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TECHNICAL PAPERS

J Biomech Eng. 1999;121(6):557-564. doi:10.1115/1.2800853.

External pneumatic compression of the lower legs is effective as prophylaxis against deep vein thrombosis. In a typical application, inflatable cuffs are wrapped around the patient’s legs and periodically inflated to prevent stasis, accelerate venous blood flow, and enhance fibrinolysis. The purpose of this study was to examine the stress distribution within the tissues, and the corresponding venous blood flow and intravascular shear stress with different external compression modalities. A two-dimensional finite element analysis (FEA) was used to determine venous collapse as a function of internal (venous) pressure and the magnitude and spatial distribution of external (surface) pressure. Using the one-dimensional equations governing flow in a collapsible tube and the relations for venous collapse from the FEA, blood flow resulting from external compression was simulated. Tests were conducted to compare circumferentially symmetric (C ) and asymmetric (A ) compression and to examine distributions of pressure along the limb. Results show that A compression produces greater vessel collapse and generates larger blood flow velocities and shear stresses than C compression. The differences between axially uniform and graded-sequential compression are less marked than previously found, with uniform compression providing slightly greater peak flow velocities and shear stresses. The major advantage of graded-sequential compression is found at midcalf. Strains at the lumenal border are approximately 20 percent at an external pressure of 50 mmHg (6650 Pa) with all compression modalities.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(6):565-573. doi:10.1115/1.2800855.

Axial and secondary velocity profiles were measured in a model human central airway to clarify the oscillatory flow structure during high-frequency oscillation. We used a rigid model of human airways consisting of asymmetrical bifurcations up to third generation. Velocities in each branch of the bifurcations were measured by two-color laser-Doppler velocimeter. The secondary velocity magnitudes and the deflection of axial velocity were dependent not only on the branching angle and curvature ratio of each bifurcation, but also strongly depended on the shape of the path generated by the cascade of branches. Secondary flow velocities were higher in the left bronchus than in the right bronchus. This spatial variation of secondary flow was well correlated with differing gas transport rates between the left and right main bronchus.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(6):574-583. doi:10.1115/1.2800856.

A network thermodynamic model has been devised to describe the coupled movement of water and a permeable additive within a kidney during perfusion under the combined action of diffusive, hydrodynamic, and mechanical processes. The model has been validated by simulating perfusions with Me2 SO, glycerol, and sucrose and comparing predicted weight and vascular resistance with experimental results obtained by Pegg (1993). The flows of CPA, water, colloid, and cellular impermeants are governed by a combination of the individual osmotic potential and pressure differences between compartments of the kidney, the viscoelastic behavior of the tissue, and the momentum transferred between the flows. The model developed in this study presents an analytical tool for understanding the dynamics of the perfused kidney system and for modifying perfusion protocols to minimize the changes in cell volume, internal pressure build-up, and increases in vascular resistance that currently present barriers to the successful perfusion of organs.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(6):584-590. doi:10.1115/1.2800857.

The heating pattern of a transurethral radio frequency (RF) applicator and its induced steady-state temperature field in the prostate during transurethral hyperthermia treatment were investigated in this study. The specific absorption rate (SAR) of the electromagnetic energy was first quantified in a tissue-equivalent gel phantom. It was used in conjunction with the Pennes bioheat transfer equation to model the steady-state temperature field in prostate during the treatment. Theoretical predictions were compared to in vivo temperature measurements in the canine prostate and good agreement was found to validate the model. The prostatic tissue temperature rise and its relation to the effect of blood perfusion were analyzed. Blood perfusion is found to be an important factor for removal of heat especially at the higher RF heating level. To achieve a temperature above 44°C within 10 percent of the prostatic tissue volume, the minimum RF power required ranges from 5.5 W to 36.4 W depending on the local blood perfusion rate (ω = 0.2−1.5 ml/gm/min). The corresponding histological results from the treatment suggest that to obtain better treatment results, either higher RF power level or longer treatment time (>180 minutes) is necessary. This is consistent with the predictions from the theoretical model developed in this study.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(6):591-597. doi:10.1115/1.2800858.

Mature tissues can often adapt to changes in their chemical, mechanical, or thermal environment. For example, in response to sustained increases or decreases in mechanical loads, some tissues grow and remodel so as to restore the stress or strain to its homeostatic state. Whereas most previous work addresses gross descriptors of tissue growth, this paper introduces a possible cell-mediated mechanism by which remodeling may occur in a soft connective tissue—that the kinetics of collagen deposition and degradation is similar regardless of the configuration of the body at which it occurs. The proposed theoretical framework applies to three-dimensional settings, but it is illustrated by focusing on the remodeling of a uniaxial collagenous tissue that is maintained at a fixed length for an extended period. It is shown that qualitative features expected of such remodeling (e.g., an increased compliance and increased stress-free length when remodeling occurs at an extended length) are easily realized. Growth and remodeling are complex phenomena, however, and are likely accomplished via multiple complementary mechanisms. There is a need, therefore, to identify other candidate mechanisms and, of course, to collect experimental data suitable for testing and refining the possible theories.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(6):598-604. doi:10.1115/1.2800859.

These studies sought to investigate quantitative relationships between the complex composite structure and mechanical properties of tendon. The isolated mouse tail tendon fascicle was chosen as an appropriate model for these so-called “structure-function” investigations. Specifically, collagen fibril diameters and mechanical properties were measured in fascicles from immature (3 week) control, adult (8 week) control, and adult (8 week) Mov13 transgenic mice. Results demonstrated a moderate correlation between mean fibril diameter and fascicle stiffness (r = 0.73, p = 0.001) and maximum load (r = 0.75, p < 0.001), whereas a weak correlation with fascicle modulus (r = 0.39, p = 0.11) and maximum stress (r = 0.48, p = 0.04). An analysis of pooled within-group correlations revealed no strong structure-function trends evidenced at the local or group level, indicating that correlations observed in the general structure-function analyses were due primarily to having three different experimental groups, rather than significant correlations of parameters within the groups.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(6):605-611. doi:10.1115/1.2800860.

This paper investigates the dynamic, distributed pressure response of the human fingerpad in vivo when it first makes contact with an object. A flat probe was indented against the fingerpad at a 20 to 40 degree angle. Ramp-and-hold and sinusoidal displacement trajectories were applied to the fingerpad within a force range of 0–2 N. The dynamic spatial distribution of the pressure response was measured using a tactile array sensor. Both the local pressure variation and the total force exhibited nonlinear stiffness (exponential with displacement) and significant temporal relaxation. The shape of the contact pressure distribution could plausibly be described by an inverted paraboloid. A model based on the contact of a rigid plane (the object) and a linear viscoelastic sphere (the fingerpad), modified to include a nonlinear modulus of elasticity, can account for the principal features of the distributed pressure response.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(6):612-615. doi:10.1115/1.2800861.

Experimental data (Thornton et al., 1997) show that relaxation proceeds more rapidly (a greater slope on a log-log scale) than creep in ligament, a fact not explained by linear viscoelasticity. An interrelation between creep and relaxation is therefore developed for ligaments based on a single-integral nonlinear superposition model. This interrelation differs from the convolution relation obtained by Laplace transforms for linear materials. We demonstrate via continuum concepts of nonlinear viscoelasticity that such a difference in rate between creep and relaxation phenomenologically occurs when the nonlinearity is of a strain-stiffening type, i.e., the stress-strain curve is concave up as observed in ligament. We also show that it is inconsistent to assume a Fung-type constitutive law (Fung, 1972) for both creep and relaxation. Using the published data of Thornton et al. (1997), the nonlinear interrelation developed herein predicts creep behavior from relaxation data well (R ≥ 0.998). Although data are limited and the causal mechanisms associated with viscoelastic tissue behavior are complex, continuum concepts demonstrated here appear capable of interrelating creep and relaxation with fidelity.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(6):616-621. doi:10.1115/1.2800862.

An experimental study examined the tensile stress-strain behavior of cortical bone during rapid load cycles to high strain amplitudes. Machined bovine and human cortical bone samples were subjected to loading cycles at a nominal load/unload rate of ±420 MPa/s. Loads were reversed at pre-selected strain levels such that load cycles were typically completed in 0.5-0.7 seconds. Axial strain behavior demonstrated considerable nonlinearity in the first load cycle, while transverse strain behavior was essentially linear. For the human bone 29.1 percent (S.D. = 4.7 percent), and for the bovine bone 35.1 percent (S.D. = 10.8 percent) of the maximum nonlinear strain accumulated after load reversal, where nonlinear strain was defined as the difference between total strain and strain corresponding to linear elastic behavior. Average residual axial strain on unloading was 35.4 percent (S.D. = 1.2 percent) for human bone and 35.1 percent (S.D. = 2.9 percent) of maximum nonlinear strain. Corresponding significant volumetric strains and residual volumetric strains were found. The results support the conclusions that the nonlinear stress-strain behavior observed during creep loading also occurs during transient loading at physiological rates. The volume increases suggest that damage accumulation, i.e., new internal surfaces and voids, plays a major role in this behavior. The residual volume increases and associated disruptions in the internal structure of bone provide a potential stimulus for a biological repair response.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(6):622-628. doi:10.1115/1.2800864.

It was hypothesized that damage to bone tissue would be most detrimental to the structural integrity of the vertebral body if it occurred in regions with high strain energy density, and not necessarily in regions of high or low trabecular bone apparent density, or in a particular anatomic location. The reduction in stiffness due to localized damage was computed in 16 finite element models of 10-mm-thick human vertebral sections. Statistical analyses were performed to determine which characteristic at the damage location — strain energy density, apparent density, or anatomic location — best predicted the corresponding stiffness reduction. There was a strong positive correlation between regional strain energy density and structural stiffness reduction in all 16 vertebral sections for damage in the trabecular centrum (p < 0.05, r2 = 0.43–0.93). By contrast, regional apparent density showed a significant negative correlation to stiffness reduction in only four of the sixteen bones (p < 0.05, r2 = 0.47 – 0.58). While damage in different anatomic locations did lead to different reductions in stiffness (p < 0.0001, ANOVA), no single location was consistently the most critical location for damage. Thus, knowledge of the characteristics of bone that determine strain energy density distributions can provide an understanding of how damage reduces whole bone mechanical properties. A patient-specific finite element model displaying a map of strain energy density can help optimize surgical planning and reinforcement of bone in individuals with high fracture risk.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(6):629-635. doi:10.1115/1.2800865.

The convergence behavior of finite element models depends on the size of elements used, the element polynomial order, and on the complexity of the applied loads. For high-resolution models of trabecular bone, changes in architecture and density may also be important. The goal of this study was to investigate the influence of these factors on the convergence behavior of high-resolution models of trabecular bone. Two human vertebral and two bovine tibial trabecular bone specimens were modeled at four resolutions ranging from 20 to 80 μm and subjected to both compressive and shear loading. Results indicated that convergence behavior depended on both loading mode (axial versus shear) and volume fraction of the specimen. Compared to the 20 μm resolution, the differences in apparent Young’s modulus at 40 μm resolution were less than 5 percent for all specimens, and for apparent shear modulus were less than 7 percent. By contrast, differences at 80 μm resolution in apparent modulus were up to 41 percent, depending on the specimen tested and loading mode. Overall, differences in apparent properties were always less than 10 percent when the ratio of mean trabecular thickness to element size was greater than four. Use of higher order elements did not improve the results. Tissue level parameters such as maximum principal strain did not converge. Tissue level strains converged when considered relative to a threshold value, but only if the strains were evaluated at Gauss points rather than element centroids. These findings indicate that good convergence can be obtained with this modeling technique, although element size should be chosen based on factors such as loading mode, mean trabecular thickness, and the particular output parameter of interest.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(6):636-643. doi:10.1115/1.2800866.

Blood cell interaction with vascular endothelium is important in microcirculation, where rolling adhesion of circulating leukocytes along the surface of endothelial cells is a prerequisite for leukocyte emigration under flow conditions. HL-60 cell rolling adhesion to surface-immobilized P-selectin in shear flow was investigated using a side-view flow chamber, which permitted measurements of cell deformation and cell-substrate contact length as well as cell rolling velocity. A two-dimensional model was developed based on the assumption that fluid energy input to a rolling cell was essentially distributed into two parts: cytoplasmic viscous dissipation, and energy needed to break adhesion bonds between the rolling cell and its substrate. The flow fields of extracellular fluid and intracellular cytoplasm were solved using finite element methods with a deformable cell membrane represented by an elastic ring. The adhesion energy loss was calculated based on receptor-ligand kinetics equations. It was found that, as a result of shear-flow-induced cell deformation, cell-substrate contact area under high wall shear stresses (20 dyn/cm2 ) could be as much as twice of that under low stresses (0.5 dyn/cm2 ). An increase in contact area may cause more energy dissipation to both adhesion bonds and viscous cytoplasm, whereas the fluid energy input may decrease due to the flattened cell shape. Our model predicts that leukocyte rolling velocity will reach a plateau as shear stress increases, which agrees with both in vivo and in vitro experimental observations.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(6):644-649. doi:10.1115/1.2800867.

This research was directed toward predicting postural equilibrium configurations in normal humans for asymmetric locations of the feet. The objective of the study was to identify trends in the variation of the location of ground center of pressure (COP) with increasing levels of asymmetry in the foot placement. The procedure developed here minimized the muscular effort (active torques) in the lower extremities while maximizing postural stability margins for given foot locations. Minimizing muscular effort led to fully extended knees, and maximal stability margin led to the COP moving toward the rear foot in asymmetric stance. A combined analytical-numerical optimization scheme was used to avoid singularities that can arise due to the fact that at equilibrium postural configurations, the torso lies at or near the workspace boundary of the lower extremities. Experiments were conducted and the results obtained were in keeping with the model predictions. This basic understanding of asymmetric stance is important for studying asymmetric postural mechanics in the presence of external disturbances, and for extending the results from normal subjects to humans at both ends of the life span.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(6):650-656. doi:10.1115/1.2800868.

Improper patellar tracking is often considered to be the cause of patellar-femoral pain. Unfortunately, our knowledge of patellar-femoral-tibial (knee) joint kinematics is severely limited due to a lack of three-dimensional, noninvasive, in vivo measurement techniques. This study presents the first large-scale, dynamic, three-dimensional, noninvasive, in vivo study of nonimpaired knee joint kinematics during volitional leg extensions. Cine-phase contrast magnetic resonance imaging was used to measure the velocity profiles of the patella, femur, and tibia in 18 unimpaired knees during leg extensions, resisted by a 34 N weight. Bone displacements were calculated through integration and then converted into three-dimensional orientation angles. We found that the patella displaced laterally, superiorly, and anteriorly as the knee extended. Further, patellar flexion lagged knee flexion, patellar tilt was variable, and patellar rotation was fairly constant throughout extension.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(6):657-662. doi:10.1115/1.2800871.

This paper presents a three-dimensional finite element tibio-femoral joint model of a human knee that was validated using experimental data. The geometry of the joint model was obtained from magnetic resonance (MR) images of a cadaveric knee specimen. The same specimen was biomechanically tested using a robotic/universal force-moment sensor (UFS) system and knee kinematic data under anterior-posterior tibial loads (up to 100 N) were obtained. In the finite element model (FEM), cartilage was modeled as an elastic material, ligaments were represented as nonlinear elastic springs, and menisci were simulated by equivalent-resistance springs. Reference lengths (zero-load lengths) of the ligaments and stiffness of the meniscus springs were estimated using an optimization procedure that involved the minimization of the differences between the kinematics predicted by the model and those obtained experimentally. The joint kinematics and in-situ forces in the ligaments in response to axial tibial moments of up to 10 Nm were calculated using the model and were compared with published experimental data on knee specimens. It was also demonstrated that the equivalent-resistance springs representing the menisci are important for accurate calculation of knee kinematics. Thus, the methodology developed in this study can be a valuable tool for further analysis of knee joint function and could serve as a step toward the development of more advanced computational knee models.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEF

J Biomech Eng. 1999;121(6):663-665. doi:10.1115/1.2800872.

A corrected derivation is provided for the relationship between the impulse response of a wave tube termination and pressure signals measured at two different locations within the tube. This derivation yields exactly the same final result as was reported previously by Louis et al. (1993), despite the omission of the active source term in that earlier derivation. This technique has become the basis of an important medical diagnostic technology. This report revises and corrects the earlier theory upon which that technology rests.

Commentary by Dr. Valentin Fuster

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