Biophysical Model of the Spatial Heterogeneity of Myocardial Flow

The blood flow in the myocardium has significant spatial heterogeneity. The objective of this study was to develop a biophysical model based on detailed anatomical data to determine the heterogeneity of regional myocardial flow during diastole. The model predictions were compared with experimental measurements in a diastolic porcine heart in the absence of vessel tone using nonradioactive fluorescent microsphere measurements. The results from the model and experimental measurements showed good agreement. The relative flow dispersion in the arrested, vasodilated heart was found to be 44% and 48% numerically and experimentally, respectively. Furthermore, the flow dispersion was found to have fractal characteristics with fractal dimensions (D) of 1.25 and 1.27 predicted by the model and validated by the experiments, respectively. This validated three-dimensional model of normal diastolic heart will play an important role in elucidating the spatial heterogeneity of coronary blood flow, and serve as a foundation for understanding the interplay between cardiac mechanics and coronary hemodynamics.     

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.     

Dynamics of coronary circulation in rats]

The blood flow velocities in left anterior descending coronary artery and ascending aorta have been measured in anesthetized rats by high frequency Doppler technique. The measurement of coronary blood flow velocity by miniature ultrasonic probe (2.0 x 1.5 mm) was performed through myocardial surface. Two different forms of coronary blood flow curves were recorded. These forms of the curves depend on the value of the coronary blood flow velocity and are connected with the ascending aorta blood flow velocity. The dynamics of the coronary blood flow reactions under coronary artery occlusion and asphyxia in the rat is similar to the one in the cat and the dog, but less expressive. In experiments with vasodilators the direct dependence between linear and volume coronary artery velocities under the measurement through myocardial surface was found.     

心房钠尿因子对麻醉家兔局部血流的影响

在42只麻醉家兔,观察了静脉注射心房肽Ⅱ(AtriopeptinⅡ,APⅡ)对局部血流量以及动脉内注射 AP Ⅱ 对局部血管阻力的影响。结果如下:(1)静脉注射 APⅡ(30μg/kg)5min后,平均动脉压(MAP)降低11.0±1.5mmHg(n=8,M±SE,下同),与溶剂对照组相比有明显差异(P相似文献   

Flow Regulation in Coronary Vascular Tree: A Model Study

Background

Coronary blood flow can always be matched to the metabolic demand of the myocardium due to the regulation of vasoactive segments. Myocardial compressive forces play an important role in determining coronary blood flow but its impact on flow regulation is still unknown. The purpose of this study was to develop a coronary specified flow regulation model, which can integrate myocardial compressive forces and other identified regulation factors, to further investigate the coronary blood flow regulation behavior.

Method

A theoretical coronary flow regulation model including the myogenic, shear-dependent and metabolic responses was developed. Myocardial compressive forces were included in the modified wall tension model. Shear-dependent response was estimated by using the experimental data from coronary circulation. Capillary density and basal oxygen consumption were specified to corresponding to those in coronary circulation. Zero flow pressure was also modeled by using a simplified capillary model.

Result

Pressure-flow relations predicted by the proposed model are consistent with previous experimental data. The predicted diameter changes in small arteries are in good agreement with experiment observations in adenosine infusion and inhibition of NO synthesis conditions. Results demonstrate that the myocardial compressive forces acting on the vessel wall would extend the auto-regulatory range by decreasing the myogenic tone at the given perfusion pressure.

Conclusions

Myocardial compressive forces had great impact on coronary auto-regulation effect. The proposed model was proved to be consistent with experiment observations and can be employed to investigate the coronary blood flow regulation effect in physiological and pathophysiological conditions.     

Assessment of coronary microcirculation in a swine animal model

Coronary microvascular dysfunction has important prognostic implications. Several hemodynamic indexes, such as coronary flow reserve (CFR), microvascular resistance, and zero-flow pressure (P(zf)), were used to establish the most reliable index to assess coronary microcirculation. Fifteen swine were instrumented with a flow probe, and a pressure wire was advanced into the distal left anterior descending artery. Adenosine was used to produce maximum hyperemia. Microspheres were used to create microvascular dysfunction. An occluder was used to produce stenosis. Blood flow from the probe (Q(p)), aortic pressure, distal coronary pressure, and right atrium pressure were recorded. Angiographic flow (Q(a)) was calculated using a time-density curve. Flow probe-based CFR and angiographic CFR were calculated using Q(p) and Q(a), respectively. Flow probe-based (NMR(qh)) and angiographic normalized microvascular resistance (NMR(ah)) were determined using Q(p) and Q(a), respectively, during hyperemia. P(zf) was calculated using Q(p) and distal coronary pressure. Two series of receiver operating characteristic curves were generated: normal epicardial artery model (N model) and stenosis model (S model). The areas under the receiver operating characteristic curves for flow probe-based CFR, angiographic CFR, NMR(qh), NMR(ah), and P(zf) were 0.855, 0.836, 0.976, 0.956, and 0.855 in N model and 0.737, 0.700, 0.935, 0.889, and 0.698 in S model. Both NMR(qh) and NMR(ah) were significantly more reliable than CFR and P(zf) in detecting the microvascular deterioration. Compared with CFR and P(zf), NMR provided a more accurate assessment of microcirculation. This improved accuracy was more prevalent when stenosis existed. Moreover, NMR(ah) is potentially a less invasive method for assessing coronary microcirculation.     

Pulsatile blood flow in the entire coronary arterial tree: theory and experiment

The pulsatility of coronary circulation can be accurately simulated on the basis of the measured branching pattern, vascular geometry, and material properties of the coronary vasculature. A Womersley-type mathematical model is developed to analyze pulsatile blood flow in diastole in the absence of vessel tone in the entire coronary arterial tree on the basis of previously measured morphometric data. The model incorporates a constitutive equation of pressure and cross-section area relation based on our previous experimental data. The formulation enables the prediction of the impedance, the pressure distribution, and the pulsatile flow distribution throughout the entire coronary arterial tree. The model is validated by experimental measurements in six diastolic arrested, vasodilated porcine hearts. The agreement between theory and experiment is excellent. Furthermore, the present pulse wave results at low frequency agree very well with previously published steady-state model. Finally, the phase angle of flow is seen to decrease along the trunk of the major coronary artery and primary branches toward the capillary vessels. This study represents the first, most extensive validated analysis of Womersley-type pulse wave transmission in the entire coronary arterial tree down to the first segment of capillaries. The present model will serve to quantitatively test various hypotheses in the coronary circulation under pulsatile flow conditions.     

Outcomes of Middle Cardiac Vein Arterialization via Internal Mammary/Thoracic Artery Anastomosis

Objective

Cardiac vein arterialization is seldom applied for treating right coronary artery disease. This study aimed to improve outcomes of cardiac vein arterialization in a porcine model using intramammary artery anastomosis.

Methods

A chronic, stenotic coronary artery model was established in 12 of 14 Chinese experimental miniature pigs of either sex, which were randomly divided into equal control (n = 6) and experimental (n = 6) groups. In experimental animals, blood flow was reconstructed in the right coronary artery using intramammary artery. Arterialization involved dissection of right internal mammary artery from bifurcation to apex of thorax followed by end-to-side anastomosis of internal mammary artery and middle cardiac vein plus posterior descending branch of right coronary artery. Intraoperative heart rate was maintained at 110 beats/min. Graft flow assessment and echocardiography were performed when blood pressure and heart rate normalized.

Results

The experimental group had significantly higher mean endocardial and epicardial blood flow postoperatively than control group (mean endocardial blood flow: 0.37 vs. 0.14 ml/(g*min), p<0.001; mean epicardial blood flow: 0.29 vs. 0.22, p = 0.014). Transmural blood flow was also higher in experimental group than in control group (0.33 vs. 0.19, p<0.001); ejection fraction increased from 0.46% at baseline to 0.51% (p = 0.0038) at 6 hours postoperatively, and mean blood flow of internal mammary artery was 44.50, perfusion index 0.73 at postoperative 6 months, 43.33 and 0.80 at 3 months.

Conclusion

Successful cardiac vein arterialization via intramammary artery in a porcine model suggests that this may be a viable method for reconstructing blood flow in chronic, severe coronary artery disease.     

Pulmonary vascular compliance and viscoelasticity

When dog lung lobes were perfused at constant arterial inflow rate, occlusion of the venous outflow (VO) produced a rapid jump in venous pressure (Pv) followed by a slower rise in both arterial pressure (Pa) and Pv. During the slow rise Pa(t) and Pv(t) tended to converge and become concave upward as the volume of blood in the lungs increased. We compared the dynamic vascular volume vs. pressure curves obtained after VO with the static volume vs. pressure curves obtained by dye dilution. The slope of the static curve (the static compliance, Cst) was always larger than the slope of the dynamic curve (the dynamic compliance, Cdyn). In addition, the Cdyn decreased with increasing blood flow rate. When venous occlusion (VO) was followed after a short time interval by arterial occlusion (AO) such that the lobe was isovolumic, both Pa and Pv fell with time to a level that was below either pressure at the instant of AO. In an attempt to explain these observations a compartmental model was constructed in which the hemodynamic resistance and vascular compliance were volume dependent and the vessel walls were viscoelastic. These features of the model could account for the convergence and upward concavity of the Pa and Pv curves after VO and the pressure relaxation in the isovolumic state after AO, respectively. According to the model analysis, the difference between Cst and Cdyn and the flow dependence of Cdyn are due to wall viscosity and volume dependence of compliance, respectively. Model analysis also suggested ways of evaluating changes in the viscoelasticity of the lobar vascular bed. Hypoxic vasoconstriction that increased total vascular resistance also decreased Cst and Cdyn and appeared to increase the vessel wall viscosity.     

Quantification of coronary microvascular resistance using angiographic images for volumetric blood flow measurement: in vivo validation

Structural coronary microcirculation abnormalities are important prognostic determinants in clinical settings. However, an assessment of microvascular resistance (MR) requires a velocity wire. A first-pass distribution analysis technique to measure volumetric blood flow has been previously validated. The aim of this study was the in vivo validation of the MR measurement technique using first-pass distribution analysis. Twelve anesthetized swine were instrumented with a transit-time ultrasound flow probe on the proximal segment of the left anterior descending coronary artery (LAD). Microspheres were injected into the LAD to create a model of microvascular dysfunction. Adenosine (400 μg·kg(-1)·min(-1)) was used to produce maximum hyperemia. A region of interest in the LAD arterial bed was drawn to generate time-density curves using angiographic images. Volumetric blood flow measurements (Q(a)) were made using a time-density curve and the assumption that blood was momentarily replaced with contrast agent during the injection. Blood flow from the flow probe (Q(p)), coronary pressure (P(a)), and right atrium pressure (P(v)) were continuously recorded. Flow probe-based normalized MR (NMR(p)) and angiography-based normalized MR (NMR(a)) were calculated using Q(p) and Q(a), respectively. In 258 measurements, Q(a) showed a strong correlation with the gold standard Q(p) (Q(a) = 0.90 Q(p) + 6.6 ml/min, r(2) = 0.91, P < 0.0001). NMR(a) correlated linearly with NMR(p) (NMR(a) = 0.90 NMR(p) + 0.02 mmHg·ml(-1)·min(-1), r(2) = 0.91, P < 0.0001). Additionally, the Bland-Altman analysis showed a close agreement between NMR(a) and NMR(p). In conclusion, a technique based on angiographic image data for quantifying NMR was validated using a swine model. This study provides a method to measure NMR without using a velocity wire, which can potentially be used to evaluate microvascular conditions during coronary arteriography.     

Influence of arterial wall compliance on the pressure drop across coronary artery stenoses under hyperemic flow condition

Hemodynamic endpoints such as flow and pressure drop are often measured during angioplasty procedures to determine the functional severity of a coronary artery stenosis. There is a lack of knowledge regarding the influence of compliance of the arterial wall-stenosis on the pressure drop under hyperemic flows across coronary lesions. This study evaluates the influence in flow and pressure drop caused by variation in arterial-stenosis compliance for a wide range of stenosis severities. The flow and pressure drop were evaluated for three different severities of stenosis and tested for limiting scenarios of compliant models. The Mooney-Rivlin model defined the non-linear material properties of the arterial wall and the plaque regions. The non-Newtonian Carreau model was used to model the blood flow viscosity. The fluid (blood)-structure (arterial wall) interaction equations were solved numerically using the finite element method. Irrespective of the stenosis severity, the compliant models produced a lower pressure drop than the rigid artery due to compliance of the plaque region. A wide variation in the pressure drop was observed between different compliant models for significant (90% area occlusion) stenosis with 41.0, 32.1, and 29.8 mmHg for the rigid artery, compliant artery with calcified plaque, and compliant artery with smooth muscle cell proliferation, respectively. When compared with the rigid artery for significant stenosis the pressure drop decreased by 27.7% and 37.6% for the calcified plaque and for the smooth muscle cell proliferation case, respectively. These significant variations in pressure drop for the higher stenosis may lead to misinterpretation and misdiagnosis of the stenosis severity.     

A3 adenosine receptor agonist IB-MECA reduces myocardial ischemia-reperfusion injury in dogs

We examined the effect of the A3 adenosine receptor (AR) agonist IB-MECA on infarct size in an open-chest anesthetized dog model of myocardial ischemia-reperfusion injury. Dogs were subjected to 60 min of left anterior descending (LAD) coronary artery occlusion and 3 h of reperfusion. Infarct size and regional myocardial blood flow were assessed by macrohistochemical staining with triphenyltetrazolium chloride and radioactive microspheres, respectively. Four experimental groups were studied: vehicle control (50% DMSO in normal saline), IB-MECA (100 microg/kg iv bolus) given 10 min before the coronary occlusion, IB-MECA (100 microg/kg iv bolus) given 5 min before initiation of reperfusion, and IB-MECA (100 microg/kg iv bolus) given 10 min before coronary occlusion in dogs pretreated 15 min earlier with the ATP-dependent potassium channel antagonist glibenclamide (0.3 mg/kg iv bolus). Administration of IB-MECA had no effect on any hemodynamic parameter measured including heart rate, first derivative of left ventricular pressure, aortic pressure, LAD coronary blood flow, or coronary collateral blood flow. Nevertheless, pretreatment with IB-MECA before coronary occlusion produced a marked reduction in infarct size ( approximately 40% reduction) compared with the control group (13.0 +/- 3.2% vs. 25.2 +/- 3.7% of the area at risk, respectively). This effect of IB-MECA was blocked completely in dogs pretreated with glibenclamide. An equivalent reduction in infarct size was observed when IB-MECA was administered immediately before reperfusion (13.1 +/- 3.9%). These results are the first to demonstrate efficacy of an A3AR agonist in a large animal model of myocardial infarction by mechanisms that are unrelated to changes in hemodynamic parameters and coronary blood flow. These data also demonstrate in an in vivo model that IB-MECA is effective as a cardioprotective agent when administered at the time of reperfusion.     

Myocardial blood flow regulation relative to left ventricle pressure and volume in anesthetized dogs

The influence of left ventricle pressure and volume changes on coronary blood flow was investigated in eight anesthetized dogs. Coronary artery pressure-flow relationships were determined at two levels of left ventricular pressure and volume. The distribution of blood flow within the myocardium was also determined when these relationships varied. Reducing left ventricle pressures and volumes increased heart rate. Rate-pressure product, diastolic coronary pressure, myocardial O2 consumption, total, subendocardial and subepicardial flow decreased. Hematocrit and blood gas data were unchanged. The pressure-flow relationships were shifted leftward (p = 0.001) but the range of autoregulation was not altered. At low left ventricle pressures and volumes, the lower coronary artery pressure limit was shifted leftward (from 75 to 45 mm Hg (1 mm Hg = 133.3 Pa)), while total, subendocardial, and subepicardial blood flow did not change compared with the control. Below the lower coronary artery pressure limit, subendocardial but not subepicardial flow decreased, resulting in maldistribution of flow across the left ventricular wall. When coronary pressure was reset between control and the lower coronary artery pressure limit, subendocardial flow was restored. These results show that the lower coronary artery pressure limit can be shifted leftward while the distribution of blood flow across the left ventricular wall is preserved.     

Analysis of blood flow in the entire coronary arterial tree

A hemodynamic analysis of coronary blood flow must be based on the measured branching pattern and vascular geometry of the coronary vasculature. We recently developed a computer reconstruction of the entire coronary arterial tree of the porcine heart based on previously measured morphometric data. In the present study, we carried out an analysis of blood flow distribution through a network of millions of vessels that includes the entire coronary arterial tree down to the first capillary branch. The pressure and flow are computed throughout the coronary arterial tree based on conservation of mass and momentum and appropriate pressure boundary conditions. We found a power law relationship between the diameter and flow of each vessel branch. The exponent is approximately 2.2, which deviates from Murray's prediction of 3.0. Furthermore, we found the total arterial equivalent resistance to be 0.93, 0.77, and 1.28 mmHg.ml(-1).s(-1).g(-1) for the right coronary artery, left anterior descending coronary artery, and left circumflex artery, respectively. The significance of the present study is that it yields a predictive model that incorporates some of the factors controlling coronary blood flow. The model of normal hearts will serve as a physiological reference state. Pathological states can then be studied in relation to changes in model parameters that alter coronary perfusion.     

Myocardial blood volume and coronary resistance during and after coronary angioplasty

Animal experiments have shown that the coronary circulation is pressure distensible, i.e., myocardial blood volume (MBV) increases with perfusion pressure. In humans, however, corresponding measurements are lacking so far. We sought to quantify parameters reflecting coronary distensibility such as MBV and coronary resistance (CR) during and after coronary angioplasty. Thirty patients with stable coronary artery disease underwent simultaneous coronary perfusion pressure assessment and myocardial contrast echocardiography (MCE) of 37 coronary arteries and their territories during and after angioplasty. MCE yielded MBV and myocardial blood flow (MBF; in ml · min(-1) · g(-1)). Complete data sets were obtained in 32 coronary arteries and their territories from 26 patients. During angioplasty, perfusion pressure, i.e., coronary occlusive pressure, and MBV varied between 9 and 57 mmHg (26.9 ± 11.9 mmHg) and between 1.2 and 14.5 ml/100 g (6.7 ± 3.7 ml/100 g), respectively. After successful angioplasty, perfusion pressure and MBV increased significantly (P < 0.001 for both) and varied between 64 and 118 mmHg (93.5 ± 12.8 mmHg) and between 3.7 and 17.3 ml/100 g (9.8 ± 3.4 ml/100 g), respectively. Mean MBF increased from 31 ± 20 ml · min(-1) · g(-1) during coronary occlusion, reflecting collateral flow, to 121 ± 33 ml · min(-1) · g(-1) (P < 0.01), whereas mean CR, i.e., the ratio of perfusion pressure and MBF, decreased by 20% (P < 0.001). In conclusion, the human coronary circulation is pressure distensible. MCE allows for the quantification of CR and MBV in humans.     

Epicardial coronary blood flow including the presence of stenoses and aorto-coronary bypasses--I: Model and numerical method

A computer model and numerical method for calculating left epicardial coronary blood flow has been developed. This model employs a finite-branching geometry of the coronary vasculature and the one-dimensional, unsteady equations for flow with friction. The epicardial coronary geometry includes the left main and its bifurcation, the left anterior descending and left circumflex coronary arteries, and a selected number of small branches. Each of the latter terminate in an impedance, whose resistive component is related to intramyocardial compression through a linear dependence on left ventricular pressure. The elastic properties of the epicardial arteries are taken to be non-linear and are prescribed by specifying the local small-disturbance wave speed. The model allows for the incorporation of multiple stenoses as well as aorto-coronary bypasses. Calculations using this model predict pressure and flow waveform development and allow for the systematic investigation of the dependence of coronary flow on various parameters, e.g., peripheral resistance, wall properties, and branching pattern, as well as the presence of stenoses and bypass grafts. Reasonable comparison between calculations and earlier experiments in horses has been obtained.     

Influence of heart rate on fractional flow reserve, pressure drop coefficient, and lesion flow coefficient for epicardial coronary stenosis in a porcine model

A limitation in the use of invasive coronary diagnostic indexes is that fluctuations in hemodynamic factors such as heart rate (HR), blood pressure, and contractility may alter resting or hyperemic flow measurements and may introduce uncertainties in the interpretation of these indexes. In this study, we focused on the effect of fluctuations in HR and area stenosis (AS) on diagnostic indexes. We hypothesized that the pressure drop coefficient (CDP(e), ratio of transstenotic pressure drop and distal dynamic pressure), lesion flow coefficient (LFC, square root of ratio of limiting value CDP and CDP at site of stenosis) derived from fluid dynamics principles, and fractional flow reserve (FFR, ratio of average distal and proximal pressures) are independent of HR and can significantly differentiate between the severity of stenosis. Cardiac catheterization was performed on 11 Yorkshire pigs. Simultaneous measurements of distal coronary arterial pressure and flow were performed using a dual sensor-tipped guidewire for HR < 120 and HR > 120 beats/min, in the presence of epicardial coronary lesions of <50% AS and >50% AS. The mean values of FFR, CDP(e), and LFC were significantly different (P < 0.05) for lesions of <50% AS and >50% AS (0.88 ± 0.04, 0.76 ± 0.04; 62 ± 30, 151 ± 35, and 0.10 ± 0.02 and 0.16 ± 0.01, respectively). The mean values of FFR and CDP(e) were not significantly different (P > 0.05) for variable HR conditions of HR < 120 and HR > 120 beats/min (FFR, 0.81 ± 0.04 and 0.82 ± 0.04; and CDP(e), 95 ± 33 and 118 ± 36). The mean values of LFC do somewhat vary with HR (0.14 ± 0.01 and 0.12 ± 0.02). In conclusion, fluctuations in HR have no significant influence on the measured values of CDP(e) and FFR but have a marginal influence on the measured values of LFC. However, all three parameters can significantly differentiate between stenosis severities. These results suggest that the diagnostic parameters can be potentially used in a better assessment of coronary stenosis severity under a clinical setting.     

Simple physical model of coronary vasodilation

The coronary diastolic pressure-flow relationship was studied in two groups of dogs; in one group coronary circulation was characterized by normal tone of vascular smooth muscle, while in the other group, complete relaxation of smooth muscle fibres was produced by intravenous infusion of dipyridamole. The coronary flow (CF) was measured in both groups for several values of mean aortic blood pressure (ABP), the variations being obtained by means of a 10 s arterial haemorrhage. The measured CF versus ABP data were found to be well represented by best fit curves calculated by power regression methods. These curves were quite different in the presence and absence of dipyridamole infusion. A simple physical model is proposed for analysis of these curves; the model is based on the Poiseuille equation, modified to take into proper account the variations of the vessel radii under different ABP values during ventricular diastole. These variations are expressed by means of Laplace and Hooke's laws by equating wall tension due to APB, to the sum of tensions due to elastic and smooth muscle forces. Analysis of CF versus APB curves, performed on the basis of this model, shows that to account for the large change of coronary bed conductance observed under dipyridamole infusion one must assume not only that the smooth muscle tone is absent but also that some relevant variations occur in the whole coronary bed, thus pointing to possible recruitment of new blood vessel paths.     

Effects of increased pressure inside or outside ventricles on total and regional myocardial blood flow

Increasing pressures to 30 mmHg in right (RV) and left (LV) ventricles and surrounding heart (SH) in isolated, arrested, maximally vasodilated, blood-perfused dog hearts shifted pressure-flow (PF) curves rightward and increased zero flow pressure (P(zf)) by an amount equal to the RV applied pressure, SH applied pressure, or two-thirds of the LV applied pressure. There were comparable increases in coronary venous pressures. Increasing LV or SH pressures decreased coronary blood flows, especially in the subendocardium. Decreases in driving pressure decreased flows in all layers, but even with driving pressure of 5 mmHg, a few subepicardial pieces had flow. We conclude with the following: 1) raising pressures inside or outside the heart shifts PF curves and raises P(zf) by increasing coronary venous pressure; 2) the effects are most prominent in the subendocardial muscle layer; and 3) as driving pressures are decreased, there is a range of P(zf) in the heart with the final P(zf) recorded due to the last little piece of muscle to be perfused.     

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.