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A S Popel

Publications and source records attributed to A S Popel.

At least 19 recordsLinked to original sources
PubMed1996

Measurements and a model of the outer hair cell hydraulic conductivity.

The hydraulic conductivity of the cochlear outer hair cell (OHC) is central to the maintenance of the positive intracellular pressure necessary for its function as the cochlear amplifier. A mathematical model of osmotic water transport across the OHC membrane is formulated. The model relates the OHC hydraulic conductivity, Lp, to the rate of volume change in response to osmotic stimuli. Lp is evaluated from osmotic experiments in which isolated OHCs are exposed to an hypotonic solution. The rate of volume increase in response to the hypotonic challenge was determined by a morphometric analysis of video images of cells. Lp was found to be about 10(-14) m s-1 Pa-1 or equivalently, Pf approximately 10(-4) cm s-1. This is on the low side of values reported for different lipid bilayers and is 2 orders of magnitude lower than the hydraulic conductivity of red blood cells. The relation of the low OHC hydraulic conductivity to the composition and morphology of its membranes is discussed.

Animals↗
PubMed1996

The ratio of elastic moduli of cochlear outer hair cells derived from osmotic experiments.

Outer hair cells (OHCs) were subjected to three different hypo-osmotic challenges which induced shape changes in OHCs. The longitudinal and circumferential strains, epsilon z and epsilon c, respectively, were extracted from a morphometric analysis of video images of the cells. A value of epsilon z/epsilon c = -0.72 was obtained and was found to be independent of the applied osmotic gradient. Using an elastic isotropic membrane model for the OHC lateral wall, the ratio of the elastic shear modulus mu to the elastic area expansion modulus K was calculated yielding a value of 0.054. The contribution of this ratio to OHC mechanics is discussed.

Animals↗
PubMed1996

Theoretical predictions of end-capillary PO2 in muscles of athletic and nonathletic animals at VO2max.

Characterizing the resistances to O2 transport from the erythrocyte to the mitochondrion is important in understanding potential transport limitations. A steady-state model of this process was developed to predict the minimum (critical) end-capillary PO2 required to prevent hypoxia at maximal O2 consumption (VO2max) in a circular region of tissue surrounding the venular end of a capillary. Capillary density was used as a measure of O2 delivery, and mitochondrial density was used as a measure of O2 consumption. The effects of oxyhemoglobin dissociation kinetics and diffusion facilitation by hemoglobin in the erythrocytes and facilitation by myoglobin in the tissue were taken into account. Calculations made for selected skeletal muscles, diaphragm, and myocardium in three adaptive animal pairs (dog and goat, horse and cow, and pony and calf) yielded values of end-capillary PO2 that were consistent with measured values of mixed venous PO2 in maximally working animals. Values of end-capillary PO2 were found to be uncorrelated with values of VO2max in different muscles. No significant difference in end-capillary PO2 was found between similar muscles of athletic versus nonathletic animals. Predicted intracapillary O2 transport resistance ranged from 18 to 54% of the total transport resistance in the O2 pathway. Further investigation is required to explore the extent to which spatial and temporal heterogeneities in O2 delivery and consumption play a role in O2 transport.

Animals↗
PubMed1995

A theoretical analysis of intracellular oxygen diffusion.

Oxygen diffusion rates within cells may be heterogeneous, with more rapid diffusion occurring along intracellular pathways of high oxygen solubility, such as mitochondria. Recent experimental data indicate that tissue oxygen permeability rises sharply in a temperature range associated with phase transitions in lipid membranes suggesting that membranes may function as oxygen "pathway". The experimental data have been analyzed using theoretical models of diffusion in two-phase media. By assuming muscles to be composed entirely of aqueous cytosol and lipids, cytosolic permeability was determined as a function of temperature by matching the experimental values of tissue permeability with those of model predictions using in vitro values of lipid permeability. Cytosolic permeability ranged from 50% of water permeability (low temperature) to 90% of water permeability (high temperature) and its temperature dependence was distinctly different from that of water. An upper bound for cytosolic permeability was calculated using a physiologic value for protein volume fraction, and lipid permeability was obtained using this cytosolic permeability. A model with a parallel arrangement of lipid and cytosol yielded a value of lipid permeability that was 71% higher than the in vitro value. Intracellular permeabilities calculated from tissue permeability values were found to be inconsistent with experimentally reported values for rat cardiac myocytes. Comparison of three different muscles exhibited the same trend of higher permeability with higher lipid content. It is concluded that both lipid and cytosol permeabilities and, hence, tissue permeabilities are different among different muscles and one should exercise caution when data from one muscle is used to calculate or extrapolate values in other muscles. It is conceivable that muscles with very high mitochondrial content, such as diaphragm and cardiac muscles may exhibit an oxygen permeability which is significantly higher than commonly accepted values. These results warrant additional measurements of tissue oxygen permeability at 37 degrees C, especially for oxidative muscles with high lipid content.

Animals↗
PubMed1995

Outer hair cell length changes in an external electric field. I. The role of intracellular electro-osmotically generated pressure gradients.

Brownell et al. [Science 227, 194-196 (1985)] observed that an isolated, cylindrically shaped cochlear outer hair cell can change its length when an electric field is applied. In their experiments, the cell was fixed at one end, and located between two electrodes which lie on the cell axis but were positioned far from the cell. Kachar et al. [Nature 322, 365-368 (1986)] had suggested that the cell's electrically evoked elongation could be caused by pressure gradients resulting from electro-osmosis of the intracellular fluid. A mathematical model is developed which predicts the length change that would result from electro-osmotically generated pressure gradients inside the cell. Estimated parameter values are included to demonstrate that the pressures generated by electro-osmosis inside the cell would result in elongations that are at least two orders of magnitude below the experimentally measured values.

Cytoplasm↗
PubMed1995

Outer hair cell length changes in an external electric field. II. The role of electrokinetic forces on the cell surface.

An isolated cochlear outer hair cell can elongate or shorten when electrically stimulated, as discovered by Brownell et al. [Science 227, 194-196 (1985)]. In their experiments, the cylindrically shaped cell was fixed at one end, and was positioned between two electrodes which lie on the cell axis, but were far from the cell (transcellular stimulation). A model is developed to predict the component of the cell's elongation which arises from only electrokinetic phenomena. Outside the cell, electro-osmosis produces a drag on the lateral wall which almost exactly balances the electrophoretic force. In contrast to previous theories, we find that the electrokinetic response is governed by the free end of the cell, not the lateral wall. If the surface charge density of the free end lies between -0.004 and -0.07 C/m2 (corresponding to the zeta potential between -5 and -60 mV), then our model predicts elongations that are comparable in magnitude to experimentally measured values.

Electric Stimulation↗
PubMed1994

A numerical study of plasma skimming in small vascular bifurcations.

Owing in part to a plasma-skimming mechanism, the distribution of red blood cells (RBCs) into branches of microvascular bifurcations typically differs from the distribution of the bulk blood flow. This paper analyzes the plasma-skimming mechanism that causes phase separation due to uneven distribution of red blood cells at the inlet cross section of the parent vessel. In a previous study, the shape of the surface that divides the flow into the branches was found by numerical simulation of three-dimensional flow of a homogeneous Newtonian fluid in T-type bifurcations. Those findings are used in this study to determine, as a first approximation, the side-to-parent vessel RBC flux ratio and discharge hematocrit ratio as a function of corresponding flow ratios. Calculations are based on the assumption that RBCs move along streamlines of a homogeneous Newtonian fluid and are uniformly distributed within a concentric core at the inlet cross section of the parent vessel. The results of our calculations agree well for a wide range of flow parameters with experimental data from in vivo and in vitro studies.

Blood Flow Velocity↗
PubMed1994

Capacity for red blood cell aggregation is higher in athletic mammalian species than in sedentary species.

The purpose of this study was to show that two rheological parameters, red blood cell (RBC) sedimentation rate and apparent blood viscosity at low shear rate, characterizing the degree of RBC aggregation, correlate significantly with the maximal mass-specific rate of oxygen consumption or aerobic capacity (VO2max). Comparisons were made within two groups of similarly sized athletic and sedentary species: group 1, pronghorn antelope, dog, goat, and sheep; and group 2, horse and cow. The pronghorn antelope (Antilocapra americana) is one of the most athletic mammals, and we have obtained data on the rheological properties of blood from this species for the first time. The values of apparent viscosity at hematocrit = 40% and shear rate = 0.277 s-1 measured in a rotational viscometer were 59.5, 42.6, and 9.1 cP for antelope, dog, and sheep blood, respectively, and 55.3 and 11.5 cP for horse and cow blood, respectively. The viscosity values for antelope, dog, and sheep blood can be correlated with aerobic capacity: ln viscosity = 4.48-106.3 VO2(-1)max (r2 = 0.998; P < 0.05). The values of RBC sedimentation rate at hematocrit = 40% were 12.8, 7.0, and 0 mm/h for antelope, dog, and sheep blood, respectively, and 45.3 and 0.1 mm/h for horse and cow blood, respectively. Therefore, the data showed that the athletic species exhibit a consistently higher degree of RBC aggregation than do the corresponding nonathletic species.

Animals↗
PubMed1993

Effect of red blood cell shape on oxygen transport in capillaries.

A mathematical model of oxygen (O2) transport within a capillary utilizes axisymmetric red blood cell (RBC) shapes that were predicted theoretically by Zarda et al. in 1977. Chemical kinetics and both free and facilitated diffusion of O2 are accounted for in this time-dependent model. The finite-element method is used to solve the governing partial differential equations. It is found that the shape of RBCs, characterized by the shape parameter theta adapted from Zarda et al., affects such important O2 transport characteristics as capillary wall O2 flux and hemoglobin (Hb) saturation. At an RBC residence time (time for an RBC to travel from the capillary inlet to a given point) of 0.22 s, a change in the shape parameter theta from 0 (undeformed cell) to 26 (parachute-shaped cell) decreases the spatially averaged O2 flux by 26%. The dependence of O2 flux on RBC shape diminishes as the RBC residence time increases. The difference in Hb saturation at the RBC residence time of 0.22 s can be as large as 10% for different values of theta. The mass transfer Nusselt number, which is inversely proportional to transport resistance, decreases with increases in theta. The fractional transport resistance in the plasma region accounts for approximately 65-80% of the total intracapillary resistance. Calculations show that local chemical equilibrium in the O2-Hb chemical reaction is attained everywhere except within a thin boundary layer adjacent to the erythrocyte membrane, where significant deviation from chemical equilibrium occurs.

Animals↗
PubMed1993

Sternal force-displacement relationship during cardiopulmonary resuscitation.

A viscoelastic model is presented to describe the dynamic response of the human chest to cyclic loading during manual cardiopulmonary resuscitation (CPR). Sternal force and displacement were measured during 16 clinical resuscitation attempts and during compressions on five CPR training manikins. The model was developed to describe the clinical data and consists of the parallel combination of a spring and dashpot. The human chests' elastic and damping properties were both augmented with increasing displacement. The manikins' elastic properties were stiffer and both elastic and damping properties were less dependent on displacement than the humans'.

Biomechanical Phenomena↗
PubMed1992

Modeling the circulation with three-terminal electrical networks containing special nonlinear capacitors.

Development, first of analog and later of digital computers, as well as algorithms for analysis of electrical circuits, stimulated the use of electrical circuits for modeling the circulation. The networks used as building blocks for electrical models can provide accurate representation of the hydrodynamic equations relating the inflow and outflow of individual segments of the circulation. These networks, however, can contain connections in which voltages and currents have no analogues in the circulation. Problems arise because (a) electrical current must flow in closed loops, whereas no such constraints exist for hydraulic models; and (b) electrical capacitors have a number of characteristics that are not analogous to those of hydraulic compliant chambers. Disregarding these differences can lead to erroneous results and misinterpretation of phenomena. To ensure against these errors, we introduce an imaginary electrical element, the nonlinear residual-charge capacitor (NRCC), with characteristics equivalent to those of a compliant chamber. If one uses appropriate circuit connections and incorporates the residual-charge capacitor, then all voltages and currents in the model are proper analogues of pressures and flows in the circulation. It is shown that the capacitive current represents the rate of change of volume of blood inside the vessel, as well as the rate of the corresponding displacement of volume of the surrounding tissue.

Blood Circulation↗
PubMed1992

A numerical study of the shape of the surface separating flow into branches in microvascular bifurcations.

The shape of the separating surface formed by the streamlines entering the branches of microvascular bifurcations plays a major role in determining the distribution of red blood cells and other blood constituents downstream from the bifurcation. Using the finite element method, we determined the shape of the surface through numerical solution of three dimensional Navier-Stokes equations for fluid flow at low Reynolds numbers in a T-type bifurcation of circular tubes. Calculations were done for a wide range of daughter branch to parent vessel diameter ratios and flow ratios. The effect of Reynolds number was also studied. Our numerical results are in good agreement with previously reported experimental data of Rong and Carr (Microvascular Research, Vol. 39, pp. 186-202, 1990). The numerical results of this study will be used to predict the concentration of blood constituents downstream from microvascular bifurcations providing that the inlet concentration profile is known.

Blood Flow Velocity↗
PubMed1990

Effect of convection in capillaries on oxygen removal from arterioles in striated muscle.

Based on experimental data that show the presence of significant oxygen saturation gradients in precapillary arterioles, it has been suggested that the in vivo permeability to oxygen of resting striated muscle may be significantly higher than the corresponding in vitro value obtained in unperfused tissue samples (Popel et al., 1989b, Adv. expl. Med. Biol. 247, 215). The present study performs two analyses to further compare theoretical predictions with experimental data obtained under control conditions and during hemodilution and hemoconcentration. First, it is shown that, in principle, a capillary-perfused tissue layer with a thickness of a few hundred microns is necessary to convectively carry the experimentally determined amount of oxygen released by precapillary arterioles under control and hemodiluted conditions. This capacity to convect oxygen depends strongly on the resting tissue oxygen tension. Second, a more general version of a previous model (Weerappuli & Popel, 1989, J. Biomech. Eng. 111, 24) is used to examine whether changes made in the model parameters within the physiological range of values can explain the experimentally measured flux. The results show that the theoretical predictions can be made compatible with experimental observations if the in vivo permeability of perfused tissue to oxygen is assumed to be one to two orders of magnitude higher than the in vitro value. Furthermore, the predicted in vivo permeability for perfused tissue surrounding an arteriole varies with the arteriolar luminal oxygen tension and flow. This may be due to simplifying approximations made in the model or possible experimental artifacts. Alternatively, it could also be speculated that this variability indicates the flow dependency of the permeability of perfused tissue to oxygen.

Animals↗
PubMed1990

Identification of dynamic mechanical parameters of the human chest during manual cardiopulmonary resuscitation.

Survival from cardiac arrest is dependent on timely cardiopulmonary resuscitation (CPR). Since CPR is often unsuccessful, the outcome may be improved by a better understanding of the relationship between force applied to the sternum and the resulting hemodynamic effects. The first step in this complex chain of interactions is the mechanical response of the chest wall to cyclical compression. We formulated a dynamic mechanical model of the chest response and developed a method of identification of the model parameters based on force, displacement, and acceleration data acquired during cyclical compressions. The elasticity, damping, and equivalent mass of the human chest were estimated with a constrained nonlinear least-mean-square identification technique. The method was validated on data acquired from a test apparatus built for this purpose. The model fit was measured with the normalized chi-square statistic on residuals obtained between recorded force and force predicted by the model. In the analysis of one human chest, the elasticity was found to be nonlinear and statistically different during compression and release. A considerable amount of damping was found, with no significant difference between compression and release. The equivalent mass was too small to be determined accurately. This method can be used to obtain the dynamic mechanical parameters of the human chest and may lead to a better understanding of CPR.

Biomechanical Phenomena↗
PubMed1990

Shape and orientation of arterial loops in cat sartorius muscle.

A method is described to quantify the shape and orientation of vascular loops (arcades). Shape is characterized by an ellipticity factor, calculated from area and perimeter values. Orientation is measured as the angle formed by the great axis of the loop with the muscle fibers. These parameters were calculated for 772 arteriolar loops of the cat sartorius muscle. The results show that, on the average, the ellipticity factor is a linear function of the number of segments. The observed values change in the opposite direction from the expected values for regular polygons. Simple calculations are presented to rectify this discrepancy. Most loops are oriented parallel to the muscle fibers.

Animals↗
PubMed1989

The cost of departure from optimal radii in microvascular networks.

In the Murray optimality model of branching vasculatures, the radii of vessels are related to blood viscosity, vascular metabolic rate, and blood flow rate, in such a way as to minimize the total work (hydraulic and metabolic) of the system. The model predicts that flow is proportional to the cube of a vessel radius, and that at junctions the cube of the radius of the parent vessel equals the sum of the cubes of the daughter radii. In comparing real vasculatures to the Murray model, we have previously had no expressions for evaluating the apparent energy cost for departures from the optimal junction exponent of 3. Such expressions are derived here. They show that junction exponents, from about 1.5 to large positive values, are within 5% of the energy minimum. With the new equations, observed individual junctions or entire vascular trees can be compared, energy-wise, with the Murray optimum. Junctions in the transverse arteriolar trees of cat sartorius muscle were compared to the Murray optimality model, using these new expressions. The junction exponents for these small pre-capillary vessels had a broad range, with a median value greater than the Murray optimum of 3. The exponents were restricted, however, to values requiring, at individual junctions, little increase in energy. The majority of junctions had energy costs less than 1% above the Murray minimum. For entire trees involving many junctions the departures from optimality averaged less than 10%. Thus, while the branching geometry for these microvascular trees deviates significantly from the Murray optimum in the direction of larger daughter to parent ratios, the departures are small in energy terms.

Animals↗