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PubMed1994

Functional origin of reflected pressure waves in a multibranched model of the human arterial system.

The effects of wave travel and wave reflection were simulated in a mathematical model of the whole arterial tree consisting of 142 uniform transmission line segments. The arterial model was partitioned into three separate segments: upper limbs, trunk, and lower limbs. Aging was simulated by increasing average pulse wave velocities of these segments (10.9-12.9, 8.0-11.7, and 9.0-11.3 m/s for upper limbs, trunk, and lower limbs, respectively). Reflection coefficients at the terminal elements were altered to simulate vasodilation (0.0) and vasoconstriction (0.95). The impedance patterns and spatial distribution of pressure waveforms generated by the model simulating aging and vasoconstriction were similar to in vivo measurements by other investigators. Reflected pressure waves from each segment reached the ascending aorta and contributed differently to the late systolic peak on the aortic pressure wave. Aging does not alter the origin of these reflected pressure waves in the trunk. Aortic impedance and pressure wave changes induced by simulation of dilation of splanchnic bed were similar to those observed experimentally with nitroglycerin.

Aorta↗
PubMed1994

Determinants of end-systolic pressure during different load alterations in the in situ left ventricle.

Because of the strong dependency of the end-systolic pressure-volume relation on the type of transient loading intervention in the in situ left ventricle (LV), experiments in the basal inotropic state in 16 open-chest anesthetized dogs were reanalyzed to find additional variables to model and predict end-systolic pressure (ESP) of both afterloading and preloading interventions by a single equation. Random-coefficients regression analysis was performed on 22 experiments in the basal inotropic state simultaneously, yielding an overall R2 of 0.97. The major part of total variance of ESP was due to linear terms of end-systolic volume (ESV) (74%) and stroke volume (SV) (19%). The SV effect was consistently negative and quantitatively quite important. An average load-independent end-systolic elastance of 6.7 mmHg/ml and an average SV effect of -5.7 mmHg/ml ejected were estimated, separating the "force-length" property from shortening effects in the in situ LV. History-related effects appeared to be only minor.

Analysis of Variance↗
PubMed1994

In vivo visualization of oxygen transport in microvascular network.

Oxygen transport from the blood to the tissues is a diffusive process driven by the gradient of oxygen tension (PO2). We developed an oxygen-quenching fluorescent membrane that allowed visualization of the PO2 distribution near the microvessels as optical patterns on the membrane by epifluorescence microscopy. This membrane was highly gas permeable to allow PO2 measurement and was transparent enough to also permit observation of the microcirculation. In combination with a newly devised gastight chamber and a micropositioning system, this membrane technique made it possible to visualize the PO2 distribution in the rat mesenteric microvascular network under well-defined conditions. Our preliminary findings indicate that the oxygen distribution in the microvascular network is heterogeneous and suggest that there is considerable release of oxygen from the arterioles. The time lag of the system for tracking rapid PO2 changes in vitro was shown to be negligible, indicating that dynamic PO2 changes occurring in vivo can also be assessed. This technique should provide a novel tool for the study of oxygen transport and metabolism under normal and abnormal conditions.

Animals↗
PubMed1995

Exercise training effects on collateral and microvascular resistances in rat model of arterial insufficiency.

Experiments were performed to determine if exercise training reduces collateral or microvascular resistances in the hindlimb of rats with arterial insufficiency. After right femoral arterial ligation (age 10 wk), rats were divided into sedentary (Sed) and treadmill-trained (Tr) groups (7-9 wk, final intensity: 27 m/min, 6 degree grade, 60 min/day). Minimal resistances (mmHg.ml-1.min.100 g) of the total limb (RT), collateral vessels (RC), and the microcirculations distal (Rfmc) and proximal (Rimc) to the ligation site were determined during pump perfusion of the hindlimbs. RT was lower in nonligated (open) and acutely ligated limbs of Tr than Sed rats (open: 0.69 +/- 0.011 vs. 0.93 +/- 0.071; acute: 0.92 +/- 0.028 vs. 1.18 +/- 0.070 mmHg.ml-1.min.100 g) but not in chronically ligated limbs (chronic: 0.88 +/- 0.072 vs. 1.00 +/- 0.046 mmHg.ml-1.min.100 g). RC was similar between the chronically ligated limbs of Sed and Tr rats (1.69 +/- 0.165 vs. 1.97 +/- 0.227 mmHg.ml-1.min.100 g) and was approximately 70% lower than in acutely ligated limbs of both groups. Rfmc and Rimc were not affected by arterial ligation, but Rimc was significantly lower in Tr than in Sed rats (acute: 1.05 +/- 0.026 vs. 1.54 +/- 0.163; chronic: 1.24 +/- 0.071 vs. 1.81 +/- 0.202 mmHg.ml-1.min.100 g). These results indicate that the primary site of vascular adaptations to chronic arterial ligation is in the collateral vessels. Exercise training does not significantly alter the collateralization process but may provide protection against acute arterial occlusion by stimulating microvascular growth.

Animals↗
PubMed1995

Permeability of cat skeletal muscle capillaries to small solutes.

Permeability-surface area products (PS) for 51Cr-EDTA, [3H]mannitol, [14C]urea, and 22Na were measured in isolated, perfused, lower hindlimb muscles of anesthetized cats. The tracers were added stepwise to the arterial inflow, and Evans blue-labeled albumin was the reference indicator. At flow rates > 70 ml.min-1.100 g-1, the PS values (+/- SE) were 5.0 +/- 0.5, 7.6 +/- 1.2, 17.8 +/- 1.4, and 21.0 +/- 1.4 (n = 7, 4, 5, and 3 animals, respectively). The ratio of simultaneous PS measurements of mannitol and urea was 0.42 +/- 0.02 (n = 9), significantly less than the free diffusion coefficient ratio (0.49), indicating the presence of restricted diffusion. PS measurements were also made during osmotic flow (4.2 +/- 0.6 ml.min-1.100 g-1) induced by 20% NaCl. The data clearly showed that osmotic transients did not alter small solute permeability. Pore models were used to show that the PS data and previously reported reflection coefficient data were consistent with a single description of the capillary wall. This model contained a water-only pathway containing 60% of the hydraulic capacity and an extracellular route modeled by pores of 4 nm radius having 21,000 cm of area per unit membrane thickness (A/delta x).

Animals↗
PubMed1995

Muscle length alters geometry of arterioles and venules in hamster retractor.

We investigated how changes in muscle length (Lm) would alter the geometry of arterioles and venules and whether such an effect would depend on the orientation of microvessels to muscle fibers. The parallel-fibered retractor muscle of anesthetized (pentobarbital sodium, 65 mg/kg) male hamsters (n = 20, 105 +/- 4 g) was exposed and irrigated with physiological saline solution (pH 7.4; 35 degrees C). Sarcomere length (Ls) was measured at x2,400 magnification after topical application (3 min, 10(-5) M) of a fluorescent dye [4-(4-diethylaminostyryl)-N-methylpyridinium iodide]. In vivo Ls at resting Lm (i.e., at Lm = 100%) was 3.00 +/- 0.02 microns. The origin and insertion of the retractor were cut, and the muscle was reflected dorsally while the circulation arising from the ventral surface was preserved. Polystyrene "tendons" were glued to each end of the muscle to control Lm, which was varied in 10% increments from 80 to 130% of in situ Lm; Ls increased linearly (r2 = 0.82) from 2.58 +/- 0.03 to 3.89 +/- 0.07 microns, respectively. Arteriole and venule branches and the centerline of "Y" bifurcations were classified based on orientation angles (theta) with respect to muscle fibers at Lm = 100%; three categories were defined using trigonometry (detailed in the APPENDIX) based on microvessel behavior during changes in Lm: parallel (P), 0 degree < or = theta < or = 32.6 degrees; intermediate (I), 32.6 degrees < theta < 59.4 degrees; and normal (N), 59.4 degrees < or = theta < or = 90 degrees.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗
PubMed1995

Mathematical model that characterizes transmitral and pulmonary venous flow velocity patterns.

The transmitral and pulmonary venous flow velocity (TMFV and PVFV, respectively) patterns are related to the physiological state of the left heart by use of an electrical analog model. Filling of left ventricle (LV) through the mitral valve is characterized by a quadratic Bernoulli's resistance in series with an inertance. Filling of the left atrium (LA) through the pulmonary veins is represented by a lumped network of linear resistance, capacitance, and inertance. LV and LA are each represented by a time-varying elastance. A volume dependency is incorporated into the LV model to produce physiological pressure-volume loops and Starling curves. The state-space representation of the analog model consists of 10 simultaneous differential equations, which are solved by numerical integration. Model validity is supported by the following. First, the expected effects of aging and decreasing LV compliance on TMFV and PVFV are accurately represented by the model. Second, the model-generated TMFV and PVFV waveforms fit well to pulsed-Doppler recordings in normal and postinfarct patients. It is shown that the TMFV deceleration time is prolonged by the increase in LV compliance and, to a lesser extent, by the increase in LA compliance. A shift from diastolic dominance to systolic dominance in PVFV occurs when LA compliance or pulmonary perfusion pressure increases or when LV compliance or mitral valve area decreases. The present model should serve as a useful theoretical basis for echocardiographic evaluation of LV and LA functions.

Animals↗
PubMed1995

Predicting the potential gradient field in ventricular fibrillation from shocks delivered in paced rhythm.

A method of defibrillation threshold determination that utilizes low-strength shocks delivered in a benign rhythm would be desirable. Because the two-dimensional epicardial potential gradient (PG) is a shock parameter that is linked to defibrillation, we examined whether the epicardial PG measured for shocks delivered in paced rhythm could be used to predict the PG for defibrillation-strength shocks delivered in ventricular fibrillation (VF). In six open-chest pentobarbital-anesthetized pigs with left ventricular apex and right atrial internal defibrillation patches, we measured the epicardial PG field for shocks delivered in paced rhythm and during VF. We determined that there was a linear relationship between epicardial PG and shock strength for shocks delivered in paced rhythm. However, prediction of the PG measured for shocks in VF from those measured in paced rhythm resulted in a statistically significant overestimation of the PG in VF. We conclude that, for equivalent strength shocks, the epicardial PG field is weaker for shocks delivered in VF. This change in the potential gradient field can have an effect on defibrillation threshold estimates that are based on shocks delivered in paced rhythm.

Animals↗
PubMed1995

Modeling pressure-area relations of coronary blood vessels embedded in cardiac muscle in diastole and systole.

Pressure-cross-sectional area (P-A) relations of a (thick-walled) arteriole and (thin-walled) small vein (both maximally dilated), embedded in cardiac muscle in both static systole and diastole at slack length and at 90% of maximal length (Lmax), were calculated. The elastic properties of cardiac muscle and vessel wall per se were taken into account. Muscle fibers and vessels were assumed to run in parallel. The muscle tissue (fibers + collagen) was assumed to be incompressible, homogeneous, nonlinearly elastic, and transversely isotropic. Cross-fiber stress-strain relations were assumed to be proportional to those in fiber direction. It is predicted that cardiac muscle in diastole has little effect on the P-A relation of the arteriole but strongly affects that of the small vein. In systole, the myocardium strongly affects the P-A relations of both vessels. Isometric transition from static diastole to static systole (isometric "contraction") was found to reduce arteriolar and venous area (at constant pressures of 35 and 7 mmHg, respectively) by approximately 50 and 40, respectively. Contraction with a 14% shortening was found to reduce these areas by 48 and 32%, respectively. The differences in the results for the two vessels were found to be determined mainly by their difference in the ratio of outer to inner radius. Furthermore, it was found that the area reductions are much larger for contractions (with or without shortening) than for muscle stretch per se. It is concluded that the change in elastic properties and, more specifically, development of stress in cross-fiber direction of the cardiac muscle during contraction causes the area reductions of coronary vessels.

Animals↗
PubMed1995

Cardiac quick-release contraction mechanoenergetics analysis using a cardiac muscle cross-bridge model.

Huxley's sliding filament cross-bridge muscle model coupled with parallel and series elastic components was simulated to examine the conflicting reports on the amount of energy saved by quick release at the peak contraction time. Cross-bridge energy utilization was determined by considering the ATP hydrolysis for the cross-bridge cycling. The quick-release cases were simulated by letting the muscle fiber suddenly shorten to the resting fiber length at peak systole, and then the contraction was allowed to continue at the resting length. Simulation results demonstrated that, using realistic parameter values, typically approximately 15% of the muscle fiber energy is used after peak systole (and approximately 30% of the cross-bridge energy), but this is also a function of the muscle fiber properties characterized by cross-bridge association and dissociation rate constants. Increasing the kinetic rate constants, the series elasticity, the initial fiber length, or the time of peak intracellular calcium will increase the amount of energy left, which may explain some of the discrepancies in the literature. Cardiac muscle hypertrophy will increase the fraction of muscle fiber energy left after peak systole to approximately 30%. The strongest indicator of the percent energy left at peak systole was the time the fiber reached peak systole, and as the fiber reached peak systole faster, the amount of energy saved by quick release increased.

Animals↗
PubMed1995

A method to assess endocardial regional longitudinal curvature of the left ventricle.

Knowledge of the instantaneous geometry of the left ventricular (LV) chamber is necessary to calculate LV function and wall stresses. We describe a method utilizing myocardial markers that does not rely on any a priori assumptions of global LV geometry. Five dogs underwent placement of 25 endocardial and 3 epicardial miniature LV markers. Six weeks later, the animals were studied during conscious closed-chest conditions. The three-dimensional coordinates of the LV markers were used to compute longitudinal fitted curves for LV walls and septum during steady-state conditions; endocardial radii of curvature (rcurv) were then computed for each region at the midequatorial (rcurv-eq) and apical levels. There was a uniform decrease in rcurv in each LV wall during systole (compared with diastole, P < 0.01); at end systole, rcurv was regionally heterogeneous between opposing walls, e.g., anterior and posterior rcurv-eq values were 17.2 +/- 2.0 and 17.7 +/- 1.8 (SD) cm, respectively (P < 0.05). At end diastole, only septal-lateral rcurv-eq was different (16.9 +/- 2.1 vs. 18.7 +/- 1.3 cm: P < 0.05). Normalization of rcurv (to instantaneous LV volume) removed the systolic-diastolic differences, but a similar pattern of regional heterogeneity persisted. The data presented pertain to the LV endocardial surface, but the method described can be applied to the epicardial surface as well; this new method offers promise in assessing dynamic changes in longitudinal LV endocardial curvature.

Analysis of Variance↗
PubMed1996

Cardiac transient outward potassium current: a pulse chemistry model of frequency-dependent properties.

Recent voltage-clamp studies of isolated myocytes have demonstrated widespread occurrence of a transient outward current (I(to)) carried by potassium ions. In the canine ventricle, this current is well developed in epicardial cells but not in endocardial cells. The resultant spatial dispersion of refractoriness is potentially proarrhythmic and may be amplified by channel blockade. The inactivation and recovery time constants of this channel are in excess of several hundred milliseconds, and consequently channel availability is frequency dependent at physiological stimulation rates. When the time constants associated with transitions between different channel conformations are rapid relative to drug binding kinetics, the interactions between drugs and an ion channel can be approximated by a sequence of first-order reactions, in which binding occurs in pulses in response to pulse train stimulation (pulse chemistry). When channel conformation transition time constants do not meet this constraint, analytical characterizations of the drug-channel interaction must then be modified to reflect the channel time-dependent properties. Here we report that the rate and steady-state amount of frequency-dependent inactivation of I(to) are consistent with a generalization of the channel blockade model: channel availability is reduced in a pulsatile exponential pattern as the stimulation frequency is increased, and the rate of reduction is a linear function of the pulse train depolarizing and recovery intervals. I(to) was reduced in the presence of quinidine. After accounting for the use-dependent availability of I(to) channels, we found little evidence of an additional use-dependent component of block after exposure to quinidine, suggesting that quinidine reacts with both open and closed I(to) channels as though the binding site is continuously accessible. The model provides a useful tool for assessing drug-channel interactions when the reaction cannot be continuously monitored.

Animals↗
PubMed1997

Relationship of the fourth heart sound to atrial systolic transmitral flow deceleration.

The fourth heart sound (S4) is thought to be due to cardiohemic vibrations, powered by deceleration of transmitral blood flow, that occur when atrial systole leads to a disproportionately high rise in ventricular end-diastolic pressure (relative to diastasis), associated with an enhanced atrial systolic blood filling volume or a stiff ventricular wall. To characterize S4 production, we modeled the cardiohemic system as a forced, damped nonlinear harmonic oscillator. The forcing term used a closed-form expression for the Doppler A-wave contour. We simultaneously recorded transthoracic phonocardiograms and Doppler A waves in subjects with and without audible S4 and compared model predictions for S4 amplitude, frequency, and power spectrum with those of the recorded S4. Excellent agreement was observed between the model-predicted amplitude, duration, timing, and power spectrum and those of the phonocardiographic S4. We conclude that, with a normal mitral valve, there should always be an oscillation of the cardiohemic system during A-wave deceleration. However, oscillations may not have high enough amplitude, frequency, or coupling to the chest wall to be clinically audible as an S4.

Atrial Function↗
PubMed1997

Regional perfusion parameters from pulmonary microfocal angiograms.

An indicator-dilution model was developed to describe transport of vascular contrast medium through an organ during acquisition of vascular dynamic contrast images. The model provides the theoretical basis for methods of determining regional blood flow, blood volume, and mean transit time from time-absorbance curves acquired from the images of tissue regions of interest (ROI) distal from the inlet site. The robustness of these methods was evaluated using a computer-simulated vessel network, which simulated the passage of a bolus of contrast medium through arterioles, networks of capillaries, and venules. The network was used to evaluate the reliability of ROI parameter estimation methods when the underlying model assumptions are violated. The shape of the ROI inlet concentration curve and moderate amounts of random noise did not affect the ability of the method to recover accurate parameter estimates. The estimates of ROI flow and transit time were degraded in the presence of significant dispersion of the inlet concentration curve as it traveled through arteries upstream from the microvascular ROI or when the flow was redistributed within the ROI. The estimates of ROI volume were relatively robust. The method was applied to image data of the dog pulmonary vasculature obtained using microfocal X-ray angiography to show that the results obtained from the simulations are consistent with actual data.

Angiography↗
PubMed1997

Macromolecular transport in the arterial intima: comparison of chronic and acute injuries.

Hypertension is a known risk factor for the development of atherosclerosis, which is characterized by the abnormal accumulation of low-density lipoprotein and other plasma-borne macromolecules. The goal of this study was to measure accumulation of a plasma-borne macromolecular marker, horseradish peroxidase (HRP; 44 kDa), in the aortic intima and media of chronically hypertensive rats. HRP transport in 2-yr-old spontaneously hypertensive rats (SHR) was compared with that in age-matched Wistar-Kyoto rats (WKY) under conditions in which blood pressures were not significantly different during the 15-min HRP circulation. Intimal accumulation and medial HRP concentration profiles were obtained from methacrylate-embedded sections after reaction with 3,3'-diaminobenzidine and H2O2. Data were analyzed using a mathematical model of macromolecular transport to quantify the permeabilities of endothelium and internal elastic lamina (IEL). Chronic hypertension increased endothelial permeability without a change in IEL permeability. An apparent convective flux of HRP into the intima of SHR raised intimal HRP to a concentration higher than that of HRP in the plasma. Our results suggest that the intimal accumulation of plasma-borne macromolecules from pressure-driven convection is normally minimized by an intact endothelium. Similar changes resulted from acute injury by lipopolysaccharide, suggesting endothelial injury could account for transport changes associated with hypertension. After either chronic or acute endothelial damage, transport of macromolecules into the intima increases, but the IEL continues to retard transport of macromolecules beyond the intima, resulting in increased intimal accumulation.

Animals↗
PubMed1997

Interaction between adenosine and flow-induced dilation in coronary microvascular network.

Previous studies have demonstrated that coronary microvessels are regulated by at least three possible means: metabolite-induced, shear-induced, and pressure-induced (myogenic) mechanisms. Adenosine, a putative metabolic vasodilator, preferentially dilates downstream coronary microvessels, whereas the shear-sensitive mechanism is detected predominantly in upstream larger microvessels. However, the interaction of these mechanisms and the significance of the heterogeneous vascular responsiveness in flow regulation have not been evaluated. These tasks cannot be performed experimentally because of several confounding factors that cannot be separated. Therefore, the present study employed a data-based modeling approach to investigate the role of response heterogeneity in a coronary vascular network and to test the hypothesis that shear-sensitive mechanism or the myogenic mechanisms will enhance the vascular sensitivity to adenosine due to the heterogeneity of the vascular responsiveness. We obtained necessary data and developed empirical models for the responsiveness of single vessels to pressure, shear stress, and adenosine. With the single-vessel models, a network model was established based on the branching pattern of coronary microvessels, mass balance, and fluid mechanics laws. Model simulation predicted an enhanced vascular response to adenosine in the network. Such an enhancement is caused by the heterogeneous vascular response to adenosine and the predominant flow-induced dilation in the large arterioles. Preferential dilation of the downstream small arterioles to adenosine initiates an increase in flow and a decrease in pressure at upstream vessels. The increased flow activates the shear-sensitive mechanism of the upstream large arterioles and further enhances the flow. This hemodynamic interaction contributes up to approximately 20% of the adenosine-induced flow increase and also reduces the adenosine-induced pressure drop. In contrast to the shear-sensitive mechanism, myogenic response contributes relatively little to the vascular response to adenosine. These results suggest that various vascular regulation mechanisms and the response heterogeneity of vessels of different sizes may act in an integrative fashion for the optimal control of microvascular perfusion.

Adenosine↗
PubMed1997

Modulation of propagation from an ectopic focus by electrical load and by extracellular potassium.

We previously developed a technique (R. Kumar, R. Wilders, R. W. Joyner, H. J. Jongsma, E. E. Verheijck, D. A. Golod, A. C. G. van Ginneken, and W. N. Goolsby. Circulation 94: 833-841, 1996) for study of a mathematical model cell with spontaneous activity, viz. a "real-time" simulation of a rabbit sinoatrial node cell (SAN model cell; R. Wilders, H. J. Jongsma, and A. C. van Ginneken. Biophys. J. 60: 1202-1216, 1991) simultaneously being electrically coupled via our "coupling clamp" [H. Sugiura and R. W. Joyner. Am. J. Physiol. 263 (Heart Circ. Physiol. 32): H1591-H1604, 1992] circuit to a real, isolated ventricular myocyte. We now apply this technique to investigate effects of coupling conductance (Gc), cell size, and the modulation of membrane potential by elevated extracellular potassium concentration on the ability of an ectopic focus, represented by the SAN model cell, to successfully drive a ventricular cell. Values of Gc and the relative sizes of the two cells define three possible outcomes: 1) spontaneous pacing of the SAN model cell but not driving of the ventricular cell, 2) cessation of spontaneous pacing, or 3) pacing of the SAN model cell and driving of the ventricular cell. Below a critical size of the SAN model cell only the first two of these outcomes is possible. Above this critical size there is a range of Gc that allows successful operation of the system as an ectopic focus. Elevation of extracellular potassium concentration from 4 to 8 mM increases both the lower bound and upper bound of Gc for this range. Elevation of extracellular potassium concentration, as commonly observed in myocardial ischemia, may have effects on either inhibiting or releasing from inhibition an ectopic focus.

Animals↗
PubMed1997

Electrode for recording direction of activation, conduction velocity, and monophasic action potential of myocardium.

Conduction velocity and recovery of excitability are central facets of reentry arrhythmias, and yet there are no satisfactory techniques for the simultaneous measurement of both from the same area of myocardium. We have developed an electrode arrangement that allows the simultaneous recording of conduction velocity, repolarization of the myocardium together with an index of dispersion, and direction of activation of the myocardium. Three silver/silver chloride electrodes were arranged in an equilateral triangle with a reference electrode at the center. From this arrangement three monophasic action potentials were recorded. From the time of arrival of the wavefront of activation at each electrode the direction of activation and conduction velocity were calculated in real time by a computer. There was a good correlation for the in vivo signals from the circular electrode and the new electrode both for conduction velocity (r = 0.99, P < 0.001) and for direction of activation (r = 0.99, P < 0.001). This new mathematical method and electrode design allows the simultaneous measurement of conduction velocity and direction and monophasic action potential, and this can give a beat-by-beat indication of wavelength and dispersion of action potential duration.

Action Potentials↗