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RESEARCH PAPERS

J Biomech Eng. 1980;102(1):1-7. doi:10.1115/1.3138193.

A finite element model is formulated for determining the macroscopic stress, strain and deformation of the lung parenchyma. The effects of nonlinear elastic behavior, finite deformation, and interfacial tension are included. An incremental approach is used. Illustrative results for deformation of the lung due to its weight are included. The necessity of including surface tension explicitly is demonstrated.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1980;102(1):8-22. doi:10.1115/1.3138203.

Collapse of arteries subjected to a band of hydrostatic pressure of finite length is analyzed. The vessel is treated as a long, thin, linearly elastic, orthotropic cylindrical shell, homogeneous in composition, and with negligible radial stresses. Blood in the vessel is treated as a Newtonian fluid and the Reynolds number is of order 1. Results are obtained for effects of the following factors on arterial collapse: intraluminal pressure, length of the pressure band, elastic properties of the vessel, initial stress both longitudinally and circumferentially, blood flow Reynolds number, compressibility, and wall thickness to radius ratio. It is found that the predominant parameter influencing vessel collapse for the intermediate range of vessel size and blood flow Reynolds numbers studied is the preconstricted intraluminal pressure. For pressure bands less than about 10 vessel radii the collapse pressure increases sharply with increasing intraluminal pressure. Initial axial prestress is found to be highly stabilizing for small band lengths. The effects of fluid flow are found to be small for pressure bands of less than 100 vessel radii. No dramatic orthotropic vessel behavior is apparent. The analysis shows that any reduction in intraluminal pressure, such as that produced by an upstream obstruction, will significantly lower the required collapse pressure. Medical implications of this analysis to Legg-Perthes disease are discussed.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1980;102(1):23-27. doi:10.1115/1.3138194.

Flow of a liquid through distensible tubes is of interest primarily in biological systems, and some properties of shock waves in such tubes are discussed. In shock-fixed coordinates, these flows are steady, and the shock is associated with an increase of pressure and cross-sectional area. Shock transition is analyzed for two flow models, namely, immediate flow separation, when the flow enters the shock zone, and no separation. Shock properties are expressed in terms of the speed index (ratio of the velocity of the shock to that of a small-amplitude wave) and dissipation (loss of total pressure). Examples are worked out for the thoracic aorta of an anesthetized dog, a perfectly elastic tube, and a partially collapsed tube. Appreciable differences in shock velocity and dissipation result if either flow separation or no separation is assumed.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1980;102(1):28-33. doi:10.1115/1.3138195.

When measuring blood pressure indirectly, oscillations in the cuff pressure are observed. The cuff pressure for which these oscillations reach a maximum and its relationship to the true mean arterial pressure was investigated using a simple one-dimensional theoretical model of the cuff-arm-artery system. Results from this model indicate that the cuff pressure for maximal oscillation is strongly dependent on compression chamber air volume, pulse pressure, and arterial elasticity. Parallel experimental studies indicate general agreement with the theoretical model. The cuff pressure for maximal oscillations appears to provide a reasonable estimation of the true mean arterial pressure provided compression chamber air volume is kept small.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1980;102(1):34-41. doi:10.1115/1.3138196.

Although prosthetic heart valves have been in existence for many years, the need for new improved designs and in-vitro evaluation techniques are apparent. This paper presents details on the design considerations, fabrication techniques and heart valve evaluation equipment. A valve performance index is discussed in light of various valve and mock circulatory test section designs. The need for national and indeed international valve evaluation techniques is made apparent.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1980;102(1):42-49. doi:10.1115/1.3138197.

An analysis of the temperature fields developed in a biological tissue undergoing a monoactive electrical coagulating process is presented, including thermal recovery following prolonged heating. The analysis is performed for the passage of alternating current and assumes a homogeneous and isotropic tissue model which is uniformly perfused by blood at arterial temperature. Solution for the one-dimensional spherical geometry is obtained by a Laplace transform and numerical integrations. Results obtained indicate the major role which blood perfusion plays in determining the effects of the coagulating process; tissue temperatures and depth of destruction are drastically reduced as blood perfusion increases. Metabolic heat generation rate is found to have negligible effects on tissue temperatures whereas electrode thermal inertia affects temperature levels appreciably. However, electrodes employed in practice would have a low thermal inertia which might be regarded as zero for all practical purposes. It is also found that the depth of tissue destruction is almost directly proportional to the electrical power and duration of application. To avoid excessively high temperatures and charring, it would be advantageous to reduce power and increase the time of application. Results of this study should be regarded as a first approximation to the rather complex phenomena associated with electrocoagulation. They may, nevertheless, serve as preliminary guidelines to practicing surgeons applying this technique.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1980;102(1):50-56. doi:10.1115/1.3138198.

It is known that the surface of articular cartilage is rough and it has been suggested that this is likely to affect the lubrication of human joints. This paper describes the direct measurement of a cartilage surface with a stylus instrument. It is found that the height distribution is Gaussian with an inverse-square power spectrum. It is thus possible to calculate the elastic deflection of the surface under normal walking loads and it is shown that the mean separation of the cartilage surfaces in a human joint varies rather slowly with load. In one particular hip joint at heel strike the real area of contact was calculated to be about 1.3 cm2 , the mean gap to be about 60 μm and the trapped volume to be about 80 percent of that when standing.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1980;102(1):57-61. doi:10.1115/1.3138199.

A quantitative mechanical description of the heart organ requires information on the mechanical behavior of its muscle in reasonable unity and completeness. In this respect, a fundamental constitutive law for soft biological tissues was proposed by Fung in 1972. This article presents evidence to show that Fung’s law is a useful law to describe the mechanical behavior of heart muscle in the unstimulated (diastolic) state with sufficient generality. A visco-elastic relaxation phenomenon is studied in the isolated cardiac muscle of cat and rabbit with the purpose of constructing a mathematical model for relaxation. Experimental results show that passive relaxation behavior of heart muscle can be adequately described by a generalized standard linear solid with a continuous distribution of relaxation times. The form of the relaxation function devised permits the application of linear visco-elasticity theory to the nonlinear cardiac muscle. The relaxation model is used to predict the force-length (stress-strain) behavior of papillary muscle with reasonable accuracy.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1980;102(1):62-66. doi:10.1115/1.3138200.

Measurements of segmental deformation made on papillary muscles obtained from cat, rabbit, dog and pig hearts suggest that the deformational behavior in these specimens is appreciably nonuniform both in the resting (passive) state and in the stimulated (active) state. In view of this, in the mechanical testing of papillary muscles, it is necessary to establish a minimum size of segment “sufficiently” far from the disturbing influence of end fixtures generally used to hold the specimen in the testing machine. The segment size should be large enough to average out the nonuniform aspects of deformation. Thus, the shape and size of the specimen dictated by the nonuniformities in the mechanical response, the thinness of the specimen dictated by the viability considerations and aspects of the testing machines and method dictated by the visco-elastic features of the specimen should be given due consideraton in the selection and testing of papillary muscles.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1980;102(1):67-72. doi:10.1115/1.3138201.

An experimental study was performed to determine the extent of shear-induced augmentation of oxygen diffusion in blood. The results were obtained using whole human blood in laminar flow through semipermeable membrane tubes. Transfer enchancement in whole blood was found to be dependent on the fluid shear rate and the hemoglobin saturation level. Very little agumentation was observed in saturated blood for shear rates up to 2500 s−1 . However, with partially unsaturated blood, oxygen transfer was increased up to 250 percent at the higher shear rates. The implications for modeling oxygen transfer in blood are discussed.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1980;102(1):73-84. doi:10.1115/1.3138202.

Articular cartilage is a biphasic material composed of a solid matrix phase (∼ 20 percent of the total tissue mass by weight) and an interstitial fluid phase (∼ 80 percent). The intrinsic mechanical properties of each phase as well as the mechanical interaction between these two phases afford the tissue its interesting rheological behavior. In this investigation, the solid matrix was assumed to be intrinsically incompressible, linearly elastic and nondissipative while the interstitial fluid was assumed to be intrinsically incompressible and nondissipative. Further, it was assumed that the only dissipation comes from the frictional drag of relative motion between the phases. However, more general constitutive equations, including a viscoelastic dissipation of the solid matrix as well as a viscous dissipation of interstitial fluid were also developed. A constant “average” permeability of the tissue was assumed, i.e., independent of deformation, and a solid content function Vs /Vf (the ratio of the volume of each of the phases) was assumed to vary with depth in accordance with the experimentally determined weight ratios. This linear, nonhomogeneous theory was applied to describe the experimentally obtained biphasic creep and biphasic stress relaxation data via a nonlinear regression technique. The determined intrinsic “aggregate” elastic modulus, from ten creep experiments, is 0.70 ± 0.09 MN/m2 and, from six stress relaxation experiments, is 0.76 ± 0.03 MN/m2 . The “average” permeability of the tissue is (0.76 ± 0.42) × 10−14 m4 /N•s. We concluded that the large spread in the permeability coefficients is due to the assumption of a constant deformation independent permeability. We also concluded that 1) a nonlinearly permeable biphasic model, where the permeability function is given by an experimentally determined empirical law: k = A(p) exp [α(p)e], can be used to describe more accurately the rheological properties of articular cartilage, and 2) the frictional drag of relative motion is the most important factor governing the fluid/solid viscoelastic properties of the tissue in compression.

Commentary by Dr. Valentin Fuster

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