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RESEARCH PAPERS

J Biomech Eng. 1989;111(1):1-8. doi:10.1115/1.3168334.

This paper considers the flow of an inelastic liquid which is generated by contractions like those of the intestine. Unlike regular peristaltic motion, these contractions occur locally over a finite length and have a finite amplitude. We adopt a contraction model due to Macagno and Christensen and repeat their analysis for an inelastic liquid. Our analysis, which is based on a Boundary Element Method, indicates that the net flow rate depends very weakly on the power-law index. The pumping action is therefore similar to that of a positive displacement pump.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(1):9-16. doi:10.1115/1.3168349.

A numerical investigation of pulmonary flow properties was carried out in a monoalveolar model composed of a balloon and a compliant tube in series, subjected to pressure ramps. The flow is shown to become quickly limited by a wave-speed mechanism, occurring at the peak flow. The critical point then travels upstream, while the main part of the exit flow rate is provided by the tube collapse. After the critical flow period, the flow becomes subcritical and viscous effects are predominant in the deeply collapsed tube.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(1):17-23. doi:10.1115/1.3168333.

Mean pressures within the lungs and lung volume, respectively, are clinically important parameters. During ventilation by way of high-frequency oscillation (HFO), these parameters have been shown to be strongly frequency dependent. To identify mechanisms leading to mean pressure formation during HFO, findings of the theory of stationary flow were extended to oscillatory flow by a quasi-stationary approach. To confirm the theoretical findings, in-vitro experiments on HFO-models were performed. Flow separation was found to be an important mechanism in the formation of mean pressure. Flow separation causes a significant flow resistance, which may be distinctly different for in- and outflow. During oscillatory flow, a mean pressure difference thus results. This mechanism is of particular importance in bifurcations, which are present in the HFO-circuit as well as in the airways. With the direction-dependent flow separation, a general mechanism was found, which accounts for differing mean pressure values within the lungs with different HFO-circuits. This mechanism also contributes to interregionally different mean pressure values within the lungs.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(1):24-31. doi:10.1115/1.3168335.

A mathematical model is developed to study the effect of capillary convection on oxygen transport around segments of arterioles and venules that are surrounded by capillaries. These capillaries carry unidirectional flow perpendicular to the vessel. The discrete capillary structure is distributed in a manner determined by the capillary blood flow and capillary density. A nonlinear oxyhemoglobin dissociation curve described by the Hill equation is used in the analysis. Oxygen flux from the vessel is expressed as a relationship between Sherwood and Peclet numbers, as well as other dimensionless combinations involving parameters of the capillary bed. A numerical solution is obtained with a finite difference method. The numerical results obtained within the physiological range of parameters allow the prediction of longitudinal gradients of hemoglobin-oxygen saturation along the arterioles and venules.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(1):32-36. doi:10.1115/1.3168336.

We measured the Fahraeus effect of blood flowing in a sheet flow model formed with two glass slides. The number of red blood cells in the sheet flow was counted to determine a sheet hematocrit Hs and the discharge hemotocrit Hd was measured from blood collection. For a Hd in the range of 3 to 30 percent, we find that Hs /Hd is about .83 for a gap of 4.1 μm. When the discharge hematocrit is 30 percent, the ratio decreases to .66 as the gap approaches 7 μm and then increases as the gap becomes thicker. The results indicate that the hematocrit ratio for a gap thicker than 4.1 μm is an increasing function of the discharge hematocrit. The value of Hs /Hd found for the sheet flow models and its dependence on Hd are comparable to those of circular tubes when their diameter equals the gap thickness.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(1):37-41. doi:10.1115/1.3168337.

In an experiment motivated by the study of arterial blood flow along the lines suggested by the traditional Chinese medicine, the flow in a pipe whose lumen was blocked by a semi-circular plug two tube-diameters long was visualized by suspended particles, recorded by cinematography, and analyzed digitally. The Reynolds number was in the range of 100 to 450 based on the pipe diameter, similar to that of blood flow in the radial artery in the arms of man. The blockage was found to have a profound effect on the velocity profile of the flow in the wake, but it had little influence on the symmetry of the velocity profile upstream of the block, except in its immediate neighborhood. When the end conditions far away from the block were steady, the flow in the wake was steady. The asymmetry of the flow in the wake can be judged by the deviation of the location of the maximum axial velocity from the center line of the pipe as seen in the plane of symmetry of the blockage. Our results show that the deviation can be described as the sum of two components. The first is a strong one which decays exponentially in an entry length which is about twice as long as the classical Boussinesq entry length of axisymmetric flow. The second is a weaker component which is wavy spatially and persists far downstream (many times the entry length). The separated flow and vortex system behind the blockage are sensitive to the flow rate. The relevance of these findings to the arterial pulse wave diagnosis methods used in the traditional Chinese medicine is discussed. We show that the human arteries are shorter than the entry length, hence nonaxisymmetric disturbances can be propagated throughout the circulation system. We propose that the propagation of the persistent, small, wavy asymmetric wave is relevant to the “localization” of the spheres of influence of internal and external organs in a two-inch region of the radial artery. We propose further that the method of pressing hard on the artery to “feel” the pulse is to amplify the signal by creating a wake that is very sensitive to velocity of flow.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(1):42-46. doi:10.1115/1.3168338.

A frequency domain approach that incorporates a matched filter was examined for discriminating between ordered velocity fluctuations with band-limited frequency content and random velocity variations in pulsatile disturbed flows. Fluctuations at pseudo-discrete frequencies may yield a significant contribution to the apparent stress tensor computed from the unsteady Navier Stokes equations, and an estimate of the stresses arising from these ordered structures can be obtained once the velocity variations have been decomposed. This type of decomposition permits the estimation of the apparent stresses in turbulent flows, consisting of coherent and random parts, in blood flow applications such as diseased constricted arteries or downstream of artificial heart valves.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(1):47-54. doi:10.1115/1.3168339.

The distributions of mass transfer rate and wall shear stress in sinusoidal laminar pulsating flow through a two-dimensional asymmetric stenosed channel have been studied experimentally and numerically. The distributions are measured by the electrochemical method. The measurement is conducted at a Reynolds number of about 150, a Schmidt number of about 1000, a nondimensional pulsating frequency of 3.40, and a nondimensional flow amplitude of 0.3. It is suggested that the deterioration of an arterial wall distal to stenosis may be greatly enhanced by fluid dynamic effects.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(1):55-61. doi:10.1115/1.3168340.

The thermal pulse-decay method, as developed and analyzed by Chen et al. [1–6], is a thermal clearance technique that uses a small thermistor probe for determining the blood perfusion and thermal conductivity of the tissue immediately surrounding the probe. They described the energy transfer of the probe/tissue system mathematically with a simple analytical model, the point source model, which assumes that the heating source is infinitely small. This paper introduces a new, more accurate analytical description that assumes the heating source is spherically symmetric with a finite radius. A numerical study of these two alternative mathematical models is presented in which the solutions of each model are compared to transient temperature decay data generated from a detailed finite difference simulation of the probe/tissue system. The accuracy and sensitivity of the predictions of each of these models to variations in tissue thermal conductivity and perfusion, probe characteristics, and heating time are presented. In all cases, the accuracy of the spherical source model was better than the point source model. It is also shown that the spherical source model can accurately predict low rates of perfusion (on the order of 1 kg/m3 s) unlike the point source model. The spherical source model also allows for the possibility of the measurement probes to be calibrated for an “effective bead radius” which accounts for the nonideal characteristics of the probe, thereby giving even more accurate determinations of perfusion.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(1):62-68. doi:10.1115/1.3168341.

Many medical applications involving lasers rely upon the generation of heat within the tissue for the desired therapeutic effect. Determination of the absorbed light energy in tissue is difficult in many cases. Although UV wavelengths of the excimer laser and 10.6 μm wavelength of the CO2 laser are absorbed within the first 20 μm of soft tissue, visible and near infrared wavelengths are scattered as well as absorbed. Typically, multiple scattering is a significant factor in the distribution of light in tissue and the resulting heat source term. An improved model is presented for estimating heat generation due to the absorption of a collimated (axisymmetric) laser beam and scattered light at each point r and z in tissue. Heat generated within tissue is a function of the laser power, the shape and size of the incident beam and the optical properties of the tissue at the irradiation wavelength. Key to the calculation of heat source strength is accurate estimation of the light distribution. Methods for experimentally determining the optical parameters of tissue are discussed in the context of the improved model.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(1):69-77. doi:10.1115/1.3168342.

A one-dimensional steady state continuum mechanics model of retraction of pseudopod in leukocytes is developed. The retracting pseudopod is assumed to move bodily toward the main cell body, the bulk motion of which can be represented by cytoplasmic flow within a typical stream tube through the leukocyte. The stream tube is approximated by a frictionless tube with prescribed geometry. The passive rheological properties of cytoplasm in the main cell body and in the pseudopod are modeled, respectively, by Maxwell fluid and Hookean solid. The two regions are assumed to be separated by a sharp interface at which actin gel solates and thereby changes its rheological properties as it flows from the pseudopod to the main cell body. The driving mechanism responsible for the active retraction motion is hypothesized to be a spontaneous deformation of the actin gel, analogous but not necessarily equal to the well known actin-myosin interaction. This results in an active contractile stress being developed in the pseudopod as well as in the cell cortex. The transverse traction pulls against the inclined wall of the stream tube and is transduced into an axial stress gradient, which in turn drives the flow. The tension on the tube wall is picked up by the prestressed cortical shell. Governing equations and boundary conditions are derived. A solution is obtained. Sample data are computed. Comparison of the theory with experiments shows that the model is compatible to the observations.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(1):78-87. doi:10.1115/1.3168343.

The objective of this study is to establish and verify the set of boundary conditions at the interface between a biphasic mixture (articular cartilage) and a Newtonian or non-Newtonian fluid (synovial fluid) such that a set of well-posed mathematical problems may be formulated to investigate joint lubrication problems. A “pseudo-no-slip” kinematic boundary condition is proposed based upon the principle that the conditions at the interface between mixtures or mixtures and fluids must reduce to those boundary conditions in single phase continuum mechanics. From this proposed kinematic boundary condition, and balances of mass, momentum and energy, the boundary conditions at the interface between a biphasic mixture and a Newtonian or non-Newtonian fluid are mathematically derived. Based upon these general results, the appropriate boundary conditions needed in modeling the cartilage-synovial fluid-cartilage lubrication problem are deduced. For two simple cases where a Newtonian viscous fluid is forced to flow (with imposed Couette or Poiseuille flow conditions) over a porous-permeable biphasic material of relatively low permeability, the well known empirical Taylor slip condition may be derived using matched asymptotic analysis of the boundary layer at the interface.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J Biomech Eng. 1989;111(1):88-91. doi:10.1115/1.3168344.

A rich group of fluid mechanical problems are suggested in the classical Chinese books Nei Jing and Mai Jing. In this article the methods of pulse wave palpation described in these books are briefly explained, and an attempt to understand some of their statements is presented.

Commentary by Dr. Valentin Fuster

LETTERS TO THE EDITOR

J Biomech Eng. 1989;111(1):92-93. doi:10.1115/1.3168345.
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Abstract
Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(1):93-94. doi:10.1115/1.3168346.
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Abstract
Topics: Biomechanics
Commentary by Dr. Valentin Fuster

BOOK REVIEWS

J Biomech Eng. 1989;111(1):95. doi:10.1115/1.3168347.
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Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(1):95-96. doi:10.1115/1.3168348.
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Abstract
Commentary by Dr. Valentin Fuster

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