P. Sipkema

Comparison of models used to calculate left ventricular wall force.

Myocardial wall force per area (=stress) is a major determinant of muscle function and oxygen consumption. It cannot be measured accurately but has to be derived from a mathematical model. Many models have been presented in the literature but a comparison between models has not been available. In this study angiographic data from the literature are used to calculate left ventricular wall force for normal and diseased hearts using a thin-walled spherical model, a thick-walled spherical model and six ellipsoidal models, and the results are compared. There appeared to be large differences between the stresses yielded by the models for the same cardiac geometry. The thick-walled sphere yields circumferential stresses that are approximately 25% lower than the stresses yielded by most of the ellipsoidal models. Of the ellipsoidal models the one suggested by Streeter el al. gives circumferential stresses that are 25% higher than those of the other ellipsoids. Similar differences are found for left ventricular wall stress in the longitudinal direction. However, all models correspond closely in the prediction of the deviation from normal stress in the various pathological states studied.Some of the models give information about the stress distribution over the thickness of the wall as well. We found substantial differences in this predicted stress distribution for models that employ similar assumptions. These differences plus the uncertainties with regard to the properties of the myocardial wall material, that change during the cardiac cycle, call for some scepticism concerning the calculated stress distribution over the wall. The ellipsoidal model suggested by Falsetti et al. is very simple and yields approximately the same mean wall stress values as the more complicated models that we studied. This model therefore appears to be the best choice.

Endothelium Function Is Protected by Albumin and Flow-Induced Constriction Is Independent of Endothelium and Tone in Isolated Rabbit Femoral Artery

To investigate the preservation of endothelial function, we perfused two segments of one rabbit femoral artery (n = 8) in a pressure myograph in parallel, both with Tyrode, but one with 0.6% albumin added. The change in the outer diameter of the vessels [preconstricted with norepinephrine (NE) to 70%] in response to acetylcholine as an indicator of the endothelial function, was repeatedly measured over 5 h after the equilibration. The difference between the acetylcholine responses of the two vessel segments was significant (p < 0.05) after a perfusion period of 4 h. We also investigated whether flow-induced constriction is dependent on (1) the presence of endothelium and (2) the level of preconstriction. We therefore perfused segments of rabbit femoral arteries (n = 5) with Tyrode with 0.6% albumin. If acetylcholine-induced dilatation was present, a flow-diameter relation was determined at two constriction levels: about 60% (high) and 90% (low) of the passive outer diameter. Both determinations were repeated after mechanical endothelium removal (checked functionally and histologically). A similar decrease in diameter (about 7%) with an increase in flow ranging from 0 to 1,330 microliters/min was found in all conditions. We conclude that the addition of (0.6%) albumin protects endothelial function in the rabbit femoral artery when perfused in the low-flow range for a period longer than 4 h. We also found that flow-dependent constriction is neither influenced by the presence of the endothelium nor by the level of tone induced with NE.

A dynamic nonlinear lumped parameter model for skeletal muscle circulation

A dynamic nonlinear lumped parameter model of the circulation of skeletal muscle for constant vasoactive state is presented. This model consists of four compartments that represent the large arteries, the arterioles, the capillaries and venules, and the veins, respectively. The first compartment consists of a linear compliance (C1) and resistance (R1). The third compartment possesses no compliance and is represented by a linear resistance (R3). The second and fourth compartments each consist of a nonlinear pressure-volume relation, resulting in a pressure dependent compliance (C2, C4, respectively) and nonlinear resistance (R2, R4, respectively). The eleven model parameters were collected in a complementary way: they were partly obtained from a priori knowledge including, information at the microscopic level, and partly determined by means of an estimation algorithm. Estimated values of the compliances (in cm3·kPa−1·100 g−1, 1kPa=7.5 mmHg) and resistances (in kPa·s·cm−3·100 g) at an (arterial) inflow pressure of 10 kPa and a (venous) outflow pressure of 0 kPa were: C1: 0.014; R1: 6.6; C2: 0.565; R2: 84.6; R3: 37.9; C4: 1.044; R4: 24.5. The model (with the nonlinear pressure-volume relations) is able to predict the static and dynamic instantaneous (i.e., for constant vasomotor tone) pressure-flow relation and the instantaneous zero flow pressure intercept. These phenomena are therefore not necessarily the result of the rheological properties of blood. The secondary or delayed dilatation upon a positive inflow pressure step (or negative step in venous pressure) is predicted by the model implying that delayed dilatation is not necessarily related to changes in vasomotor tone. Venous outflow delay, upon a positive inflow pressure step (starting from zero flow), is also predicted by the model.

Mechanics of a thin walled collapsible microtube

The purpose of this study is to measure the transmural pressure-cross sectional area relation of micro tubes (240 μm diameter) and to compare the measured perfusion pressure-flow relation with the pressure-flow relation calculated from the experimental pressure-cross sectional area relation. The microtubes are made by dipping a glass mould in a latex solution and glueing their outside ends to the inside of glass pipettes. The pressure-cross sectional area relation is determined both with a microplethysmograph (pressure-volume relation) and the microscope (pressure-diameter relations). Heparinized blood is used to include the rheological properties of blood as a perfusion medium. Static pressure-flow relations are obtained with a constant velocity piston pump for two values of external pressure (0 and 10 kPa) and with two downstream resistor settings (0 and 380 kPa cm−3 sec). The calculated pressure-flow relations using length and the experimental pressure-cross sectional area relation, Poiseuilles law, and accounting for the diameter-and shear-dependent viscosity compared well with the relations obtained from the experiments. It is also found that the pressure-flow relation shows an apparent zero flow pressure axis intercept (the extrapolation of the pressure-flow relation to the pressure axis), which can therefore be explained on the basis of the shape of the pressure-area relations.

Rate of the myogenic response increases with the constriction level in rabbit femoral arteries

The myogenic response forms an important aspect of blood flow regulation and is usually quantified by the steady-state relation between pressure and diameter. The aim of the present study is to analyze the dynamics of the myogenic response. In six isolated rabbit femoral arteries, the time course of the active part of the diameter response to a pressure step from 95 to 110 cm H2O (from 9.5 to 11 kPa), at two levels of norepinephrine (NE)-induced constriction, was fitted to a monoexponential curve to obtain the time constant. The NE concentrations used in the superfusion solution were between 0.8 and 1.5 μM for high constriction and between 0.2 and 0.6 μM for low constriction. Acetylcholine (1 μM in perfusion) was used to check endothelial function. The respective median values of the time constants with and without endothelium, are 13.2 and 15.5 sec (NS) for the high level of constriction and 49.5 and 58.5 sec (NS) for the low constriction level. Time constants at the two constriction levels were significantly different (p=0.002). In seven separate experiments using 40 mM KCl, in the superfusion fluid, to constrict femoral arteries to the same level as during the high level of NE constriction, it was found that the amplitude of the myogenic response was much smaller, compared with the norepinephrine experiments, and the time constant was significantly longer (median: 80.8 sec). We conclude that the dynamics of the myogenic response in the rabbit femoral artery is independent of the endothelium, but is dependent on the constriction level and type of constricting agent.

Effects of Oxygen and Flow on the Diameter of the Femoral Artery of the Rabbit

Contradictory results concerning the effects of oxygen and flow on blood vessel dimensions have been published. The aim of this study was to investigate the diameter changes in isolated, cannulated femoral arteries (n = 5) of the rabbit in a preconstricted state (two norepinephrine levels) during high and low pO2 (both inside and outside) at different flow levels. In this way the interaction between oxygen and flow is also investigated. Results were normalized to relative diameters, where the diameter at zero flow, during high pO2 and low norepinephrine concentration was considered as a control diameter (100%). We found three effects in this study: (1) going from high to low oxygen, there was a global vasoconstriction (repeated measures, analysis of variance, p = 0.016 with low norepinephrine and p = 0.015 with high norepinephrine); (2) when flow was increased from 1 to 100 ml/h, we found a significant (p less than 0.001) flow-dependent constriction under all four conditions, and (3) there is an interaction between flow and oxygen, for example at low norepinephrine the constriction due to low oxygen is 16% at zero flow and 1% at a flow of 1 ml/h, at high norepinephrine these numbers are 22 and 10%, respectively.

Responses to mechanical stimuli of isolated basilar and femoral arteries of the Rhesus monkey are different.

SummaryThe present study aimed to determine regional differences in diameter response to mechanical stimuli such as flow (shear stress) and transmural pressure (myogenic response) of the isolated basilar artery and femoral artery from Rhesus monkeys. Whether or not spontaneous tone developed, a transmural pressure-diameter relation was determined after the equilibration period. Vessels were then constricted with a submaximal dose of prostaglandin-F2α (PGF2α; 1.23–2µM) and a flow-diameter relation (0–2,000µl/min) and a pressure-diameter (15–125cmH2O) relation were determined. Endothelium function was tested with the calcium ionophore A-23187 (1.0 µM). The vessels were then maximally dilated (papaverine, 100µM) and a passive pressure-diameter relation was determined. The responses of the basilar and the femoral arteries were markedly different. The basilar artery developed spontaneous tone, while the femoral artery did not. The basilar artery showed flow-induced constriction (P = 0.024), while the femoral artery dilated when flow was increased (P = 0.0005). The myogenic index of the two arteries during treatment with PGF2α was not different (P = 0.49) and the strength of the myogenic response was such that the diameter of both arteries stayed constant over the pressure range studied. We conclude that the responses to mechanical stimuli of the basilar artery and the femoral artery of the Rhesus monkey are markedly different.

Smooth muscle responses of the rat septal artery are not influenced by surrounding passive cardiac tissue

SummaryWe investigated the possible contribution of surrounding passive cardiac tissue to the smooth muscle responses of coronary arteries. The vasoactive properties of the intramyocardial septal artery (outer diameter 350–400 µm) of the rat heart were investigated when it was freed from the surrounding cardiac tissue (dissected artery) and when it remained in the left ventricle and was thus embedded in passive cardiac tissue (in situ). The changes in external diameter relative to the maximal diameter (isoproterenol) resulting from the application of 125 mM KCl and 1,000 µU/ml vasopressin were measured at 37°C, a transmural pressure of 100cm H2O, and zero flow. In the dissected septal arteries (n = 5) the maximum diameter was 402 ± 16 µm, while during exposure to KCl and vasopressin the diameter was reduced to 66.1 ± 4.6% and 74.2 ± 3.0%, respectively. For the in situ arteries (n = 6), the maximal diameter was 386 ± 28 µm, a value not statistically different from the dissected vessels and the diameters reduced to 63.2 ± 5.5% and 65.6 ± 7.2% due to KCl and vasopressin, respectively. The constrictions of dissected arteries and in situ arteries were statistically not different. The results show that the maximally-dilated diameter and the constriction responses of intramyocardial conduit arteries of the rat heart are not affected by the surrounding passive cardiac tissue.

Vasoactive properties of rat coronary artery : in the tissue and isolated

Perfusion of the heart takes place mainly in diastole. It is therefore important to study the factors that affect coronary diastolic flow. One of the factors that may limit coronary artery vasoactive responses is the surrounding cardiac tissue. We have therefore studied the intramyocardial septal artery, both when still embedded in the diastolic, unstretched myocardial tissue and after complete dissection (n = 6). In situ, the average external diameter was 351 +/- 21 microns; after dissection, it was 362 +/- 21 microns. These values were not significantly different. The average response of the vessel to KCl (125 mM, receptor-independent constriction) reduced the diameter to 56.1 +/- 5.0% and 69.4 +/- 3.7% of the maximal diameter for in situ and dissected vessels, respectively. The reduction in diameter after dissection was significantly less than the reduction in situ. The response to vasopressin (1,000 microU/ml, a receptor-dependent constrictor) was a reduction to 62.6 +/- 4.7% and 70.4 +/- 4.5%, respectively. The reduction in diameter of the dissected vessel is significantly smaller than that of the in situ vessel. The average values of the ratios of the diameter reductions for vasopressin and KCl were 0.85 +/- 0.06 in the in situ condition and 0.95 +/- 0.08 after dissection and were not significantly different (paired t-test). The results show that the dilated diameter and the diameter responses of intramyocardial conduit arteries are not affected by the surrounding diastolic cardiac tissue.