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RESEARCH PAPERS

J Biomech Eng. 1989;111(3):177-179. doi:10.1115/1.3168362.
Abstract
Topics: Flow (Dynamics)
Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(3):180-184. doi:10.1115/1.3168363.

This paper examines mainly oscillatory behavior of a fluid-conveying collapsible tube using a two-dimensional flexible channel made of a pair of membranes. The equation of equilibrium of the membrane in a large deflection theory is coupled with the equations of continuity and momentum of an incompressible flow in a one-dimensional flow theory accounting for flow separation. An explicit finite difference method was used to solve the governing equations numerically. According to numerical results, the fluids in the inlet and outlet rigid channels have strong effects on the oscillation of the system. Depending on initial values for the numerical integration, there may exist both a stable static equilibrium and an oscillatory solution for the same parameter values, but only if the external pressure is sufficiently large.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(3):185-191. doi:10.1115/1.3168364.

To determine whether self-excited oscillations in a Starling resistor are relevant to physiological situations, a collapsible tube conveying an aqueous flow was externally pressurized along only a central segment of its unsupported length. This was achieved by passing the tube through a shorter and wider collapsible sleeve which was mounted in Starling resistor fashion in a pressure chamber. The tube size and material, and all other experimental parameters, were as used in our previous Starling resistor studies. Both low- and high-frequency self-excited oscillations were observed, but the low-frequency oscillations were sensitive to the sleeve type and length relative to unsupported distance. Pressure-flow characteristics showed multiple oscillatory modes, which differed quantitatively from those observed in comparable Starling resistors. Slow variation of driving pressure gave differing behavior according to whether the pressure was rising or falling, in accord with the hysteresis noted on the characteristics and in the tube law. The results are discussed in terms of the various possible mechanisms of collapsible tube instability, and reasons are presented for the absence of the low-frequency mode under most physiological circumstances.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(3):192-199. doi:10.1115/1.3168365.

Numerical calculations were performed to study the influence of several physiologic parameters on a forced expiration. It was found that the axial distribution of airway compliance produced profound changes in the detailed flow pattern, as characterized by the axial distributions of speed index and area ratio, but had little effect on the flow-volume curve. Similar results were obtained when the expression for frictional losses was changed to reflect new experimental results. In contrast, changes in airway size and geometry altered both the detailed flow pattern and the mean expiratory flow rate. The shape of the flow-volume curve remained unchanged.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(3):200-205. doi:10.1115/1.3168366.

A model has been developed for expiration from human lungs in which the mechanical properties of the airways and parenchyma can be varied between regions. The model is based on an existing homogeneous model. The fluid mechanical problem of the merging of dissimilar flows from adjacent regions is underspecified by the conservation laws of mass and energy. An existing, empirically derived result, provides the required extra equation. Model simulation of a nonhomogeneously distributed mild constriction of the peripheral airways gives results for maximal flows and alveolar pressure differences which are in good agreement with recent experimental findings.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(3):206-211. doi:10.1115/1.3168367.

In steady flow through nonuniform collapsible tubes a key concept is the compressive zone, at which flow limitation can occur at both high and low Reynolds numbers. Ureteral peristalsis can be considered as a series of compressive zones, corresponding to waves of active muscular contraction, that move at near-constant speed along the ureter towards the bladder. One-dimensional, lubrication-theory analysis shows that peristalsis can pump urine from kidney into the bladder only at relatively low mean rates of urine flow. Under these circumstances isolated boluses of urine are propelled steadily through the ureter (assumed uniform) by the contraction waves. At higher mean rates of flow the behavior depends on whether the frequency of peristalsis is higher or lower than a critical value. For frequencies above the critical value steady propagation of boluses that are in contact with contraction waves at both ends is possible. As the flow rate rises the urine begins to leak through the contraction waves and steady peristaltic flow breaks down. There is an upper limit to the mean flow rate that can be carried by steady peristalsis, which depends on the mechanical properties of the ureter. At high flow rates the peristaltic contractions do not pump but hinder the flow of urine through the ureter.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(3):212-221. doi:10.1115/1.3168368.

Velocity profiles and the pressure drop across two mild (62 percent) coronary stenoses in series have been investigated numerically and experimentally in a perspex-tube model. The mean flow rate was varied to correspond to a Reynolds number range of 50–400. The pressure drop across two identical (62 percent) stenoses show that for low Reynolds numbers the total effect of two stenoses equals that of two single stenoses. A reduction of 10 percent is found for the higher Reynolds numbers investigated. Numerical and experimental results obtained for the velocity profiles agree very well. The effect of varying the converging angle of a single mild (62 percent) coronary stenosis on the fluid flow has been determined numerically using a finite element method. Pressure-flow relation, especially with respect to relative short stenoses, is discussed.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(3):222-227. doi:10.1115/1.3168369.

To study the flow behavior in regions where hemodynamic effects have been suggested to participate in atherogenesis, we evaluated flow in a mold of the aorta and renal arteries of a previously healthy 27-year-old woman who died of trauma. A birefringent solution (vanadium-pentoxide) was used. When diluted, this material behaves like a Newtonian fluid. This method gives a complete picture of the entire flow field. Zones of flow separation and disturbed flow can be seen and the location and size of disturbed areas observed. Unseparated flow regions downstream from disturbed zones can be properly visualized and the method can be used for pulsatile flow as well as steady flow. During steady flow (only at branch to-trunk flow ratios > 0.20), zones of flow separation were observed in the aorta distal to the renal arteries. During pulsatile flow, disturbances were found at nearly all branch-to-trunk flow ratios.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(3):228-232. doi:10.1115/1.3168371.

The influence of tilting disk valve orientation on pulsatile flow through a curved tube model of the human aorta was studied. Simultaneous, two-component laser Doppler velocimeter measurements were made in a tube having a 22 mm diameter and 41 mm radius of curvature which simulated the average dimensions of the adult aorta. The blood analog fluid had a viscosity of 3.0 cp and matched the refractive index of the glass model aorta. Results at mid-arch showed low turbulence levels in early systole and no influence of valve orientation. During mid-systole, fluid from the ventricle reached mid-arch exhibiting strong influence of valve orientation and increased turbulence levels. With the major orifice of the valve adjacent to the inner curved wall, the peak turbulent shear stress was 307 dynes/cm2 at mid-arch during mid-systole. When the major orifice was rotated 180 degrees, the peak value was reduced to 91 dynes/cm2 at the same location and time. At the exit of the curved section, the flow was independent of the valve orientation and the turbulent shear stress levels were an order of magnitude lower than the peak value at the inlet. This study demonstrated that orienting the major orifice of a tilting disk valve adjacent to the outer curved wall minimized turbulent shear stress levels.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(3):233-240. doi:10.1115/1.3168372.

The artero-venous system is often stressed by accelerative perturbation, not only during exceptional performances, but also in normal life. For example, when the body is subject to fast pressure changes, accelerative perturbations combined with a change in hydrostatic pressure could have severe effects on the circulation. In such cases a preliminary mathematical inquiry, whose results allow qualitative evaluation of the perturbation produced is useful. Pressure variations are studied in this work when the body is subjected both to rectilinear and rotational movements as well as posture change. The dominant modes of the hemodynamic oscillations are emphasized and the numerical simulation results presented. The artery model used for simulation is obviously simplified with respect to the anatomical structure of an artery. Nevertheless, behavior of the main arteries (like the common carotid and aorta) can be approximately described, choosing suitable model parameters. The frequency of blood oscillations strictly depends on the Young modulus of the arterial wall. This connection could be employed for new clinical tests on the state of the arteries.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(3):241-249. doi:10.1115/1.3168373.

Diffuse axonal injury (DAI) with prolonged coma has been produced in the primate using an impulsive, rotational acceleration of the head without impact. This pathophysiological entity has been studied subsequently from a biomechanics perspective using physical models of the skull-brain structure. Subjected to identical loading conditions as the primate, these physical models permit one to measure the deformation within the surrogate brain tissue as a function of the forces applied to the head. An analytical model designed to approximate these experiments has been developed in order to facilitate an analysis of the parameters influencing brain deformation. These three models together are directed toward the development of injury tolerance criteria based upon the shear strain magnitude experienced by the deep white matter of the brain. The analytical model geometry consists of a rigid, right-circular cylindrical shell filled with a Kelvin-Voigt viscoelastic material. Allowing no slip on the boundary, the shell is subjected to a sudden, distributed, axisymmetric, rotational load. A Fourier series representation of the load allows unrestricted load-time histories. The exact solution for the relative angular displacement (V) and the infinitesimal shear strain (ε ) at any radial location in the viscoelastic material with respect to the shell was determined. The strain response for brain tissue (μ = 345 Poise, G = 1.38 × 104 Pa) was examined at the non-dimensional radial location R = 0.3. The size (1.8<R0 <6.8 cm) and constitutive properties of the brain, and the magnitude, duration (2<TD <100 msec) and waveform (sine, square, triangle) of the applied load were varied independently; each contributed to the response of the tissue. Strain increased linearly with increasing magnitude of the applied load and exponentially with increasing brain size (where the exponent n was frequency-dependent). Peak angular acceleration (Θ̈ p ) and peak angular velocity (ΔΘ̇ p ) were defined as appropriate load descriptors. As ΔΘ̇ p increased, strain rose rapidly and was independent of Θ̈ p , then levelled off and was highly sensitive to Θ̈ p .

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(3):250-255. doi:10.1115/1.3168374.

Cervical spine injuries such as wedge, burst, and tear drop fractures are often associated with compressive axial loads delivered to the human head-neck complex. Understanding the injury mechanisms, the kinematics of the anatomic structure, and the tissue tolerances can improve clinical prognosis and facilitate a better design for anthropomorphic devices. The axial compressive response of human cadaveric preparations was compared with the 50th percentile anthropomorphic Hybrid III manikin under various loading rates. Ten fresh human cadavers were used in the study. Intact cadaver torsos, head-cervical spines, and ligamentous cervical columns were tested. The head-neck structure and the neck (without head) of the Hybrid III manikin were also tested. Responses of the human cadaveric preparations and manikin structures were nonlinear at all rates of loading. However, axial stiffness, a measure of the ability of the structure to withstand external force, was higher under all rates of loading for manikin preparations when compared with the human cadaveric tissues.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(3):256-260. doi:10.1115/1.3168375.

The compressive yield strain was measured for 61 specimens of bovine cancellous bone from three distal femora. There was no significant relationship (p = 0.08, R 2 = 0.051) between yield strain and the degree of trabecular orientation. There was a significant positive correlation (p <0.00001, R 2 = 0.319) between yield strain and structural (apparent) density and significant negative correlation (p <0.0025, R 2 = 0.145) between yield strain and bone density. Yield strain correlated best with bone solid volume fraction Vv (εy = 0.592 + 1.446vv , R 2 = 0.337). The quantity, yield strain, is highly dependent on specific definitions of the yield point and the point of zero strain. For this study the yield point was defined by a 0.0003 offset criterion, and the point of zero strain was defined as the point where the tangent at 15 percent of yield crosses zero. The results using these definitions were compared with results using yield strain values determined by other definitions of the yield point and zero strain. The correlations between yield strain and trabecular orientation, structural density and bone density changed very little for differing definitions of yield. The results suggest that yield strain in cancellous bone is isotropic or independent of textural anisotropy, so the yield behavior may be characterized by a maximum strain yield criterion. The results also suggest that the primary mode of yield in cancellous bone is buckling of the trabeculae.

Commentary by Dr. Valentin Fuster

ERRATA

TECHNICAL BRIEFS

J Biomech Eng. 1989;111(3):261-262. doi:10.1115/1.3168376.

The novelty in the proposed seat design consists in allowing a free vertical motion of the back rest, so as to decrease the strain on the spinal column. Road and vibrating table tests show that the strain is indeed considerably reduced. A simple mathematical model of the seated human body provides a qualitative explanation of this improvement.

Commentary by Dr. Valentin Fuster

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