Pulsatile pressure and flow in the skeletal muscle microcirculation

Although blood flow in the microcirculation of the rat skeletal muscle has negligible inertia forces with very low Reynolds number and Womersley parameter, time-dependent pressure and flow variations can be observed. Such phenomena include, for example, arterial flow overshoot following a step arterial pressure, a gradual arterial pressure reduction for a step flow, or hysteresis between pressure and flow when a pulsatile pressure is applied. Arterial and venous flows do not follow the same time course during such transients. A theoretical analysis is presented for these phenomena using a microvessel with distensible viscoelastic walls and purely viscous flow subject to time variant arterial pressures. The results indicate that the vessel distensibility plays an important role in such time-dependent microvascular flow and the effects are of central physiological importance during normal muscle perfusion. In-vivo whole organ pressure-flow data in the dilated rat gracilis muscle agree in the time course with the theoretical predictions. Hemodynamic impedances of the skeletal muscle microcirculation are investigated for small arterial and venous pressure amplitudes superimposed on an initial steady flow and pressure drop along the vessel.     

The pressure-flow relation for plasma in whole organ skeletal muscle and its experimental verification.

The whole-organ pressure-flow relation in resting rat skeletal muscle is examined for the flow of plasma. Due to the small size of the blood vessels in this organ, inertia and convective forces in the blood are negligible and viscous forces dominate. Direct measurements in the past have shown that skeletal muscle blood vessels are distensible. Theoretical formulations based on these measurements lead to a third order polynomial model for the pressure-flow relation. The purpose of the current study is to examine this relation experimentally in an isolated muscle organ. A high precision feedback controlled pump is used to perfuse artificial plasma into the vasodilated rat gracilis muscle. The results indicate that the pressure-flow curve in this tissue is nonlinear in the low flow region and almost linear at physiological flow rates, following closely the third order polynomial function. Vessel fixation with glutaraldehyde causes the curves to become linear at all pressures, indicating that vessel distention is the primary mechanism causing the nonlinearity. Furthermore, the resistance of the post-fixed tissue is determined by the pressure at which the fixative is perfused. At fixation pressures below 10 mmHg, the resistance is three times higher than in vessels fixed at normal physiological pressures. Dextran (229,000 Dalton) is used to obtain Newtonian perfusates at different viscosities. The pressure-flow relation is found to be linearly dependent on viscosity for all flow rates.(ABSTRACT TRUNCATED AT 250 WORDS)     

Dynamic viscous flow in distensible vessels of skeletal muscle microcirculation: application to pressure and flow transients

Blood flow in the microcirculation of the rat skeletal muscle during transient changes of arterial pressure is analyzed theoretically. Although flow in such small vessels is quasi-steady and has a very low Reynolds number, time-dependent nonuniform flows along the length of the blood vessels can be observed due to vessel distensibility. The governing equations for a single microvessel are derived using previously measured microvessel elasticity, and several solutions to different inflow and outflow pressures and flow conditions are investigated. The results indicate that when such distensible microvessels are subjected to a step increase of arterial pressure, the arterial flow shows a rapid overshoot followed by a progressive decay to steady-state. An arterial step flow induces a different response which takes the form of a monotonically increasing pressure. Pressure and flows are nonuniform along the vessel length during such transients. In-vitro whole organ pressure-flow data are presented in the dilated rat gracilis muscle which qualitatively agree with the theoretical predictions.     

The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model.

Laser Doppler anemometry experiments and finite element simulations of steady flow in a three dimensional model of the carotid bifurcation were performed to investigate the influence of non-Newtonian properties of blood on the velocity distribution. The axial velocity distribution was measured for two fluids: a non-Newtonian blood analog fluid and a Newtonian reference fluid. Striking differences between the measured flow fields were found. The axial velocity field of the non-Newtonian fluid was flattened, had lower velocity gradients at the divider wall, and higher velocity gradients at the non-divider wall. The flow separation, as found with the Newtonian fluid, was absent. In the computations, the shear thinning behavior of the analog blood fluid was incorporated through the Carreau-Yasuda model. The viscoelastic properties of the fluid were not included. A comparison between the experimental and numerical results showed good agreement, both for the Newtonian and the non-Newtonian fluid. Since only shear thinning was included, this seems to be the dominant non-Newtonian property of the blood analog fluid under steady flow conditions.     

Studies of fluids simulating blood-like rheological properties and applications in models of arterial branches

We studied several non-Newtonian fluids to determine how closely they simulate the flow behavior of human blood. The viscous and viscoelastic properties of these fluids were compared with human blood samples in steady flow and transient flow Couette viscometers and in an oscillatory tube flow viscoelasticity analyzer. We examined: 1) A polyacrylamide suspension (Separan AP30 and AP45) to which we added 4% isopropanol and 0.01% magnesium chloride. 2) A suspension of 2% Dextran with 16% by weight biconcave disc-shaped particles simulating red blood cells. 3) 40% ghost cells prepared according to Dodge in Tri (hydroxymethyl) aminomethane. These ghost cells were used to simulate the two-phase flow behavior of blood. 4) A suspension of 5% Dextran (70,000) with 12% polystyrene particles (diameter of 1 micron) and 10 mMol calcium chloride. All these fluids closely approximate the flow behavior of blood and can be used in a variety of different experimental situations. To measure velocity distribution using a laser-Doppler-anemometer, we used fluids #1 and #3 in a rigid T-junction simulating the first septal branch of the left descending coronary artery. The measurements were done in steady and pulsatile flow experiments at different flow rate ratios. The fluids showed large differences in velocity profiles compared to Newtonian fluids.     

The superposition of steady on oscillatory shear and its effect on the viscoelasticity of human blood and a blood-like model fluid

To understand the pulsatility of human blood flow in vivo, it is necessary to separately investigate (1) steady shear and oscillatory flow, and (2) the superposition of steady shear flow on oscillatory flow performed under in vitro conditions. In this study a variable steady shear rate was superimposed in parallel on oscillatory shear at a constant frequency (0.5 Hz) for human blood (45% hematocrit), and an aqueous polyacrylamide polymer solution (AP 30E, concentration 300 ppm). The effect of superposition of the above two shear flows on the viscoelasticity of blood was more pronounced for the elastic (η′') than for the viscous (η′) component of viscoelasticity. With increasing superimposed shear rate, both η′ and η′' decreased, especially at the low shear region. This behavior can be explained by the viscoelastic properties of blood and the phenomena of blood aggregation and disaggregation. Quantitatively, the dependence of the viscous component of complex viscosity on superimposed shear for both blood and polymer solution is described by a modified Carreau equation. The elastic component of complex viscosity decreased exponentially with increasing superimposed shear, and it is described by an exponential model. © 1997 Elsevier Science Ltd     

The influence of the non-Newtonian properties of blood on the flow in large arteries: unsteady flow in a 90 degrees curved tube.

A numerical and experimental investigation of unsteady entry flow in a 90 degrees curved tube is presented to study the impact of the non-Newtonian properties of blood on the velocity distribution. The time-dependent flow rate for the Newtonian and the non-Newtonian blood analog fluid were identical. For the numerical computation, a Carreau-Yasuda model was employed to accommodate the shear thinning behavior of the Xanthan gum solution. The viscoelastic properties were not taken into account. The experimental results indicate that significant differences between the Newtonian and non-Newtonian fluid are present. The numerical results for both the Newtonian and the non-Newtonian fluid agree well with the experimental results. Since viscoelasticity was not included in the numerical code, shear thinning behavior of the blood analog fluid seems to be the dominant non-Newtonian property, even under unsteady flow conditions. Finally, a comparison between the non-Newtonian fluid model and a Newtonian fluid at a rescaled Reynolds number is presented. The rescaled Reynolds number, based on a characteristic rather than the high-shear rate viscosity of the Xanthan gum solution, was about three times as low as the original Reynolds number. Comparison reveals that the character of flow of the non-Newtonian fluid is simulated quite well by using the appropriate Reynolds number.     

The pressure-flow relation in resting rat skeletal muscle perfused with pure erythrocyte suspensions

In spite of numerous investigations of erythrocyte rheology, there is limited information about the influence of erythrocyte suspensions on whole organ pressure-flow relationships. In this study, we present whole organ pressure-flow curves for resting vasodilated gracilis muscle of the rat, in which the microanatomy and vessel properties have been determined previously. For pure erythrocyte suspensions from donor rats, the organ resistance increases only mildly with perfusion time (less than a 5% shift over a one-hour perfusion time), while in contrast, erythrocyte suspensions containing leukocytes show an increases of resistance near 100% over a period of 25 min. Variation in pressure-flow curves in the muscle at the same arterial hematocrit between different rats is less than 15%. The pressure-flow relation for pure erythrocyte suspensions depends on hematocrit. Shear thinning is exhibited at high hematocrits, while Newtonian behavior is approached at arterial hematocrits below 15%. The whole organ apparent viscosity for pure erythrocyte suspensions (normalized by cell-free plasma resistance) is a non-linear function of hematocrit; at physiological pressures, it reaches values comparable to those of apparent viscosities measured in rotational viscometers or in in vitro tube flow (diameters greater than 0.8 mm). The apparent viscosities estimated from the whole organ experiments tend to be higher than those measured in straight tubes under in vitro conditions. The pressure-flow curves for pure erythrocyte suspensions are shifted towards lower pressures than the curves for mixed suspensions of erythrocytes at the same hematocrit and with leukocytes at physiological cell counts. These acute experiments show that pure erythrocyte suspensions yield highly reproducible resistances in the skeletal muscle microcirculation with dilated arterioles. Relative apparent viscosities measured in vivo are higher than those measured in straight glass tubes of comparable dimesions.     

Hypoxic pulmonary vasoconstriction during steady and pulsatile flow in ferrets

We examined the effects of hypoxia and pulsatile flow on the pressure-flow relationships in the isolated perfused lungs of Fitch ferrets. When perfused by autologous blood from a pump providing a steady flow of 60 ml/min, the mean pulmonary arterial pressure rose from 14.6 to 31.3 Torr when alveolar PO2 was reduced from 122 to 46 Torr. This hypoxic pressor response was characterized by a 10.1-Torr increase in the pressure-axis intercept of the extrapolated pressure-flow curves and an increase in the slope of these curves from 130 to 240 Torr X l-1 X min. With pulsatile perfusion from a piston-type pump, mean pulmonary arterial pressure increased from 17.5 to 36.3 Torr at the same mean flow. This hypoxic pressor response was also characterized by increases in the intercept pressure and slope of the pressure-flow curves. When airway pressure was raised during hypoxia, the intercept pressure increased further to 25 +/- 1 Torr with a further increase in vascular resistance to 360 Torr X l-1 X min. Thus, in contrast to the dog lung, in the ferret lung pulsatile perfusion does not result in lower perfusion pressures during hypoxia when compared with similar mean levels of steady flow. Since the effects of high airway pressure and hypoxia are additive, they appear to act at or near the same site in elevating perfusion pressure.     

A model for shear stress-induced deformation of a flow sensor on the surface of vascular endothelial cells

Fluid mechanical shear stress elicits humoral, metabolic, and structural responses in vascular endothelial cells (ECs); however, the mechanisms involved in shear stress sensing and transduction remain incompletely understood. Beyond being responsive to shear stress, ECs distinguish among and respond differently to different types of shear stress. Recent observations suggest that endothelial shear stress sensing may occur through direct interaction of the flow with cell-surface structures that act as primary flow sensors. This paper presents a mathematical model for the shear stress-induced deformation of a flow sensor on the EC surface. The sensor is modeled as a cytoskeleton-coupled viscoelastic structure exhibiting standard linear solid behavior. Since ECs respond differently to different types of flow, the deformation and resulting velocity of the sensor in response to steady, non-reversing pulsatile, and oscillatory flow have been studied. Furthermore, the sensitivity of the results to changes in various model parameters including the magnitude of applied shear stress, the constants that characterize the viscoelastic behavior, and the pulsatile flow frequency (f) has been investigated. The results have demonstrated that in response to a suddenly applied shear stress, the sensor exhibits a level of instantaneous deformation followed by gradual creeping to the long-term response. The peak deformation increases linearly with the magnitude of the applied shear stress and decreases for viscoelastic constants that correspond to stiffer sensors. While the sensor deformation depends on f for low f values, the deformation becomes f -independent above a critical threshold frequency. Finally, the peak sensor deformation is considerably larger for steady and non-reversing pulsatile flow than for oscillatory flow. If the extent of sensor deformation correlates with the intensity of flow-mediated endothelial signaling, then our results suggest possible mechanisms by which ECs distinguish among steady, non-reversing pulsatile, and oscillatory shear stress.     

Estimation of blood flow distribution in skeletal muscle from inert gas washout

A new method is evaluated for the estimation of blood flow-to-volume distribution in skeletal muscle from inert gas washout kinetics. Acetylene washout from the isolated, blood-perfused canine gracilis muscle was measured continuously with a blood gas catheter in combination with a mass spectrometer. The washout curves were transformed to flow-to-volume ratio distributions by means of a 50-compartment model. The algorithm fits the expression for the washout curve derived from the model by a least-squares method with enforced smoothing. The algorithm was evaluated using computer simulations in which artificial washout curves were generated by a multicompartment model with a known flow distribution. A wide range of given flow distributions could be recovered from the simulated data. The data were also analyzed using a linear programming technique. Analysis of the experimental data with the least-squares method showed that there is considerable heterogeneity in the distribution of perfusion in resting gracilis muscle. The distribution is characterized by at least two modes and a single compartment with a very low perfusion-to-volume ratio. Experimental noise made it impossible to obtain feasible flow distributions by means of linear programming.     

A model for shear stress sensing and transmission in vascular endothelial cells

Arterial endothelial cell (EC) responsiveness to flow is essential for normal vascular function and plays a role in the development of atherosclerosis. EC flow responses may involve sensing of the mechanical stimulus at the cell surface with subsequent transmission via cytoskeleton to intracellular transduction sites. We had previously modeled flow-induced deformation of EC-surface flow sensors represented as viscoelastic materials with standard linear solid behavior (Kelvin bodies). In the present article, we extend the analysis to arbitrary networks of viscoelastic structures connected in series and/or parallel. Application of the model to a system of two Kelvin bodies in parallel reveals that flow induces an instantaneous deformation followed by creeping to the asymptotic response. The force divides equally between the two bodies when they have identical viscoelastic properties. When one body is stiffer than the other, a larger fraction of the applied force is directed to the stiffer body. We have also probed the impact of steady and oscillatory flow on simple sensor-cytoskeleton-nucleus networks. The results demonstrated that, consistent with the experimentally observed temporal chronology of EC flow responses, the flow sensor attains its peak deformation faster than intracellular structures and the nucleus deforms more rapidly than cytoskeletal elements. The results have also revealed that a 1-Hz oscillatory flow induces significantly smaller deformations than steady flow. These results may provide insight into the mechanisms behind the experimental observations that a number of EC responses induced by steady flow are not induced by oscillatory flow.     

Non-Newtonian Blood Flow in Left Coronary Arteries with Varying Stenosis: A Comparative Study

This paper presents Computational fluid dynamic (CFD) analysis of blood flow in three different 3-D models of left coronary artery (LCA). A comparative study of flow parameters (pressure distribution, velocity distribution and wall shear stress) in each of the models is done for a non-Newtonian (Carreau) as well as the Newtonian nature of blood viscosity over a complete cardiac cycle. The difference between these two types of behavior of blood is studied for both transient and steady states of flow. Additionally, flow parameters are compared for steady and transient boundary conditions considering blood as non-Newtonian fluid. The study shows that the highest wall shear stress (WSS), velocity and pressure are found in artery having stenosis in all the three branches of LCA. The use of Newtonian blood model is a good approximation for steady as well as transient blood flow boundary conditions if shear rate is above 100 s-1. However, the assumption of steady blood flow results in underestimating the values of flow parameters such as wall shear stress, pressure and velocity.     

Physiological and immunocytochemical evidence for a new concept of blood flow regulation in the corpus luteum

To explain the high rate of blood flow in the corpus luteum, we hypothesize that luteal blood vessels offer minimal resistance to flow and are incapable of vasomotion. This hypothesis was tested in rabbits at mid-pseudopregnancy by measuring blood flow in the corpus luteum and ovarian stroma with tracer-labeled microspheres at three levels of arterial blood pressure, which was manipulated by constricting the aorta above the ovarian artery. In addition, the distribution of vascular smooth muscle in the ovary was evaluated with morphological and immunocytochemical techniques. Decreases in arterial pressure were paralleled by reductions in blood flow in the corpus luteum, whereas ovarian stromal blood flow was unchanged. Consistent with our hypothesis, there was no change in the low level of vascular resistance offered by blood vessels in the corpus luteum, supporting the view that they are maximally dilated and incapable of autoregulation. Morphologically, the vessels within the corpus luteum appeared as large sinusoidal capillaries without smooth muscle, providing an anatomical explanation for the lack of vasomotor control demonstrated physiologically. The absence of vascular smooth muscle was confirmed with immunocytochemistry using an antibody against the muscle-specific intermediate filament, desmin. The fluorescein-labeled antibody decorated arteries and arterioles within the ovarian stroma and near the capsule of the corpus luteum, but did not decorate vessels in the corpus luteum of pseudopregnancy, providing additional evidence that the vessels of the corpus luteum lack the smooth muscle investment necessary to change vascular caliber. From these findings, we have proposed a novel scheme to explain intraovarian blood flow regulation. Vascular resistance in the ovarian stroma, as in most tissues, is acutely regulated by dilation or constriction of intratissue arterioles. In contrast, vascular resistance within the corpus luteum is modeled as a relatively invariable parameter, fixed at a low level by the morphological characteristics of the luteal vasculature. Therefore, the corpus luteum operates on a linear (maximally "vasodilated") pressure-flow curve, does not actively regulate intratissue blood flow, and is subject to acute regulation of perfusion only through changes in extra-luteal vessels.     

Vasomotion in critically perfused muscle protects adjacent tissues from capillary perfusion failure

We analyzed the incidence and interaction of arteriolar vasomotion and capillary flow motion during critical perfusion conditions in neighboring peripheral tissues using intravital fluorescence microscopy. The gracilis and semitendinosus muscles and adjacent periosteum, subcutis, and skin of the left hindlimb of Sprague-Dawley rats were isolated at the femoral vessels. Critical perfusion conditions, achieved by stepwise reduction of femoral artery blood flow, induced capillary flow motion in muscle, but not in the periosteum, subcutis, and skin. Strikingly, blood flow within individual capillaries was decreased (P < 0.05) in muscle but was not affected in the periosteum, subcutis, and skin. However, despite the flow motion-induced reduction of muscle capillary blood flow during the critical perfusion conditions, functional capillary density remained preserved in all tissues analyzed, including the skeletal muscle. Abrogation of vasomotion in the muscle arterioles by the calcium channel blocker felodipine resulted in a redistribution of blood flow within individual capillaries from cutaneous, subcutaneous, and periosteal tissues toward skeletal muscle. As a consequence, shutdown of perfusion of individual capillaries was observed that resulted in a significant reduction (P < 0.05) of capillary density not only in the neighboring tissues but also in the muscle itself. We conclude that during critical perfusion conditions, vasomotion and flow motion in skeletal muscle preserve nutritive perfusion (functional capillary density) not only in the muscle itself but also in the neighboring tissues, which are not capable of developing this protective regulatory mechanism by themselves.     

A perturbation model for the oscillatory flow of a Bingham plastic in rigid and periodically displaced tubes.

An approximate analytical model for the pulsatile flow of an ideal Bingham plastic fluid in both a rigid and a periodically displaced tube has been developed using regular perturbation methods. Relationships are derived for the velocity field and dimensionless flow rate. The solution compares adequately with available experimentally measured oscillatory non-Newtonian fluid flow data. These solutions provide useful analytical models supporting experimental and computation studies of arterial blood flow.     

Numerical investigation of the non-Newtonian pulsatile blood flow in a bifurcation model with a non-planar branch

The pulsatile flow of non-Newtonian fluid in a bifurcation model with a non-planar daughter branch is investigated numerically by using the Carreau-Yasuda model to take into account the shear thinning behavior of the analog blood fluid. The objective of this study is to deal with the influence of the non-Newtonian property of fluid and of out-of-plane curvature in the non-planar daughter vessel on wall shear stress (WSS), oscillatory shear index (OSI), and flow phenomena during the pulse cycle. The non-Newtonian property in the daughter vessels induces a flattened axial velocity profile due to its shear thinning behavior. The non-planarity deflects flow from the inner wall of the vessel to the outer wall and changes the distribution of WSS along the vessel, in particular in systole phase. Downstream of the bifurcation, the velocity profiles are shifted toward the flow divider, and low WSS and high shear stress temporal oscillations characterized by OSI occur on the outer wall region of the daughter vessels close to the bifurcation. Secondary motions become stronger with the addition of the out-of-plane curvature induced by the bending of the vessel, and the secondary flow patterns swirl along the non-planar daughter vessel. A significant difference between the non-Newtonian and the Newtonian pulsatile flow is revealed during the pulse cycle; however, reasonable agreement between the non-Newtonian and the rescaled Newtonian flow is found. Calculated results for the pulsatile flow support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology.     

Viscoelastic properties of microvessels in rat spinotrapezius muscle

In order to establish a quantitative model of blood flow in skeletal muscle, the mechanical properties of the blood vessels need to be measured. We present measurements of the viscoelastic properties of arterioles, venules, and capillaries in exteriorized rat spinotrapezius muscle. Muscles were perfused with an inert silicone polymer and a uniform static pressure was established by occlusion of the venous outflow. Vessel diameters were then measured as a function of the static pressure. This study provides the first measurements of the viscoelastic properties of microvessels in skeletal muscle in situ. Over a pressure range of 20-200 mmHg, the transverse arterioles are the most distensible vessels, while the arcade venules are the stiffest. In response to a step change in pressure, all vessels show an initial elastic deformation, followed by a nonlinear creep. Based on the experimental results for different pressure histories a constitutive equation relating vessel diameter to the local transmural pressure is proposed. Diameter changes are expressed in the form of a diameter strain, analogous to a Green's strain, and are related to the local transmural pressure using a standard linear solid model. This model has only three empirical coefficients and could be fitted to all experimental results for all vessels within error of measurement.     

Effect of non-Newtonian and pulsatile blood flow on mass transport in the human aorta

To investigate the effects of both non-Newtonian behavior and the pulsation of blood flow on the distributions of luminal surface LDL concentration and oxygen flux along the wall of the human aorta, we numerically compared a non-Newtonian model with the Newtonian one under both steady flow and in vivo pulsatile flow conditions using a human aorta model constructed from MRI images. The results showed that under steady flow conditions, although the shear thinning non-Newtonian nature of blood could elevate wall shear stress (WSS) in most regions of the aorta, especially areas with low WSS, it had little effect on luminal surface LDL concentration (c(w)) in most regions of the aorta. Nevertheless, it could significantly enhance c(w) in areas with high luminal surface LDL concentration through the shear dependent diffusivity of LDLs. For oxygen transport, the shear thinning non-Newtonian nature of blood could slightly reduce oxygen flux in most regions of the aorta, but this effect became much more apparent in areas with already low oxygen flux. The pulsation of blood flow could significantly reduce c(w) and enhance oxygen flux in these disturbed places. In most other regions of the aorta, the oxygen flux was also significantly higher than that for the steady flow simulation. In conclusion, the shear shining non-Newtonian nature of blood has little effect on LDL and oxygen transport in most regions of the aorta, but in the atherogenic-prone areas where luminal surface LDL concentration is high and oxygen flux is low, its effect is apparent. Similar is for the effect of pulsatile flow on the transport of LDLs. But, the pulsation of blood flow can apparently affect oxygen flux in the aorta, especially in areas with low oxygen flux.     

Subendocardial and subepicardial pressure-flow relations in the rat heart in diastolic and systolic arrest

Ischemic heart disease is more apparent in the subendocardial than in subepicardial layers. We investigated coronary pressure-flow relations in layers of the isolated rat left ventricle, using 15 microm microspheres during diastolic and systolic arrest in the vasodilated coronary circulation. A special cannula allowed for selective determination of left main stem pressure-flow relations. Arterio-venous shunt flow was derived from microspheres in the venous effluent. We quantitatively investigated the pressure-flow relations in diastolic arrest (n=8), systolic arrest at normal contractility (n=8) and low contractility (n=6). In all three groups normal and large ventricular volume was studied. In diastolic arrest, at a perfusion pressure of 90 mmHg, subendocardial flow is larger than subepicardial flow, i.e., the endo/epi ratio is approximately 1.2. In systolic arrest the endo/epi ratio is approximately 0.3, and subendocardial flow and subepicardial flow are approximately 12% and approximately 55% of their values during diastolic arrest. The endo/epi ratio in diastolic arrest decreases with increasing perfusion pressure, while in systole the ratio increases. The slope of the pressure-flow relations, i.e., inverse of resistance, changes by a factor of approximately 5.3 in the subendocardium and by a factor approximately 2.2 in the subepicardium from diastole to systole. Lowering contractility affects subendocardial flow more than subepicardial flow, but both contractility and ventricular volume changes have only a limited effect on both subendocardial and subepicardial flow. The resistance (inverse of slope) of the total left main stem pressure-flow relation changes by a factor of approximately 3.4 from diastolic to systolic arrest. The zero-flow pressure increases from diastole to systole. Thus, coronary perfusion flow in diastolic arrest is larger than systolic arrest, with the largest difference in the subendocardium, as a result of layer dependent increases in vascular resistance and intercept pressure. Shunt flow is larger in diastolic than in systolic arrest, and increases with perfusion pressure. We conclude that changes in contractility and ventricular volume have a smaller effect on pressure-flow relations than diastolic-systolic differences. A synthesis of models accounting for the effect of cardiac contraction on perfusion is suggested.