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RESEARCH PAPERS

J Biomech Eng. 1986;108(3):193-200. doi:10.1115/1.3138602.

In order to establish a quantitative model of blood flow in skeletal muscle, the mechanical properties of the blood vessels need to be measured. We present measurements of the viscoelastic properties of arterioles, venules, and capillaries in exteriorized rat spinotrapezius muscle. Muscles were perfused with an inert silicone polymer and a uniform static pressure was established by occlusion of the venous outflow. Vessel diameters were then measured as a function of the static pressure. This study provides the first measurements of the viscoelastic properties of microvessels in skeletal muscle in situ. Over a pressure range of 20–200 mmHg, the transverse arterioles are the most distensible vessels, while the arcade venules are the stiffest. In response to a step change in pressure, all vessels show an initial elastic deformation, followed by a nonlinear creep. Based on the experimental results for different pressure histories a constitutive equation relating vessel diameter to the local transmural pressure is proposed. Diameter changes are expressed in the form of a diameter strain, analogous to a Green’s strain, and are related to the local transmural pressure using a standard linear solid model. This model has only three empirical coefficients and could be fitted to all experimental results for all vessels within error of measurement.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1986;108(3):201-207. doi:10.1115/1.3138603.

The elastic properties of marginal band, a microtubular structure isolated from the newt (notophthalmus viridescens ) have been measured. Bands were isolated using Triton X-100 and pepsin at pH 6.8 according to the method of Cohen (1978). Isolated bands were manipulated with a glass microhook in a buffer-filled chamber under the microscope. Single bands were stretched between the hook and a thin glass fiber. The fiber was calibrated so that the force on the band could be calculated from the displacement of the fiber. The data pairs of force versus band deflection were analyzed according to the theoretical work of Libai and Simmonds (1983) to obtain the flexural and extensional rigidities of the band. Band dimensions calculated from the data were consistent with microscopically determined values. The average flexural rigidity of the bands (EI ) was 5.3 × 10−13 dyn•cm2 and the average extensional rigidity (EA ) was 0.017 dyn. Compared to the cell membrane, the marginal band is nearly inextensible and has a much greater resistance to bending, indicating that the band makes an important contribution to the deformability of the circulating cell.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1986;108(3):208-214. doi:10.1115/1.3138604.

Presented here is a theoretical analysis of the recently developed thermal pulse decay (TPD) method for a simultaneous measurement of local tissue conductivity and blood perfusion rate. The paper describes the theoretical model upon which the TPD method is based and details its capabilities and limitations. The theoretical aspects that affected the development of the measurement protocol are also discussed. The performance of the method is demonstrated with an experimental example which compares the measurements of local kidney blood perfusion rates made using the TPD method with the total renal blood flow obtained coincidentally using a blood flowmeter, in an anesthetized dog.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1986;108(3):215-221. doi:10.1115/1.3138605.

In the last two decades, several multi-segmented mathematical models of the total-human-body have appeared in the literature. While these models can handle very sophisticated load-motion situations, their effectiveness depends heavily on the proper biomechanical description and simulation of the major articulating joints of the human body. Among these joints, the most complicated and the least successfully modeled one has been the shoulder complex mainly due to the lack of an appropriate biomechanical data base as well as the anatomical complexity of the shoulder region. In 1984, the senior author and his associates proposed a new kinematic data collection methodology by means of sonic emitters and associated data analysis technique. Based on this data collection methodology, Part I of this paper establishes a statistical data base for the shoulder complex sinus of the male population of ages 18–32. Estimates for the population mean and standard deviation as well as their confidence intervals are presented. The results are expressed in functional expansion form relative to a locally defined joint axis system as well as relative to the torso-fixed coordinate system in the form of globographic representation.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1986;108(3):222-227. doi:10.1115/1.3138606.

In mathematical modeling of multi-segmented articulating total-human-body, there is no doubt that the shoulder complex plays one of the most important roles. However, proper biomechanical passive resistive force data have been lacking in the literature. This paper presents determination of the three-dimensional passive resistive joint properties beyond the maximal voluntary shoulder complex sinus. A functional expansion with two spherical angular variables in the local joint axis system is proposed to fit the overall restoring force (moment) data. A constant restoring force (moment) contour map as well as a three-dimensional perspective view of the results are presented in a new coordinate system defined in this study. Finally, a statistical data base is established by utilizing the statistical analysis procedures discussed in Part I [9] of this paper.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1986;108(3):228-231. doi:10.1115/1.3138607.

The accuracy of a flush-mounted hot film anemometer probe for wall shear stress measurements in physiological pulsatile flows was evaluated in fully developed pulsatile flow in a rigid straight tube. Measured wall shear stress waveform based on steady flow anemometer probe calibrations were compared to theoretical wall shear stress waveforms based on well-established theory and measured flow rate waveforms. The measured and theoretical waveforms were in close agreement during systole (average deviation of 14 percent at peak systole). As expected, agreement was poor during diastole because of flow reversal and diminished frequency response at low shear rate.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1986;108(3):232-238. doi:10.1115/1.3138608.

In this study we have employed a single channel, pulsed ultrasonic Doppler velocimeter to measure instantaneous velocity distributions within the pumping chamber of a ventricular assist device. Instantaneous velocities have been decomposed into periodic mean and turbulent fluctuating components from which estimates of Reynolds stresses within the chamber and mean shear stresses along the wall of the chamber have been obtained. A review of the complete data set indicates a maximum value of the mean wall shear stress of 25 dynes/cm2 and a maximum Reynolds stress of 212 dynes/cm2 . These values are lower than those measured distal to aortic valve prostheses in vitro and are well below levels known to damage blood components. Core flow patterns, wall washing patterns and flow stagnation points are also revealed.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1986;108(3):239-245. doi:10.1115/1.3138609.

The theoretical basis, practical design considerations, and prototype testing of a perfused model suitable for simulation studies of microwave heated tissue are presented. A parallel tube heat exchanger configuration is used to simulate the internal convection effects of blood flow. The global thermal response of the phantom, on a scale of several tube spacings, is shown theoretically to be nearly identical to that predicted by Pennes’ bioheat equation, which is known to give a reasonable representation of tissue under many conditions. A parametric study is provided for the relationships between the tube size, spacing and material properties and the simulated perfusion rate. A prototype with a physiologically reasonable perfusion rate was tested using a typical hyperthermia applicator. The measured thermal response of the phantom compares favorably with the numerical solution of the bioheat equation under the same irradiation conditions. This similarity sheds light on the unexpected success of the bioheat equation for modeling the thermal response of real tissue.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1986;108(3):246-250. doi:10.1115/1.3138610.

We develop analytical expressions (scaling laws) for the local temperature fluctuations near isolated and countercurrent blood vessels during hyperthermia. These scaling laws relate the magnitude of such fluctuations to the size of the heated region and to the thermal equilibration length of the vessels. A new equilibration length is identified for countercurrent vessels. Significant temperature differences are predicted between the vessels and the immediately adjacent tissue when the equilibration length is comparable to or longer than the size of the heated tissue region. Countercurrent vessels are shown to have shorter equilibration lengths and produce smaller temperature fluctuations than isolated vessels of the same size.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1986;108(3):251-258. doi:10.1115/1.3138611.

Phasic and spatial time-averaged pressure distributions were measured in a 60-deg femoral artery branch model over a large range of branch flow ratios and at physiological Reynolds numbers of about 120 and 700. The results obtained with an in-vivolike flow wave form indicated spatial adverse time average pressure gradients in the branch vicinity which increased in magnitude with branch flow ratio, and the importance of the larger inertial effects at the higher Reynolds numbers. Pressure losses in the branch entrance region were relatively large, and corresponding flow resistances may limit branch flow, particularly at higher Reynolds numbers. The effect of branch flow was to reduce the pressure loss in the main lumen.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1986;108(3):259-265. doi:10.1115/1.3138612.

Blood flow velocity was measured in the dog aorta distal to mechanically induced constrictions of various degrees of severity employing an 8-MHz pulsed Doppler ultrasound velocimeter and a phase-lock loop frequency tracking method for extracting velocity from the Doppler quadrature signals. The data were analyzed to construct ensemble average velocity waveforms and random velocity disturbances. In any individual animal the effect of increasing the degree of stenosis beyond approximately 25 percent area reduction was to produce increasing levels of random velocity disturbance. However, variability among animals was such that the sensitivity of random behavior to the degree of stenosis was degraded to the point that it appears difficult to employ Doppler ultrasound measurements of random disturbances to discriminate among stenoses with area reductions less than approximately 75 percent. On the other hand, coherent vortex structures in velocity waveforms consistently occurred distal to mild constrictions (25–50 percent area reduction). Comparison of the phase-lock loop Doppler ultrasound data with simultaneous measurements using invasive hot-film anemometry, which possesses excellent frequency response, demonstrates that the ultrasound method can reliably detect those flow phenomena in such cases. Thus, the identification of coherent, rather than random, flow disturbances may offer improved diagnostic capability for noninvasively detecting arteriosclerotic plaques at relatively early stages of development.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1986;108(3):266-272. doi:10.1115/1.3138613.

Axial mass transport due to the combined effects of flow oscillation and a turbulent jet was studied both experimentally and with a simple theoretical model. The experiments show that the distance over which turbulence enhances transport is greatly increased by flow oscillation, and is particularly sensitive to tidal volume. The jet flow rate and jet configuration are relatively less important. To analyze the results, the region influenced by the jet is divided into two zones: a near field in which the time-mean flow velocities are larger than the turbulent fluctuations, and a far field where the time-mean flow is essentially zero. In the far field, axial mass transport is increased due to the turbulence which decays in strength away from the jet. When oscillatory flow is superimposed upon the steady jet flow, the turbulence in the far field interacts with the flow oscillations to augment the transport of turbulence energy and of mass. This transport enhancement is modeled by introducing an effective axial diffusivity analogous to that used in laminar oscillatory flow.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1986;108(3):273-280. doi:10.1115/1.3138614.

Stable internal fixation usually results in a unique histological healing pattern which involves direct cortical reconstruction and an absence of periosteal bridging callus. While it has been suggested that longitudinal interfragmentary strain levels control this healing pattern, the complex, multiaxial strain fields in the interfragmentary region are not well understood. Based on an in-vivo study of gap healing in the sheep tibia by Mansmann et al. [13], we used several finite element models of simplified geometry to: 1) explore modeling assumptions on material linearity and deformation kinematics, and 2) examine the strain distribution in a healing fracture gap subjected to known levels of interfragmentary strain. We found that a general nonlinear material, nonlinear geometric analysis is necessary to model an osteotomy gap subjected to a maximum longitudinal strain of 100 percent. The large displacement, large strain conditions which were used in the in-vivo study result in complex, multiaxial strain fields in the gap. Restricting the maximum longitudinal strain to 10 percent allows use of a linear goemetric formulation without compromising the numerical results. At this reduced strain level a linear material model can be used to examine the extent of material yielding within a homogeneous osteotomy gap. Severe local strain variations occurred both through the thickness of the gap and radially from the endosteal to periosteal gap surfaces. The bone/gap interface represented a critical plane of high distortional and volumetric change and principal strain magnitudes exceeded the maximum longitudinal strains.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1986;108(3):281-288. doi:10.1115/1.3138615.

The phenomenon of high-amplitude inflation waves resulting from a sharp axial acceleration of the aorta, as may ocur in road accidents, is investigated theoretically. The aorta is modeled as an axisymmetric tapered membranic shell (tube) made of an incompressible, nonlinear viscoelastic material with cylindrical orthotropy. It is filled with an inviscid, incompressible fluid whose flow is considered as quasi-one dimensional along the tube axis. The equations of motion of the tube and of the fluid are solved numerically, by using a two-step explicit scheme, for several axial acceleration profiles. The solutions shows that an inflation wave is generated and it propagates in opposite direction to that of the acceloeration. The wall stresses, deformations and their time derivatives as well as fluid velocity and pressure are determined along the tube at different time intervals. Peak axial and circumferential stresses are high, with the latter far exceeding the former. These stresses may cause rupture of the aorta.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1986;108(3):289-293. doi:10.1115/1.3138616.

The geometry of the pulmonary arterial tree of six adult dogs was measured by a high-speed, volume-scanning, X-ray tomographic technique. After the dogs were anesthetized a catheter was advanced to the right ventricular outlfow tract and 2 mL/kg Renovist contrast agent injected rapidly. During the subsequent pulmonary arterial phase of the angiogram the dogs were scanned. Three-dimensional geometry of the pulmonary arterial tree was measured in terms of vessel segment cross-sectional area, branching angles and interbranch segment lengths along axial pathways. The effect of lung inflation and phase of the cardiac cycle on geometry was shown to be most marked on vessel cross-sectional area. The geometric branching patterns in all dogs were similar. The observed, in-vivo branching pattern behaved somewhat like the branching pattern predicted from optimized models proposed by Murray [4, 5], Zamir [10, 11] and Uylings [7].

Commentary by Dr. Valentin Fuster

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