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RESEARCH PAPERS

J Biomech Eng. 1984;106(1):1. doi:10.1115/1.3138450.
Abstract
Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(1):2-9. doi:10.1115/1.3138452.

Studies of red blood cell deformation have shown that there are a number of membrane material properties that affect the deformation process. In this paper various types of deformation are modeled using geometrical and constitutive simplifications so that the effect of intrinsic elastic and viscous membrane properties and of major geometric constraints is made obvious while other factors are ignored. To this end, numerical solutions are shunned in favor of exact analytical (“closed-form”) solutions to simple and basic membrane deformation problems in order to reveal functional dependence.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(1):10-18. doi:10.1115/1.3138448.

A new continuum mechanical theory for protopod extension in leukocytes is developed. Protopod formation is an active process which is the basis for amoeboid displacement on substrates. Leukocytes may form protopods both when adhering to a substrate and when freely suspended in plasma. Therefore the required energy is derived from the cell itself. Protopods are depleted of granules and other organelles, they have a fine fibrillar ultrastructure, and they are covered by a cell membrane. They grow at about 5 μm/min until they reach a length of 4–5 μm. A period of protopod retraction follows during which granules re-enter via the protopod base by Brownian motion. Micropipette experiments have indicated that the protoplasm in the leukocyte has viscoelastic properties, whereas the protopod is stiffer and shows elastic behavior. We propose a continuum theory based on the polymerization of the actin matrix in the cell which results in gelation with a preferred orientation. It is triggered by influx of Ca++ across local regions of the cell membrane and the polymerization occurs along an interface at the base of the polymerized protopod. As cytoplasm passes through the interface it is subject both to a volumetric strain due to exclusion of granules and a shear strain due to alignment of actin molecules. The polymerization provides an active force leading to projection of the protopod and cell deformation. The base of the protopod rests on the unpolymerized cytoplasm along the interface. As the external plasma medium and the cell membrane, if it is not stretched taut, offer little resistance, the projection of the protopod proceeds outward with simultaneous unfolding of the membrane. On the other hand, in osmotically swollen cells the membrane offers considerable resistance as it is under tension and the actin polymerization proceeds inward. A general set of equations are formulated and some special solutions are discussed.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(1):19-24. doi:10.1115/1.3138449.

A method has been developed for the study of the forces which individual cells exert during their locomotion. Polydimethyl-siloxane (silicone fluid) was crosslinked on its surface by brief flaming to form a thin layer of silicone rubber. Tissue culture cells of many types were then plated out onto these rubber substrata and the propulsive forces these cells exert as they adhere and spread became visible as wrinkles and other distortions in the rubber. From time-lapse films of these distortions, it appears that the component cells of the body move by exerting shearing forces through their plasma membranes. How these forces are exerted and how this technique for observing them could be made more quantitative are discussed.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(1):25-30. doi:10.1115/1.3138451.

Intact single cells were isolated from adult rat hearts by enzymatic digestion and suspended in 0.25 mM Ca++ Tyrode’s solution. Quiescent, clearly striated rodlike cells were selected for study of the elastic properties of the cells at various stages of membrane and myofilament extraction. Selected cells were placed in a relaxing solution (pCa + 9, 10 mn EGTA) and then each end gently pulled into the tip of a closely fitting suction micropipette for attachment to a force transducer and length perturbation driver. This procedure was performed in low Ca++ to prevent Ca++ loading of the cell during attachment and at room temperature to prevent chemical skinning of the cell [1]. Stiffness was measured by applying a 5-Hz sinusoidal length perturbation (5 percent L0 ) to one end of the cell while measuring the induced tension change at the other. The ratio of sinusoidal tension change to applied length change (stiffness) was determined for each cell over a length range of about 1–1.3 L0 before removal of the contractile filaments and up to 3.0 L0 after treatment with 0.6 M KI. The stiffness-length relation was measured first in relaxing solution and then in 0.25 mM Ca++ Tyrode’s. If spontaneous contractions or contracture occurred the cell was rejected. If the cell remained quiescent and relaxed it was treated again with relaxing solution and 1 percent Triton X-100 to remove the membranes. The stiffness-length relation was again measured and then the cell was superfused with 0.47 M KCl/10 mM pyrophosphate solution to remove the myosin filaments. The stiffness-length relation was again determined and the cell finally perfused with 0.6 M KI to remove all the contractile filaments. A rodlike, faintly striated structure remained at this point whose stiffness could still be measured. In cells which remained quiescent during the entire extraction procedure and did not develop contracture the following results were obtained. In the relaxing solution and in 0.25 mM Ca++ the stiffness-length relation was similar to that of rat papillary muscle [2]. When the cell membranes were removed with detergent a transient increase in stiffness sometimes occurred which declined within a few minutes to a level near that in the relaxing solution. With KC1 treatment the stiffness declined variably to about half its control value. Immediately upon treatment of the cell with KI solution the major striation pattern disappeared and stiffness fell dramatically. Also the cell became highly extensible such that is could be reversibly extended in length to 2.5–3 L0 with the faintly striated pattern uniformly following the extension. At 3 L0 the sinusoidally measured stiffness was about equal to that of the intact cell at L0 . These data indicate that a significant source of the high resting stiffness of rat heart muscle resides within the muscle cells and is dependent to a large extent on the presence of the myofilaments [3]. Also, a measurable stiffness remains in the cells after contractile filament extraction, which may be attributable to the cytoskeletal intermediate filaments.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(1):31-35. doi:10.1115/1.3138453.

Shear stress produced by a flowing fluid has been found to cause changes in the structure and function of vascular endothelial cells. They tend to become elongated and aligned with the direction of flow. They respond to changes in fluid shear stress (either from low shear to high shear or vice versa) by transiently increasing fluidphase endocytosis. And they are capable of producing intracellular actin and myosin filaments that are oriented in the flow direction.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(1):36-41. doi:10.1115/1.3138454.

Recent efforts to model the mechanical interaction of aggregates of biological cells are reviewed. Differential adhesion is discussed as a means of creating a field of stress equivalent to tension elements at interfaces between unlike cell types. Several numerical algorithms are described and applied to shortening and folding of cell sheets, three-dimensional monolayers, and two-dimensional cell aggregates.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(1):42-47. doi:10.1115/1.3138455.

Nonlinear viscoelasticity is important in a variety of studies in biomechanics. One of the subject areas is the necessity to characterize the dynamic properties of blood vessels. This study concerns a theoretical formulation to examine the higher order nonlinear viscoelastic relaxation functions for arterial tissue based on the assumption of transversely isotropic material properties. Simple numerical results for the first-order theory are compared with those available in the literature.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(1):48-53. doi:10.1115/1.3138456.

An in-vitro flow study was conducted in a mildly atherosclerotic main coronary artery casting of man using sugar-water solutions simulating blood viscosity. Steady flow results indicated substantial increases in pressure drop, and thus flow resistance at the same Reynolds number, above those for Poiseuille flow by 30 to 100 percent in the physiological Reynolds number range from about 100 to 400. Time-averaged pulsatile flow data showed additional 5 percent increases in flow resistance above the steady flow results. Both pulsatile and steady flow data from the casting were found to be nearly equal to those from a straight, axisymmetric model of the casting up to a Reynolds number of about 200, above which the flow resistance of the casting became gradually larger than the corresponding values from the axisymmetric model.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(1):54-61. doi:10.1115/1.3138457.

An investigation was carried out to quantitatively evaluate left ventricular volume flow rate, momentum, force and impulse derived from application of conservation principles for mass and momentum of blood within the ventricle during the ejection phase. An automated digital image processing system was developed and applied to left ventricular angiograms which are computer processed and analyzed frame by frame to determine the dynamical relations by numerical methods. Our initial experience with force and impulse has indicated that neither quantity seemed to be a sensitive indicator of coronary artery disease as evaluated by qualitative angiography for the particular patient group studied. Utilization of the dynamical relations in evaluating human left ventricular performance requires improved means of measurement and interpretation of clinical studies.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(1):62-65. doi:10.1115/1.3138458.

We determine the pressure distribution behind a soft contact lens that is necessary to keep the lens in conformity with an axisymmetric substrate. The substrate consists of two regions: a central portion, the cornea, supposed to be an ellipsoid; and a peripheral region, the sclera, taken to be a sphere. The pressure is obtained as part of a numerical solution of the axisymmetric equilibrium equations for an initially curved, linearly elastic membrane. The relaxed shape of the lens is assumed to be an axisymmetric ellipsoid with a central curvature and a shape factor different from those of the cornea. The variation in the thickness of the lens from its center to edge is approximated by a polynomial. Pressure distributions are obtained for several typical soft contact lens fittings.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(1):66-71. doi:10.1115/1.3138459.

To determine the extent of backflow encountered with currently used prosthetic valves, four types of aortic valves with comparable orifice diameters were tested in a pulse duplicating system. These were a Hancock porcine valve, a Lillehei-Kaster pivoting disk valve, a St. Jude bileaflet valve and a Björk-Shiley tilting disk valve. Mean aortic pressure was sequentially increased from 83 to 147 mmHg, keeping the pump rate essentially constant (69–73 strokes/min). The porcine valve produced the least amount of total backflow (backflow due to closure plus leakage backflow) (1.6 to 2.4 mL/stroke). Among the mechanical valves the Björk-Shiley valve showed the least amount of total backflow (5.0 to 6.0 mL/stroke). At a mean aortic pressure of 100 mmHg and a low cardiac output of 2 L/min, the total backflow with the porcine valve was only 6 percent of forward flow; whereas it was 19 percent with the Lillehei-Kaster valve, 22 percent with the St. Jude valve and 18 percent with the Björk-Shiley valve. Leakage backflow at a given level of mean aortic pressure was, as expected, directly related to the annular clearance area. It is concluded that the Hancock valve showed the least amount of backward flow, which would be particularly beneficial in low output states. In the presence of normal hemodynamics, the amount of backflow with the three mechanical valves appeared to be well below the level of backflow considered to be clinically significant.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(1):72-78. doi:10.1115/1.3138460.

This report describes the theory and operation of a pulsed-probe anemometer designed to measure steady three-dimensional velocity fields typical of pulmonary tracheo-bronchial airflows. Local velocities are determined by measuring the transport time and orientation of a thermal pulse initiated at an upstream wire and sensed at a downstream wire. The transport time is a reproducible function of velocity and the probe wire spacing, as verified by a theoretical model of convective heat transfer. When calibrated the anemometer yields measurements of velocity accurate to ±5 percent and resolves flow direction to within 1 deg at airspeeds ≥10 cm/s. Spatial resolution is ±0.5 mm. Measured flow patterns typical of curved circular pipes are included as examples of its application.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(1):79-82. doi:10.1115/1.3138461.

Steady and pulsatile flows were passed through casts of human aortic bifurcations and, by means of a laser Doppler anemometer, fluid velocities were measured at selected sites near the ventral and dorsal walls. At these sites, in the vicinity of the bifurcation, the influence of secondary flow is significant and therefore an appreciation of the phasic variation of secondary flow patterns is important. Results are presented comparing the flow direction in both steady and pulsatile flow at sites in three casts. The common features of the flow at these sites were the persistence of the flow direction during the accelerating and decelerating phases of the pulsatile cycle, and the consistently smaller angle (measured from the inlet centerline) of the pulsatile flow direction as compared to the angle of the flow direction in steady flow.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(1):83-88. doi:10.1115/1.3138463.

This paper demonstrates a modeling technique of prosthetic heart valves. In the modeling, a pumping cycle is divided into four phases, in which the state of the valve and flow is different. The pressure-flow relation across the valve is formulated separately in each phase. This technique is developed to build a mathematical model used in the real time estimation of the hemodynamic state under artificial heart pumping. The model built by this technique is simple enough for saving the computational time in the real time estimation. The model is described by the first-order ordinary differential equation with 12 parameters. These parameters can be uniquely determined beforehand from in-vitro experimental data. It is shown that the model can adapt, with sufficient accuracy, to a change in the practical pumping condition and the viscosity of the fluid in their practical range, and is also demonstrated that the estimated backflow volume by model agrees closely with the actual one.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J Biomech Eng. 1984;106(1):89-90. doi:10.1115/1.3138464.
Abstract
Topics: Pulsatile flow
Commentary by Dr. Valentin Fuster

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