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RESEARCH PAPERS

J Biomech Eng. 1998;120(5):549-558. doi:10.1115/1.2834744.

Successful improvement of cryopreservation protocols for cells in suspension requires knowledge of how such cells respond to the biophysical stresses of freezing (intracellular ice formation, water transport) while in the presence of a cryoprotective agent (CPA). This work investigates the biophysical water transport response in a clinically important cell type—isolated hepatocytes—during freezing in the presence of dimethylsulfoxide (DMSO). Sprague-Dawley rat liver hepatocytes were frozen in Williams E media supplemented with 0, 1, and 2 M DMSO, at rates of 5, 10, and 50°C/min. The water transport was measured by cell volumetric changes as assessed by cryomicroscopy and image analysis. Assuming that water is the only species transported under these conditions, a water transport model of the form dV/dT = f(Lpg ([CPA]), ELp ([CPA]), T(t)) was curve-fit to the experimental data to obtain the biophysical parameters of water transport—the reference hydraulic permeability (Lpg ) and activation energy of water transport (ELp )—for each DMSO concentration. These parameters were estimated two ways: (1) by curve-fitting the model to the average volume of the pooled cell data, and (2) by curve-fitting individual cell volume data and averaging the resulting parameters. The experimental data showed that less dehydration occurs during freezing at a given rate in the presence of DMSO at temperatures between 0 and −10°C. However, dehydration was able to continue at lower temperatures (<−10°C) in the presence of DMSO. The values of Lpg and ELp obtained using the individual cell volume data both decreased from their non-CPA values—4.33 × 10−13 m3 /N-s (2.69 μm/min-atm) and 317 kJ/mol (75.9 kcal/mol), respectively—to 0.873 × 10−13 m3 /N-s (0.542 μm/min-atm) and 137 kJ/mol (32.8 kcal/mol), respectively, in 1 M DMSO and 0.715 × 10−13 m3 /N-s (0.444 μm/min-atm) and 107 kJ/mol (25.7 kcal/mol), respectively, in 2 M DMSO. The trends in the pooled volume values for Lpg and ELp were very similar, but the overall fit was considered worse than for the individual volume parameters. A unique way of presenting the curve-fitting results supports a clear trend of reduction of both biophysical parameters in the presence of DMSO, and no clear trend in cooling rate dependence of the biophysical parameters. In addition, these results suggest that close proximity of the experimental cell volume data to the equilibrium volume curve may significantly reduce the efficiency of the curve-fitting process.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(5):559-569. doi:10.1115/1.2834745.

There is currently a need for experimental techniques to assay the biophysical response (water transport or intracellular ice formation, IIF) during freezing in the cells of whole tissue slices. These data are important in understanding and optimizing biomedical applications of freezing, particularly in cryosurgery. This study presents a new technique using a Differential Scanning Calorimeter (DSC) to obtain dynamic and quantitative water transport data in whole tissue slices during freezing. Sprague-Dawley rat liver tissue was chosen as our model system. The DSC was used to monitor quantitatively the heat released by water transported from the unfrozen cell cytoplasm to the partially frozen vascular/extracellular space at 5°C/min. This technique was previously described for use in a single cell suspension system (Devireddy, et al. 1998). A model of water transport was fit to the DSC data using a nonlinear regression curve-fitting technique, which assumes that the rat liver tissue behaves as a two-compartment Krogh cylinder model. The biophysical parameters of water transport for rat liver tissue at 5°C/min were obtained as Lpg = 3.16 x 10−13 m3 /Ns (1.9 μm/min-atm), ELp = 265 kJ/mole (63.4 kcal/mole), respectively. These results compare favorably to water transport parameters in whole liver tissue reported in the first part of this study obtained using a freeze substitution (FS) microscopy technique (Pazhayannur and Bischof, 1997). The DSC technique is shown to be a fast, quantitative, and reproducible technique to measure dynamic water transport in tissue systems. However, there are several limitations to the DSC technique: (a) a priori knowledge that the biophysical response is in fact water transport, (b) the technique cannot be used due to machine limitations at cooling rates greater than 40°C/min, and (c) the tissue geometric dimensions (the Krogh model dimensions) and the osmotically inactive cell volumes Vb , must be determined by low-temperature microscopy techniques.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(5):570-578. doi:10.1115/1.2834746.

The objective of this investigation was to gain a deeper understanding of the intracellular events that precede photolysis of cells. A model system, consisting of malignant melanoma cells pretreated with the calcium sensitive fluorescent dye, Fluo-3, was used to examine the intracellular calcium dynamics in single-cell photolysis experiments. Exposure of the cells to 632 nm laser light in the presence of photosensitizer, tin chlorin e6, resulted in a rise in intracellular calcium. The increase in intracellular calcium was blocked using a variety of calcium channel blocking agents, including verapamil, nifedipine, and nickel. Treatment with the channel blockers was also effective in either decreasing or eliminating cell death despite the presence of lethal doses of photosensitizer and irradiation. These results show that intracellular calcium rises prior to plasma membrane lysis, and that this early rise in intracellular calcium is necessary for membrane rupture.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(5):579-583. doi:10.1115/1.2834747.

The intraluminal thrombus (ILT) commonly found within abdominal aortic aneurysm (AAA) may serve as a barrier to oxygen diffusion from the lumen to the inner layers of the aortic wall. The purpose of this work was to address this hypothesis and to assess the effects of AAA bulge diameter (dAAA ) and ILT thickness (δ) on the oxygen flow. A hypothetical, three-dimensional, axisymmetric model of AAA containing ILT was created for computational analysis. Commercial software was utilized to estimate the volume flow of O2 per cell, which resulted in zero oxygen tension at the AAA wall. Solutions were generated by holding one of the two parameters fixed while varying the other. The supply of O2 to the AAA wall increases slightly and linearly with dAAA for a fixed δ. This slight increase is due to the enlarged area through which diffusion of O2 may take place. The supply of O2 was found to decrease quickly with increasing δ for a fixed dAAA due to the increased resistance to O2 transport by the ILT layer. The presence of even a thin, 3 mm ILT layer causes a diminished O2 supply (less than 4 × 10−10 μmol/min/cell). Normally functioning smooth muscle cells require a supply of 21 × 10−10 μmol/min/cell. Thus, our analysis serves to support our hypothesis that the presence of ILT alters the normal pattern of O2 supply to the AAA wall. This may lead to hypoxic cell dysfunction in the AAA wall, which may further lead to wall weakening and increased potential for rupture.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(5):584-593. doi:10.1115/1.2834748.

To provide a quantitative description of the convection field of gas transport through the lung under both low and high-frequency ventilation conditions, volume-cycled, purely oscillatory flow has been investigated in a symmetrically bifurcating model bronchial bifurcation. Significant differences in the flow properties that developed as the Reynolds number varied from 750 to 950 and the dimensionless frequency varied from 3 to 12 are described. At low frequency, the axial velocity field was found to approximate closely that of a steady flow through a bifurcation. However, even at α = 3, secondary velocity fields were confined to within a few diameters of the bifurcation, with less than 10 percent of the magnitude of the axial velocity. At high frequency they were still slower and more limited. These secondary velocity observations are discussed in terms of a physical mechanism balancing inviscid centripetal acceleration with viscous retardation. As the dimensionless frequency increased but the flow amplitude decreased, the magnitude of the axial drift velocity field was found to decrease. In addition, a burst of high-frequency velocity fluctuations was detected in both the axial and secondary velocity measurements in the parent tube, in low-frequency flow, during the deceleration phase of expiration. The position and timing of this burst suggest that it derives from the free shear layer in the parent tube. Stability criteria for the flow were therefore evaluated.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(5):594-601. doi:10.1115/1.2834749.

The study of steady and unsteady oscillatory static fluid pressures acting on the internal wall of a collapsible tube is essential for investigation of the complicated behavior observed when a flow is conveyed inside a tube. To examine the validity of two one-dimensional nonsteady theoretical flow models, this paper presents basic experimental observations of flow separation and reattachment and measured data on the static pressure distributions of the flow in a quasi-two-dimensional channel with a throat, together with information on the corresponding shape of the wall deflection and motion. For combinations of moderate Reynolds numbers and angles of the divergent segment of the channel, a smooth flow is separated from the wall downstream of the minimum cross section and reattached to the wall farther downstream. The measured data are compared with numerical results calculated by the two flow models.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(5):602-607. doi:10.1115/1.2834750.

An experimental technique was developed to determine the finite strain field in heterogeneous, diseased human aortic cross sections at physiologic pressures in vitro. Also, the distributions within the cross sections of four histologic features (disease-free zones, lipid accumulations, fibrous intimal tissue, and regions of calcification) were quantified using light microscopic morphometry. A model incorporating heterogeneous, plane stress finite elements coupled the experimental and histologic data. Tissue constituent mechanical properties were determined through an optimization strategy, and the distributions of stress and strain energy in the diseased vascular wall were calculated. Results show that the constituents of atherosclerotic lesions exhibit large differences in their bilinear mechanical properties. The distributions of stress and strain energy in the diseased vascular wall are strongly influenced by both lesion structure and composition. These results suggest that accounting for heterogeneities in the mechanical analysis of atherosclerotic arterial tissue is critical to establishing links between lesion morphology and the susceptibility of plaque to mechanical disruption in vivo.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(5):608-613. doi:10.1115/1.2834751.

Stress analysis of contact models for isotropic articular cartilage under impacting loads shows high shear stresses at the interface with the subchondral bone and normal compressive stresses near the surface of the cartilage. These stress distributions are not consistent, with lesions observed on the cartilage surface of rabbit patellae from blunt impact, for example, to the patello-femoral joint. The purpose of the present study was to analyze, using the elastic capabilities of a finite element code, the stress distribution in more morphologically realistic transversely isotropic biphasic contact models of cartilage. The elastic properties of an incompressible material, equivalent to those of the transversely isotropic biphasic material at time zero, were derived algebraically using stress-strain relations. Results of the stress analysis showed the highest shear stresses on the surface of the solid skeleton of the cartilage and tensile stresses in the zone of contact. These results can help explain the mechanisms responsible for surface injuries observed during blunt insult experiments.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(5):614-619. doi:10.1115/1.2834752.

The in situ mechanical conditions of cartilage in the articulated knee were quantified during joint loading. Six porcine knees were subjected to a 445 N compressive load while cartilage deformations and contact pressures were measured. From roentgenograms, cartilage thickness before and during loading allowed the calculation of tissue deformation on the lateral femoral condyle at different times during the loading process. Contact pressures on the articular surface were measured with miniature fiber-optic pressure transducers. Results showed that the medial side of the lateral femoral condyle had higher contact pressures, as well as deformations. To begin to correlate the pressures and resulting deformations, the intrinsic material properties of the cartilage on the lateral condyle were obtained from indentation tests. Data from four normal control specimens indicated that the aggregate modulus of the medial side was significantly higher than in other areas of the condyle. These experimental measures of the in situ mechanical conditions of articular cartilage can be combined with theoretical modeling to obtain valuable information about the relative contributions of the solid and fluid phases to supporting the applied load on the cartilage surface (see Part II).

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(5):620-624. doi:10.1115/1.2834753.

Experimental measurements in conjunction with theoretical predictions were used to determine the extent of load supported by the fluid phase of cartilage at the articular surface. The u-p finite element model was used to simulate the loading of six separate porcine knee joints and to predict surface deformations of the cartilage layer on the lateral femoral condyle. Representative geometry for the condyle, contact pressures, and intrinsic material properties of the cartilage layer were supplied from experimental measures (see Part I). The u-p finite element predictions for surface deformations of the cartilage layer were obtained for several load partitioning states between the solid and fluid phases of cartilage at the articular surface. These were then compared to actual surface deformations obtained experimentally. It appeared from the comparison that approximately 75 percent of the applied load was borne by the fluid phase at the articular surface under this loading regime. This was qualitatively in agreement with the hypothesis that an applied load to articular joints is partitioned at the surface to the two phases according to the surface area ratios of the solid and fluid phases. It appeared that the solid phase was shielded from the total applied stress on the articular surface by the fluid and could be a reason for the excellent durability of the tissue under the demanding conditions in a diarthrodial joint.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(5):625-633. doi:10.1115/1.2834754.

The direction of rotation (DOR) of individual elbow muscles, defined as the direction in which a muscle rotates the forearm relative to the upper arm in three-dimensional space, was studied in vivo as a function of elbow flexion and forearm rotation. Electrical stimulation was used to activate an individual muscle selectively, and the resultant flexion-extension, supination-pronation, and varus-valgus moments were used to determine the DOR. Furthermore, multi-axis moment-angle relationships of individual muscles were determined by stimulating the muscle at a constant submaximal level across different joint positions, which was assumed to result in a constant level of muscle activation. The muscles generate significant moments about axes other than flexion-extension, which is potentially important for actively controlling joint movement and maintaining stability about all axes. Both the muscle DOR and the multi axis moments vary with the joint position systematically. Variations of the DOR and moment-angle relationship across muscle twitches of different amplitudes in a subject were small, while there were considerable variations between subjects.

Topics: Rotation , Muscle , Stability
Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(5):634-639. doi:10.1115/1.2834755.

Although the contributions of passive structures to stability of the elbow have been well documented, the role of active muscular resistance of varus and valgus loads at the elbow remains unclear. We hypothesized that muscles: (1) can produce substantial varus and valgus moments about the elbow, and (2) are activated in response to sustained varus and valgus loading of the elbow. To test the first hypothesis, we developed a detailed musculoskeletal model to estimate the varus and valgus moment-generating capacity of the muscles about the elbow. To test the second hypothesis, we measured EMGs from 11 muscles in four subjects during a series of isometric tasks that included flexion, extension, varus, and valgus moments about the elbow. The EMG recordings were used as inputs to the elbow model to estimate the contributions of individual muscles to flexion-extension and varus-valgus moments. Analysis of the model revealed that nearly all of the muscles that cross the elbow are capable of producing varus or valgus moments; the capacity of the muscles to produce varus moment (34 Nm) and valgus moment (35 Nm) is roughly half of the maximum flexion moment (70 Nm). Analysis of the measured EMGs showed that the anconeus was the most significant contributor to valgus moments and the pronator teres was the largest contributor to varus moments. Although our results show that muscles were activated in response to static varus and valgus loads, their activations were modest and were not sufficient to balance the applied load.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(5):640-646. doi:10.1115/1.2834756.

An alternative concept of the relationship between morphological and elastic properties of trabecular bone is presented and applied to human tissue from several anatomical locations using a digital approach. The three-dimensional morphology of trabecular bone was assessed with a microcomputed tomography system and the method of directed secants as well as the star volume procedure were used to compute mean intercept length (MIL) and average bone length (ABL) of 4 mm cubic specimens. Assuming isotropic elastic properties for the trabecular tissue, the general elastic tensors of the bone specimens were determined using the homogenization method and the closest orthotropic tensors were calculated with an optimization algorithm. The assumption of orthotropy for trabecular bone was found to improve with specimen size and hold within 6.1 percent for a 4 mm cube size. A strong global relationship (r2 = 0.95) was obtained between fabric and the orthotropic elastic tensor with a minimal set of five constants. Mean intercept length and average bone length provided an equivalent power of prediction. These results support the hypothesis that the elastic properties of human trabecular bone from an arbitrary anatomical location can be estimated from an approximation of the anisotropic morphology and a prior knowledge of tissue properties.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(5):647-654. doi:10.1115/1.2834757.

Repetitive, low-intensity loading from normal daily activities can generate fatigue damage in trabecular bone, a potential cause of spontaneous fractures of the hip and spine. Finite element models of trabecular bone (Guo et al., 1994) suggest that both creep and slow crack growth contribute to fatigue failure. In an effort to characterize these damage mechanisms experimentally, we conducted fatigue and creep tests on 85 waisted specimens of trabecular bone obtained from 76 bovine proximal tibiae. All applied stresses were normalized by the previously measured specimen modulus. Fatigue tests were conducted at room temperature; creep tests were conducted at 4, 15, 25, 37, 45, and 53°C in a custom-designed apparatus. The fatigue behavior was characterized by decreasing modulus and increasing hysteresis prior to failure. The hysteresis loops progressively displaced along the strain axis, indicating that creep was also involved in the fatigue process. The creep behavior was characterized by the three classical stages of decreasing, constant, and increasing creep rates. Strong and highly significant power-law relationships were found between cycles-to-failure, time-to-failure, steady-state creep rate, and the applied loads. Creep analyses of the fatigue hysteresis loops also generated strong and highly significant power law relationships for time-to-failure and steady-state creep rate. Lastly, the products of creep rate and time-to-failure were constant for both the fatigue and creep tests and were equal to the measured failure strains, suggesting that creep plays a fundamental role in the fatigue behavior of trabecular bone. Additional analysis of the fatigue strain data suggests that creep and slow crack growth are not separate processes that dominate at high and low loads, respectively, but are present throughout all stages of fatigue.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(5):655-659. doi:10.1115/1.2834758.

Fuji film has been widely used in studies aimed at obtaining the contact mechanics of articular joints. Once sealed for practical use in biological joints, Fuji Pressensor film has a total effective thickness of 0.30 mm, which is comparable to the cartilage thickness in the joints of many small animals. The average effective elastic modulus of Fuji film is approximately 100 MPa in compression, which is larger by a factor of 100–300 compared to that of normal articular cartilage. Therefore, inserting a Pressensor film into an articular joint will change the contact mechanics of the joint. The measurement precision of the Pressensor film has been determined systematically; however, the changes in contact mechanics associated with inserting the film into joints have not been investigated. This study was aimed at quantifying the changes in the contact mechanics associated with inserting sealed Fuji Pressensor film into joints. Spherical and cylindrical articular joint contact mechanics with and without Pressensor film and for varying degrees of surface congruency were analyzed and compared by using finite element models. The Pressensor film was taken as linearly elastic and the cartilage was assumed to be biphasic, composed of a linear elastic solid phase and an inviscid fluid phase. The present analyses showed that measurements of the joint contact pressures with Fuji Pressensor film will change the maximum true contact pressures by 10–26 percent depending on the loading, geometry of the joints, and the mechanical properties of cartilage. Considering this effect plus the measurement precision of the film (approximately 10 percent), the measured joint contact pressures in a joint may contain errors as large as 14–28 percent.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(5):660-666. doi:10.1115/1.2834759.

We predicted and measured the evolution of smooth muscle cell (SMC) orientation in media-equivalents (MEs) for four fabrication conditions (F−, M−, F+, M+) under Free or Mandrel compaction (F/M) with and without magnetic prealignment of the collagen fibrils in the circumferential direction (±). Mandrel compaction refers to SMC-induced compaction of the ME that is constrained by having a nonadhesive mandrel placed in the ME lumen. Predictions were made using our anisotropic biphasic theory (ABT) for tissue-equivalent mechanics. Successful prediction of trends of the SMC orientation data for all four fabrication cases was obtained: maintenance of the initial isotropic state for F−, loss of initial circumferential alignment for F+, development of circumferential alignment for M−, and enhancement of initial circumferential alignment for M+. These results suggest two mechanisms by which the presence of the mandrel leads to much greater mechanical stiffness in the circumferential direction reported for mandrel compacted MEs relative to free compacted MEs: (1) by inducing an increasing circumferential alignment of the SMC and collagen, and (2) by inducing a large stress on the SMC, resulting in secretion and accumulation of stiffening components.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(5):667-675. doi:10.1115/1.2834760.

To isolate the primary variables influencing acetabular cup and interface stresses, we performed an evaluation of cup loading and cup support variables, using a Statistical Design of Experiments (SDOE) approach. We developed three-dimensional finite element (FEM) models of the pelvis and adjacent bone. Cup support variables included fixation mechanism (cemented or noncemented), amount of bone support, and presence of metal backing. Cup loading variables included head size and cup thickness, cup/head friction, and conformity between the cup and head. Interaction between and among variables was determined using SDOE techniques. Of the variables tested, conformity, head size, and backing emerged as significant influences on stresses. Since initially nonconforming surfaces would be expected to wear into conforming surfaces, conformity is not expected to be a clinically significant variable. This indicates that head size should be tightly toleranced during manufacturing, and that small changes in head size can have a disproportionate influence on the stress environment. In addition, attention should be paid to the use of nonmetal backed cups, in limiting cup/bone interface stresses. No combination of secondary variables could compensate for, or override the effect of, the primary variables. Based on the results using the SDOE approach, adaptive FEM models simulating the wear process may be able to limit their parameters to head size and cup backing.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(5):676-685. doi:10.1115/1.2834761.

Shape-memory alloys have properties that make them well suited to a variety of applications. One application for which their unique combination of properties (large elastic range, low modulus of elasticity, ability to deliver nearly constant forces over a wide range of deformations) seems ideally suited is for orthodontic retraction appliances where these properties are very desirable. The mechanical response of shape-memory alloys is modeled by a simple constitutive model that captures the essential superelastic behavior of the shape-memory wires. An initial value approach that iteratively converges to the appropriate boundary conditions is utilized to deliver numerical solutions. Qualitative agreement is shown with previous experimental works. The possible benefits of using such wires in an orthodontic retraction appliance are then investigated.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J Biomech Eng. 1998;120(5):686-689. doi:10.1115/1.2834762.

Unified constitutive equations for elastic–viscoplastic materials were modified and used to model the highly nonlinear elastic and rate-dependent inelastic response exhibited in recent experiments on excised facial tissues. These included the skin and the underlying supportive tissue SMAS (the Superficial Musculoaponeurotic System). This study indicates a number of relevant results: The skin is more strain rate dependent than the SMAS; the nonlinearity of the elasticity of the skin is greater than that of the SMAS; both tissues exhibit a hardening effect indicated by increased resistance to inelastic deformation due to stress acting over a time period; the hardening effect leads to a decrease in time dependence and an increased elastic range, which is more pronounced for SMAS. Consequently, the SMAS can be viewed as the firmer elastic foundation of the more viscous skin. Moreover, the relaxation time for the skin is fairly short so the skin would be expected to conform to the deformation of the SMAS if it remained attached to the SMAS during stretching. This is relevant when it is undesirable to separate the skin from the SMAS for physiological reasons.

Commentary by Dr. Valentin Fuster

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