Download Coronary Blood Flow Models

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 contracHng myocardium inhibits its own blood flow. •  Porter, WT. (1898) observed that Hme averaged flow increased with heart contracHon and hence increased coronary flow. •  Sabiston and Gregg (1957) concluded that contracHon is an impeding factor to coronary blood flow. Coronary Systolic Flow Impediment (CSFI) Systolic flow is lower than diastolic flow. The inhibiHon of blood flow during systole, due to contracHon, 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 creaHng vascular waterfalls; thus, the primary impediment to coronary blood flow is pressure in the ventricle. Flow is proporHonal to the difference between the perfusion pressure and the Hssue pressure (waterfall pressure). •  This model assumes that intramyocardial pressure (or Hssue 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 !ssue pressure that is varying over the myocardial wall, from LV pressure at the endocardium, to thoracic pressure at the epicardium. It assumes that the Hssue pressure acts on the outer surface of the intramural vessels as a fluid pressure. In case Hssue pressure exceeds coronary arterial pressure, coronary flow would cease. •  With a lower Hssue pressure, only intramural veins are expected to locally collapse and at this collapse point, intramural pressure would be equal to Hssue pressure. Downey & Kirk, Circ Res, 1975. Vascular Waterfall Mechanism •  It explains the reducHon of coronary flow due to increase in resistance, but it is unable to explain the arterial inflow and venous ouclow. •  It can t account for retrograde systolic flow. •  Ignores resistance variaHons 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 ouclow resistance that roughly corresponds to the resistance of the arterioles and venules respecHvely. •  Cardiac contracHon squeezes blood volume out of the compliance, reducing arterial inflow and augmenHng venous ouclow. The elasHcity of the intramural vessels would then form a restoraHon force for intramural volume, augmenHng arterial inflow in the subsequent diastole and decreasing venous ouclow. 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 direcHon in systole. •  The capacitor in the electrical analog implies that during maintained contracHon (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 observaHon 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 Hme-­‐
varying ventricular wall sHffness, 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 ouclow. It fails to explain why the epicardial and endocardial flows are not Westerhof N. et al, Physiol Rev 2006; 86:1263-­‐1308. impaired to the same degree. ContracHlity induced changes in CBF •  CBF amplitude is strongly related to levels of contracHlity. ContracHlity has ~10 Hmes stronger effect than PLV on amplitude of CBF. •  It is the difference in sHffness 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 microcirculaHon. … during systole… White arrows indicate flow direcHon. Black arrows vessels indicate 10-­‐20% change in diameter. Epicardial arteries and midmyocardial venules change lijle. My model: Time-­‐Varying EffecHve Resistance using Wave Intensity Analysis (WIA) •  It is derived from one-­‐dimensional theory of flow in elasHc tubes; solved using the method of characterisHcs; holding the advantage of Hme-­‐
domain 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 propagaHon in the cardiovascular system. •  Wave speed is required for separaHng the wave travel into their forward and backward direcHons. The CirculaHon is NOT in Steady State OscillaHon Brief Introduction to WIA:
Windkessel + Wave P in the ventriculo-arterial coupling
•  We model Pressure as:
P Ao = PWk + Pex
•  Using conservation of
mass and assuming the
system is compliant
dPWk (t ) dPWk dVWk (t ) Qin (t ) ! Qout (t )
=
=
dt
dVWk dt
C
•  And the solution:
PWk (t ) " P$ = ( P0 " P$ )e
"
1
RC
+e
"
t!
Qin (t !) RC
#t C e dt!
0
1 t
RC
Wang, J.J., et al. Am. J. Heart Circ. Physiol., 2003, 284, H1358--H1368.
Reservoir-­‐Wave separaHon 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 Separa!on before and a1er extrac!on of the Reservoir component Measured
waveform
Forward
wave
Reflected
wave
Reservoir
component
© Imperial College London Reservoir-­‐Wave separa!on in the Coronary Arteries P waveforms are almost idenHcal Page 21 Velocity measurements in the Coronary Arteries •  Velocity waveforms are parHcularly determined by the systolic impediment due to myocardial contracHon. •  It cannot be assumed that the wave pressure (p) drives the blood flow into the coronaries
© Imperial College London Page 22 AssumpHons: •  It is noHceable 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 resisHve behaviour to flow. Calcula!on of the reservoir-­‐wave separa!on in the coronary arteries © Imperial College London Page 24 Time-­‐varying EffecHve Resistance •  We can then calculate an effecHve Hme-­‐varying resistance imposed by the coronary microcirculaHon for each of the measurement locaHons, 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 RelaHon between effecHve resistance and ventricular pressure EffecHve resistance is different in each vessel and varies depending its spaHal locaHon and the region of the myocardium they perfuse. © Imperial College London Page 26 Wave speed calculaHon and wave separaHon •  If we esHmate the wave speed, we can separate the waves into their forward and backward components and we can further use WIA to bejer understand coronary haemodynamics and the cross talk with myocardial contracHon. For example, in the LAD: Τ=1.02 s
c∑²= 10.94 m/s a= 9.6 m/s
Forward P wave
dist Forward U wave
prox Backward U wave
dist prox Page 27 Backward P wave
© Imperial College London Wave travel analysis provides evidence that perfusion into the myocardium is both due to the reservoir component and the acHve sucHon of the myocardium during its relaxaHon. 2
4
1
6
Wave Intensity Analysis in the Coronary Arteries 5
© Imperial College London Modified from Davies et al, CirculaHon 2006; 113:1768-­‐1778. What models lack: •  Effects on CBF of muscle shortening and thickening. •  Vascular deformaHon with contracHon, that involves changes of shape, vascular cross secHons, branching angles, vessel tortuosity) •  Subject specific parameterizaHon. ComputaHonal Models (Smith NP, 2004) •  Anatomically based, coupled to biomechanics. •  EsHmaHon of IMP from mechanical deformaHon. •  Arterioles, capillaries and venules (≈vessels<100μm) are represented with a lumped parameter model (intramyocardial pump). •  SoluHon of Navier-­‐Stokes equaHons of flow reduced to a 1D case. ComputaHonal Models Extra Assignment Use the Intramyocardial Pump Model, and add a variaHon to it. Ideas can be found in: •  Burarni 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.