Download here

Am J Physiol Heart Circ Physiol 301: H2198–H2206, 2011.
First published September 16, 2011; doi:10.1152/ajpheart.00781.2011.
Review
Pressure-volume relation analysis of mouse ventricular function
Oscar H. Cingolani and David A. Kass
Division of Cardiology, Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, Maryland
Submitted 3 August 2011; accepted in final form 12 September 2011
hemodynamics
THIS ARTICLE is part of a collection on Assessing Cardiovascular Function in Mice: New Developments and Methods.
Other articles appearing in this collection, as well as a full
archive of all collections, can be found online at http://
ajpheart.physiology.org/.
A comprehensive assessment of mouse cardiac hemodynamics in vivo can be essential to define the physiological significance of a given genetic or pharmacological modification.
This is often measured using imaging tools (e.g., Doppler/
echocardiography or MRI) and left ventricular (LV) pressure
data. However, a more detailed analysis may be desired, and
this can be provided by ventricular pressure-volume (P-V)
analysis. The P-V approach provides a comprehensive method
to assess cardiac systolic and diastolic function in a manner
less affected by arterial and venous loading while at the same
time quantifying this load. Methods to derive P-V relations in
mice, principally using a conductance catheter, were developed
in the late 1990s in our laboratory and are now commercially
available. The method and analysis require some appreciation
of the signals and potential sources of error, as well as the
underlying hemodynamics. The original work regarding P-V
analysis dates back 40 years, when it was the focus of bioengineering and systems biologists (34). Its emergence in an era
of molecular physiology in mice has made it all the more valuable
to revisit the principles, assumptions, and limitations of these
analytical approaches and the methodologies used to apply them.
The contents of this review are not new; however, as the constellation of investigators using P-V analysis has dramatically
changed from physiologist/engineers to molecular biologists, we
Address for reprint requests and other correspondence: D. A. Kass, Johns
Hopkins Univ. SOM, Ross 858, 720 Rutland Ave., Baltimore, MD 21205
(e-mail: [email protected]).
H2198
thought it useful to update (remind) researchers of the details and
provide contemporary examples of how P-V analysis is providing
unique insights into molecular physiology.
A Bit of History
The first studies regarding ventricular P-V relations were
reported from frog ventricle and date to the late 19th century
with the work of Otto Frank (7). However, it was the seminal
work from the Sagawa laboratory in the 1970s and 80s that
truly advanced the understanding of these relations and their
utility (41, 44 – 46). These investigators established the concept
that ventricular contraction behaves as a time-varying elastance, like a spring with a stiffness constant that changes from
diastole to systole and back. They examined the end-systolic
P-V relation (ESPVR), the set of P-V points from multiple
cardiac cycles generated under different loading conditions,
each reflecting maximal elastance for that condition. Over
several years, they established the relative (though not absolute) independence of the ESPVR from changes in cardiac
filling volume (preload) and aortic impedance (afterload) (44),
its modulation by chamber size/geometry (42), nonlinear ESPVR behavior (3, 15), how to couple the ESPVR to the arterial
loading system (46, 47), and how to analyze myocardial
energetic efficiency (43). All of this work was performed in
isolated, excised, blood-perfused canine hearts, and it was not
until the mid-1980s that in vivo translation occurred with the
arrival of a conductance catheter (2, 20) and sonomicrometer
measurements (23) to determine LV volume. Of these, the
catheter method was applicable to humans, and by the late
1980s, work by Kass and others (16, 18, 19) revealed the utility
of P-V analysis for studies of human heart disease. The
conductance (inverse of electrical resistance) catheter was
inserted into the LV so it lie along the longitudinal axis. It
0363-6135/11 Copyright © 2011 the American Physiological Society
http://www.ajpheart.org
Downloaded from http://ajpheart.physiology.org/ by 10.220.33.1 on October 5, 2016
Cingolani OH, Kass DA. Pressure-volume relation analysis of mouse ventricular function. Am J Physiol Heart Circ Physiol 301: H2198 –H2206, 2011. First
published September 16, 2011; doi:10.1152/ajpheart.00781.2011.—Nearly 40
years ago, the Sagawa laboratory spawned a renaissance in the use of instantaneous
ventricular pressure-volume (P-V) relations to assess cardiac function. Since then,
this analysis has taken hold as the most comprehensive way to quantify ventricular
chamber function and energetics and cardiovascular interactions. First studied in
large mammalian hearts and later in humans employing a catheter-based method,
P-V analysis was translated to small rodents in the late 1990s by the Kass
laboratory. Over the past decade, this approach has become a gold standard for
comprehensive examination of in vivo cardiac function in mice, facilitating a new
era of molecular cardiac physiology. The catheter-based method remains the most
widely used approach in mice. In this brief review, we discuss this instrumentation,
the theory behind its use, and how volume signals are calibrated and discuss
elements of P-V analysis. The goal is to provide a convenient summary of earlier
investigations and insights for users whose primary interests lie in genetic/molecular studies rather than in biomedical engineering.
Review
ASSESSMENT OF CARDIAC FUNCTION IN MICE
H2199
From Conductance to Volume
The original P-V catheters designed for larger experimental
animals and humans consisted of 8 –12 equally spaced electrodes, with a micromanometer mounted between electrodes 3
and 4 so it would lie within the LV. The catheter was placed
with its distal tip in the LV apex, and proximal electrode just
beyond the aortic valve. A high-frequency (⬃20 kHz), lowamplitude (⬃10 ␮A) alternating current was injected between
the most proximal and distal electrodes, generating a current
field about the heart, and voltage was measured between pairs
of the intervening electrodes. As equal-voltage planes were
perpendicular to the current field and thus catheter shaft, this
allowed for a reasonable assumption to be made: voltage
between two neighboring electrodes would be inversely related
to conductivity of the material between the electrodes (blood ⫹
heart muscle), and the time-varying component of this voltage
largely depended on varying blood volume during the cardiac
cycle. One added up the signals from sequential pairs of
electrodes, like a summation of disks, to calculate total volume.
For the mouse, it was impractical to scale this to a catheter ⬍0.5
mm in diameter, so the electrode count was simplified to four: two
outer pairs for stimulation and two inner for voltage determination
(Fig. 1). Blood conductivity is approximately three times more
than myocardium, and as this source more than myocardial
conductivity varies during the cardiac cycle, the signal is thought
to primarily reflect blood volume change. This is not absolute
volume; there is an offset due to conductance of the wall and
surrounding structures and a signal gain that is not unity. Calibration is needed to convert to absolute volume.
The primary equation relating conductance to volume is V ⫽
1/␣(␳L2)(G ⫺ Gp)(2), where ␳ is the blood resistivity, L is the
distance between sensing electrodes, G represents conductance
(inverse of voltage with a constant current circuit), Gp is
conductance from muscle wall and surrounding tissues (parallel conductance), and ␣ is the gain. If the current was injected
from parallel plates at base and apex, the field lines would all
pass linearly and the assumptions in this equation would be
perfectly met. However, we have point sources (ring electrodes) for the current, so the field lines are curved as are the
voltage planes perpendicular to them. This introduces a nonlinearity that is more and more evident the larger the heart is
(further distance away from the point sources). While this
impacts large mammalian and human hearts that are substanAJP-Heart Circ Physiol • VOL
Fig. 1. Cartoon showing positioning of a pressure-conductance catheter inside the
left ventricle (LV). For this example, insertion is via an apical stab, although a
retrograde introduction through the aortic valve is also feasible. The catheter shaft
is aligned along the LV longitudinal axis, with the outermost electrodes (E1, E4)
positioned right next to the aortic valve and apical endocardial border, respectively.
The pressure sensor is localized between the inner electrode pair. The dashed lines
depict the current field, and voltage is measured between electrodes E2 and E3 to
determine the volume signal. RV, right ventricle.
tially dilated, small rodents such as the mouse are at an
advantage here, since the short axis is 1 to 2 mm and wall
thickness is around 1 mm (relatively hypertrophied even in
normal mouse compared with human). Even when the mouse
heart is dilated severalfold, one is still dealing with a field
distribution that is close to the catheter shaft. This helps
stabilize the signal, improves linearity versus gold standard
volumes, and also insulates the signal from far field artifacts
(10). LV volumes acquired by the conductance catheter correlate quite well with those obtained by other imaging methods,
such as cardiac MRI, even in mice with postinfarction cardiomyopathy, where volumes are larger and LV walls present
fibrosis (48). In many ways, the small rodent heart has turned
out to be the ideal application for this methodology.
A pressure signal can be integrated with other imaging
methods to obtain volume such as MRI or echocardiography to
convert P-V data to stress/strain (4). However, this has its own
limitations requiring careful signal synchronization and is hard
to use for transient manipulations, such as load change, used to
derive the full set of relations.
Depending on the parameters to be examined, calibration of
the conductance signal is important. There are several different
methods that have been proposed, some being provided with
commercial systems. One is the external cuvette calibration,
where a Plexiglas block with cylinder-shaped holes of known
volume is filled with heparinized blood. By dipping the catheter into these holes, conductance signals are obtained and plot
against known volume to obtain a correlation. However, this
method is rarely accurate, since the in vivo electric field
distribution is quite different than in this external system and
the offset and gain are thus different. Another method is based
on a comparison with another “gold standard” measure of flow,
301 • DECEMBER 2011 •
www.ajpheart.org
Downloaded from http://ajpheart.physiology.org/ by 10.220.33.1 on October 5, 2016
provided an alternating constant current field between base and
apex and sensed voltage differences between intervening electrode pairs to generate a blood volume signal (volume was
inversely proportional to resistance, directly to conductance).
P-V relations were obtained by combining a micromanometer
sensor with the volume signal.
In 1998, P-V analytic methods were miniaturized by the
generation of very thin catheters and custom instrumentation
(10). Whereas the use of P-V analysis in humans has remained
limited to a few research laboratories worldwide, its use in
mice has exploded, and it is now considered the gold standard
for ventricular functional analysis. Understanding the principles and use of the method involves two components: the
methodology of the volume measurement [see also Pacher et
al. (30)] and the analysis of the data obtained. We will deal
with both in this order.
Review
H2200
ASSESSMENT OF CARDIAC FUNCTION IN MICE
ment of both parallel conductance and gain variability during
the cardiac cycle, based on admittance dynamic analysis and
Wei’s equation (21, 33). This requires a determination of
myocardial admittance (inverse of impedance) but then automates a real-time estimation of any time-varying myocardial
admittance contribution to the volume signal and compensates
for time-varying gain. Commercial systems with this algorithm
are available (ADVantage, Scisense, London, Ontario, Canada), and studies have proposed this as superior to the traditional approach and more forgiving of catheter misalignment in
the LV (21). Validation of this claim in various disease conditions has not been reported. In our hands, the traditional
approaches work very well and strongly correlate with echocardiographic or cardiac MRI-based volumes. Nonetheless, the
flow probe and saline calibration methods are tricky, and a
robust automated approach would indeed be valuable.
Surgical Technique and Common Pitfalls
To obtain reproducible, good quality P-V hemodynamics in
mice, a skillful operator is crucial. The following steps need to
be followed carefully: 1) induction of anesthesia and preparation of the skin for the procedure, 2) intubation and correct
placement of the mouse over a heating pad, 3) intravenous
access for hydration/volume expansion, 4) surgical approach to
Fig. 2. A: baseline pressure-volume (P-V) loop
for the LV, with stroke volume (SV) defined
as the average width of the loop (averaging
volumes from the 2 “vertical” sides). B: calibration of the parallel conductance. A set of
loops are recorded after rapid bolus injection
of hypertonic saline (⬃10 ␮l). Ventricular
pressures are minimally altered if this is performed correctly. C: peak and trough volumes
[end-diastolic volume (EDV) and end-systolic
volume (ESV)] are plotted, and a regression
between them is extrapolated to the line of
identity (dashed line) to determine parallel
conductance (Vp). Once done, this can be
subtracted from the conductance signal to obtain calibrated LV volume.
AJP-Heart Circ Physiol • VOL
301 • DECEMBER 2011 •
www.ajpheart.org
Downloaded from http://ajpheart.physiology.org/ by 10.220.33.1 on October 5, 2016
Doppler ultrasound, thermodilution, or other methods (5, 10,
30). One determines the stroke volume (SV) by this approach
and then calibrates the conductance signal to match it. This is
done by estimating the average width of the P-V loop and
setting this to the independently determined SV. This gives us
the “true” SV (Fig. 2A).
To assess the offset or parallel conductance, one can use the
hypertonic saline calibration method first proposed by Baan et
al. (2) and later applied and validated by our group in mice (9).
This is based on the principle that if one only varies the
conductivity of blood (introducing a very low volume of
hypertonic saline into the venous return) but not actual blood
volume, the catheter would interpret this as an increase in
volume from one beat to the next (Fig. 2B). This is then used
to estimate what the catheter signal would be if there was no
blood conductance volume, i.e., signal from non-blood sources
(Fig. 2C). This becomes the parallel conductance. Details of
this as well as pitfalls have been previously reported (9, 30).
Key issues are that LV pressures should be stable during this
injection and beats during the initial wash-in phase of rising
volume signals are used. Anything else reflects changes in real
LV function because of the hypertonic saline typically depressing function.
Most recently, another method to calibrate the conductance
signal has been proposed that is based on a real-time assess-
Review
H2201
ASSESSMENT OF CARDIAC FUNCTION IN MICE
exposing the diaphragm where a window is performed with an
electrocautery device (this is crucial since the diaphragm is
vascularized and bleeds after sectioning without cauterization).
The LV apex is punctured with a 26- to 27-gauge needle, and
the catheter is carefully introduced via this puncture. It is
important to use the correct needle size, large enough to allow
the introduction of the catheter without damaging it, but not too
large that the blood will flow back from a hole bigger than the
catheter’s diameter. LV catheterization retrograde, with the
catheter introduced via the right carotid artery, has also been
used by many. Our group prefers the apical approach since
there is never a question of placement: the possibility of being
trapped along the wall in trabeculae or papillary muscle is
minimized, and one knows where the electrodes are.
Once inside the LV, a correct positioning of the catheter is
also important. Its shaft needs to be aligned with the LV major
(longitudinal) axis, with both outer electrodes right below the
aortic valve and adjacent to the apical endocardial border,
respectively (Fig. 1). Correct volume and pressure signals
should be identified, together with generally squared- to ovalshaped loops (Fig. 2A). Before recording data, a change in
loading conditions [either via inferior vena cava (IVC) occlusion or aortic constriction maneuver] should be performed to
ensure that the electrodes are not in contact with intracardiac
structures (i.e., papillary muscles) during the loading-changing
maneuver. The catheter itself has a cross-sectional diameter of
0.625 mm, and with a 7-mm long axis, this occupies a bit more
than 2 ␮l. This is ⬍10% of end-diastolic volume (EDV) but
could be a substantial percentage of end-systolic volume, and
Table 1. Schematic of P-V catheter placement via left ventricular apex in the mouse
Anesthetic Agent
Parameter
Body weight, g
Heart rate, beats/min
MAP, mmHg
ESP, mmHg
EDP, mmHg
ESV, ␮l
EDV, ␮l
Stroke volume, ␮l
CO, ml/min
CI, ml 䡠 min⫺1 䡠 kg
Ea, mmHg/␮l
TPR, mmHg 䡠 ml⫺1 䡠 min
Systolic indexes
Ejection fraction, %
dP/dtmax, mmHg/s
SW, mmHg 䡠 ␮l
Ees (Emax), mmHg/␮l
dP/dtmax-EDV, mmHg 䡠 s⫺1 䡠 ␮l⫺1
PRSW, mmHg
Efficiency, %
Diastolic indexes
⫺dP/dtmin, mmHg/s
␶ (W), ms
␶ (G), ms
EDPVR
Urethane ⫹ Etomidate ⫹ Morphine
Ketamine ⫹ Xylazine
Pentobarbital Sodium
80–120
2–8
2–12
20–33
14–26
7–16
280–557
4–6
—
20–34
470–620
81–105
92–118
1–6
7–21
25–53
17–30
8–16
350–580
3–7
6–12
20–34
340–510
93–109
104–125
1–9
9–20
25–39
14–21
6–10
225–400
5–9
10–19
20–34
365–550
72–90
90–110
2–8
10–29
28–54
17–25
6–13
226–480
4–6
7–14
50–88
9,500–16,000
1,200–2,700
6–14
360–600
70–130
70–85
55–72
8,200–14,200
1,500–2,600
7–14
180–470
58–93
60–75
49–63
7,700–14,480
1,600–2,200
—
—
—
—
44–62
6,900–11,000
1,100–2,100
6–9
160–390
51–86
55–68
6,000–12,000
—
7–9
—
6,700–10,500
4.4–7.6
7–12
0.04–0.12
6,900–10,400
4.8–8.5
8–13
—
5,400–9,500
4.9–10
7–15
0.06–0.2
20–30
490–655
Isoflurane
CI, cardiac index; CO, cardiac output; dP/dtmax-EDV, relation of peak rate of pressure rise and end-diastolic volume; ⫺dP/dtmin, peak rate of pressure decline;
Ea, arterial elastance (measure of ventricular afterload); EDP, end-diastolic pressure; EDPVR slope, end-diastolic pressure-volume (P-V) relation slope; EDV,
end-diastolic volume; Ees (Emax), end-systolic elastance (slope of the end-systolic relationship); Efficiency [stroke work (SW)/P-V area]; ESP, end-systolic
pressure; ESV, end-systolic volume; MAP, mean arterial pressure; PRSW, preload-recruitable stroke work (slope of stroke work-EDV relationship); ␶ (G),
relaxation time constant calculated by Glantz method (regression of dP/dt vs. pressure); ␶ (W), relaxation time constant calculated by Weiss method [regression
of log(pressure)]; TPR, total peripheral resistance, MAP/CO. Values were calculated with correction based on aortic flow measurements and saline calibrations
as described from P-V loops obtained with open-chest approach (modified from Ref. 30; used with permission).
AJP-Heart Circ Physiol • VOL
301 • DECEMBER 2011 •
www.ajpheart.org
Downloaded from http://ajpheart.physiology.org/ by 10.220.33.1 on October 5, 2016
expose the cardiac apex, and 5) correct introduction and
positioning of the catheter into the LV.
Different anesthetics are available (Table 1), though we
continue to prefer a combination of etomidate-urethane or
etomidate-isoflurane. After the mouse has been placed in a
Plexiglas box with isoflurane for several seconds, an injection
of ethomidate (5–10 mg/kg ip) is given, the chest and neck are
shaved (internal jugular vein access is necessary for intravenous fluid administration), and the animal is intubated (or
tracheostomized). The mouse is placed on a heating pad to
keep body temperature around ⬃37°C and ventilated (for a
25-g intubated mouse, we use a respiratory rate of 130 –150/
min and tidal volume of 200 –250 ␮l). Temperature control in
anesthetized mice is critical. The mouse heart rate is exquisitely sensitive to changes in temperature, and HR (and contractility) can easily decreased by half the normal values if
heating is inappropriate. A warm pad at 40 – 45°C will keep
body temperature close to 37°C. If possible, monitoring is
preferred with a rectal thermometer. It is important to achieve
normal baseline contractility parameters, such as HR and peak
rate of pressure rise (dP/dtmax) (see Table 1), and maintain
them steady throughout the procedure while data are being
acquired.
The internal jugular vein should be accessed (e.g., a PE-10
silastic tubing connected to a 30-gauge needle), and a constant
infusion of 12.5% albumin in normal saline is given at 5
␮l/min, after an initial 50-␮l bolus. This is necessary to
counteract the peripheral vasodilatation and hypotension induced by anesthesia. A subxyphoid incision is made next,
Review
H2202
ASSESSMENT OF CARDIAC FUNCTION IN MICE
Assessment of Ventricular Function
Ventricular P-V data are the in vivo chamber correlate of
isolated muscle force-length relations; active and passive
force-length relations correspond to the end-diastolic and endsystolic P-V relations. P-V data are affected not only by
myocyte properties, however, but also by vascular and extracellular matrix, as well as by chamber geometry. Various
parameters derived from these relations can therefore be impacted by nonmyocyte behavior, and this needs to be kept in
mind. One can divide the parameters typically obtained into
several groupings: 1) resting function, 2) systolic relations,
3) diastolic relations, 4) ventricular-vascular coupling, and
5) energetics.
Resting function. Baseline P-V data provide standard measures of volumetric function (e.g., ejection fraction and stroke
work) but also peak ventricular power (maximal pressure-flow
product), pressures and pressure derivatives, relaxation time
constants, and other parameters. Loops are not always perfectly
vertical during isovolumic contraction and relaxation, even
without any physiological mechanism for deviation. This is
most often due to slight signal artifacts which become obvious
when pressure is changing rapidly as it does in these two
Fig. 3. A: P-V loops obtained after decreasing
preload through inferior vena cava occlusion
(left) or increasing afterload by constricting
the ascending aorta (right). Two potential fit
methods are shown, a linear (based on perpendicular regression) or nonlinear (logarithmic). B: stroke work (SW) versus EDV plots
for each data set. With preload reduction, the
slope (called preload-recruitable SW) is positive, highly linear, and a robust refection of
systolic function that is chamber size independent. For the afterload example, the slope
was negative and is uninterpretable as a contractility index. C: another useful systolic
performance index is the slope of the peak
rate of pressure rise (dP/dtmax)-EDV dependence. This can be derived if a preload
change maneuver is generated, but as dP/
dtmax is little altered by afterload, such data
are inadequate to generate this index.
AJP-Heart Circ Physiol • VOL
301 • DECEMBER 2011 •
www.ajpheart.org
Downloaded from http://ajpheart.physiology.org/ by 10.220.33.1 on October 5, 2016
during transient IVC occlusion, where these volumes decline
further, this can lead to pressure spiking at end systole often
because of entrapment. This can be usually fixed with some
modest additional fluid repletion. Other than this, having the
catheter occupy blood volume space in the chamber does not
impact function, and as the signal is calibrated to external
standards, this “dead volume” is corrected for.
As mentioned earlier, to change the loading conditions,
transient occlusion of the IVC or aorta is usually performed.
For the former, this is achieved by either pushing with a cotton
tip right before the IVC enters the right atrium or pulling from
a suture placed around the vessel. For the aorta, the suture
technique is recommended given the higher pressures. For the
latter, we personally prefer to perform an incision at the second
and third ribs left to the sternum, following the surgical
technique used for transverse aortic coarctation (4), and expose
the ascending aorta, where a 5-0 to 7-0 suture is passed around
the vessel. Several P-V loops are then recorded while changing
loading conditions (examples shown in Fig. 3A). P-V analysis
is not identical based on these different loading maneuvers, and
for a variety of reasons, including analytical and physiological,
preload modulation is preferable. This is discussed in more
detail below.
Review
ASSESSMENT OF CARDIAC FUNCTION IN MICE
AJP-Heart Circ Physiol • VOL
Fig. 4. Alternative methods to assess “inotropic” change from sets of nonlinear
end-systolic P-V relations. Rather than comparing linear slopes or curvilinear
fit parameters, one can determine the area bounded between two relations
within the physiologically measured pressure range. This is done by analytical
integration using in this instance nonlinear fits to each end-systolic P-V
relation. See Ref. 37 for details.
and involve physiological pressures. The area is determined
from the nonlinear fits using analytical integration, and it
represents an altered P-V area that the heart can operate within
as a result of an ESPVR change. Third, the ESPVR is relatively
but not absolutely load independent. Studies performed in the
mid-1980s demonstrated the impact of high afterload on the
ESPVR (shifting it leftward) (8), and differences in ESPVRs
derived from preload versus afterload modulated contractions
(1, 12). The latter more than the former impacts the duration of
systole and the extent of shortening, so different loops may not
really be derived from identical resting contractile states (17).
This is less prominent with preload change.
Diastolic relations. One of the common uses of P-V relations is to define the diastolic P-V relation (DPVR), something
difficult to do from imaging methods. This ideally requires
more than single steady-state beats, as the relations are impacted by relaxation processes, right ventricular load, and
pericardial constraint (14). Using a set of loops measured over
a range of loading (typically IVC occlusion), one identifies the
lower boundary, fitting the data to linear, exponential, logarithmic (14), or harmonic oscillator models (27). The most
common is an exponential model: P ⫽ ␣(e␤V ⫺ 1) ⫹ P0, where
␣ is a stiffness and scaling coefficient, and ␤ is chamber
stiffness coefficient, and P0 offset pressure at a volume of 0.
Figure 5 shows an example of marked differences in DPVR
between mice with desmin-related cardiomyopathy and controls. While Doppler indexes of filling can be used to assess
such restrictive type physiology, the direct analysis of P-V
relations during diastole is valuable to determine stiffness
modulation.
As with ESPVR, one needs to be careful about analyzing
DPVRs. The most common fit using an exponential is overparameterized for the data being fit, i.e., that while one can
identify parameters by the curve fit algorithm, alternative fits
with quite different parameter sets can fit the data virtually as
well. Examining the displacement between relations by area
integration or other subtraction methods (19), which do not
rely solely on the model fits, can be used.
There are other indexes of diastolic function that are
derivable from P-V relations. The first is the rate of decline
301 • DECEMBER 2011 •
www.ajpheart.org
Downloaded from http://ajpheart.physiology.org/ by 10.220.33.1 on October 5, 2016
periods. Rather than use maximum and minimum volumes to
determine SV, we prefer averaging multiple volumes from the
mid-two sides of the loop, taking advantage of the additional
data available. This reduces a bias of selecting one point over
another and uses more of the available data. SV is then the
mean width of the loop. This calibration impacts other parameters, so it is worth considering. Data are typically derived
from multiple signal-averaged beats or can be determined from
multiple beats and then averaged.
Systolic relations. The primary P-V relation identified by
Sagawa and colleagues was the ESPVR. Ideally, this is determined by finding the points of maximal P/(V ⫺ Vo) for each
beat, using an iterative method to identify Vo and then fitting
the data using perpendicular regression. The latter is preferred
over linear regression, since it does not designate a dependent
and independent variable but minimizes the perpendicular
distance of each point to the regression line. Nonlinear models
have also been described, typically a parabolic model (15) or a
theoretically based logarithmic model (26). As shown in the
two examples in Fig. 3A, the ESPVR may be fit to a linear
model, though it is often curvilinear. In the measured data
range, the difference may be subtle, but extrapolations clearly
differ.
There are a number of alternative systolic relations that have
been derived from the same P-V data, all with the goal of
deriving a systolic index less susceptible to changes in LV
load. Little et al. (22) studied the dP/dtmax-EDV relation (22),
which is more sensitive to inotropic change from PKA phosphorylation than is the ESPVR. Rankin and colleagues (11)
developed preload-recruitable stroke work (PRSW), a linear
version of the Sarnoff relation (35), and Sharir and Kass (39)
pursued maximal power-EDV relations. Each of these ordinate
parameters, dP/dtmax, stroke work, and maximal power, vary
with preload but less with afterload (unless pushed to extremes). Thus, if a set of P-V data are obtained by transient
aortic occlusion, none of these is useful, whereas all can be
derived from preload modified data. This is shown in Fig. 3B.
Only the preload reduction-derived data are interpretable,
whereas the relations from the afterload increase analysis are
not. PRSW is particularly useful because its units are force
(pressure) and errors in volume calibration are removed. As a
result, it is chamber size independent, so mice, rats, dogs, pigs,
sheep, and humans all have the same normal rest value of
70 –90 mmHg. This is a useful independent check on P-V
analysis and on the condition of the hearts being studied.
Reports of PRSW values in the 30 – 40 mmHg range in control
animals raise concerns about cardiac depression and experimental conditions and would make corresponding transgenic
analysis suspect.
There are several important issues pertinent to comparing
ESPVRs. First, the position as well as slope are relevant, a
relation that is acutely leftward shifted but with a lower slope
does not indicate depressed contractility but more likely nonlinear behavior (15). Acute interventions with inotropes or
pacing can impact both slope and extrapolated Vo. Second, a
quantitation of shifts of these relations to acute interventions
may be misleading when based solely on slope, particularly if
the data are nonlinear. As depicted in prior studies (28, 40) and
in Fig. 4, differences between nonlinear ESPVRs can easily be
assessed by an area defined between them. This P-V area is
constrained to lie within the measured range of the data sets
H2203
Review
H2204
ASSESSMENT OF CARDIAC FUNCTION IN MICE
Fig. 5. Use of P-V analysis to assess the diastolic P-V relation. Data from mice harboring a
R120G mutation in B-crystalin (CryABR120G)
that causes desmin-related cardiomyopathy and
littermate controls are shown. The former was
associated with chamber dilation, and marked
diastolic stiffening reflected by the end-diastolic
P-V relation (EDPVR) are shown here fit by a
3-parameter monoexponential relation.
the case in depressed ventricles with dilated cardiomyopathy. Here, an alternative logistic model has proven to be the
better choice (25, 37). If one assumes an exponential decay
when the actual pressure decline waveform does not follow
this trajectory, then the calculated ␶ will be artificially high
and sensitive to the absolute value of pressure estimated at
end diastole. Lastly, one can determine end-diastolic pressure, which with P-V loops is often defined as the pressure
at the lower right corner. Without volume data, it is often
defined as the pressure at peak QRS or pressure when dP/dt
exceeds 10% of maximum. A visual determination from
pressure waves alone is often unreliable.
Fig. 6. A: use of effective arterial elastance (Ea)
to assess LV afterload. Three loops at different
levels of aortic occlusion are shown, and Ea ⫽
end-systolic pressure/SV is shown for each.
B: normalized time-varying elastance [En(t)] derived from mice lacking myosin-binding protein C (MyBPC⫺/⫺) and from 4 different genetic models of heart failure. MyBPC deletion
results in a unique temporal shortening of the
time course, abbreviating systole. This was a
primary mechanical defect in this model. Mycard, myocardium; MKK3a, MAPK kinase 3a;
TnI t/t, troponin I truncation mutation. C: effect
of omecamtiv mecarbil (myosin ATPase activator) on En(t). Unlike dobutamine (left), which
accelerates ventricular stiffening and abbreviates systole, omecamtiv mecarbil had no impact on the initial rising phase but markedly
prolonged the duration of systolic stiffening.
Thus the time to reach peak En(t) was lengthened. This is a novel mechanism of action for a
cardiac inotrope, and one that required P-V
analysis to identify. TEmax and TEmin, time at
maximal and minimal elastance, respectively.
AJP-Heart Circ Physiol • VOL
301 • DECEMBER 2011 •
www.ajpheart.org
Downloaded from http://ajpheart.physiology.org/ by 10.220.33.1 on October 5, 2016
of ventricular pressure during isovolumetric relaxation, assessed from micromanometer data. Here too, assumptions
are often made that may not be appropriate. The most
common model is a monoexponential decay fit to the pressure from peak rate of pressure decline to the estimated
onset of LV filling (end-diastolic pressure ⫹ 2–5 mmHg).
The time constant ␶ is reported. However, some models
assume pressure decays to zero, and this may not be the case
(more often not in intact humans). Assuming this when not
the case will yield a falsely high ␶ value (37, 38). Second,
these models assume that pressure decay follows a monoexponential. This is reasonable for normal hearts but is not
Review
ASSESSMENT OF CARDIAC FUNCTION IN MICE
AJP-Heart Circ Physiol • VOL
faster heart rates and load dependence of relaxation (28). The
second example pertains to a pharmaceutical study of a drug
currently in clinical trials for heart failure. The drug, omecamtiv mecarbil, activates the myosin ATPase (24), enhancing the
probability of forming a tightly bound cross bridge. This
results in a prolongation of the systolic phase of En(t) without
accelerating early contraction as would dobutamine (Fig. 6C).
Here too, dP/dtmax was unaltered by the drug, though ejection
properties were. The P-V relation analysis proved central to
defining the mechanism of action.
Conclusion
P-V analysis remains the most detailed and precise analytic
approach to chamber heart function yet developed. Its introduction into mouse research has truly ignited interest from
many investigators outside the biomechanics field, though
some more sophisticated hemodynamic understanding is
needed to employ it correctly. The more one appreciates the
pitfalls and strengths, the more likely real insights will be
derived. Most of the primary resources for this analysis are old,
and to our knowledge there are no recent monograms summarizing the work for nonengineers. Hopefully, this review
helped address that gap.
DISCLOSURES
No conflicts of interest, financial or otherwise, are declared by the author(s).
AUTHOR CONTRIBUTIONS
Author contributions: O.H.C. and D.A.K. prepared figures; O.H.C. and
D.A.K. drafted manuscript; O.H.C. and D.A.K. edited and revised manuscript;
D.A.K. approved final version of manuscript.
REFERENCES
1. Baan J, Van der Velde ET. Sensitivity of left ventricular end-systolic
pressure-volume relation to type of loading intervention in dogs. Circ Res
62: 1247–1258, 1988.
2. Baan J, Van der Velde ET, de Brun HG, Smeenk GJ, Koops J, van
Dijk AD, Temmerman D, Senden J, Buis B. Continuous measurement of
left ventricular volume in animals and humans by conductance catheter.
Circulation 70: 812–823, 1984.
3. Burkhoff D, Sugiura S, Yue DT, Sagawa K. Contractility-dependent
curvilinearity of end-systolic pressure- volume relations. Am J Physiol
Heart Circ Physiol 252: H1218 –H1227, 1987.
4. Cingolani OH, Perez NG, Ennis IL, Alvarez MC, Mosca SM, Schinella
GR, Escudero EM, Console G, Cingolani HE. In vivo key role of
reactive oxygen species and NHE-1 activation in determining excessive
cardiac hypertrophy. Pflugers Arch. 2011 Aug 26. [Epub ahead of print.]
5. Cingolani OH, Yang XP, Cavasin MA, Carretero OA. Increased
systolic performance with diastolic dysfunction in adult spontaneously
hypertensive rats. Hypertension 41: 249 –254, 2003.
6. de Tombe PP, Jones S, Burkhoff D, Hunter WC, Kass DA. Ventricular
stroke work and efficiency both remain nearly optimal despite altered
vascular loading. Am J Physiol Heart Circ Physiol 264: H1817–H1824,
1993.
7. Frank O. Dynamik des Herzmuskels. Z Biol 32: 370 –370, 1895.
8. Freeman GL. Effects of increased afterload on left ventricular function in
closed-chest dogs. Am J Physiol Heart Circ Physiol 259: H619 –H625,
1990.
9. Georgakopoulos D, Kass DA. Estimation of parallel conductance by
dual-frequency conductance catheter in mice. Am J Physiol Heart Circ
Physiol 279: H443–H450, 2000.
10. Georgakopoulos D, Mitzner WA, Chen CH, Byrne BJ, Millar HD,
Hare JM, Kass DA. In vivo murine left ventricular pressure-volume
relations by miniaturized conductance micromanometry. Am J Physiol
Heart Circ Physiol 274: H1416 –H1422, 1998.
11. Glower DD, Spratt JA, Snow ND, Kabas JS, Davis JW, Olsen CO,
Tyson GS, Sabiston DC, Rankin JS. Linearity of the Frank-Starling
301 • DECEMBER 2011 •
www.ajpheart.org
Downloaded from http://ajpheart.physiology.org/ by 10.220.33.1 on October 5, 2016
Ventricular-arterial coupling. While P-V relations can yield
characterizations of the heart that are relatively less impacted
by the loading constraints imposed on the ventricle, they also
yield metrics of this load. EDV, for example, is the most
straightforward translation of preload, since it more than pressure relates to the actual stretch of the myocardium before
systole. Aortic impedance can also be examined, using the
effective arterial elastance proposed by Sunagawa and colleagues (46, 47). This is most commonly derived from the
end-systolic pressure-to-SV ratio and is largely dictated by
systemic resistance and heart rate (Fig. 6A). The coupling ratio
of arterial elastance to end-systolic elastance generally falls
between 0.7 and 1.2, a range where heart and vessels are
optimally linked to provide the greatest work, power, and
efficiency (6). The capacity to selectively manipulate heart
versus vascular cells using genetic engineering of mice means
that an analysis of the interaction between them can be quite
important to the phenotype.
Energetics. P-V relations have also been extensively analyzed as a means to extract useful mechanoefficiency information. The total P-V area as first defined by Suga and colleagues
(29) includes the external work of a P-V loop and “internal
work” bounded by the left side of the loop, ESPVR, and
DPVR. P-V area is linearly related to total myocardial oxygen
consumption and has been useful for examining mechanisms
by which energetics of the heart are altered by disease and
molecular processes. Most applications of this analysis have
been conducted in isolated hearts, where precise changes in the
P-V area and global measures of oxygen consumption are
feasible. This has been achieved in isolated mouse hearts as
well (13, 32).
Other applications: normalized time-varying elastance. The
preceding discussion has reviewed traditional uses of P-V
relations, i.e., more comprehensively examined systolic and
diastolic function of the heart, identified cardiac-loading interactions, and quantified energetic efficiency status. However,
there are other parameters that are not a traditional focus but
can be very important. A major example is analysis of the time
course of ventricular elastance {E(t) ⫽ P(t)/[V(t) ⫺ Vo]} itself.
While the absolute magnitude of E(t) clearly varies with
contractility and heart size (mouse is ⬃4,000⫻ human) and its
time course is influenced by heart rate, a binormalized curve
(to both amplitude and time to peak) is remarkably conserved.
This was first shown in patients encompassing a broad range of
clinical heart diseases, heart rates, inotropic status, and other
features (36). The human relation is very similar to mouse (10).
Two recent studies have revealed how normalized timevarying elastance [En(t)] can be profoundly altered by either
genetic or pharmacological interventions to greatly impact
systolic function. In both instances, more traditional measures
such as dP/dtmax were little impacted. The first example is a
genetic model involving the absence of myosin binding protein
C. In these mice, the En(t) curve was profoundly abbreviated,
peaking just before the onset of ejection and then declining
(Fig. 6B). By contrast, En(t) was little altered in mice with a
broad array of genetic manipulations that altered calcium
cycling, signaling kinases, myofilament, and cytoskeletal proteins (31) (Fig. 6B). The impact of myosin-binding protein C
on contraction and relaxation kinetics was subsequently explored by P-V relations, in a study that revealed the criticality
of this protein to shortening of the diastolic filling period at
H2205
Review
H2206
12.
13.
14.
15.
16.
17.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
relationship in the intact heart: the concept of preload recruitable stroke
work. Circulation 71: 994 –1009, 1985.
Hunter WC. End-systolic pressure as a balance between opposing effects
of ejection. Circ Res 64: 265–275, 1989.
Kameyama T, Chen Z, Bell SP, Fabian J, LeWinter MM. Mechanoenergetic studies in isolated mouse hearts. Am J Physiol Heart Circ Physiol
274: H366 –H374, 1998.
Kass DA. Assessment of diastolic dysfunction. Invasive modalities. Cardiol Clin 18: 571–586, 2000.
Kass DA, Beyar R, Lankford E, Heard M, Maughan WL, Sagawa K.
Influence of contractile state on curvilinearity of the in situ end-systolic
pressure-volume relations. Circulation 79: 167–178, 1989.
Kass DA, Chen CH, Curry C, Talbot M, Berger R, Fetics B, Nevo E.
Improved left ventricular mechanics from acute VDD pacing in patients
with dilated cardiomyopathy and ventricular conduction delay. Circulation 99: 1567–1573, 1999.
Kass DA, Maughan WL. From ‘Emax’ to pressure-volume relations: a
broader view. Circulation 77: 1203–1212, 1988.
Kass DA, Midei M, Brinker J, Maughan WL. Influence of coronary
occlusion during PTCA on end-systolic and end-diastolic pressure-volume
relations in humans. Circulation 81: 447–460, 1990.
Kass DA, Wolff MR, Ting CT, Liu CP, Chang MS, Lawrence W,
Maughan WL. Diastolic compliance of hypertrophied ventricle is not
acutely altered by pharmacologic agents influencing active processes. Ann
Intern Med 119: 466 –473, 1993.
Kass DA, Yamazaki T, Burkhoff D, Maughan WL, Sagawa K. Determination of left ventricular end-systolic pressure-volume relationships by
the conductance (volume) catheter technique. Circulation 73: 586 –595,
1986.
Kottam AT, Porterfield J, Raghavan K, Fernandez D, Feldman MD,
Valvano JW, Pearce JA. Real time pressure-volume loops in mice using
complex admittance: measurement and implications. Conf Proc IEEE Eng
Med Biol Soc 1: 4336 –4339, 2006.
Little WC. The left ventricular dP/dtmax-end-diastolic volume relation in
closed-chest dogs. Circ Res 56: 808 –815, 1985.
Little WC, Freeman GL, O’Rourke RA. Simultaneous determination of
left ventricular end-systolic pressure-volume and pressure-dimension relationships in closed- chest dogs. Circulation 71: 1301–1308, 1985.
Malik FI, Hartman JJ, Elias KA, Morgan BP, Rodriguez H, Brejc K,
Anderson RL, Sueoka SH, Lee KH, Finer JT, Sakowicz R, Baliga R,
Cox DR, Garard M, Godinez G, Kawas R, Kraynack E, Lenzi D, Lu
PP, Muci A, Niu C, Qian X, Pierce DW, Pokrovskii M, Suehiro I,
Sylvester S, Tochimoto T, Valdez C, Wang W, Katori T, Kass DA,
Shen YT, Vatner SF, Morgans DJ. Cardiac myosin activation: a potential therapeutic approach for systolic heart failure. Science 331: 1439 –
1443, 2011.
Matsubara H, Takaki M, Yasuhara S, Araki J, Suga H. Logistic time
constant of isovolumic relaxation pressure-time curve in the canine left
ventricle. Better alternative to exponential time constant. Circulation 92:
2318 –2326, 1995.
Mirsky I, Tajimi T, Peterson KL. The development of the entire
end-systolic pressure-volume and ejection fraction-afterload relations: a
new concept of systolic myocardial stiffness. Circulation 76: 343–356,
1987.
Mossahebi S, Shmuylovich L, Kovacs SJ. The thermodynamics of
diastole: kinematic modeling-based derivation of the P-V loop to transmitral flow energy relation with in vivo validation. Am J Physiol Heart
Circ Physiol 300: H514 –H521, 2011.
Nagayama T, Takimoto E, Sadayappan S, Mudd JO, Seidman JG,
Robbins J, Kass DA. Control of in vivo left ventricular contraction/
relaxation kinetics by myosin binding protein C: protein kinase A phosphorylation dependent and independent regulation. Circulation 116:
2399 –2408, 2007.
Nozawa T, Yasumura Y, Futaki S, Tanaka N, Igarashi Y, Goto Y,
Suga H. Relation between oxygen consumption and pressure-volume area
of in situ dog heart. Am J Physiol Heart Circ Physiol 253: H31–H40,
1987.
AJP-Heart Circ Physiol • VOL
30. Pacher P, Nagayama T, Mukhopadhyay P, Batkai S, Kass DA. Measurement of cardiac function using pressure-volume conductance catheter
technique in mice and rats. Nat Protoc 3: 1422–1434, 2008.
31. Palmer BM, Georgakopoulos D, Janssen PM, Wang Y, Alpert NR,
Belardi DF, Harris SP, Moss RL, Burgon PG, Seidman CE, Seidman
JG, Maughan DW, Kass DA. Role of cardiac myosin binding protein C
in sustaining left ventricular systolic stiffening. Circ Res 94: 1249 –1255,
2004.
32. Palmer BM, Noguchi T, Wang Y, Heim JR, Alpert NR, Burgon PG,
Seidman CE, Seidman JG, Maughan DW, LeWinter MM. Effect of
cardiac myosin binding protein-C on mechanoenergetics in mouse myocardium. Circ Res 94: 1615–1622, 2004.
33. Porterfield JE, Kottam AT, Raghavan K, Escobedo D, Jenkins JT,
Larson ER, Trevino RJ, Valvano JW, Pearce JA, Feldman MD.
Dynamic correction for parallel conductance, GP, and gain factor, alpha,
in invasive murine left ventricular volume measurements. J Appl Physiol
107: 1693–1703, 2009.
34. Sagawa K, Maughan WL, Suga H, Sunagawa K. Cardiac Contraction
and the Pressure-Volume Relationship. New York, NY: Oxford University
Press, 1988.
35. Sarnoff SJ, Mitchell JH. The regulation of the performance of the heart.
Am J Med 30: 747–747, 1961.
36. Senzaki H, Chen CH, Kass DA. Single-beat estimation of end-systolic
pressure-volume relation in humans. A new method with the potential for
noninvasive application. Circulation 94: 2497–2506, 1996.
37. Senzaki H, Fetics B, Chen CH, Kass DA. Comparison of ventricular
pressure relaxation assessments in human heart failure: quantitative influence on load and drug sensitivity analysis. J Am Coll Cardiol 34:
1529 –1536, 1999.
38. Senzaki H, Kass DA. Analysis of isovolumic relaxation in failing hearts
by monoexponential time constants overestimates lusitropic change and
load dependence: mechanisms and advantages of alternative logistic fit.
Circ Heart Fail 3: 268 –276, 2010.
39. Sharir T, Feldman MD, Haber H, Feldman AM, Marmor A, Becker
LC, Kass DA. Ventricular systolic assessment in patients with dilated
cardiomyopathy by preload-adjusted maximal power. Validation and noninvasive application. Circulation 89: 2045–2053, 1994.
40. Soergel DG, Georgakopoulos D, Stull LB, Kass DA, Murphy AM.
Augmented systolic response to the calcium sensitizer EMD-57033 in a
transgenic model with troponin I truncation. Am J Physiol Heart Circ
Physiol 286: H1785–H1792, 2004.
41. Suga H. Ventricular Energetics. Physiol Rev 70: 247–277, 1990.
42. Suga H, Hisano R, Goto Y, Hamada O. Normalization of end-systolic
pressure-volume relation and Emax of different sized hearts. Jpn Circ J
48: 136 –143, 1984.
43. Suga H, Hisano R, Goto Y, Yamada O, Igarashi Y. Effect of positive
inotropic agents on the relation between oxygen consumption and systolic
pressure volume area in canine left ventricle. Circ Res 53: 306 –318, 1983.
44. Suga H, Sagawa K, Demer L. Determinants of instantaneous pressure in
canine left ventricle: time and volume specification. Circ Res 46: 256 –
256, 1980.
45. Suga H, Sagawa K, Shoukas AA. Load independence of the instantaneous pressure-volume ratio of the canine left ventricle and effects of
epinephrine and heart rate on the ratio. Circ Res 32: 314 –314, 1973.
46. Sunagawa K, Maughan WL, Burkhoff D, Sagawa K. Left ventricular
interaction with arterial load studied in isolated canine ventricle. Am J
Physiol Heart Circ Physiol 245: H773–H780, 1983.
47. Sunagawa K, Maughan WL, Sagawa K. Optimal arterial resistance for
the maximal stroke work studied in isolated canine left ventricle. Circ Res
56: 586 –586, 1985.
48. Winter EM, Grauss RW, Atsma DE, Hogers B, Poelmann RE, van der
Geest RJ, Tschope C, Schalij MJ, Gittenberger-de Groot AC,
Steendijk P. Left ventricular function in the post-infarct failing mouse
heart by magnetic resonance imaging and conductance catheter: a comparative analysis. Acta Physiol (Oxf) 194: 111–122, 2008.
301 • DECEMBER 2011 •
www.ajpheart.org
Downloaded from http://ajpheart.physiology.org/ by 10.220.33.1 on October 5, 2016
18.
ASSESSMENT OF CARDIAC FUNCTION IN MICE