Download Coronary Circulation

Coronary Blood Flow Models
Dr. Jazmin Aguado-Sierra
Brief History of Coronary Blood Flow
Modelling
• Scaramucci, J. (1695) was the earliest physiologist to postulate
that during systole, the contracting myocardium inhibits its
own blood flow.
• Porter, WT. (1898) observed that time averaged flow
increased with heart contraction and hence increased
coronary flow.
• Sabiston and Gregg (1957) concluded that contraction is an
impeding factor to coronary blood flow.
Coronary Systolic Flow Impediment
(CSFI)
Systolic flow is lower than diastolic flow. The inhibition of
blood flow during systole, due to contraction, is the CSFI.
Intramural blood volume varies throughout the cardiac cycle.
In systole, blood volume is squeezed out of the
intramyocardial vessels, but intramural blood volume is
restored during diastole. The level of perfusion
impediment depends on the balance between these two
processes.
At higher HR, there will be less net intramural vascular volume
and thereby on average coronary resistance will be
increased.
Coronary Blood Flow Models
• Systolic Extravascular Resistance (Gregg, 1957)
• Vascular waterfall mechanism (Downey & Kirk,
1975)
• Intramyocardial pump (Spaan, 1981)
• Time-varying elastance (Suga, 1973; Krams, 1989)
• Latest models
Systolic Extravascular Resistance
(Gregg, 1957)
• It assumes that coronary resistance in systole
is higher than in diastole due to extravascular
compression, without specifying the
mechanism.
• It assumed the compression effect fades away
quickly in diastole, so that at the end of
diastole, the coronary resistance could be
measured unrelated to the compression
effect.
Vascular Waterfall Mechanism
(Downey & Kirk, 1975)
• Intramyocardial pressure reduces coronary blood flow by creating vascular
waterfalls; thus, the primary impediment to coronary blood flow is pressure
in the ventricle. Flow is proportional to the difference between the perfusion
pressure and the tissue pressure (waterfall pressure).
• This model assumes that intramyocardial pressure (or tissue pressure)
changes from zero at the epicardium, to peak at ventricular pressure at the
endocardium.
Westerhof N. et al, Physiol Rev 2006; 86:1263-1308.
Vascular Waterfall Model
• It assumes that radial stress in the
ventricular wall generates a tissue
pressure that is varying over the
myocardial wall, from LV pressure at
the endocardium, to thoracic pressure
at the epicardium. It assumes that the
tissue pressure acts on the outer
surface of the intramural vessels as a
fluid pressure. In case tissue pressure
exceeds coronary arterial pressure,
coronary flow would cease.
• With a lower tissue pressure, only
intramural veins are expected to locally
collapse and at this collapse point,
intramural pressure would be equal to
tissue pressure.
Downey & Kirk, Circ Res, 1975.
Vascular Waterfall Mechanism
• It explains the reduction of coronary flow due to
increase in resistance, but it is unable to explain the
arterial inflow and venous outflow.
• It can’t account for retrograde
systolic flow.
• Ignores resistance variations
during cardiac cycle
Downey & Kirk, Circ Res, 1975.
Intramyocardial Pump (Spaan, 1981)
• This model ads the concept of
compliance of the intramural vessels
to the other models.
• The intramural vascular
compartment is represented by a
lumped compliance.
• The resistance of the intramural vessels is distributed into an inflow and
an outflow resistance that roughly corresponds to the resistance of the
arterioles and venules respectively.
• Cardiac contraction squeezes blood volume out of the compliance,
reducing arterial inflow and augmenting venous outflow. The elasticity of
the intramural vessels would then form a restoration force for intramural
volume, augmenting arterial inflow in the subsequent diastole and
decreasing venous outflow.
Intramyocardial Pump Model
• This model assumes that intramyocardial pressure changes from
zero at the epicardium, to peak at ventricular pressure at the
endocardium.
• It explains the arterio-venous lag by introducing the role of
compliance. Compliant vessels are filled during diastole and
discharged through the low-pressure venous direction in systole.
• The capacitor in the electrical analog implies that during maintained
contraction (heart arrested in systole) flow is not different from
arrest in diastole.
Westerhof N. et al, Physiol Rev 2006; 86:1263-1308.
Elastance (Krams, 1989)
• This model relies on the observation of similar flow
impediment in “isovolumic” and “isobaric” states.
Krams et al. Am J. Physiol. 1990; 258:H1889-98.
Elastance (Krams, 1989)
•
Applied the concept of Elastance to
the coronary artery flow.
E
•
•
•
P
V
It emphasizes the effect of timevarying ventricular wall stiffness,
which is assumed as independent
of the ventricular pressure.
The rate of change of vascular
volume determines the sum of the
decrease in arterial flow and
increase of venous outflow.
It fails to explain why the epicardial
and endocardial flows are not
impaired to the same degree.
Westerhof N. et al, Physiol Rev 2006; 86:1263-1308.
Contractility induced changes in CBF
• CBF amplitude is
strongly related to
levels of contractility.
Contractility has ~10
times stronger effect
than PLV on amplitude
of CBF.
• It is the difference in
stiffness of cardiac
muscle in systole and
diastole that
determines CBF
amplitude.
Krams et al. Am J. Physiol. 1989; 258:H1936-1944.
Recent Models (Kajiya, 2008)
Lumped model of intramyocardial microcirculation.
… during systole…
White arrows indicate
flow direction. Black
arrows vessels indicate
10-20% change in
diameter. Epicardial
arteries and
midmyocardial venules
change little.
My model: Time-Varying Effective
Resistance using Wave Intensity Analysis
(WIA)
• It is derived from one-dimensional theory of flow
in elastic tubes; solved using the method of
characteristics; holding the advantage of timedomain analysis and retaining the non-linear
treatment of flow in arteries.
• It allows the analysis of non-periodic, transient
flow.
• It refers to the analysis of wave energy and wave
propagation in the cardiovascular system.
• Wave speed is required for separating the wave
travel into their forward and backward directions.
The Circulation is NOT in Steady State Oscillation
Brief Introduction to WIA:
Windkessel + Wave P in the ventriculo-arterial coupling
• We model Pressure as:
P Ao  PW k  Pex
• Using conservation of
mass and assuming the
system is compliant
• And the solution:
Wang, J.J., et al. Am. J. Heart Circ. Physiol., 2003, 284, H1358--H1368.
Reservoir-Wave separation in systemic arteries
P( x, t )  P (t )  p ( x, t )
U ( x, t )  U (t )  u ( x, t )
Asc ao
Ao arch
Thor ao
Page 18
© Imperial College London
Abd ao
Separation of
reservoir and
wave pressure
along the aorta
P (measured pressure)
P (reservoir pressure)
U (measured velocity)
p (wave pressure)
The exponential decay in diastole is
very similar throughout the arterial
system.
The wave pressure is driving the
inflow to the arterial system.
Page 19
Aguado-Sierra J. JEM, 2007.
Wave Separation before and after
extraction of the Reservoir component
Measured
waveform
Forward
wave
Reflected
wave
Reservoir
component
© Imperial College London
Reservoir-Wave separation in the Coronary Arteries
P waveforms are
almost identical
Page 21
Velocity measurements in the Coronary Arteries
• Velocity waveforms are
particularly determined by the
systolic impediment due to
myocardial contraction.
• It cannot be assumed that the
wave pressure (p) drives the
blood flow into the coronaries
© Imperial College London
Page 22
Assumptions:
• It is noticeable that velocity in
diastole in the coronaries
follows the diastolic decay of
pressure.
Westerhof N. et al, Physiol Rev 2006; 86:1263-1308.
• Assuming that the reservoir component of Pressure drives the
flow into the coronary arteries and that during diastole, the
coronaries hold mostly a resistive behaviour to flow.
Calculation of the reservoir-wave separation
in the coronary arteries
© Imperial College London
Page 24
Time-varying Effective Resistance
• We can then calculate an effective time-varying resistance imposed by the
coronary microcirculation for each of the measurement locations, that can
describe the blood flow impediment in the coronary arteries, mainly
occurring during systole.
P(t )  Pv
R ( x, t ) 
U ( x, t )
Page 25
© Imperial College London
Relation between effective resistance and
ventricular pressure
Effective
resistance is
different in
each vessel and
varies
depending its
spatial location
and the region
of the
myocardium
they perfuse.
© Imperial College London
Page 26
Wave speed calculation and wave separation
•
If we estimate the wave speed, we can separate the waves into their forward and
backward components and we can further use WIA to better understand coronary
haemodynamics and the cross talk with myocardial contraction.
For example, in the LAD:
Τ=1.02 s
c∑²= 10.94 m/s a= 9.6 m/s
Forward P wave
dist
Backward P wave
Forward U wave
prox
Backward U wave
dist
prox
Page 27
© Imperial College London
Wave travel analysis provides
evidence that perfusion into
the myocardium is both due to
the reservoir component and
the active suction of the
myocardium during its
relaxation.
2
6
4
1
Wave Intensity Analysis in
the Coronary Arteries
5
© Imperial College London
Modified from Davies et al, Circulation 2006; 113:1768-1778.
What models lack:
• Effects on CBF of muscle shortening and
thickening.
• Vascular deformation with contraction, that
involves changes of shape, vascular cross
sections, branching angles, vessel tortuosity)
• Subject specific parameterization.
Computational Models
(Smith NP, 2004)
• Anatomically based, coupled to biomechanics.
• Estimation of IMP from mechanical
deformation.
• Arterioles, capillaries and venules
(≈vessels<100μm) are represented with a
lumped parameter model (intramyocardial
pump).
• Solution of Navier-Stokes equations of flow
reduced to a 1D case.
Computational Models
Extra Assignment
Use the Intramyocardial Pump Model, and add a variation to it. Ideas
can be found in:
• Burattini et al. Ann Biomed Eng 13:385-404, 1985.
• Bruinsma et al. Basic Res Cardiol 83:510-524,1988.
• Chadwick et al. Am J Physiol Heart Circ Physiol 258:H1687-H1698,
1990.
• Zinemanas et al. Ann Biomed Eng 22:638-652, 1994.
• Zinemanas et al. Am J Physiol Heart Circ Physiol 268:H633-H645,
1995.
• Hoffman and Spaan. Physiol Rev 70:331-390,1990.
• Arts T and Reneman RS, Bibl Anat 103-107, 1977.
• Arts T and Reneman RS, J Biomech Eng 107:50-56, 1985.