardiac related changes Zc , has its origin for about
61% from the lungs, 23% from the large arteries and about 13% from the skeletal muscles.
[28] The amplitude caused by the respiratory component is much larger than the amplitude
of the cardiac component, but the frequency of the cardiac component is higher than at
19
the respiratory component. Therefore, in the first derivative of ∆Z, the thoracic impedance
change from the respiratory and cardiac component together, strongly reflects the signal of
the cardiac component.[29]
4.3.1
Theory of impedance cardiography
In a simplified model the thorax can be seen as a double cylinder consisting of two parts.
These two parts consist of tissue and blood, as shown in figure 4.4. The human thorax is
composed of mostly muscles, lung, fat, skin, bone and air, which all have a relatively high
resistivity. Blood has a very low resistivity. As electrical current, emitted by the I-electrodes,
chooses the path of the least resistance, it can be assumed that the majority of the current
flowing through the thorax will travel through the blood filled aorta and vena cava. So the
changes in the impedance that are observed in the thorax are related to the volume changes
in the large vessels. The thoracic impedance is then considered as a parallel connection of the
tissue impedance, Zt and blood impedance, Zb . To relate the blood volume changes to the
Figure 4.4: Simplified cylindrical model of the human thorax with the cross-section of the blood
compartment, Ab , the cross-section of the tissue compartment At and the cylindrical length L
impedance changes, the simplified model of figure 4.4 is used. The longitudinal impedance Z
of the thorax can be modeled by the parallel of the blood and tissue impedances Zb and Zt :
Z=
Zb Zt
Zb + Zt
(4.11)
To find the relation between longitudinal impedance change and the blood impedance changes
equation 4.11 must be differentiated with respect to Zb :
d
Zb Zt
Z
(
) = ( )2
dZb Zb + Zt
Zb
(4.12)
The impedance of biological tissue is often presented as a complex number, but blood impedance
is mainly resistive and therefore the phase angles of Zb is assumed to be unimportant and
can be neglected. The blood impedance depends upon the cross-sectional area (Ab ), and
20
resistivity of blood (ρb ), then the changes in Zb can be related to the changes in volume (Vb )
of the conductor by:
L
L2
Zb = ρb ( ) = ρb ( )
(4.13)
Ab
Vb
where Vb = Ab L is the blood volume, L the distance between the electrodes and with ρb
measured in Ω cm. The resistivity of blood is assumed to be constant. By making use of
the relationship between longitudinal impedance and blood impedance of equation 4.12 the
dependency of the change in blood volume, (d(Vb )) on changes in thoracic impedance can
then be expressed as:
L2
dVb = d(LAb ) = −ρb 2 dZ
(4.14)
Z
With Z the base impedance. The contraction of the ventricles produces small cyclic changes
and Kubicek et al. investigated these changes to asses the stroke volume, resulting in the
Kubicek equation. [25] In this equation it is assumed that the rate of cardiac ejection of
blood in the systole phase is constant. In addition, it is assumed that if no blood were to
flow away from the thorax during systole, the thorax impedance would continuously decrease
during systole at a rate equal to the maximum rate of decrease of dZ, dZ/dtmax . The stroke
volume, (SV ) is then given by [25]:
SV = c(
dZ
)max tLV E
dt
(4.15)
with ( dZ
dt )max the maximum value of the first derivative of the impedance waveform, tLV E
the left ventricular ejection time. The constant c, contains the base impedance Z, blood
resistivity ρb and the length L. The accuracy of the method is limited, because of several
factors. First, a cylindrical model is a significant simplification of the human thorax. Second,
the constancy of the blood resistivity can be questioned, because it is influenced by the shape
and orientation erythrocytes in the blood, which can have a significant variation. [26] In
addition, the base impedance Z can have large variations effecting the constant c. [28] After
Kubicek et al. some other investigators have added small changes to the constant c in equation
4.15. [30, 31]
4.3.2
Theory of Physioflow
Recently a new method based on the thoracic electrical bioimpedance for the calculation of
the SV, Physioflow, was introduced. In equation (4.15) the constant c is effected by the
basal thoracic impedance Z. Z depends upon multiple factors like the thorax morphology,
homogeneity of thorax perfusion, and fluid and gas content. The precise measurement of this
variable is therefore critical and can be altered by perspiration, subcutaneous adiposity, and
is also influenced by poor electrical contact.[10] Large and rapid exercise-induced variations
of this parameter make its estimation more difficult in this situation. It is shown that ρb can
not be assumed constant.[26] Therefore a new equation was introduced where the evaluation
of Z, ρb and thoracic height is not necessary anymore. [10] The cardiac output measured by
the Physio flow is based on:
SV = SVi BSA
(4.16)
with SV the stroke volume, SVi the stroke volume index [mL/m2 ], which is equal to SV
divided by Body Surface Area, BSA. BSA is the defined by the Haycock formula BSA =
21
0.02BM 0.54 H 0.40 , with BM the body mass in kg and H the height in cm. [10] SVi is given
by:
s
(dZ/dt)max T F ITcal
SVi = SV ical 3
(4.17)
(dZ/dt)max,cal T F IT
where (dZ/dt)max,cal and T F ITcal are the values obtained during the calibration. As shown
in this equation the changes of the value of SV is correlated with variation in dZ/dtmax , but
inversely correlated with variations in left ventricular ejection time. [32]
SV ical is calculated in the calibration phase by measuring several consecutive heart beats in
rest condition. The calculation of the calibrated SVi is described by:
SV ical = k[
(dZ/dt)max
]w(T F ITcal )
(Zmax − Zmin )
(4.18)
where k is a constant. In this calibration the largest impedance variation of ∆Z is taken into
account (Zmax −Zmin ) and the largest rate of variation of the impedance signal (dZ/dt)max or
called contractility index, CT I. The calculation of SV ical also depends on the left ventricular
ejection time tLV E . For the calculation of tLV E a slightly different parameter is chosen, called
the thoracic flow inversion time, T F IT in ms, see figure 4.5. The value of T F IT is weighted,
Figure 4.5: The ECG, ∆Z with the Zmax and Zmin and the dZ/dtmax with T F IT . Modified
from [9]
w(T F IT ), in the algorithm of Physioflow and in this specific algorithm also the pulse pressure
(P P ) and the heart rate fc is included. The P P is included because it has been demonstrated
that there is a linear relation between aortic compliance and the SV /P P ratio.[33] The SV ical
is used as reference for the calculation of the current SVi and the variation in SV is mainly
a result of the variation in dZ/dtmax and T F IT .[32]
22
4.3.3
Discussion
A major problem of the Physioflow algorithm is that no fundamental physical background
can be elucidated. Some disadvantages of the theory of bioimpedance cardiography have been
overcome, but it remains unclear, why above approach has been chosen. A calibration procedure is performed to measure absolute cardiac output values, because the aortic diameter
is specific for every patient. [34, 35] However, it remains unclear how absolute stroke volume
values can be obtained from equation 4.18. Despite the fact that the parameter dZ/dtmax
is related to rapid left ventricle ejection velocity, [36] the concept of using the constant k,
(Zmax − Zmin ) and w(T F ITcal ) for the conversion of impedance variation to stroke volume is
not known. In addition, the third root in equation 4.17 does not have a physical background,
but has been determined as producing the best agreement with reference invasive techniques
and V O2 /HR of a large extensive database with a variety of pathology statuses. Although
the Physioflow algorithm shows several drawbacks, in the study of Charloux et al. [10] and
Richard et al. [11] promising results were found compared with the direct Fick method. In
contrast, its accuracy during exercise was markedly lower in COPD patients. It was hypothesized that this may be due to specific characteristics of these patients, such as hyperinflation
and changes in lung volume. [9]
23
4.4
Pulse Contour Analysis
Pulse contour analysis is based on the principle that changes in blood flow correlate with
changes in arterial pressure. The concept of using the blood pressure waveform for the measurement of the blood flow changes was first proposed by Frank in 1899. The objective was
to derive cardiac output from the aortic pressure. His approach described the circulation in
terms of a Windkessel model. This model eventually resulted in the two-element Windkessel
model [37], see figure 4.6.
Figure 4.6: The two-element Windkessel model represented as an electrical circuit with i(t)
related to the blood flow q(t) and u(t) corresponding to the pressure p(t). R, the resistance
and C the conductor, related to the arterial compliance.
The following equation corresponds with this model:
dp(t)
p(t)
+C
(4.19)
q(t) =
R
dt
where q(t) is the blood flow, p(t) the pressure as a function of time. R, the peripheral
resistance and C the arterial compliance. The difficulty of measuring the stroke volume is
that the relation of the pressure change and the volume change of the aorta has a non-linear
behaviour and depends on its compliance. This prevents a simple approach to calculate stroke
volume by pulse contour. At low pressures the aortic complies more than at high pressures
resisting the overstretching of the aortic wall. The non-linear relation of pressure and volume
of the human aorta was investigated by Remington and Langewouters. [38, 39]
4.4.1
The three element model
An extension of the two element model was proposed by Wesseling using a three-element
model to measure cardiac output continuously. [35] The flow is computed from the response
of the three-element model of the arterial input impedance to arterial pressure, see figure
4.7. This model consists of three elements, which represent the three major properties of
the aorta and the arterial system. The first element is the aortic characteristic impedance
Z0 representing the dynamic property of the aorta that impedes pulsatile outflow from the
ventricle. The second component is the windkessel compliance Cw, representing the capacity
to store an amount of blood in the aorta and arterial system. The last element is the peripheral
resistance, which corresponds with the total peripheral resistance of the vascular bed together.
To calculate the cardiac output the parameters Cw , Z0 and Rp of the model must be known.
The aortic characteristic impedance Z0 can be estimated by:
r
ρ
Z0 =
(4.20)
AC 0
24
Figure 4.7: In this model p(t) is the arterial pressure waveform, q(t) the blood flow, Z0 the
aortic characteristic impedance, Cw the variable compliance of the arterial system, Rp the
variable resistance. Modified from [35].
0
where ρ is the density of blood, A the cross-sectional area of the aorta and C the derivative
of area with respect to pressure (P ) given by:
dA
dP
0
C =
(4.21)
where the windkessel compliance is assumed to be equal to the compliance of one unit length
of thoracic aorta times an aortic effective length l:
Cw = lC
0
(4.22)
where l is assumed to be 80cm for adults.[35] The last component of the three-element model,
Rp is defined as the ratio of the average pressure to average flow. Because this value changes
slowly compared to heart rate this value is computed every heart beat and used as input for
the next beat. The relation of the pressure and the cross-sectional area is given by [39]:
A(P ) = Amax [0.5 +
P − P0
1
arctan(
)]
π
P1
(4.23)
with Amax the maximal cross-sectional area at very high pressure. The values of P0 and P1
are defined as the position of the inflection point on the pressure axis at one-half of Amax (P0 )
0
and the inflection point of three-quarter of Amax , (P0 + P1 ). The compliance C can then be
found by inserting equation 4.23 into equation 4.21:
0
C (P ) =
1
Amax
πP1
0 2
+ ( P P−P
1 )
(4.24)
This relationship of the cross-sectional area and compliance with the blood pressure is illustrated in figure 4.8.
25
Relation of cross−sectional area and the blood pressure
5
A [cm2]
4
3
2
1
0
0
50
100
150
200
P [mmHg]
Relation of compliance of unit length with the blood pressure
C [cm2/mmHg]
0.06
0.04
0.02
0
0
50
100
P [mmHg]
150
200
Figure 4.8: The cross-sectional are and compliance of unit length related to blood pressure
from equation 4.23 and equation 4.24
4.4.2
Theory of PulseCO system
Recently a new method based on pulse contour analysis has been developed. In this section
the algorithm of the PulseCO system will be discussed. Absolute levels of cardiac output
cannot determined with certainty, however changes in cardiac output can be followed with
precision. [34] This is caused by the fact that, although the influence of age, gender, distending pressure, arteriosclerosis on the properties of the aorta has been investigated frequently,
the aortic diameter at maximal pressure can vary up to 40%. [39] Therefore it was proposed
already in 1904 to calibrate the pulse contour method by another method like the indicator
dilution. [34] Because of this the relative cardiac output of the PulseCO method is calibrated
by making use of Lithium Chloride as indicator dilution to get absolute values of the cardiac
output. This calibration is performed in rest. [40, 41, 42] This method is described in section
4.2.
The PulseCO algorithm operates in several steps. In the first step the pressure waveform
is converted into an arbitrary volume waveform. A volume changes results in an arterial
pressure change and this relation can be expressed as compliance. The relation of pressure
and volume used in this algorithm is determined from data of Remington. [38] The equation
used for this relation can be written as:
V (p) = Cal250[1 − e−kp ]
(4.25)
The value 250 corresponds with the saturation volume of the aorta of 250 ml and this value
is scaled during the calibration with lithium dilution by the constant Cal. The constant k is
derived from an analysis of cadaveric aortas and p the pressure in mmHg. In the second step
26
the DC component of the arbitrary volume waveform is removed and by autocorrelation of
this signal the heart beat is detected and for every heart beat the corresponding root mean
square (rms) value of the arbitrary volume waveform is calculated.
Vuncal (t) = Vuncal,mean + Vuncal,dyn (t)
s
Z
1 T
Vuncal,rms =
(Vuncal,dyn (t))2
T 0
(4.26)
Where Vuncal (t) is the arbitrary volume waveform, which consist of the DC component,
Vuncal,mean and the dynamic component Vuncal,dyn (t). The rms-value, Vuncal,rms , is calculated from the dynamic component over the heart beat of duration T in sec. The variable
Vuncal,rms is the uncalibrated stroke volume. In the last step the lithium dilution is used
to calculate the calibration factor Cal to scale the uncalibrated stroke volume and cardiac
output as shown in the next equation:
Vnocal,rms = SVnocal −→ COnocal = SVnocal HR
COli
Cal =
−→ SVcal = SVnocal Cal
COuncal
4.4.3
(4.27)
(4.28)
Discussion
In the PulseCO algorithm the pressure waveform is converted into an arbitrary volume waveform. Only two studies are known where human aortas have been used to investigate the
non-linear relationship of pressure changes and volume changes. [38, 39] In the PulseCO
algorithm the relationship of Remington is used. Only in the second step it is not clear in
the concept of the PulseCO algorithm why the RMS-value of the dynamic component of the
volume waveform is taken as uncalibrated stroke volume for calibration with lithium dilution.
In analogy with the electrical circuit the RMS-value of a periodic function represents the
effective value. However, if the volume waveform is chosen to calculate the stroke volume it
is theoretically seen more logical to calculate the mean volume of during a heart beat. Then
the uncalibrated mean volume can be used as uncalibrated stroke volume to scale to absolute
stroke volume with lithium dilution. Several studies were performed with the PulseCO system and have shown promising results. [13, 14] In these studies thermodilution and lithium
dilution were used as reference methods.
27
Chapter 5
Data processing
The goal of this study is to validate the cardiac output measurements during exercise in
patients with chronic heart failure. The data of the different devices have to be collected
and processed to validate the equipment. The data output of the respiratory gas exchange
system, the Vigilance monitor, the LidCO monitor, the Physioflow monitor are analyzed in
Matlab (Mathworks Inc., USA). Several steps have to be performed before analyzing the final
results. These steps include importing the data, outlier detection, synchronizing the data and
processing the data for statistical analysis.
5.1
Characteristics of equipment
An overview of the equipment used in this study is shown in figure 5.1a and figure 5.1b. The
patient is seated on the bicycle (1). In front the Physioflow system is shown (2a), which is
connected to a laptop computer for acquisition and analysis of the data(2b). The impedance
signal measured by the six electrodes on the thorax (2c) is connected with the Physioflow
system. The pulmonary catheter is connected with the Vigilance monitor (3), which is also
connected with the laptop computer. The radial catheter is connected with the hemodynamic
pressure monitor (4a) through the pressure transducer (4b). The pressure monitor is eventually connected with the LiDCO monitor. (4c) The ECG electrodes (5a) were connected with
ZAN computer for continuously monitoring ECG. (5b) The test subject breathed through a
mask with a mouthpiece, which was connected by a capillary line of small bore, and the gases
were analyzed for O2 and CO2 concentrations by optical spectrometer and infrared absorption
analyzers (ZAN680, USB, Germany), (5c) and was connected with the ZAN computer.
The sensing of the ventilation through the mask is based on pressure differences with variable
diaphragm (Pneumotachometry). Pneumotachometry is a method used to measure frequency,
tidal volume and peak air flow of breathing. A pressure exist across a semipermeable resistive
membrane. The high pressure on one side of the membrane forces the air to flow to the low
pressure zone on the other side of the membrane. This air flow is directly proportional to the
resistance of the membrane. Since the airflow cannot be directly, the pressure difference is
measured by pressure transducers on both sides of the membrane. Before every test the flow
sensor was calibrated with a 3L syringe. The gas analyzers were calibrated from both room
air and gas of known concentration. Together with a integrated 12 lead ECG the system was
connected to a computer which monitored online, several variables like, heart rate, the load
28
Figure 5.1: A schematic view of the equipement used in this study. (a,b)
performed on the bicycle, V O2 , V CO2 breath-by-breath.
SvO2 can be measured continuously in the pulmonary artery with the Swan-Ganz Oximetry
TD system (Edwards Lifesciences, Irvine, CA, USA). The measurement of SvO2 is based on
reflection spectrophotometry. This involves transmitting light in the catheter body to the
blood flowing past the catheter tip. The reflected light is then transmitted back through
the second fiberoptic filament to a photodetector located in the optical module. The absorption spectra of oxyhemoglobin and deoxyhemoglobin differ. At a wavelength of λ = 660
nm oxyhemoglobin has significantly lower absorption, than deoxyhemoglobin, while at λ =
940 nm its absorption is slightly higher. [19] These two wavelengths are both subject to
the same interferences, so when a ratio of readings is used to calculated SvO2 , the effects of
these interferences are cancelled. The most significant interference in SvO2 measurement is
usually caused by changes in hematocrit. To correct for this in the calibration of the SwanGanz Oximetry TD system the hematocrit value is entered. The calibration in this study is
performed in vivo, thereby also a blood sample is taken from the Swan-Ganz catheter and
analyzed to enter a start value of SvO2 which is used as calibration for the start ratio of the
readings. The Vigilance monitor is connected with a RS232 serial null modem cable with
a PC. The Vigilance system software on the PC (Multi Data logger, Edwards Lifesciences)
imports the data of the Vigilance monitor. During a test markers are set at several important
timepoints, in rest and during exercise for synchronizing the data of the equipment.
5.2
Outlier detection
After importing all data into Matlab, the first step that has to be performed is to detect
samples in the data, which are caused by noise and contains no underlying physiological
meaning. There can be several reasons for the noise in the data.
In the breath-by-breath data occasionally breath values can occur that are clearly artificial;
this can be caused by swallowing, coughing, premature ending of the breath or possibly wrong
detection of end of breath.
29
In the PulseCO system the radial blood pressure signal is used to calculate the cardiac output
beat-to-beat. Occasionally the beat detection can be wrong and can therefore give values
which have no physiological meaning. During the exercise test blood samples are taken from
catheter in the radial artery. When blood samples are taken no blood pressure signal can be
measured by the PulseCO system. In this period there is no beat-to-beat signal and will result
in an incorrect data output in this period too. The beat-to-beat calculations of the Physioflow
equipment also contains incorrect values. Because of all these possible occurrences of incorrect
data points a method has been developed to detect outliers in the data. The method has to
detect single outliers and also detect several outliers after each other.
In this study a median filtering is developed to remove the outliers in the data. It is assumed
that the generation of outliers can be described by an additive outlier model [43]:
yk = xk + ok
(5.1)
Where yk is the measured data, xk the ’real’ data with contains several contaminating outliers
ok . The value of ok is assumed to be zero except for a few data points in the data set where
ok is large compared to the nominal variation seen in the data. In the first step all values of
the variable of the data set is replaced by the median value. Then the new data set contains
the global trend of the variable and is not influenced by the outliers. From the global trend
a new threshold is chosen to determine the predicted value for the outliers. Based on the
breath-by-breath data set and the beat-to-beat data set of all variables the threshold for the
breath-by-breath data is chosen as 50% above and below the global trend line and for the
beat-to-beat data as 30% as the best option. In figure 5.2a an example is shown of the first
step. In the second step the data set is investigated at a smaller time scale to preserve the
local dynamics by taking a smaller window by choosing a smaller window size. The threshold
are similar as in the previous step. As shown in figure 5.2b at about beat number 450 the
threshold will follow the local variation of the cardiac output. An example of the heart rate
Heart rate data of PulseCO during submaximal exercise
Cardiac output of PulseCO during submaximal exercise
140
20
Raw data
Filtered data
18
120
16
Cardiac output [L/min]
Heart rate [bts/min]
100
80
60
40
14
12
10
8
6
4
20
2
0
0
100
200
300
400
500
Time [sec]
600
700
0
800
0
100
200
300
400
500
Time [sec]
600
700
800
Figure 5.2: (a) The heart rate of patient 1 with the raw data (blue), the global trend (purple)
and the lower limit and upper of 30%. (b) The cardiac output of patient 1 during submaximal
exercise. The upper limit and lower limit with the 30% threshold and with the raw data (blue)
and in the filtered data. (red)
data output before filtering and after filtering of the PulseCO system is shown in figure 5.3a
30
Heart rate data of PulseCO during submaximal exercise
Heart rate data of PulseCO during submaximal exercise
140
140
120
120
1.
1.
80
60
60
40
20
20
0
100
200
300
400
500
Time [sec]
600
700
0
800
1.
80
40
0
2.
2.
100
Heart rate [bts/min]
Heart rate [bts/min]
100
1.
2.
2.
0
100
200
300
400
500
Time [sec]
600
700
800
Figure 5.3: (a) The raw heart rata data. With arrow nr. 1 the blood pressure signal is
not available for the PulseCO system, because blood samples are taken. With arrow nr. 2
occasional outliers can be seen. (b) The filtered signal is shown of the method used in this
study. The outliers are removed and replaced by representative values.
and figure 5.3b. The outliers in the data are finally neglected in the averaging procedure to
statistically analyze the data.
5.3
Re-sampling the data
All the devices differ in their data output. Therefore the variables in the data output of all
devices are measured in different kind of time intervals. The data output contains beat-to-beat
intervals, breath-by-breath intervals and intervals of 2sec. Because the different equipment
have data containing non-equidistant sample intervals and equidistant sampling intervals, it is
important for synchronization of the data to have uniform sampling intervals. The next step
before validation is to re-sample all data to have all data sets with uniform sampling intervals.
In addition, for comparing the data output it is necessary to have the same sample intervals
for all data sets from all equipment. The data is re-sampled with the principle called boxcar
re-sampling. [44] A boxcar window is convoluted with the equidistant and non-equidistant
signals from the equipment and expressed as:
(
1
0
if |t|> fres
(5.2)
Wbc (t) =
fres
1
if |t|≤ fres
2
where Wbc (t) is the boxcar window at time t. fres is the re-sample frequency of the data.
The resulting filtered signal will be re-sampled at 4Hz, because 4Hz is the smallest re-sample
frequency above the highest heart rate that can occur. [44] The result of this operation is
shown in figure 5.4. In this figure the red window represents the boxcar window of height fres
2
2
and width fres
.
31
Heart rate with non−equidistant time intervals
Heart rate [bts/min]
100
95
90
85
80
0
0.5
1
1.5
2
2.5
3
3.5
Time [sec]
Heart rate with non− and even equidistant time intervals
0.5
1
1.5
4
Heart rate [bts/min]
100
95
90
85
80
0
2
2.5
Time [sec]
3
3.5
4
Figure 5.4: An example of heart rate signal with at the y-axis the heart rate and on the x-axis
the corresponding non-equidistant time intervals. In the graph below the re-sampled signal at
4Hz is shown in circles and in red the rectangular moving window. The red window represents
the boxcar window.
5.4
Synchronizing the data
The last step in the data processing procedure is to synchronize the data sets. The method
used to synchronize the data is based on least mean square error of the heart rate. The
data sets of PulseCO, Physioflow and the ZAN contains the heart rate in the data output.
The PulseCO measures the heart rate from the blood pressure signal, the Physioflow and
ZAN from the ECG signal. The data set of the Vigilance and Pulse Oximeter and also the
Physioflow and ZAN register the absolute time during the measurements. The heart rate data
from PulseCO and Physioflow are crosscorrelated to obtain the minimum least square error.
After this synchronization the Vigilance, Pulse Oximeter and ZAN are synchronized with
the absolute time column of the ZAN. Only the heart rate of PulseCO and Physioflow were
crosscorrelated, because the Physioflow does not determine the absolute time insufficiently
accurate. The data sets of the equipment do not have all the same length.
To obtain the least mean square error the shortest heart rate dataset is shifted over the other
heart rate dataset. For every shift the mean square error is calculated. For a data column x
with length n and data column y with length m and it states that n < m then:
Pn
P
2
M SE(j + 1) = n+m−1
[ n1
i=1 [x(i + j) − y(i + j + 1 − n)] ]
j=0
(5.3)
(if i + j − n + 1≤0 and i + j − n + 1≥m→y = 0)
where An example of the synchronization procedure is shown in figure 5.5. The heart rate of
Physioflow and PulseCO of the submaximal exercise and the maximal exercise is shown. A
time shift is seen from this figure. The outliers are already detected in both signals.
32
Heart rate of Physioflow and PulseCO
160
PulseCO
Physioflow
140
Heart rate [bts/min]
120
100
80
60
40
20
0
0
1000
2000
3000
Time [sec]
4000
5000
Figure 5.5: An example of heart rate signal of the Physioflow and PulseCO of patient 8.
5.5
Averaging the data
Before validation of the Physioflow and PulseCO with the Fick method, the data are averaged
in intervals of 30sec. During the test markers are set at the beginning of every exercise stage.
The data are then averaged from the beginning of exercise test. Because outliers are present
in the data, these values are not taken into account for averaging into intervals of 30sec. If
more then 25% in an interval is detected as outlier, the averaging value will be rejected. An
example of the averaging procedure is shown in figure 5.6.
Cardiac output of PulseCO
8
PulseCO
Averaging at 30%
Averaging at 80%
7
Cardiac output [L/min]
6
5
4
3
2
1
0
0
100
200
300
400
Time [sec]
500
600
700
Figure 5.6: An example of averaging in intervals of 30sec of PulseCO cardiac output at 30%
(square) and 80% (circle) of submaximal exercise test. The rejected averaging values are set
to zero.
33
Chapter 6
Materials and Methods
6.1
Methodology
Ten male patients with stable CHF were selected at the cardiology outdoor clinic of Máxima
Medical Center (Veldhoven, The Netherlands). Criteria for eligibility were stable systolic
heart failure attributed to either dilated cardiomyopathy or ischemic heart disease due to
myocardial infarction, New York Heart Association (NYHA) Class II or III, left ventricular
ejection fraction ≤ 40% (assessed by echocardiography or radionuclide ventriculography) and
sinus rhythm. Exclusion criteria were recent myocardial infarction (< 3 months prior), angina
pectoris at rest, peripheral vascular, neurological or orthopaedic disease limiting the ability to
exercise and chronic airway obstruction, defined as FEV1/FVC <60%. Subject characteristics
are listed in Table 6.1. The research protocol was approved by the local Research Ethics
Committee of Máxima Medical Center, and all patients provided written informed consent.
Variables
Age (yrs)
Height (cm)
Weight (kg)
BMI (kg/m2 )
LVEF (%)
Mean ± SD
63 ± 8
178 ± 8
89 ± 13
28 ± 3.5
33 ± 7
Medication
Diuretics
ACE inhibitors/ ARB
Beta-blockers
Digoxin
nr. of patients
9
10
9
0
NYHA functional class II/III
Aetiology ICM/DCM
6/4
9/1
Table 6.1: Characteristics of CHF patients. LVEF = left ventricular ejection fraction, NYHA
= New York Heart Association, ICM = ischaemic cardiomyopathy, DCM = dilated cardiomyopathy, ACE = angiotensin converting enzyme, ARB = angiotensin II receptor blocker.
34
6.1.1
Exercise protocol
Exercise tests were performed on a cycle ergometer (Lode, Corival, Groningen) in sitting
position. Test subjects were asked to cycle during the exercise test at a pedal rate of 70 per
min. The exercise protocol consisted of 3 periods, see figure 6.1. The first stage was a resting
period and has a duration of 15 min, this was performed in supine position. In this stage
the lithium dilution was performed with the direct Fick method in the 10th min. The next
stage was a sub-maximal exercise test. In the first 2min of this stage the test subject had
to cycle unloaded, followed by a minimum of 5 min at 30% and at 80% of the ventilatory
threshold of the test subject, determined in an earlier maximal exercise test. If steady-state
was not reached, 5 minutes was added to the exercise stage. Next, between the steady-state
test and the maximal exercise test consisted of a resting period 10 min. The last stage was
an incremental maximal exercise test. The test subject has to cycle again first unloaded for 2
min, then the maximal exercise test starts. In this procedure the test subjects had to cycle up
to maximal effort. The maximal load of the previous maximal exercise test was used as input
for this study. The aim is to have an exercise duration of about 8-12 min. [3] The computer
was programmed to reach the maximal load of the previous test after 10 min. For example,
if a test subject had a maximal load of 200 Watt, the load increases every 6 sec with 2 Watt.
During exercise, cardiac output was measured continuously by the Physioflow and PulseCO.
6.1.2
The continuous and direct Fick method
Before the resting period, a pulmonary artery catheter (CCOmbo, 7F, Edwards Lifesciences,
Irvine, USA) is inserted into the right antecubital vein and positioned in the right pulmonary
artery under fluoroscopic guidance. The pulmonary catheter was connected to a hemodynamical monitor (Vigilance II, Edwards, Irvine, USA) Every 2 sec, SvO2 is measured with a
sensor attached to the pulmonary catheter. Measurements of V O2 and V CO2 are obtained
breath by breath (Zan 680 USB, Germany). Volumes and gas analyzers were calibrated before each test.By making use of a pulse oximeter (Onyx 9500, Nonim Medical Inc) SaO2
is measured continuously attached on a finger. Blood samples were drawn from the distal
port of the pulmonary artery catheter and the radial artery and collected in a heparinized
syringe at rest (2 times with 5 minute-intervals), at the end of both constant load tests, before the symptom limited, incremental exercise test and in the last minute of this test. The
samples were immediately analyzed for hemoglobin, O2 saturation and hematocrit (ABL800
Flex, Radiometer America Inc., Copenhagen, Denmark) From the Hb, SaO2 , SvO2 obtained
from blood samples together with the V O2 , obtained from ZAN, direct Fick cardiac output
is determined, see figure 6.1. The continuous Fick cardiac output is determined continuously
in the steady-state period and maximal exercise period from the V O2 from ZAN, Hb from
the blood samples, SaO2 from the pulse oximeter and the SvO2 from the pulmonary artery
catheter. The different Hb-values from the blood samples during the test were taken into
account for the calculation of continuous Fick cardiac output. The continuous Fick method
are averaged over intervals of 30sec to determine the cardiac output during the 2 stages of the
protocol as described in section 4.1. These values are used for the validation of Physioflow
and PulseCO.
35
Figure 6.1: The protocol of the study consists of three major stages: The resting period,
steady-steady exercise and incremental exercise.
36
6.1.3
Lithium dilution
2 ml Lithium Chloride (150mM) is injected into the distal port of the pulmonary artery
catheter. Once lithium is injected, it will be detected by a sensor, that consist of a lithiumselective electrode. The lithium electrode is attached to the radial artery catheter with a
three-way tap. If the line is open, the blood flow is kept constant at a rate of 4ml/min
by a peristaltic pump. The voltage is measured by an isolated amplifier, digitized and then
analyzed on the monitor (LIDCO, London, UK), see figure 6.2. The cardiac output calculated
by the lithium dilution method is compared to the direct Fick method in the 5th and 10th
minute of the resting period.
Figure 6.2: Schematic view of lithium dilution method. Modified from [24]
6.1.4
Impedance cardiography
In the two exercise stages Physioflow (P F − 05, Manatec Biomedical) is used to measure
cardiac output. Physioflow emits a high-frequency (75 kHz) and low-amperage (3.8 mA)
alternating current via the electrodes. Six Ag/AgCl electrodes (Skintact, F50) are positioned
on the human thorax. 2 sets of 2 electrodes for the measurement of the impedance signal
and 2 electrodes for measuring the ECG signal, see figure 6.3 The outer electrodes (white,
black) are the transmitting electrodes and the inner electrodes (blue, green) are the receiving
electrodes. The calculation of the cardiac output is explained in section 4.3. Before the
exercise tests the subject must sit immobile on the cycling ergometer for the calibration
procedure of the Physioflow. The impedance device is connected with a standard notebook
where data collection takes place and where cardiac output is displayed beat-to-beat.
6.1.5
Pulse contour analysis
In addition to the pulmonary catheter, before the resting period, under local anaesthesia
a short radial artery catheter is inserted into the radial artery (20Ga, 8.5F, Edwards Life
Sciences, Irvine, CA, USA). The radial artery catheter is connected to a pressure monitor
(SC9000, Siemens Medical Systems Inc., Germany) using a disposable pressure transducer
(Safedraw, Becton Dickinson, USA). The cardiac output from PulseCO is calibrated with the
cardiac output obtained from lithium dilution in the resting period.
37
Figure 6.3: The positions of the Physioflow electrodes. The white and blue at the base of the
neck, the green and black at the xiphoid point and the red and orange for the ECG to register
the heart rate. Modified from [9].
6.1.6
Statistical analysis
The data will be analyzed by calculating correlation, linear regression and bias and limits
of agreement described by Bland and Altman. [45, 46] The linear regression models y = ax
and y = ax + b are used for investigating the best fit between the methods. In addition the
results are presented by the percentage bias and percentage limits of agreement proposed
by Critchley and Critchley. [47] In this method the proportionality of the magnitude of the
cardiac output is taken into account by calculating the percentage error. Because, for example,
an absolute difference of 1 L/min has remarkable more influence in the agreement between
methods at low cardiac output values compared to high cardiac output values. Also, stroke
volume measurements were validated using the approach, proposed by Linton and Linton.
[48]. Statistical significantly was assumed for p-values <0.05.
38
Chapter 7
The reliability of continuous
measurement of mixed venous
oxygen saturation during exercise in
patients with chronic heart failure1
Boudewijn T.H.M. Sleutjes1 ,Hareld M.C. Kemps2 ,Eric J.M. Thijssen3 ,Goof Schep2
Frans N. van de Vosse1 ,Chris H.L. Peters4 ,Pieter F.F. Wijn4,5
1:
2:
3:
4:
5:
Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands
Department of Sports Medicine, Máxima Medical Centre, Veldhoven, The Netherlands
Department of Cardiology, Máxima Medical Centre, Veldhoven, The Netherlands
Department of Clinical Physics, Máxima Medical Centre, Veldhoven, The Netherlands
Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
Abstract
Continuous assessment of mixed venous oxygen saturation (cSvO2 ) during exercise using a
fiberoptic pulmonary artery catheter can provide valuable information on the physiological
determinants of the exercise capacity in patients with chronic heart failure (CHF). However,
the accuracy of continuous SvO2 measurements is not well established during exercise. Therefore this study evaluates the reliability of a fiberoptic pulmonary artery catheter for measuring
SvO2 during exercise in CHF patients. Ten patients with stable CHF performed steady state
exercise tests at 30% and 80% of the maximum workload and consequently a symptom limited
incremental exercise test was performed. During the tests SvO2 was monitored continuously
using a fiberoptic pulmonary artery catheter (CCOmbo, Edwards Lifesciences, Irvine, CA,
USA) and mixed venous blood samples obtained at rest (n = 26), steady state (n = 17) and
peak exercise (n = 8) were analyzed. A significant correlation between oximetrically determined SvO2 and cSvO2 values (r = 0.97) was found. Bias between both methods was 0.6%
with limits of agreement of -8% and 9%. Limits of agreement for SvO2 values < 30% (n =
1
Concept for publication to European Journal of Applied Physiology
39
17) were wider than for SvO2 values > 30% (n = 34) (-10%, 12% and -7%, 8% respectively).
There was no significant difference between oximetrically determined SvO2 and cSvO2 values
in the lower range (1.2% ± 5%).
In conclusion, continuous measurement of SvO2 during exercise using a fiberoptic pulmonary
catheter is reliable in patients with CHF, with somewhat less accurate measurements below
30%.
Key words: Mixed venous oxygen saturation, pulmonary arterial catheter, exercise, chronic
heart failure
Introduction
Fiberoptic pulmonary artery catheters have enabled continuous measurement of mixed venous oxygen saturation (SvO2 ). [49] This measurement technique has been shown accurate
and useful in the management of critically ill patients [50, 51, 52], pediatric patients [53] and
patients undergoing cardiac surgery [54]. Continuous measurements of SvO2 might also be
useful in patients with left ventricular dysfunction for studying physiological mechanisms,
determining the exercise response and recovery from exercise [55, 56] and for the assessment
of continuous cardiac output during exercise using the continuous Fick method [57, 58]. However, the reliability of continuous SvO2 measurements during exercise in these patients is not
well established. Previous studies in patients with chronic obstructive pulmonary disease [59]
and patients with chronic heart failure (CHF) [60] have reported that fiberoptic pulmonary
artery catheters are reliable at SvO2 levels above 50%, but systematically underestimate
lower values. Since the publication of these studies, technological advances have improved
the accuracy of fiberoptic pulmonary artery catheters. Therefore in this study the reliability
of a fiberoptic pulmonary artery catheter for continuous measurement of SvO2 during steady
state and incremental exercise in patients with CHF is evaluated.
Methods
Subjects
Ten male patients with stable CHF were selected at the cardiology outdoor clinic of Máxima
Medical Center (Veldhoven, The Netherlands). Criteria for eligibility were stable systolic
heart failure attributed to either dilated cardiomyopathy or ischemic heart disease due to
myocardial infarction, New York Heart Association (NYHA) Class II or III, left ventricular
ejection fraction < 40% (assessed by echocardiography or radionuclide ventriculography) and
sinus rhythm. Exclusion criteria were recent myocardial infarction (< 3 months prior), angina
pectoris at rest, peripheral vascular, neurological or orthopaedic disease limiting the ability
to exercise and chronic airway obstruction, defined as FEV1/FVC <60%. Subject characteristics are listed in Table 7. The research protocol was approved by the local Research
Ethics Committee of the Máxima Medical Center, and all patients provided written informed
consent.
40
Table 7.1: Characteristics of included patients with CHF (n=10).
Variables
Mean ± SD
Age (yrs)
63 ± 8
Height (cm)
178 ± 8
Weight (kg)
89 ± 13
BMI (kg/m2 )
28 ± 3.5
LVEF (%)
33 ± 7
Medication
Diuretics
ACE inhibitors/ ARB
Beta-blockers
Digoxin
nr. of patients
9
10
9
0
NYHA functional class II/III
Aetiology ICM/DCM
6/4
9/1
Exercise testing
Upon entering the study, all patients performed a symptom limited, incremental exercise
test in an upright seated position on an electromagnetically braked cycle ergometer (Corival,
Lode, Groningen, The Netherlands), using an individualized ramp protocol with a total test
duration of 8-12 minutes. [3] Measurements of VE and respired fractions of O2 and CO2
were obtained breath by breath (Zan 680 USB, Germany). Volumes and gas analyzers were
calibrated before each test. During the tests all patients were instructed to maintain a pedaling frequency of 70 min−1 . A 12-lead electrocardiogram was recorded continuously. The
test was ended when the patient was not able to maintain the required pedaling frequency.
Peak- O2 was defined as the average O2 of the last 30 seconds of the test. The ventilatory threshold was determined by two independent observers using the V-slope method as
described by Beaver et al. [61] On a separate day patients underwent exercise testing with
SvO2 measurements. After arrival in the Cardiac Catheterization Room, a 7.5 F Swan-Ganz
catheter (CCOmbo, Edwards Lifesciences, Irvine, CA, USA) was inserted into the right antecubital vein and positioned in the right pulmonary artery under fluoroscopic guidance. The
pulmonary catheter was connected to a hemodynamic monitor (Vigilance II, Edwards, Irvine,
USA). After a resting period of 20 minutes, an in-vivo calibration of the fiberoptic catheter
was performed using hematocrit and oxygen saturation values obtained from a pulmonary
artery blood sample analyzed by an in-vitro oximeter (ABL800 Flex, Radiometer America
Inc., Copenhagen, Denmark). After the patient had been seated on the ergometer for at
least 5 minutes, exercise testing started with unloaded cycling for 2 minutes, followed by a
minimum of 5 minutes at 30% and thereafter 5 minutes at 80% of the previously determined
ventilatory threshold. If the patient did not reach a steady state after 5 minutes, the test
was continued for another 5 minutes. After a resting period of at least 15 minutes a symptom limited, incremental exercise test was performed. Blood samples were drawn from the
distal port of the pulmonary artery catheter and collected in a heparinized syringe at rest (2
times with 5 minute-intervals), at the end of both constant load tests, before the symptom
41
limited, incremental exercise test and in the last minute of this test. The samples were immediately analyzed for hemoglobin O2 saturation and hematocrit (ABL800 Flex, Radiometer
America Inc., Copenhagen, Denmark) and compared afterwards to the average of continuously measured SvO2 (cSvO2 ) values of 15 sec before and 15 sec after blood sample collection.
Statistical analysis
After acquisition, all data were analyzed using a statistically. Differences between continuous variables were evaluated by the paired Student’s t test. Linear regression was used to
calculate correlations between variables. Agreement between SvO2 and cSvO2 was assessed
by limits of agreement (mean difference ± 1.96 x SD) [46]. Probability values < 0.05 were
considered significant.
Results
All subjects completed the exercise tests. In the first test, the maximum workload was 133 ±
51 Watt, peak- O2 was 17.7 ± 5 mL.min-1.kg-1 and O2 at the ventilatory threshold was 14.7
± 5 mL.min−1 .kg−1 ). In total, 59 blood samples were taken from the pulmonary catheter.
Of these samples 8 were excluded because of blood clot formation in 4 cases and an unstable
cSvO2 signal in 4 cases (in one patient), leaving 51 samples for further analysis (26 at rest,
17 at steady state exercise and 8 at maximal exercise). A comparison between oximetrically
determined SvO2 and cSvO2 values is shown in 7.1. The linear correlation coefficient between
the two methods was r = 0.97 (p < 0.001, figure 7.1 (a)). The bias between both methods was
0.6% with limits of agreement of -8% and 9%, figure 7.1 (b). Visual inspection of the BlandAltman plot reveals that the relative variability of the difference between both measurement
methods increases with SvO2 values < 30% (n = 17). The limits of agreement for these
values in the lower range was wider than for SvO2 values > 30% (n = 34) (-10%, 12% and -7,
8% respectively). There was no significant difference between oximetrically determined SvO2
and cSvO2 in the range below 30% (1.2 ± 5.4%, P = ns).
Discussion
In contrast to other studies using a different fiberoptic catheter [59, 60], there was no systemic
underestimation of SvO2 by the fiberoptic catheter in the lower range. We did, however, observe a larger relative variation in the difference with oximetrically determined SvO2 values
in the range below 30%, indicating lower accuracy at lower values.
A significant increase of the hematocrit at maximal exercise (41% ± 4% at rest vs 45% ± 5%
at maximal exercise, P < 0.05) was found and may theoretically result in an underestimation
of SvO2 during exercise, because the fiberoptic catheter was not recalibrated during exercise.
However, no systemic underestimation of SvO2 by the fiberoptic catheter in the lower range
was found.
Although exercise induced changes in the pressure waveform indicating catheter tip migration
were not observed, the effect of body movements on catheter tip position could affect the accuracy of continuous SvO2 measurement during exercise. In addition, SvO2 signal intensity
42
20
70
15
60
10
SvO2−cSvO2 [%]
80
cSvO2 [%]
50
40
30
5
0
−5
20
−10
10
−15
0
0
10
20
30
40
SvO2 [%]
50
60
70
−20
80
0
10
20
30
40
50
(SvO2+cSvO2)/2 [%]
60
70
80
Figure 7.1: Comparison of continuously measured SvO2 (cSvO2 ) and oximetrically determined SvO2 (SvO2 ) (n=51).(a) Correlation plot between cSvO2 and SvO2 . (b) Bland-Altman
plot showing the difference between cSvO2 and SvO2 vs their mean. The solid line represents
the mean difference between the two tests, the dashed lines indicate the 95% confidence intervals of the difference.
was insufficient in only one patient.
Finally, the apparent lower accuracy of the fiberoptic catheter in the lower range could be
the consequence of the fact that measurements at maximal exercise were performed in a nonsteady state situation. Since cSvO2 and oximetrically determined SvO2 cannot be obtained
exactly simultaneously due to signal instability of the fiberoptic catheter during blood sampling, we may have underestimated the reliability of cSvO2 measurements during maximal
exercise.
Conclusion
This study showed that continuous measurement of mixed venous oxygen saturation is feasible
and reliable during exercise in patients with CHF. Although values < 30% seem somewhat
less accurate, there is no systemic underestimation in this lower range.
43
Chapter 8
Results
In this chapter the results of the study will be presented. In the first section the results of
the measurements at rest will be discussed. In the second section the validation performed at
submaximal exercise will be given and in the final section the results obtained during maximal
exercise.
8.1
Measurements at rest
The resting measurements include the rest periods before the submaximal exercise test and
before the maximal exercise test. First, the results of the direct Fick and Physioflow will
be discussed. Second, the PulseCO method is calibrated with lithium dilution. Therefore
lithium dilution (LidCO) measurements are compared with the direct Fick measurements in
rest. Table 8.1 shows the physical characteristics of the patients involved in this study. In
Parameters (N=10)
Weight (kg)
BMI (kg/m2 )
V O2 peak (ml/minkg)
30% VT (W att)
80% VT (W att)
Max load (W att)
Diagnosis
Mean ± SD
89 ± 13
28 ± 3.5
18 ± 6
27 ± 9
73 ± 23
108 ± 46
Ischemic
cardiomyopathy (9)
Dilating
cardiomyopathy (1)
Range
72 - 114
23 - 34
13 - 32
20 - 36
53 - 130
75 - 220
-
Table 8.1: Physical characteristics of CHF patients.
total 23 correct measurements were performed at rest. The direct Fick cardiac output ranged
from 2.8 to 5.0 L/min, the Physioflow cardiac output range was 3.6 to 9.3 L/min and the
LiDCO cardiac output ranged from 2.8 to 4.7 L/min. In patient 1 and patient 2 the PulseCO
system was not calibrated with lithium dilution. Due to the formation of blood clots and
the incorrect administration of lithium in total 17 measurements of direct Fick and lithium
44
dilution were compared. The Physioflow signal is not reliable in patient 2 and 3, because
heart rate was not correctly detected, resulting in a comparison of 21 measurements for direct
Fick and Physioflow. The average cardiac output for direct Fick, Physioflow and lithium
dilution is shown in table 8.2. To compare the cardiac output values the Bland-Altman plot
Method
COdF ick (N=23)
COphys (N=22)
COli (N=17)
Mean
3.8 ±
6.2 ±
3.8 ±
± SD (L/min)
0.6
1.7
0.5
Table 8.2: Mean cardiac output values for the three methods at rest.
for the direct Fick method and the Physioflow method is given in figure 8.1. The bias of
Bland−Altman plot of direct Fick and Physioflow in rest
Percentage difference in cardiac output [%]
120
100
80
60
40
20
0
−20
−40
−60
−80
−100
−120
0
1
2
3
4
5
Mean cardiac output [L/min]
6
7
8
Figure 8.1: Bland-Altman plot of direct Fick and Physioflow. The solid black line indicates
the percentage bias and the percentage limits of agreement are plotted with the dashed black
line.
direct Fick and Physioflow was 2.47 L/min and the limits of agreement were -0.78 L/min to
5.72 L/min. The percentage difference of continuous Fick and Physioflow is shown in figure
8.1. The percentage bias between the methods is 46% and the limits of agreement were -10%
to 102%.
The Bland-Altman plot of the cardiac output values at rest for the direct Fick method and
lithium dilution method is shown in figure 8.2. The bias between direct Fick and LiDCO
was -0.06 L/min and the limits of agreement were -1.14 L/min to 1.02 L/min, expressed
in percentage difference of the direct Fick and LiDCO the bias was -2% and the limits of
agreement were -29% to 26%. A summary of the results in rest is shown in table 8.3. There
is no significant difference between the cardiac output by the direct Fick method and the
PulseCO method as is shown in table 8.3, in contrary to the direct Fick method and the
Physioflow method where a significant difference was found.
45
Bland−Altman plot of direct Fick and lithium dilution in rest
Percentage difference in cardiac output [%]
120
100
80
60
40
20
0
−20
−40
−60
−80
−100
−120
0
1
2
3
4
5
Mean cardiac output [L/min]
6
7
8
Figure 8.2: Bland-Altman plot of continuous Fick and lithium dilution. The solid black line
indicates the percentage bias and the percentage limits of agreement are plotted with the dashed
black line.
Comparison
COphys − COdF ick (N=21)
COli − COdF ick (N=17)
Mean difference
± Limits of agreement (L/min)
2.47 ± 3.25
-0.06 ± 1.08
95% confidence interval
of mean (L/min), (p)
-1.72 - 3.23, (<0.001)
-0.34 - 0.23, (0.68)
Table 8.3: The reference method compared with Physioflow and lithium dilution.
8.2
Measurements at steady state exercise test
The results of the submaximal exercise test is divided in 2 parts. In the first part the validation of cardiac output of the continuous Fick versus Physioflow and continuous Fick versus
PulseCO is discussed. In the last part the data will be analyzed by investigating the ability
of the methods of tracking changes of stroke volume.
8.2.1
Cardiac output
In chapter 7 it was explained that the continuous Fick cardiac output is used for the validation
of the Physioflow method and PulseCO method. To illustrate the changes in cardiac output
during submaximal exercise test figure 8.3 shows the results of the submaximal exercise test
for patient 8. In figure 8.3 the errorbars correspond with standard deviations of the intervals.
The steady-state cardiac output values of the three methods were obtained in the last two
minutes. The cardiac output values are averaged over 30sec to determine 4 values at each
submaximal exercise stage for every patient. This results in 8 values in each patient. Due to
the disregarding of outliers the number of values used for comparison is less than 8 and will
differ between patients. Outliers are determined with the method described in chapter 5. In
the PulseCO method most of the outliers appeared at the moment of blood sample collection.
46
Course of cardiac output during submaximal exercise
25
3.
cFick
PulseCO
Physioflow
Cardiac output [L/min]
20
2.
1.
15
10
5
0
0
200
400
600
Time [sec]
800
1000
Figure 8.3: Cardiac output of all three methods. The errorbars expresses the standard deviation in the corresponding interval. Arrow 1: Start exercise, arrow 2: start submaximal at
80%, arrow 3: Stop exercise.
The cardiac output values during steady state of cFick ranged from 4.5 L/min to 12.9 L/min.
For Physioflow the cardiac output values varied between 5.3 L/min and 20.0 L/min and
PulseCO ranged from 4.3 L/min to 14.2 L/min. Steady-state is determined by visual inspection. The cardiac output values at 30% and 80% of steady state exercise are shown in table
8.4. In figure 8.4b the Bland-Altman plot is shown of the Physioflow cardiac output during
Method
COcF ick
COphys
COpuls
Mean ± SD (L/min)
30%
80%
6.3 ± 1.3 (N=36)
9.1 ± 1.7 (N=36)
10.6 ± 2.6 (N=30) 14.1 ± 4.3 (N=31)
6.4 ± 1.4 (N=22)
9.1 ± 2.5 (N=26)
Table 8.4: Mean cardiac output values for the three methods at steady state exercise.
submaximal exercise test for the percentage differences between cFick cardiac output and
Physioflow cardiac output. Because of outliers in cFick and Physioflow was not reliable in
patient 2 and 3, the number of patients included here are 8, resulting in 57 observations. The
bias and limits of agreement were 4.92 L/min and -0.57 L/min to 10.40 L/min, respectively.
For the percentage difference the bias and limits of agreement were 48% and -1% to 97%,
respectively. In the submaximal exercise test the absolute bias and limits of agreement were
larger compared to the rest values. The percentage difference were comparable with rest. The
relation between continuous Fick and Physioflow is shown in figure 8.4a. The linear model
y = ax is used to describe the relation between Physioflow and continuous Fick. The best fit
was y = 1.65x and the correlation coefficient was 0.70 (P<0.001).
In figure 8.5b the Bland-Altman plot of continuous Fick cardiac output and PulseCO cardiac
47
cFick and Physioflow cardiac output during submaximal exercise
22
Physioflow cardiac output [L/min]
20
Percentage difference in cardiac output [%]
30%
80%
Linear fit
18
16
14
12
10
8
6
4
2
0
Bland−Altman plot of cFick and Physioflow during submaximal exercise
120
30%
100
80%
80
60
40
20
0
−20
−40
−60
−80
−100
0
5
10
15
cFick cardiac output [L/min]
−120
20
0
5
10
15
Mean cardiac output [L/min]
20
Figure 8.4: (a)The relation of the cardiac output of Physioflow versus continuous Fick. (b)
Bland-Altman plot of Physioflow versus continuous Fick during submaximal exercise test.
(N=57) The solid black line indicates the percentage bias and the dashed black line the percentage limits of agreement.
output is shown. In this comparison 48 observations were included. In patient 1 and 2 no
lithium dilution was performed and 16 outliers were detected in the data of the other patients, caused by taking blood samples. The absolute bias was -0.02 L/min and the limits of
agreement were -2.22 L/min to 2.17 L/min. The percentage difference gave a bias of -1% and
limits of agreement of -28% to 26%. The relation of PulseCO and continuous Fick cardiac
cFick and PulseCO cardiac output during submaximal exercise
Bland−Altman plot of cFick and PulseCO during submaximal exercise
22
120
20
Percentage difference in cardiac output [%]
30%
80%
Linear fit
PulseCO cardiac output [L/min]
18
16
14
12
10
8
6
4
2
0
30%
80%
100
80
60
40
20
0
−20
−40
−60
−80
−100
0
5
10
15
cFick cardiac output [L/min]
−120
20
0
5
10
15
Mean cardiac output [L/min]
20
Figure 8.5: (a) The relation of the cardiac output of PulseCO versus continuous Fick.
(b) Bland-Altman plot of PulseCO versus continuous Fick during submaximal exercise test.
(N=48) The solid black line indicates the percentage bias and the dashed black line the percentage limits of agreement.
output is shown in figure 8.5a. The best fit was y = 1.00x and the correlation coefficient was
0.89 (P<0.001).
The results of the submaximal exercise test are summarized in table 8.5 and 8.6.
48
regression
Cardiac output
Physioflow versus cFick (N=57)
PulseCO versus cFick (N=48)
y
y
y
y
=
=
=
=
1.65x
1.35x+2.34
1.00x
1.05x-0.4
r, (p)
0.70,
0.72,
0.89,
0.89,
95% confidence interval
of slope , intercept
(<0.001)
(<0.001)
(<0.001)
(<0.001)
1.55
1.00
0.96
0.89
-
1.75,
1.70,
1.04,
1.21,
-0.32 - 5.00
-1.71 - 0.91
Table 8.5: Linear regression equations and correlation coefficient.
Cardiac output
Submaximal(L/min)
Submaximal (%)
cFick minus
Physioflow (N=57)
Bias
Limits of agreement
cFick minus
PulseCO (N=48)
Bias
Limits of agreement
4.92
48%
-0.02
-1%
-0.57 - + 10.40
-1% - + 97%
-2.22 - +2.17
-28% - +26%
Table 8.6: Results for all patients during submaximal exercise.
8.2.2
Tracking changes of stroke volume
PulseCO and Physioflow use an initial calibration before measuring the absolute values of
cardiac output. In further calculations of the absolute cardiac output the calibration value
is used as a factor. By dividing the absolute values by the calibration value it is possible to
investigate the changes of the cardiac output. So in fact the PulseCO and the Physioflow
only follow changes in cardiac output. Therefore it is important to validate the performance
of the PulseCO and the Physioflow method also by investigating these changes.
PulseCO and Physioflow measure the cardiac output by estimating the stroke volume and
then multiplying it by the heart rate. The PulseCO method determine the heart rate by
autocorrelation of the blood pressure signal and the Physioflow method and ZAN equipment
determine the heart rate from the ECG-signal. Both methods to detect the heart rate are
accurate. The best fit for the PulseCO heart rate was y = 1.01x with a correlation coefficient of 0.99 (p<0.001, N=48) and the Physioflow heart rate linear model was y = 1.00x
with a correlation coefficient of 0.99 (p<0.001, N=57). Because PulseCO and Physioflow
measures the cardiac output by making use of the heart rate it is necessary to investigate the
performance of the PulseCO and Physioflow method by neglecting the heart rate. During
exercise the heart rate changes markedly and because Physioflow and PulseCO measures the
heart rate accurately, the changes of heart rate will be accurate too. Therefore the heart rate
must also be excluded to investigate the possibility of the PulseCO and Physioflow system
of tracking changes in stroke volume, because Physioflow and PulseCO estimate the stroke
volume. Therefore the changes in stroke volume should be pooled from difference patients.
To investigate the PulseCO and the Physioflow performance in tracking changes in stroke
volume the Physioflow and PulseCO stroke volume values have to be divided by their initial
calibration, to make the measurement independent of this initial calibration. To define the
starting stroke volume the continuous Fick cardiac output is divided by the simultaneously
measured heart rate at rest before the exercise test, for the Physioflow the simultaneously
49
measured starting stroke volume is taken. Because the exact calibration stroke volume can
not be determined in the PulseCO system the lithium dilution cardiac output is divided by
the mean of the measured heart rate of the ZAN and Physioflow system. The stroke volume
used as calibration values are given again in table 8.7 together with the continuous Fick stroke
volume values. Because it was in practice not possible to simultaneously calibrate the Physioflow and PulseCO, the Physioflow stroke volume is divided by the resting value obtained
during validation, just after calibration and the PulseCO stroke volume are divided by their
initial calibration values.
In figure 8.6a the relation between PulseCO and continuous Fick stroke volume is shown relative to their starting values. Because the absolute stroke volume values are divided by their
starting values a fixed bound is created not at the origin (x=0, y=0), but at the coordinate
(x=1, y=1), because the origin or start for all methods is at a starting factor of 1. The best
fit for this relation is y = 0.91x + 0.09 and the correlation coefficient was 0.70 (P<0.001).
This shows a significant relation in changing stroke volume values within patients.
The relation of tracking changes of stroke volume between continuous Fick and Physioflow
cFick and PulseCO divided by cal. stroke volume
cFick and Physioflow divided by cal. stroke volume
3
3
30%
80%
Linear fit
2.5
Physioflow / cal. factor
PulseCO / cal. factor
2.5
30%
80%
2
1.5
1
0.5
0
2
1.5
1
0.5
0
0.5
1
1.5
cFick / cal. factor
2
2.5
0
3
0
0.5
1
1.5
cFick / cal. factor
2
2.5
3
Figure 8.6: (a) The relation of the stroke volume of PulseCO versus continuous Fick and
(b) the relation of stroke volume divided by the calibration stroke volume of Physioflow and
continuous Fick during submaximal exercise test.
is shown in figure 8.6b. No significant relation was found with a fixed bound at (1,1).
The Bland-Altman plot of continuous Fick and Physioflow for percentage difference of
stroke volume divided by cal. factor is shown in figure 8.7a. The bias and limits of agreement
are -0.06 (-3%) -0.56 to 0.44 (-38% to 32%), respectively. Also these results indicate that the
stroke volume performs better in tracking changes then measuring absolute values.
The Bland-Altman plot of percentage changes of stroke volume of continuous Fick and
PulseCO is shown in figure 8.7b. The bias and limits of agreement are -0.03 (-2%) and 0.40 to 0.34 (-28% to 24%) respectively. A summary of the results are shown in tabel 8.8 and
table 8.9 .
50
Patient
1
2
3
4
5
6
7
8
9
10
Stroke volume,
cF ickstart (ml)
62
61
42
54
70
47
53
61
52
69
Stroke volume,
P hysiof lowstart (ml)
76
117
104
89
103
104
87
72
Stroke volume,
LiDCOcal (ml)*
71**
60**
45
52
74
48
45
67
55
59
Bland−Altman plot of cFick and Physioflow during submaximal exercise
120
30%
100
80%
Bland−Altman plot of cFick and PulseCO during submaximal exercise
120
80
60
40
20
0
−20
−40
−60
−80
−100
−120
30%
80%
100
Percentage difference of SV / cal. factor [%]
Percentage difference of SV / cal. factor [%]
Table 8.7: The calibration values of stroke volume for every patient. *LiDCO stroke volume
estimated by using heart rate of other methods. **Instead of LidCO uncalibrated PulseCO
signal used
80
60
40
20
0
−20
−40
−60
−80
−100
0
0.5
1
1.5
Mean cal. factor
2
2.5
−120
3
0
0.5
1
1.5
Mean cal. factor
2
2.5
3
Figure 8.7: (a) The Bland-Altman plot of stroke volume divided by the calibration stroke
volume of continuous Fick and Physioflow and (b) continuous Fick and PulseCO during
submaximal exercise test. The solid black line indicates the percentage bias and the percentage
limits of agreement are plotted with the dashed black line.
regression
Stroke volume
Physioflow versus cFick (N=57)
PulseCO versus cFick (N=60)
y = ax+b
y = 0.91x+0.09
r, (p)
95% confidence interval
of slope, intercept
ns
0.70, (<0.001)
0.83 - 0.99, 0.01 - 0.17
Table 8.8: Linear regression and correlation coefficient for tracking changes of stroke volume.
ns: Not significant
51
Stroke volume
Submaximal
Submaximal (%)
Physioflow minus cFick (N=57)
Bias
Limits of agreement
PulseCO minus cFick (N=60)
Bias
Limits of agreement
-0.06
-3%
-0.03
-2%
-0.56-+0.44
-38% - + 32%
-0.40 - + 0.34
-28% - + 24%
Table 8.9: Results for all patients during submaximal exercise in tracking changes of stroke
volume.
8.3
Measurements during maximal exercise
The results of the maximal exercise test are evaluated in the same way as the submaximal exercise test. First the absolute cardiac output and stroke volume will be discussed, followed by
the evaluation of the ability of tracking changes of stroke volume for the Physioflow method
and the PulseCO method.
8.3.1
Cardiac output
An example of a maximal exercise test is shown in figure 8.8 of patient 4. In this figure
the errorbars indicate the standard deviation in the corresponding interval. To compare the
cardiac output of the different methods, the cardiac output is taken at 25%, 50%, 75% and at
maximal workload during the maximal exercise test by averaging the cardiac output values
30sec before and 30sec after the corresponding workload.
The cardiac output at maximal effort of the patients for continuous Fick ranged from 7.0
L/min to 14.8 L/min, for Physioflow the cardiac output at maximal effort values were between 8.2 L/min and 26.9 L/min and the PulseCO cardiac output values at maximal effort
ranged from 6.8 L/min to 16.6 L/min. The average cardiac output values at 25%, 50%, 75%
and 100% are shown in table 8.10.
Method
COcF ick (N=10)
COphys (N=8)
COpuls (N=8)
25%
6.0 ± 1.4
10.8 ± 3.2
6.0 ± 1.0
Mean ± SD (L/min)
50%
75%
7.5 ± 2.2
8.7 ± 2.3
12.6 ± 3.5 14.2 ± 4.5
7.2 ± 1.4
8.9 ± 3.1
100%
9.6 ± 2.3
15.7 ± 5.7
9.7 ± 3.1
Table 8.10: Mean cardiac output values for the three methods during incremental exercise.
The relation of continuous Fick and Physioflow together with the Bland-Altman plot of the
cardiac output during maximal exercise of continuous Fick and Physioflow is shown in figure
8.9a and 8.9b. The best fit for the model y = ax was y=1.69x and the correlation coefficient
was 0.48 (p<0.05). In total 32 observations are involved, 4 datapoints for 8 patients, because
patient 2 and 3 were excluded, because heart rate was not correctly detected. The bias and
52
Cardiac output during maximal exercise of patient 4
24
cFick
PulseCO
Physioflow
22
20
Cardiac output [L/min]
18
16
14
12
10
8
6
4
2
0
0
100
200
300
400
Time [sec]
500
600
700
Figure 8.8: The course of the cardiac output of continuous Fick, PulseCO and Physioflow
during maximal exercise for patient 4.
cFick and Physioflow cardiac output during maximal exercise
Bland−Altman plot of cFick and Physioflow maximal exercise
120
25%
50%
75%
100%
Linear fit
25
Percentage difference in cardiac output [%]
Physioflow cardiac output [L/min]
30
20
15
10
5
25%
50%
75%
100%
100
80
60
40
20
0
−20
−40
−60
−80
−100
0
0
5
10
15
20
cFick cardiac output [L/min]
25
−120
30
0
5
10
15
20
Mean cardiac output [L/min]
25
30
Figure 8.9: (a) The relation of Physioflow and continuous Fick and (b) the Bland-Altman plot
of continuous Fick and Physioflow during maximal exercise. The solid black line indicates
the percentage bias and the percentage limits of agreement are plotted with the dashed black
line.
limits of agreement were 5.69 L/min (52%) and -1.49 L/min to 12.88 L/min (-16% to 119%)
respectively. This result is slightly worse as found during submaximal exercise.
The relation between continuous Fick and PulseCO is shown in figure 8.10a. The relation
for the linear model y = ax was y=1.04x and the correlation coefficient was 0.89 (p<0.001).
The percentage bias and limits of agreement were 4% and -28% to 35% respectively, see figure
8.10b. So for in the maximal exercise test slightly larger limits of agreement were found, compared to steady state exercise. The absolute bias was 0.31 L/min and the limits of agreement
were -2.13 L/min to 2.76 L/min. Also for the comparison of continuous Fick and PulseCO
32 oberservation are involved, because patient 1 and 2 were not included.
53
Bland−Altman plot of cFick and PulseCO maximal exercise
120
20
15
10
5
25%
50%
75%
100%
100
Percentage difference in cardiac output [%]
PulseCO cardiac output [L/min]
Relation of cFick and PulseCO cardiac output during maximal exercise
30
25%
50%
75%
25
100%
Linear fit
80
60
40
20
0
−20
−40
−60
−80
−100
0
0
5
10
15
20
cFick cardiac output [L/min]
25
−120
30
0
5
10
15
20
Mean cardiac output [L/min]
25
30
Figure 8.10: (a) The relation of PulseCO and continuous Fick and (b) the Bland-Altman plot
of continuous Fick and PulseCO during maximal exercise. The solid black line indicates the
percentage bias and the percentage limits of agreement are plotted with the dashed black line.
A summary of the results are shown in table 8.11 and table 8.12.
regression
Cardiac output
Physioflow versus cFick (N=32)
PulseCO versus cFick (N=32)
y
y
y
y
=
=
=
=
1.69x
1.08x+5.06
1.04x
1.00x+0.30
r, (p)
0.48,
0.59,
0.89,
0.89,
(<0.05)
(<0.01)
(<0.001)
(<0.001)
95% confidence interval
of slope , intercept
1.51
0.53
0.98
0.81
-
1.87,
1.64,
1.09,
1.20,
0.60 - 9.53
-1.25 - 1.84
Table 8.11: Linear regression and correlation coefficient of cardiac output and stroke volume
during maximal exercise.
Cardiac output
Maximal(L/min)
Maximal (%)
cFick versus Physioflow (N=32)
Bias
Limits of agreement
cFick versus PulseCO (N=32)
Bias
Limits of agreement
5.69
52%
0.31
4%
-1.49 + 12.88
-16% - + 119%
-2.13 - +2.76
-28% - +35%
Table 8.12: Results for all patients during maximal exercise of cardiac output and stroke
volume.
8.3.2
Tracking changes of stroke volume
In this section the ability of the Physioflow and PulseCO in tracking changes of stroke volume
during maximal exercise is investigated. The same calibration values as the steady-state ex54
ercise test were chosen. The bias and limits of agreement in tracking changes for continuous
Bland−Altman plot of cFick and Physioflow during maximal exercise
120
Percentage difference of SV / cal. factor [%]
Physioflow / cal. factor
cFick and Physioflow divided by cal. stroke volume during maximal exercise
3
25%
50%
75%
2.5
100%
2
1.5
1
0.5
25%
50%
75%
100%
100
80
60
40
20
0
−20
−40
−60
−80
−100
0
0
0.5
1
1.5
cFick / cal. factor
2
2.5
−120
3
0
0.5
1
1.5
Mean cal. factor
2
2.5
3
Figure 8.11: (a) The relation of Physioflow and continuous Fick stroke volume divided by the
calibration stroke volume and (b) the Bland-Altman plot of continuous Fick and Physioflow
stroke volume divided by the calibration stroke volume during maximal exercise. The solid
black line indicates the percentage bias and the percentage limits of agreement are plotted with
the dashed black line.
Fick and Physioflow stroke volume were 0.02 (2%) and -0.63 to 0.66 (-45% to 50%), see figure
8.11b. For the relation of changes in stroke volume for continuous Fick with both methods a
linear model with a fixed bound at (x=1, y=1) is used, as explained in the previous section.
There was no significant relation as is shown in figure 8.11a.
The Bland-Altman plot in tracking changes of stroke volume for continuous Fick and
Bland−Altman plot of cFick and PulseCO during maximal exercise
120
Percentage difference of SV / cal. factor [%]
PulseCO / cal. factor
cFick and PulseCO divided by cal. stroke volume during maximal exercise
3
25%
50%
75%
2.5
100%
Linear fit
2
1.5
1
0.5
25%
50%
75%
100%
100
80
60
40
20
0
−20
−40
−60
−80
−100
0
0
0.5
1
1.5
cFick / cal. factor
2
2.5
−120
3
0
0.5
1
1.5
Mean cal. factor
2
2.5
3
Figure 8.12: (a) The relation of PulseCO and continuous Fick stroke volume divided by the
calibration stroke volume and (b) the Bland-Altman plot of continuous Fick and PulseCO
stroke volume divided by the calibration stroke volume during maximal exercise. The solid
black line indicates the percentage bias and the percentage limits of agreement are plotted with
the dashed black line.
PulseCO is shown in figure 8.12b. The bias and limits of agreement for continuous Fick
and PulseCO stroke volume were 0.05 (4%) and -0.41 to 0.52 (-28% to 36%). The relationship of the linear model y = ax + b gave a significant relation of y = 0.98x + 0.02 and the
55
correlation coefficient was 0.37 (P<0.01), see figure 8.12a. A summary of the results is shown
in table 8.13 and table 8.14.
regression
Stroke volume
Physioflow versus cFick (N=32)
PulseCO versus cFick (N=40)
y = ax+b
y = 0.98x+0.02
r, (p)
95% confidence interval
of slope, intercept
ns
0.37 (<0.01)
0.82 - 1.14, -0.14 - 0.18
Table 8.13: Linear regression and correlation coefficient during maximal exercise of changes
of stroke volume.
Stroke volume
Maximal (factor)
Maximal
Physioflow minus cFick (N=32)
Bias
Limits of agreement
PulseCO minus cFick (N=40)
Bias
Limits of agreement
0.02
2%
0.05
4%
-0.63 - + 0.66
-45% - + 50%
-0.41 - + 0.52
-28% - + 36%
Table 8.14: Results for all patients during maximal exercise of tracking changes of stroke
volume.
56
Chapter 9
Discussion
The purpose of this study was to validate cardiac output measurements during exercise in
patients with chronic heart failure by two new devices. One method was based on impedance
cardiography, Physioflow. The other method was based on pulse contour analysis, PulseCO.
In this study at rest the direct Fick was used as reference method, because the Fick principle
is considered the gold standard for the measurement of cardiac output. In chapter 7 it was
shown that the fiberoptic pulmonary catheter used in this study was feasible and reliable of
measuring SvO2 during exercise in patients with CHF. Because of this result the cFick cardiac
output was used in this study as the reference method for the validation of cardiac output
by Physioflow and PulseCO. The results were also analyzed by investigating the possibility
of the methods of tracking changes of stroke volume. As pointed out by Critchley et al. the
acceptance of a new technique should rely in limits of agreement of up to ± 30% between two
cardiac output methods. [47] However, in the study of Critchley thermodilution was used as
reference method. In this study the Fick method was used as reference method. The accuracy of the reference method depends on the accuracy of the measurement equipment and
the physiological variation, which often lacks precision of about 10%-20%. From the variables
needed to calculate Fick cardiac output, V O2 and SvO2 show the largest changes during
exercise. The variation of cardiac output by the Fick method is therefore mainly caused by
these two variables. In the patients in this study ventilatory oscillations were not uncommon,
which also influenced the accuracy of the Fick method. To reduce the influence of ventilatory
oscillations on measured V O2 relatively long sampling intervals of 30 sec. were used.
It is also important to investigate both methods in tracking changes in stroke volume, because
PulseCO and Physioflow measure the stroke volume and multiply this value with the heart
rate to measure cardiac output. Tracking changes in stroke volume is therefore important,
because changes in heart rate are accurate. Unfortunately, no study was found were tracking
changes of stroke volume is investigated. Recently, only a few studies discussed the importance of not only investigating absolute values, but also investigating methods in tracking
changes. [16, 48] Because no study was found where tracking changes of stroke volume was
investigated, the data of a few other studies have been analyzed. In Tanabe et al. [62] the
increase of stroke volume for NYHA, class II from rest to peak exercise was ± 1.5 on average
in patients with CHF. In Sullivan et al. [55] the increase from rest to maximal exercise was ±
1.4 times the rest value for CHF patients on average. In this study a slightly larger increase
from rest to peak exercise was found, ± 1.6 times rest value on average of the ten patients.
57
The main results of this study for PulseCO showed clinical acceptable agreement at rest
(LiDCO) and during exercise (PulseCO) with bias and limits of agreement of -1% and -28%
- +26% respectively. PulseCO had a significant correlation for the linear model y = ax,
(y = 1.00x, p<0.001). PulseCO has not been tested during exercise yet, but one other study
showed similar bias and limits of agreement. [13] The correlation coefficient of 0.89 was also
similar. [13, 14]
PulseCO showed clinical acceptable agreement in tracking changes of stroke volume with bias
close to 0 (-2%) and limits of agreement (-28% - +24%) close to the values found for absolute
cardiac output at steady-state (-28% - +26%). PulseCO gave a significant correlation for the
linear model y = ax + b with a fixed bound at (x=1, y=1), (y = 0.91x + 0.09, p<0.001) and
the slope was close to line of identity, indicating a correct increase of PulseCO stroke volume
with gold standard.
The main results of this study for Physioflow showed that Physioflow overestimated the
absolute cardiac output both at rest and during steady-state exercise with a bias of 46% and
48% respectively. Also wide limits of agreement were found at rest and during steady-state
exercise for absolute cardiac output (-10% - +102% and -1% - +97% respectively). The
linear model y = ax gave a significant correlation (y = 1.65x, p<0.001) The slope of the
linear model for Physioflow was significant larger compared with PulseCO also indicating the
overestimation of absolute cardiac output.
In two other studies the Physioflow device showed clinical acceptable agreement compared
with dFick cardiac output. [10, 11] In one other study by Bougault in patients with severe
COPD also an overestimation of the cardiac output was found. [9] The mean difference of
Physioflow minus Fick was 3.2 L/min (31%) with limits of agreement of -2.6 L/min to 9
L/min (-11% to 73%). Unfortunately, in this study the ability of tracking changes in cardiac
output or stroke volume was not investigated.
In tracking changes of stroke volume, Physioflow showed no overestimation with a bias close
to 0 (-3%), therefore, the overestimation of Physioflow is caused by the incorrect calibration
of absolute stroke volume. Also the incorrect calibration have contributed to the wide limits of agreement for absolute cardiac output. Physioflow showed larger limits of agreement
compared with PulseCO and continuous Fick for tracking changes of stroke volume (-38% +32%). The linear model y = ax + b with a fixed bound at (x=1, y=1) gave no significant
correlation.
In tracking changes of stroke volume Physioflow showed wider limits of agreement compared
with PulseCO, which could be due to several reasons. As was explained in section 4.3 the
variation of the impedance signal induced by the cardiac cycle are the smallest variations.
Because the new Physioflow algorithm is independent of the baseline impedance Z0 , it makes
the cardiac output calculation totally dependent on the variation of the impedance signal.
This makes it very sensitive, for motion artifact, like muscle movements and artifacts caused
by respiration. Although the respiratory motions are filtered out of the impedance signal, this
could be of significant influence of the calculation of stroke volume, because the ventilation
in patients with chronic heart failure is known to be elevated compared to healthy subjects.
Another problem can occur when muscle movements are present in the same frequency range
as the cardiac cycle, then these artifacts are not filtered out of the impedance signal, which
can contribute to the larger variation, however this has not been investigated. This all can
effect an increase of variation of the variables (dZ/dt)max and T F ITcal , which are the only
58
variables that change after calibration.
The overestimation of absolute stroke volume during calibration is a result of an incorrect
calculation of absolute stroke volume. It is not clear how absolute stroke volume can be
obtained from the variables BSA, k, Zmax − Zmin , (dZ/dt)max and w(T F IT )cal . Increased
ventilation could be a cause of the systematic overestimation during calibration.
The wide limits of agreement and sensitivity to motion artifacts for Physioflow restricts its
use for clinical applications.
During the maximal exercise test PulseCO showed slightly larger limits of agreement (-28%
- +35%) and had a bias close to 0 (2%). In tracking changes of stroke volume the bias was
4% and similar limits of agreement were found (-28% - +36%).
For Physioflow also in the maximal exercise test a systematic overestimation for absolute
cardiac output was found with a bias of 52% and limits of agreement of -16% - +119%. In
tracking changes the bias was close to 0 (2%) and larger limits of agreement compared with
steady-state exercise (-45% - +50%). This can be explained by 3 measurements (9%) that
exceed the limits of agreement in the maximal exercise test, which have large influence on the
wider limits of agreement.
The wider limits of agreement for both methods could be due to the non steady-state situation
in an incremental exercise test. It is often stated that the determination of cardiac output by
cFick should be performed in steady-state. However, several studies have used cFick in non
steady-state situations for validation of other methods in exercise. [58, 63, 64] Some problems
occur when measuring cFick cardiac output in non steady-state exercise. The assumptions
is made that the oxygen consumption can be divided by the arterio-venous oxygen concentration difference in blood in the same time period. The oxygen consumption is measured at
the mouth and has to reflect the oxygen uptake in the lungs. A time delay consist between
the oxygen in the expired gas and the alveolar gas. Also the increased oxygen uptake in
the muscles causing an increased oxygen extraction from the blood can give a time delay,
because the decrease in SvO2 is not measured in the working muscle, but in the pulmonary
circulation. But the delay in the return of the venous blood can reduce the arterio-venous
oxygen concentration difference at a given V O2 , which can have a compensatory effect to
cFick cardiac output. [63] In steady-state situation when the V O2 and SvO2 are stable the
parameters can be used in the same time period and reflects the averaged blood flow. In
the maximal exercise test where steady state is not obtained, more variation in Fick cardiac
output could be present due to above reasons resulting in wider limits of agreement found
for the PulseCO and Physioflow for absolute cardiac output and tracking changes of stroke
volume.
59
Chapter 10
Conclusion
The goal of this study was to validate two methods for the determination of cardiac output
during exercise in patients with chronic heart failure (CHF). The reference method used in
this study was the direct Fick cardiac output in rest. The results of this study showed that
continuous measurement of SvO2 is reliable during exercise in patients with CHF. Therefore
during exercise continuous Fick cardiac output was used as reference method. In conclusion,
PulseCO is a reliable method for the measurement of absolute cardiac output and in tracking
changes of stroke volume during exercise. Physioflow is not reliable for measurement of absolute cardiac output in exercise, however may be useful for tracking changes of stroke volume.
60
Chapter 11
Recommendations
In this section clinical applications where more research is necessary to clarify the role of
cardiac output as additional parameter will be discussed. In addition, technical applications
will be described where improvements of techniques for measurement of cardiac output is
necessary.
11.1
Clinical applications
An important limitation of CHF patients is exercise intolerance. It has already been studied
that left ventricular ejection fraction (LVEF) has poor correlation with exercise capacity in
heart failure. A cardiopulmonary exercise test offers a objective evaluation of the exercise
capacity for heart failure patients. An reliable parameter used in these test is the V O2peak .
For patients in revalidation programs, that are encouraged to perform physical activity, the
measurement of cardiac output in combination with V O2 during exercise tests can give valuable information about the effect of training and can therefore improve treatment in these
patients. A cardiopulmonary exercise test with simultaneously measurement of cardiac output and oxygen consumption can help to distinguish the exercise intolerance on the basis of
cardiac or pulmonary fatigue.
The V O2peak measurement in exercise testing are used for identifying risk in heart failure
patients.V O2peak has proven to be a predictive value of survival in patients with CHF. The
higher the V O2peak , the better the prognosis of patients. In addition, V O2peak values can also
help to decide which patients should continue drug therapy and which should have a heart
transplant. A V O2peak of 14 mL/kg/min is currently the recognized cut-off point for a heart
transplant. A cut-off such as 14 mL/kg/min has its shortcomings. In combination of with the
measurement of cardiac output can help to give a better prognosis in heart failure patients
and can therefore improve the treatment in CHF patients.
Onset and off set kinetics of V O2 has been proven to give additional information about
the ability of patients to adapt and recover from exercise. [65] In combination with the
measurement of cardiac output it is expected that it can add more information about the
hemodynamical state of these patients, however this has to be investigated. Exercise intolerance can also be a result of deconditioning. This means that changes of the periphery rather
than central factors can be a determinant of the exercise intolerance in CHF patients. The
measurement of the cardiac output can elucidate the underlying factors which determine the
61
exercise intolerance. It can be concluded that the measurement of cardiac output can be used
in several clinical settings where it can be of additional value.
11.2
Technical applications
The cFick cardiac output was used as reference method. A lot of studies considered this
method as golden standard. However, no study was found were the Fick method has been
modeled to identify the accuracy and possible problems occurring in non steady-state. For
further research modeling of the respiratory system together with the pulmonary circulation
focused on cFick cardiac output could give useful information on the accuracy of the method.
Physioflow was not capable of accurately measuring cardiac output during exercise in patients with chronic heart failure. The problem lies in the small contribution of the cardiac
cycle of the impedance signal especially during exercise for cardiac changes and in the algorithm used for this technique. In section 4.3.1 the theory of thoracic electrical bioimpedance
has been described. Some disadvantages of this theory were avoided by Physioflow, but it
remains unclear why the mathematical approach of Physioflow was chosen.
From this study it can be concluded that PulseCO is an accurate method for determining cardiac output during exericse in patients with chronic heart failure. The mathematical
operations described in section 4.4 are suitable for this specific patient group. However, the
mathematical theory is not completely correct. A disadvantage is that the exact physical
origin is not elucidated. For future research it is desired to further model the PulseCO and
other potential methods. Therefore in the next section a framework for a mathematical model
is created that can be used to in further research.
11.3
Modeling of the human arterial system
Several models have been developed to describe the physical principles of blood flow and
pressure in the cardiovascular system. One of the models is the windkessel model described
in section 4.4. A disadvantage of this model is that it does not include some important hemodynamical characteristics such as wave travel and reflections. To include these phenomena,
models have been developed where the distributed arterial properties of the human arterial
tree are taken into account.[66, 67] In one study the physical background of this model is used
for the estimation of cardiac output. [48] In this model the arterial system is divided in several
arterial segments that represent the largest blood vessels. The mathematical operations of
this model will be described in more detail in appendix 12.
The flow of blood through the circulatory system is governed by the equations of conservation of mass and momentum. Several assumptions are introduced to express the properties
of an arterial segment. By making use of the Navier-Stokes equations an arterial segment can
be described by an electrical model with a resistance, inertia and a compliance given by:
L =
ρl
A
62
(11.1)
R =
C =
8ηl
πa4
3πr2 ( hr + 1)2
E(2 hr + 1)
(11.2)
(11.3)
where ρ is the density of blood, η, the blood viscosity, A the cross sectional area, a, the radius,
h the wall thickness and E, the young’s modulus of an arterial segment. [66]
In the model of the human arterial system the influence of the venous part of the circulation is
neglected. Therefore the arterial segments are cut-off by end segments. The properties of the
end segments are modeled by a characteristic impedance Z1 together with a resistance Rt and
compliance Ct . [68] Because this model does not include a definition for wave reflections, this
model is modified to investigate the principle of peripheral wave reflections. Therefore the
end segment also include a proximal characteristic impedance, Zprox . [69] By assuming that
the terminal arterial vessel and his immediate proximal arterial vessel has the same physical
properties (Zprox = Z1 ) and when ω approaches zero, the reflection coefficient λ could be
could by expressed by:
Rt
(11.4)
λ0 =
Rt + 2Z1
The compliance Ct is the compliance of the vascular bed behind the end segment. The
compliance together with the peripheral resistance determine the descending slope of the
pressure wave in the diastolic phase. If the time constant is known the compliance of the
terminal segment can be calculated by:
Ct =
τ
Rt
(11.5)
The value of τ is about 1.5sec. [68].
In this study the model of Huberts is used, [68] because the pulse contour analysis of the
PulseCO system is performed on the blood pressure signal in de radial artery. In this model,
only the major branches from aorta to leg and aorta to right arm are included. The input of
the model is a flow signal in the ascending aorta from Olufsen et al. [70]. The flow signal is
scaled to simulate a cardiac output of 5 L/min and a heart rate of 71 beats/min. The input
flow is shown in figure 11.1.
63
Flow waveform used as input of model
25
20
Flow [L/min]
15
10
5
0
−5
0
0.1
0.2
0.3
0.4
0.5
Time [sec]
0.6
0.7
0.8
Figure 11.1: Input flow for the model of the human arterial system
Output of model
To investigate the wave propagation of the pressure and flow a model of the in the human
arterial system has been described. Because the PulseCO system used in this study performs
their estimation of the cardiac output by using the blood pressure waveform in the radial
artery the wave propagation is shown of the blood pressure and flow from the aorta to the
radial artery in figure 11.2a and 11.2b. In figure 11.2a the augmentation of the systolic blood
Pressure from aorta to radial
Flow from aorta to radial
180
25
Aorta ascendens
A. Subclavia
A. Axillaris
A. Brachialis
A. Radialis
20
140
15
Flow [L/min]
Pressure (mmHg)
160
120
10
100
5
80
0
60
Aorta ascendens
A. Subclavia
A. Axillaris
A.Brachialis
A. Radialis
0
0.1
0.2
0.3
0.4
0.5
Time [sec]
0.6
0.7
−5
0.8
0
0.1
0.2
0.3
0.4
0.5
Time [sec]
0.6
0.7
0.8
Figure 11.2: The blood pressure from the aorta to the radial artery (left) and the flow from
aorta to radial artery. (right)
pressure from aorta to the radial artery is seen. In the aorta ascendens the systolic blood
pressure is 128 mmHg and in the radial artery is systolic blood pressure is increased to about
147 mmHg.
64
11.4
Discussion
In this above sections a lumped parameter model has been introduced to create a basic physical framework for the development of new techniques for the estimation of cardiac output
in further research. In contrary to the 3 element windkessel model, the lumped parameter is
capable of modeling hemodynamical effects like pulse wave velocity and reflections. In one
study the lumped parameter model is used as physical background for the determination of
cardiac output by using the radial blood pressure. [48]
In this lumped parameter model the influence of cardiovascular regulation in not taken into
account. But the cardiovascular regulation has significant influence on the peripheral blood
pressure waveform. As described in chapter 3 several physiological adaptations occur during
exercise. The sympathetic nervous system causes an increase in cardiac contraction, which
has influence on the input flow of the model. Another physiological adaptation is the vasoconstriction of the inactive peripheral bed and vasodilatation of the active region by local
vasodilator, which have influence on the modeling of the end-segments and causes redistribution of blood flow. Also the increased venous return caused by the active muscles has
influence on the model. Therefore the heart has to be included in this model together with
the venous system to omit the boundary conditions of the end-segments and the aorta. In
addition the influence of long-term effects must be elucidated, like the effect of deconditioning
on the blood vessels. By incorporating the cardiovascular system further improvements can
be made.
A general model is described in above sections, but to estimate the cardiac output in patients
it is important to make the lumped parameter model more patient-specific. Therefore it is
necessary to investigate the parameters that has the largest influence on the estimation of
cardiac output.
Also the lumped parameter model can be used to elucidate the performance of the PulseCO
method. The PulseCO showed good agreement with cFick cardiac output and was capable
of measuring the stroke volume accurately. The increase in stroke volume was a result of
the pressure wave amplification from aorta to radial artery. During exercise pressure wave
amplification increased, resulting in an increase in stroke volume. The lumped parameter
model can elucidate if the origin of the increased pressure wave amplification is really a result
of the increased stroke volume or because of the cardiovascular adaptations described above.
Another possible method that has to be investigated is described by Lu et al. [71] In this
approach the peripheral blood pressure is analyzed over time scales larger then a cardiac
cycle. Because in short time scales the peripheral blood pressure is dominated by complex
forward and backward traveling waves. By analyzing the blood pressure signal over larger
times scales the wave phenomena are diminished. The underlying concept is based on a twoelement windkessel model, which consist of the cardiac output as source and the two elements
are the arterial compliance and the total peripheral resistance. In the diastolic phase the
arterial blood pressure should decay as an exponential function. To estimate this time delay
τ from a peripheral blood pressure, the peripheral blood pressure is modeled by a convolution
of a impulse function with a function representing a cardiac contraction. By dividing the
mean arterial pressure by the τ an estimate of the cardiac output is made. Improvements in
this model has also to be investigated.
65
Acknowledgement
Finally, this is one of the last parts I have to write before finishing my report. Last, but
not least, because here I have the opportunity to thank a lot of people, who are directly and
indirectly involved in my graduation project.
First of all, I would like to thank the patients by participating in this study, without them
it was just simply not possible to start the project at all. Secondly, I would like to extend
a word of thanks to Hareld Kemps. My graduation project was part of his PhD study.
His fanaticism in gaining knowledge about people suffering from chronic heart failure has
inspired me. The cooperation with him was always a pleasure. Also I would like to thank
Chris Peters, my daily supervisor at the Department of Clinical Physics from Máximal Medical
Center. When I had questions concerning the study, I admired him in its capability of directly
defining and identify the problem and to come with a clear solution. In addition, I would
like to thank Pieter Wijn, my supervisor at the Department of Clinical Physics, who made
it possible to perform my scientific research at Máximal Medical Center. In my graduation
project I had a few presentations and during these presentations he always came with useful
comment and he was capable of clearly summarize a complex problem into a few simple
and basic problems. Further I would like to thank Frans van de Vosse my supervisor from
the University of Eindhoven for his scientific contribution and useful comment during my
presentations. Further more I would like to thank Goof Schep, who made it possible for me
to improve my medical knowledge especially in the area of Sports Medicine.
During the exercise tests of the patients a lot of people from Máxima Medical Center helped
me and Hareld, so also a thanks to them. And of course I must not forget to mention the
people I worked together last year direct or indirect, Henk-Joost, Anne, Loes, Rik, Job,
Charlotte, Carola, Rian en Jolande. At the end I would like to thank my parents, my sister
and my girlfriend to support me during my study.
66
Chapter 12
Appendix
12.1
Modeling of the human arterial system
12.2
Theory of arterial system
The flow of blood through the circulatory system is governed by the equations of conservation
of mass and momentum. Several assumptions are introduced to express the properties of an
arterial segment. Blood is assumed to be a incompressible Newtonian fluid. The NavierStokes equations, the momentum equation and continuity equation then becomes:
ρ(
δ~v
+ (~v · ∇)~v ) = f~ − ∇p + η∇2~v
δt
∇ · ~v = 0
(12.1)
(12.2)
where ~v is the velocity vector, f~ is the force acting on the volume, p the pressure, ρ the
density of blood and η the dynamic fluid velocity. When the Navier-Stokes equations are
written in cylindrical coordinates and the vessel is assumed to be axi-symmetric and also the
body forces, such as gravity, are neglected, the equations will then be expressed by:
´ δ2v ´
δvr
δvr
δvr
1 δp η ³ δ ³ 1 δ
r
+ vr
+ vz
=−
+
(rvr ) +
2
δt
δr
δz
ρ δr ρ δr r δr
δz
´ δ2v ´
δvz
δvz
δvz
1 δp η ³ δ ³ 1 δ
z
+ vr
+ vz
=−
+
(vz ) +
δt
δr
δz
ρ δz ρ δr r δr
δz 2
(12.3)
1 δ
δvz
(rvr ) +
=0
(12.4)
r δr
δz
where vr and vz are the velocity components in radial and z-direction, see figure 12.1. For
fully developed flow there are no changes in z-direction and therefore also no velocity in radial
direction and pressure changes in radial direction. The momentum equation results in:
δvz
1 δp η 1 δ δvz
=−
+
(r
)
δt
ρ δz ρ r δr δr
(12.5)
This equation represents the balance between the inertial, pressure and viscous forces. So,
in general, the hemodynamics of a arterial segments originates from the interaction between
67
these forces. To examine the balance between the pressure term and the other terms, the
forces are artificially separated.
If the flow is dominated by viscous forces equation 12.5 reduces to:
1 δp
η 1 δ δvz
=
(r
)
ρ δz
ρ r δr δr
(12.6)
By integrating equation 12.6 and filling in the boundary conditions the solution for this
equation is known as the Poiseuille profile:
vz (r) =
1 dp 2
(r − a2 )
4η dz
(12.7)
where a represents the vessel radius. The flow is obtained by integration of equation 12.7 over
the cross-sectional area A. The relation of flow and the pressure gradient can be written as:
8η
dp
= − 4q
dz
πa
(12.8)
The resistance R of an arterial segment of length l equals:
R=
8ηl
πa4
(12.9)
If the inertial forces dominate the viscous forces, equation 12.5 reduces to:
1 δp
δv
=−
δt
ρ δz
(12.10)
When the pressure gradient in equation 12.10 is multiplied with the cross-sectional area A, a
relation of pressure and flow is obtained:
ρ δq
δq
δp
=L =−
A δt
δt
δz
(12.11)
The inertia along a vessel with length l can therefore be written as:
L=
ρl
A
(12.12)
Figure 12.1: The schematic view of an arterial segment
The compliance of an arterial segment depends on the material properties of the wall
and his dimensions. By making use of the stress-strain relationships based on Hooke’s law
and assuming radius of the vessel small compared to the wavelength and small variations in
radius to itself caused by the pressure waves, together with the assumptions that the vessel
68
has no movement in longitudinal direction, and neglecting the inlet effects and influences of
flow changes at branching points the expression of the compliance becomes [72]:
C=
3πr2 ( hr + 1)2
E(2 hr + 1)
(12.13)
In this equation the poisson ratio ν is assumed to be 0.5. E is the Young’s modulus, h the
wall thickness and r the radius of the vessel.
By combining the resistance, inertia and the compliance the properties of an arterial segment
can be modeled. The one-dimensional momentum equation and continuity equation modeling
the pressure and flow relations in a short segment together form the basic equations in the
model of the human arterial system:
−
δp
δz
= L
δq
+ Rq
δt
(12.14)
−
δq
δz
= C
δp
δt
(12.15)
In this equation the leakage of blood because of branching is neglected. In fig 12.2 an electrical
model of an arterial segment is shown. The compliance is divided in two parts. This is done,
because an symmetrical network reduces the errors in characteristic impedance because of
lumping, compared with a non symmetrical network. The errors become more pronounced
at higher frequencies. [66]
Figure 12.2: The schematic view of the electrical analogue of an arterial segment
12.3
End segments
In the model of the human arterial system the influence of the venous part of the circulation
is neglected. Therefore the arterial segments are cut-off by end segments. The downstream
arterial bed is modeled as a characteristic impedance Z1 together with a resistance Rt and
compliance Ct . [68] Because this model does not include a definition for wave reflections, this
model is modified to investigate the principle of peripheral wave reflections. Therefore the
end segment also include a proximal characteristic impedance, Zprox . [69] The end segment
is shown in figure 12.3.
The impedance mismatch between the two elements, results in the next expression for
wave reflection:
Zend − Zprox
λ=
(12.16)
Zend + Zprox
69
Figure 12.3: The schematic view of the electrical analogue of an arterial segment
where Zend is described by:
Zend = Z1 +
Rt
1 + jωRt Ct
(12.17)
By assuming that the terminal arterial vessel and his immediate proximal arterial vessel
has the same physical properties (Zprox = Z1 ) and when ω approaches zero, the reflection
coefficient λ could be could by expressed by:
λ0 =
Rt
Rt + 2Z1
(12.18)
The compliance Ct is the compliance of the vascular bed behind the end segment. The
compliance together with the peripheral resistance determine the descending slope of the
pressure wave in the diastolic phase. If the time constant is known the compliance of the
terminal segment can be calculated by:
Ct =
τ
Rt
(12.19)
The value of τ is about 1.5sec. [68].
In this study the model of Huberts [68] is used, because for the pulse contour analysis of
the PulseCO system is performed on the blood pressure signal in de radial artery. In this
model, only the major branches from aorta to leg and aorta to right arm are included. Other
branches are not modeled completely. In figure 12.4 and 12.5 a schematic view of the model
is shown. The ascending aorta is modeled by segment 1 and 2, the aortic arch is modeled by
segment 3 and 4, the thoracic aorta is modeled by segment 5, 6 and 7. After the aorta-iliac
bifurcation the iliac artery is modeled by segment 11, 12, 13 and cut-off by end segment E5.
12.4
The parameters used as input of model
To calculate the parameters L, R and C for the arterial segments the wall thickness, h, the
radius, r, the Young’s Modulus, E, the blood viscosity η and blood density ρ are needed
as shown in equation 12.9, 12.12 and 12.13. The density of blood, ρ, is assumed to be
1.05103 kgm− 3, the viscosity, η, is assumed to be 0.003P as. The reflection coefficient is set to
0.8 for all end segments. The values for the Young’s Moduli, wall thickness and radius were
taken from Westerhof [66] and Huberts [68].
70
Figure 12.4: The schematic view of the arterial segments
Figure 12.5: The schematic view of the arterial vessels
The relation of pressure and flow are modeled by using a system based on discrete elements.
The elements L, R and C has each two local nodal points and a flow q. The flow depends on
71
the local pressure and the derivatives of the pressure in the local nodal points, see equation
12.14. Connecting all the elements results in a set of differential equations. The procedure
follows the next rules:
- In every node the difference of the incoming external flow, Q and the total outgoing flow
to the connected elements must equal the product of capacitance and the derivative of
the pressure change in that node.
- In every node the pressure of the connected element nodes must be equal
After assembling the relations of pressure and flow of the elements, results in a set of differential equations:
Z
δ p̃(t)
C
+ Rp̃(t) + L p̃(t)dt = q̃(t)
(12.20)
δt
where p̃ and q̃ are the columns which contain the nodal point values of the pressure and flow.
C,L and R are the matrices containing the values of the compliance, inertance and resistance.
The matrices of the resistance and inertance are contain the inverse values of the resistance
and inertance, see figure 12.6
Figure 12.6: The schematic view of the elements R, L and C with there local nodal points and
equations
After proper specification of the initial conditions, the point variables and its derivatives
are determined from the set of equations. By making use of the implicit first order trapezoidal
method as numerical integration method, the solution is calculated at discrete time steps δt
of 0.005sec
72
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