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TECHNICAL PAPERS

J Biomech Eng. 1996;118(1):1-9. doi:10.1115/1.2795941.

A field theory is presented for the study of swelling in soft tissue structures that are modeled as poroelastic materials. As a first approximation, soft tissues are assumed to be linear isotropic materials undergoing infinitesimal strains. Material properties are identified that are necessary for the solution of initial boundary value problems where swelling and convection are significant. A finite element model is developed that includes the solid displacements, the relative fiuid displacements, and a representative concentration as the primary unknowns. A numerical example is presented based on a triphasic model. The finite model simulates a typical experimental protocol for soft tissue testing and demonstrates the interaction and coupling associated with relative fluid motion and swelling in a deforming poroelastic material. The theory and finite element model provide a starting point for nonlinear porohyperelastic transport-swelling analyses of soft tissue structures that include finite strains in anisotropic materials.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(1):10-16. doi:10.1115/1.2795935.

The mechanically important constituents of swelling tissues are fibers embedded in an osmotically active fluid. The tissues’ response to external loading is the sum of contribution of the axial stresses in the fibers and of the fluid pressure. The fluid osmotic properties play a key role in determining its equilibrium response. The present study examines the conditions under which the elastic response of tissues as modeled by structural constitutive equations, is thermodynamically plausible. The analysis shows that plausibility is ensured if the fibers’ axial force increases monotonically with stretch and if the fluid osmotic pressure increases convexly with concentration. Published data shows that both conditions prevail in swelling tissues. Plausibility considerations seem to pose no specific restrictions on the structure of the tissues’ fibrous network. It is thus concluded that in swelling tissues, structural constitutive formulation is compatible with thermodynamically plausible response.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(1):17-25. doi:10.1115/1.2795940.

This study investigates the influence of parameter values of the human triceps surae muscle on the torque-angle relationship. The model used consisted of three units, each containing a contractile, a series elastic and a parallel elastic element. Parameter values were based on morphological characteristics, which made it possible to model individual units. However, for a number of parameters the values reported in the literature vary considerably. It was investigated how sensitive model results were for variation of these parameters. Slack length of the series elastic element, mean moment arm, maximum force, and length of the contractile element appeared to be the most important determinants of the behavior. For mean moment arm and contractile element length, morphology-based methods of estimation could be recommended. Slack length and maximum force were obtained through optimization. It was concluded that the model does not contain parameters on which its output depends strongly and which are difficult to estimate as well, with two exceptions: slack length of the series elastic element and maximum force.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(1):26-31. doi:10.1115/1.2795942.

The mechanisms by which the human spinal column in neutral postures can resist relatively large axial compression forces with no abnormal motions or instabilities remain yet unknown. A nonlinear finite element study of the ligamentous thoracolumbar spine was performed to investigate the stabilizing role of two plausible mechanisms of combined moments and pelvic rotation on the human spine in axial compression. The passive system, by itself was able to carry only a negligible fraction of physiological compression loads without exhibiting large motions. The unconstrained spine was most flexible in the sagittal plane (least stiff plane). The existence of combined moments and pelvic rotation significantly increased the load-bearing capacity of the spine so that the free standing passive thoracolumbar spine resisted the axial compression forces of more than 1000 N with minimal displacements. The former mechanism is much more effective in stabilizing the spine in compression than is the latter one. It is postulated that the pelvic rotation and the off-centered anterior placement of the gravity force are exploited to partially stabilize the passive spine in compression and relieve the musculature. Previous and on-going studies support the validity of the proposed mechanisms.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(1):32-40. doi:10.1115/1.2795943.

This paper describes the development and evaluation of a musculoskeletal model that represents human elbow flexion-extension and forearm pronation-supination. The length, velocity, and moment arm for each of the eight musculotendon actuators were based on skeletal anatomy and joint position. Musculotendon parameters were determined for each actuator and verified by comparing analytical moment-angle curves with experimental joint torque data. The parameters and skeletal geometry were also utilized in the musculoskeletal model for the analysis of ballistic (rapid-directed) elbow joint complex movements. The key objective was to develop a computational model, guided by parameterized optimal control, to investigate the relationship among patterns of muscle excitation, individual muscle forces, and to determine the effects of forearm and elbow position on the recruitment of individual muscles during a variety of ballistic movements. The model was partially verified using experimental kinematic, torque, and electromyographic data from volunteer subjects performing both isometric and ballistic elbow joint complex movements. This verification lends credibility to the time-varying muscle force predictions and the recruitment of muscles that contribute to both elbow flexion-extension and forearm pronation-supination.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(1):41-47. doi:10.1115/1.2795944.

A rational methodology is developed for optimal design of biaxial stretch tests intended for estimating material parameters of flat tissues. It is applied to a structural model with a variety of constitutive equations and test protocols, and for a wide range of parameter levels. The results show nearly identical optimal designs under all circumstances. Optimality is obtained with two uniaxial stretch tests at mutually normal directions inclined by 22.5 deg to the axes of material symmetry. Protocols which include additional equibiaxial tests provide superior estimation with lower variance of estimates. Tests performed at angles 0, 45, and 90 deg to the axes of material symmetry provide unreliable estimates. The optimal sampling is variable and depends on the protocols and model parameters. In conclusion, the results indicate that biaxial tests can be improved over presently common procedures and show that this conclusion applies for a variety of circumstances.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(1):48-55. doi:10.1115/1.2795945.

Tactile information about an object in contact with the skin surface is contained in the spatiotemporal load distribution on the skin, the corresponding stresses and strains at mechanosensitive receptor locations within the skin, and the associated pattern of electrical impulses produced by the receptor population. At present, although the responses of the receptors to known stimuli can be recorded, no experimental techniques exist to observe either the load distribution on the skin or the corresponding stress-state at the receptor locations. In this paper, the role of mechanics in the neural coding of tactile information is investigated using simple models of the primate fingertip. Four models that range in geometry from a semi-infinite medium to a cylindrical finger with a rigid bone, and composed of linear elastic media, are analyzed under plane strain conditions using the finite element method. The results show that the model geometry has a significant influence on the surface load distribution as well as the subsurface stress and strain fields for a given mechanical stimulus. The elastic medium acts like a spatial low pass filter with the property that deeper the receptor location, the more blurred the tactile information. None of the models predicted the experimentally observed surface deflection profiles under line loads as closely as a simple heterogeneous waterbed model that treated the fingerpad as a membrane enclosing an incompressible fluid (Srinivasan, 1989). This waterbed model, however, predicted a uniform state of stress inside the fingertip and thus failed to explain the spatial variations observed in the neural response. For the cylindrical model indented by rectangular gratings, the maximum compressive strain and strain energy density at typical receptor locations emerged as the two strain measures that were directly related to the electrophysiologically recorded response rate of slowly adapting type I (SAI) mechanoreceptors. Strain energy density is a better candidate to be the relevant stimulus for SAIs, since it is a scalar that is invariant with respect to receptor orientations and is a direct measure of the distortion of the receptor caused by the loads imposed on the skin.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(1):56-61. doi:10.1115/1.2795946.

Tendon allografts are commonly used to replace damaged anterior cruciate ligaments (ACL). Some of the sterilization and preservation techniques used by tissue banks with tendon allografts are thought to impair the mechanical properties of graft tissues. The tensile mechanical properties of porcine toe extensor tendons were measured using a dynamic testing machine following either freezing, freeze-drying, freezing then irradiation at 25 kGy (2.5 MRad), freeze-drying then irradiation, or freeze-drying then ethylene oxide gas sterilization. There was a small but significant difference in Young’s modulus between the frozen group (0.88 GPa ± 0.09 SD) and both the fresh group (0.98 GPa ± 0.12 SD) and the frozen irradiated group (0.97 GPa ± 0.08 SD). No values of Young’s modulus were obtained for the freeze-dried irradiated tendons. The ultimate tensile stress (UTS) of the freeze-dried irradiated group (4.7 MPa ± 4.8 SD) was significantly different from both the fresh and the frozen irradiated groups, being reduced by approximately 90 percent. There were no significant changes in UTS or Young’s modulus between any of the other groups. If irradiation is to be used to sterilize a tendon replacement for an ACL it must take place after freeze-drying to maintain mechanical properties.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(1):62-73. doi:10.1115/1.2795947.

The effects of hypertension on the stress and strain distributions through the wall thickness were studied in the rat thoracic aorta. Goldblatt hypertension was induced by constricting the left renal artery for 8 weeks. Static pressure-diameter-axial force relations were determined on excised tubular segments. The segments were then sliced into thin ring specimens. Circumferential strain distributions were determined from the cross-sectional shape of the ring specimens observed before and after releasing residual stresses by radial cutting. Stress distributions were calculated using a logarithmic type of strain energy density function. The wall thickness at the systolic blood pressure, Psys , significantly correlated with Psys . The mean stress and strain developed by Psys in the circumferential direction were not significantly different between the hypertensive and control aortas, while those in the axial direction were significantly smaller in the hypertensive aorta than in the control. The opening angles of the stress-free ring specimens correlated well with Psys . The stress concentration factor in the circumferential direction was almost constant and independent of Psys , although the stress distributions were not uniform through the wall thickness. Histological observation showed that the wall thickening caused by hypertension is mainly due to the hypertrophy of the lamellar units of the media, especially in the subintimal layer where the stress increase developed by hypertension is larger than in the other layers. These results indicate that: (a) the aortic wall adapts itself to the mechanical field by changing not only the wall dimensions but also the residual stresses, (b) this adaptation is primarily related to the circumferential stress but not to the axial stress, and (c) the aortic smooth muscle cells seem to change their morphology in response to the mechanical stress.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(1):74-82. doi:10.1115/1.2795948.

The localization of atherosclerosis in the coronary arteries may be governed by local hemodynamic features. In this study, the pulsatile hemodynamics of the left coronary artery bifurcation was numerically simulated using the spectral element method for realistic in vivo anatomic and physiologic conditions. The velocity profiles were found to be skewed in both the left anterior descending and the circumflex coronary arteries. Velocity skewing arose from the bifurcation as well as from the curvature of the artery over the myocardial surface. Arterial wall shear stress was significantly lower in the bifurcation region, including the side walls. The greatest oscillatory behavior was localized to the outer wall of the circumflex artery. The time-averaged mean wall shear stress varied from about 3 to 98 dynes/cm2 in the left coronary artery system. The highly localized distribution of low and oscillatory shear stress along the walls strongly correlates with the focal locations of atheroma in the human left coronary artery.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(1):83-89. doi:10.1115/1.2795949.

Quantitative methods to measure the hemodynamic consequences of various endovascular interventions including balloon angioplasty are limited. Catheters measuring translesional pressure drops during balloon angioplasty procedures can cause flow blockage and thus inaccurate estimates of pre- and post-intervention flow rates. The purpose of this investigation was to examine the influence of the presence and size of an angioplasty catheter on measured mean pressure gradients across human coronary artery stenoses. Analytical flow modeling and in vitro experimental evidence, coupled with angiographic data on the dimensions and shape of stenotic vessel segments before and after angioplasty, indicated significant flow blockage effects with the catheter present.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(1):90-96. doi:10.1115/1.2795950.

In the present study, finite element calculations are performed of blood flow in the carotid artery bifurcation under physiological flow conditions. The numerical results are compared in detail with laser-Doppler velocity measurements carried out in a perspex model. It may be concluded that the numerical model as presented here is well capable in predicting axial and secondary flow of incompressible Newtonian fluids in rigid-walled three-dimensional geometries. With regard to the flow phenomena occurring, a large region with reversed axial flow is found in the carotid sinus opposite to the flow divider. This region starts to grow at peak systole, has its maximal shape at minimal flow rate and totally disappears at the start of the acceleration phase. C-shaped axial velocity contours are formed in the deceleration phase, which are highly influenced by secondary flows. These latter flows are mainly induced by centrifugal forces, flow branching, and tapering of the carotid sinus. Lowering the sinus angle, the angle between the main branch and the carotid sinus, results in a smaller region with reversed axial flow.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(1):97-105. doi:10.1115/1.2795951.

The cause of cavitation in mechanical heart valves is investigated with Medtronic Hall tilting disk valves in an in vitro flow system simulating the closing event in the mitral position. Recordings of pressure wave forms and photographs in the vicinity of the inflow surface of the valve are attempted under controlled transvalvular loading rates averaged during valve closing period. The results revealed presence of a local flow field with a very high velocity around the seat stop of mechanical heart valves that could induce pressure reduction below liquid vapor pressure and a cloud of cavitation bubbles. The analysis of the results indicates that the “fluid squeezing” between the stop and occluder as the main cause of cavitation in Medtronic Hall valves. The threshold loading rate for cavitation initiation around the stop was found to be very low (300 and 400 mmHg/s; half the predicted normal human loading rate that was estimated to be 750 mmHg/s) because even a mild impact created a high speed local flow field on the occluder surface that could induce pressure reduction below vapor pressure. The present study suggests that mechanical heart valves with stops at the edge of major orifice region are more vulnerable to cavitation, and hence, have higher potential for damage on valve components and formed elements in blood.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(1):106-110. doi:10.1115/1.2795934.

The effect of cardiac infarction on the flow patterns in cardiac left ventricular ejection was studied using a realistic model which was made from the profile of the left ventricle of a dog heart in diastole. A Coordinate measuring machine was used to measure the left ventricular coordinates, and these were input into a three-dimensional flow simulation package. The left ventricular wall motion was described by having the walls moved towards the center of the aortic outlet, and in the case of infarcted tissue, the ventricular wall movement was diminished to simulate infarction flow behavior. The final ventricular volume varied from 25 percent to 54.1 percent of the initial volume in cases without and with infarction, respectively. The maximum blood ejection velocities and ventricular pressure decreased significantly in the presence of infarction. Infarcted areas showed complex blood flow vortex formation not present in the healthy ventricles. The Computational technique presented here predicts infarction flow effects which could be observed with measurement techniques such as ultrasound and magnetic resonance imaging, allowing a finer detail of understanding than using either simulation or experimental measurements alone.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(1):111-119. doi:10.1115/1.2795936.

Two different non-Newtonian models for blood, one a simple power law model exhibiting shear thinning viscosity, and another a generalized Maxwell model displaying both shear thining viscosity and oscillatory flow viscoelasticity, were used along with a Newtonian model to simulate sinusoidal flow of blood in rigid and elastic straight arteries. When the spring elements were removed from the viscoelastic model resulting in a purely viscous shear thinning fluid, the predictions of flow rate and WSS were virtually unaltered. Hence, elasticity of blood does not appear to influence its flow behavior under physiological conditions in large arteries, and a purely viscous shear thinning model should be quite realistic for simulating blood flow under these conditions. When a power law model with a high shear rate Newtonian cutoff was used for sinusoidal flow simulation in elastic arteries, the mean and amplitude of the flow rate were found to be lower for a power law fluid compared to a Newtonian fluid experiencing the same pressure gradient. The wall shear stress was found to be relatively insensitive to fluid rheology but strongly dependent on vessel wall motion for flows driven by the same pressure gradient. The effect of wall motion on wall shear stress could be greatly reduced by matching flow rate rather than pressure gradient. For physiological flow simulation in the aorta, an increase in mean WSS but a reduction in peak WSS were observed for the power law model compared to a Newtonian fluid model for a matched flow rate waveform.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(1):120-129. doi:10.1115/1.2795937.

A fully conjugated blood vessel network model (FCBVNM) for calculating tissue temperatures has been developed, tested, and studied. This type of model represents a more fundamental approach to modeling temperatures in tissues than do the generally used approximate equations such as the Pennes’ BHTE or effective thermal conductivity equations. As such, this type of model can be used to study many important questions at a more basic level. For example, in the particular hyperthermia application studied herein, a simple vessel network model predicts that the role of counter current veins is minimal and that their presence does not significantly affect the tissue temperature profiles: the arteries, however, removed a significant fraction of the power deposited in the tissue. These more fundamental models can also be used to check the validity of approximate equations. For example, using the present simple model, when the temperatures calculated by the FCBVNM are used for comparing predictions from two approximation equations (a simple effective thermal conductivity and a simple Pennes’ bio-heat transfer equation formulation of the same problem) it is found that the Pennes’ equation better approximates the FCBVNM temperatures than does the k eff model. These results also show that the “perfusion” value (Ẇ) in the Pennes’ BHTE is not necessarily equal to the “true” tissue perfusion (Ṗ) as calculated from mass flow rate considerations, but can be greater than, equal to, or less than that value depending on (1) how many vessel levels are modeled by the BHTE, and (2) the “true” tissue perfusion magnitude. This study uses a simple, generic vessel network model to demonstrate the potential usefulness of such fully conjugated vessel network models, and the associated need for developing and applying more complicated and realistic vascular network models. As more realistic vascular models (vessel sizes, orientations, and flow rates) are developed, the predictions of the fully conjugated models should more closely model and approach the true tissue temperature distributions, thus making these fully conjugated models more accurate and valuable tools for studying tissue heat transfer processes.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J Biomech Eng. 1996;118(1):130-132. doi:10.1115/1.2795938.

This study evaluated the effects of soft tissue integrity on patellar tracking and patellofemoral joint force after total knee arthroplasty. The results indicate that partial dissection of the soft tissue integrity in the in vitro biomechanical studies of the patellofemoral joint can alter patellar tracking and joint force significantly, leading to improper conclusions.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(1):133-135. doi:10.1115/1.2795939.

An atomic force microscope was used to measure the hardness and elasticity of fully-hydrated peritubular and intertubular human dentin. The standard silicon nitride AFM tip and silicon cantilever assembly were replaced with a diamond tip and stainless steel cantilever having significantly higher stiffness. Hardness was measured as the ratio of the applied force to the projected indentation area for indentations with depths from 10–20 nm. The sample stiffness was measured by imaging specimens in a force-modulated mode. Hardness values of 2.3 ± 0.3 GPa and 0.5 ± 0.1 GPa were measured for the peritubular and intertubular dentin, respectively. Stiffness imaging revealed that the elastic modulus of the peritubular dentin was spatially homogeneous; whereas, there was considerable spatial variation in the elasticity of the intertubular dentin. The atomic force microscope can be used to measure the mechanical properties of fully hydrated calcified tissues at the submicron level of spatial resolution, thus augmenting more traditional depth sensing probes.

Commentary by Dr. Valentin Fuster

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