Showing papers in "Journal of Biomechanical Engineering-transactions of The Asme in 2002"

Energetics of Actively Powered Locomotion Using the Simplest Walking Model

Abstract: We modified an irreducibly simple model of passive dynamic walking to walk on level ground, and used it to study the energetics of walking and the preferred relationship between speed and step length in humans. Powered walking was explored using an impulse applied at toe-off immediately before heel strike, and a torque applied on the stance leg. Although both methods can supply energy through mechanical work on the center of mass, the toe-off impulse is four times less costly because it decreases the collision loss at heel strike. We also studied the use of a hip torque on the swing leg that tunes its frequency but adds no propulsive energy to gait. This spring-like actuation can further reduce the collision loss at heel strike, improving walking energetics. An idealized model yields a set of simple power laws relating the toe-off impulses and effective spring constant to the speed and step length of the corresponding gait. Simulations incorporating nonlinear equations of motion and more realistic inertial parameters show that these power laws apply to more complex models as well.

Tensile mechanical properties of three-dimensional type I collagen extracellular matrices with varied microstructure.

Abstract: The importance and priority of specific micro-structural and mechanical design parameters must be established to effectively engineer scaffolds (biomaterials) that mimic the extracellular matrix (ECM) environment of cells and have clinical applications as tissue substitutes. In this study, three-dimensional (3-D) matrices were prepared from type I collagen, the predominant compositional and structural component of connective tissue ECMs, and structural-mechanical relationships were studied. Polymerization conditions, including collagen concentration (0.3-3 mg/mL) and pH (6-9), were varied to obtain matrices of collagen fibrils with different microstructures. Confocal reflection microscopy was used to assess specific micro-structural features (e.g., diameter and length) and organization of component fibrils in 3-D. Microstructural analyses revealed that changes in collagen concentration affected fibril density while maintaining a relatively constant fibril diameter. On the other hand, both fibril length and diameter were affected by the pH of the polymerization reaction. Mechanically, all matrices exhibited a similar stress-strain curve with identifiable "toe," "linear," and "failure" regions. However the linear modulus and failure stress increased with collagen concentration and were correlated with an increase in fibril density. Additionally, both the linear modulus and failure stress showed an increase with pH, which was related to an increasedfibril length and a decreasedfibril diameter. The tensile mechanical properties of the collagen matrices also showed strain rate dependence. Such fundamental information regarding the 3-D microstructural-mechanical properties of the ECM and its component molecules are important to our overall understanding of cell-ECM interactions (e.g., mechanotransduction) and the development of novel strategies for tissue repair and replacement.

Regional, Directional, and Age-Dependent Properties of the Brain Undergoing Large Deformation

Abstract: The large strain mechanical properties of adult porcine gray and white matter brain tissues were measured in shear and confirmed in compression. Consistent with local neuroarchitecture, gray matter showed the least amount of anisotropy, and corpus callosum exhibited the greatest degree of anisotropy. Mean regional properties were significantly distinct, demonstrating that brain tissue is inhomogeneous. Fresh adult human brain tissue properties were slightly stiffer than adult porcine properties but considerably less stiff than the human autopsy data in the literature. Mixed porcine gray/white matter samples were obtained from animals at "infant" and "toddler" stages of neurological development, and shear properties compared to those in the adult. Only the infant properties were significantly different (stiffer) from the adult.

A Finite Element Model of the Human Knee Joint for the Study of Tibio-Femoral Contact

Abstract: As a step towards developing a finite element model of the knee that can be used to study how the variables associated with a meniscal replacement affect tibio-femoral contact, the goals of this study were 1) to develop a geometrically accurate three-dimensional solid model of the knee joint with special attention given to the menisci and articular cartilage, 2) to determine to what extent bony deformations affect contact behavior, and 3) to determine whether constraining rotations other than flexion/extension affects the contact behavior of the joint during compressive loading. The model included both the cortical and trabecular bone of the femur and tibia, articular cartilage of the femoral condyles and tibial plateau, both the medial and lateral menisci with their horn attachments, the transverse ligament, the anterior cruciate ligament, and the medial collateral ligament. The solid models for the menisci and articular cartilage were created from surface scans provided by a noncontacting, laser-based, three-dimensional coordinate digitizing system with an root mean squared error (RMSE) of less than 8 microns. Solid models of both the tibia and femur were created from CT images, except for the most proximal surface of the tibia and most distal surface of the femur which were created with the three-dimensional coordinate digitizing system. The constitutive relation of the menisci treated the tissue as transversely isotropic and linearly elastic. Under the application of an 800 N compressive load at 0 degrees of flexion, six contact variables in each compartment (ie., medial and lateral) were computed including maximum pressure, mean pressure, contact area, total contact force, and coordinates of the center of pressure. Convergence of the finite element solution was studied using three mesh sizes ranging from an average element size of 5 mm by 5 mm to 1 mm by 1 mm. The solution was considered converged for an average element size of 2 mm by 2 mm. Using this mesh size, finite element solutions for rigid versus deformable bones indicated that none of the contact variables changed by more than 2% when the femur and tibia were treated as rigid. However, differences in contact variables as large as 19% occurred when rotations other than flexion/extension were constrained. The largest difference was in the maximum pressure. Among the principal conclusions of the study are that accurate finite element solutions of tibio-femoral contact behavior can be obtained by treating the bones as rigid. However, unrealistic constraints on rotations other than flexion/extension can result in relatively large errors in contact variables.

Recruitment of tendon crimp with applied tensile strain.

Abstract: The tensile stress-strain behavior of ligaments and tendons begins with a toe region that is believed to result from the straightening of crimped collagen fibrils. The in situ mechanical function is mostly confined to this toe region and changes in crimp morphology are believed to be associated with pathological conditions. A relatively new imaging technique, optical coherence tomography (OCT), provides a comparatively inexpensive method for nondestructive investigation of tissue ultrastructure with resolution on the order of 15 microm and the potential for use in a clinical setting. The objectives of this work were to assess the utility of OCT for visualizing crimp period, and to use OCT to determine how crimp period changed as a function of applied tensile strain in rat tail tendon fascicles. Fascicles from rat tail tendons were subjected to 0.5 percent strain increments up to 5 percent and imaged at each increment using OCT. A comparison between OCT images and optical microscopy images taken between crossed polarizing lenses showed a visual correspondence between features indicative of crimp pattern. Crimp pattern always disappeared completely before 3 percent axial strain was reached. Average crimp period increased as strain increased, but both elongation and shortening occurred within single crimp periods during the application of increasing strain to the fascicle.

Unsteady and Three-Dimensional Simulation of Blood Flow in the Human Aortic Arch

Abstract: A three-dimensional and pulsatile blood flow in a human aortic arch and its three major branches has been studied numerically for a peak Reynolds number of 2500 and a frequency (or Womersley) parameter of 10. The simulation geometry was derived from the three-dimensional reconstruction of a series of two-dimensional slices obtained in vivo using CAT scan imaging on a human aorta. The numerical simulations were obtained using a projection method, and a finite-volume formulation of the Navier-Stokes equations was used on a system of overset grids. Our results demonstrate that the primary flow velocity is skewed towards the inner aortic wall in the ascending aorta, but this skewness shifts to the outer wall in the descending thoracic aorta. Within the arch branches, the flow velocities were skewed to the distal walls with flow reversal along the proximal walls. Extensive secondary flow motion was observed in the aorta, and the structure of these secondary flows was influenced considerably by the presence of the branches. Within the aorta, wall shear stresses were highly dynamic, but were generally high along the outer wall in the vicinity of the branches and low along the inner wall, particularly in the descending thoracic aorta. Within the branches, the shear stresses were considerably higher along the distal walls than along the proximal walls. Wall pressure was low along the inner aortic wall and high around the branches and along the outer wall in the ascending thoracic aorta. Comparison of our numerical results with the localization of early atherosclerotic lesions broadly suggests preferential development of these lesions in regions of extrema (either maxima or minima) in wall shear stress and pressure.

The Differential Interfacial Tension Hypothesis (DITH): a comprehensive theory for the self-rearrangement of embryonic cells and tissues.

Abstract: A comprehensive theory, herein named the Differential Interfacial Tension Hypothesis for the self-rearrangement of embryonic cells and tissues is presented. These rearrangements include sorting, mixing and formation of checkerboard patterns in heterotypic aggregates of embryonic cells, and total or partial engulfment, separation and dissociation of tissues. This broadly-based theory accounts for the action of all currently known cytoskeletal components and cell adhesion mechanisms. The theory is used to derive conditions for the cell and tissue rearrangements named above. Finite element-based computer simulations involving two or more cell types confirm these conditions.

Advanced Bioreactor with Controlled Application of Multi-Dimensional Strain For Tissue Engineering

Abstract: Advanced bioreactors are essential for meeting the complex requirements of in vitro engineering functional skeletal tissues. To address this need, we have developed a computer controlled bench-top bioreactor system with capability to apply complex concurrent mechanical strains to three-dimensional matrices independently housed in 24 reactor vessels, in conjunction with enhanced environmental and fluidic control. We demonstrate the potential of this new system to address needs in tissue engineering, specifically toward the development of a tissue engineered anterior cruciate ligament from human bone-marrow stromal cells (hBMSC), where complex mechanical and biochemical environment control is essential to tissue function. Well-controlled mechanical strains (resolution of < 0.1 micron for translational and < 0.1 degree for rotational strain) and dissolved oxygen tension (between 0%-95% +/- 1%) could be applied to the developing tissue, while maintaining temperature at 37 +/- 0.2 degrees C about developing tissue over prolonged periods of operation. A total of 48 reactor vessels containing cell culture medium and silk fiber matrices were run for up to 21 days under 90 degrees rotational and 2 mm translational deformations at 0.0167 Hz with only one succumbing to contamination due to a leak at an medium outlet port. Twenty-four silk fiber matrices seeded with human bone marrow stromal cells (hBMSCs) housed within reactor vessels were maintained at constant temperature (37 +/- 0.2 degrees C), pH (7.4 +/- 0.02), and pO2 (20 +/- 0.5%) over 14 days in culture. The system supported cell spreading and growth on the silk fiber matrices based on SEM characterization, as well as the differentiation of the cells into ligament-like cells and tissue (Altman et al., 2001).

An automated approach for direct measurement of two-dimensional strain distributions within articular cartilage under unconfined compression.

Abstract: An automated approachfor measuring in situ two-dimensional strain fields was developed and validated for its application to cartilage mechanics. This approach combines video microscopy, optimized digital image correlation (DIC), thin-plate spline smoothing (TPSS) and generalized cross-validation (GCV) techniques to achieve the desired efficiency and accuracy. Results demonstrate that sub-pixel accuracies can be achieved for measuring tissue displacements with this methodology with a measurement uncertainty ranging from 0.25 to 0.30 pixels. The deformational gradients (from which the strains are determined) can be evaluated directly using the optimized DIC, with a measurement uncertainty of 0.017 to approximately 0.032. In actual measurements of strain in cartilage, TPSS and differentiation can be used to achieve a more accurate measurement of the gradients from the displacement data. Using this automated approach, the two-dimensional strain fields inside immature bovine carpometacarpal joint cartilage specimens under unconfined compression were characterized (n=21). The depth-dependent apparent elastic modulus and Poisson's ratio were also determined and found to be smallest at the articular surface and increasing with depth. The apparent Poisson's ratio is found to decrease with increasing compressive strain, with values as low as 0.01 observed near the articular surface at 25% compression. The variation of the apparent Poisson's ratio with depth is found to be consistent with a theoretical model of cartilage which accounts for the disparity in its tensile and compressive moduli.

A new in vitro model to evaluate differential responses of endothelial cells to simulated arterial shear stress waveforms.

Abstract: In the circulation, flow-responsive endothelial cells (ECs) lining the lumen of blood vessels are continuously exposed to complex hemodynamic forces. To increase our understanding of EC response to these dynamic shearing forces, a novel in vitro flow model was developed to simulate pulsatile shear stress waveforms encountered by the endothelium in the arterial circulation. A modified waveform modeled after flow patterns in the human abdominal aorta was used to evaluate the biological responsiveness of human umbilical vein ECs to this new type of stimulus. Arterial pulsatile flow for 24 hours was compared to an equivalent time-average steady laminar shear stress, using no flow (static) culture conditions as a baseline. While both flow stimuli induced comparable changes in cell shape and alignment, distinct patterns of responses were observed in the distribution of actin stress fibers and vinculin-associated adhesion complexes, intrinsic migratory characteristics, and the expression of eNOS mRNA and protein. These results thus reveal a unique responsiveness of ECs to an arterial waveform and begin to elucidate the complex sensing capabilities of the endothelium to the dynamic characteristics of flows throughout the human vascular tree.

Numerical Analysis of Flow Through a Severely Stenotic Carotid Artery Bifurcation

Abstract: The results of computational simulations may supplement MR and other in vivo diagnostic techniques to provide an accurate picture of the hemodynamics in particular vessels, which may help demonstrate the risks of embolism or plaque rupture posed by particular plaque deposits. In this study, a model based on an endarterectomy specimen of the plaque in a carotid bifurcation was examined. The flow conditions include steady flow at Reynolds numbers of 300, 600, and 900 as well as unsteady, pulsatile flow. Both dynamic pressure and wall shear stress are very high, with shear values up to 70 N/m 2 , proximal to the stenosis throat in the internal carotid artery, and both vary significantly through the flow cycle. The wall shear stress gradient is also strong along the throat. Vortex shedding is observed downstream of the most severe occlusion. Two turbulence models, the Chien and Goldberg varieties of k-«, are tested and evaluated for their relevance in this geometry. The Chien model better captures phenomena such as vortex shedding. The flow distal to stenosis is likely transitional, so a model that captures both laminar and turbulent behavior is needed. @DOI: @10.1115/1.1427042#

Analytical study on bioheat transfer problems with spatial or transient heating on skin surface or inside biological bodies.

Abstract: Several closed form analytical solutions to the bioheat transfer problems with space or transient heating on skin surface or inside biological bodies were obtained using Green's function method. The solutions were applied to study several selected typical bioheat transfer processes, which are often encountered in cancer hyperthermia, laser surgery, thermal comfort analysis, and tissue thermal parameter estimation. Thus a straightforward way to quantitatively interpret the temperature behavior of living tissues subject to constant, sinusoidal, step, point or stochastic heatings etc. both in volume and on boundary were established. Further solution to the three-dimensional bioheat transfer problems was also given to illustrate the versatility of the present method. Implementations of this study to the practical problems were addressed.

Assessment of mechanical properties of adherent living cells by bead micromanipulation: comparison of magnetic twisting cytometry vs optical tweezers.

Abstract: We compare the measurements of viscoelastic properties of adherent alveolar epithelial cells by two micromanipulation techniques: (i) magnetic twisting cytometry and (ii) optical tweezers, using microbeads of same size and similarly attached to F-actin. The values of equivalent Young modulus E, derived from linear viscoelasticity theory, become consistent when the degree of bead immersion in the cell is taken into account. E-values are smaller in (i) than in (ii): approximately 34-58 Pa vs approximately 29-258 Pa, probably because higher stress in (i) reinforces nonlinearity and cellular plasticity. Otherwise, similar relaxation time constants, around 2 s, suggest similar dissipative mechanisms.

Time-dependent mechanical behavior of sheep digital tendons, including the effects of preconditioning

Abstract: The time-dependent mechanical properties of sheep digital extensor tendons were studied by sequences of stress-relaxation tests. The results exhibited irreversible preconditioning and reversible viscoelasticity. Preconditioning effects were manifested by stress decay during consecutive stretch cycles to the same strain level, accompanied by elongation of the tendon's reference length. They intensified with increased strain level, and were reduced or became negligible as the strain decreased. The significance of intrinsic response mechanisms was studied via a structural model that includes viscoelasticity, preconditioning, and morphology of the tendon's collagen fibers. Model/data comparisons showed good agreement and good predictive power, suggesting that preconditioning can be integrated into comprehensive material characterization of tendons.

Computational analysis of coupled blood-wall arterial LDL transport.

Abstract: The transport of macromolecules, such as low density lipoproteins (LDLs), across the artery wall and their accumulation in the wall is a key step in atherogenesis. Our objective was to model fluid flow within both the lumen and wall of a constricted, axisymmetric tube simulating a stenosed artery, and to then use this flow pattern to study LDL mass transport from the blood to the artery wall. Coupled analysis of lumenal blood flow and transmural fluid flow was achieved through the solution of Brinkman's model, which is an extension of the Navier-Stokes equations for porous media. This coupled approach offers advantages over traditional analyses of this problem, which have used possibly unrealistic boundary conditions at the blood-wall interface; instead, we prescribe a more natural pressure boundary condition at the adventitial vasa vasorum, and allow variations in wall permeability due to the occurrence of plaque. Numerical complications due to the convection dominated mass transport process (low LDL diffusivity) are handled by the streamline upwind/Petrov-Galerkin (SUPG) finite element method. This new fluid-plus-porous-wall method was implemented for conditions typical of LDL transport in a stenosed artery with a 75 percent area reduction (Peclet number=2 x 10(8)). The results show an elevated LDL concentration at the downstream side of the stenosis. For the higher Darcian wall permeability thought to occur in regions containing atheromatous lesions, this leads to an increased transendothelial LDL flux downstream of the stenosis. Increased transmural filtration in such regions, when coupled with a concentration-dependent endothelial permeability to LDL, could be an important contributor to LDL infiltration into the arterial wall. Experimental work is needed to confirm these results.

Predicting local cell deformations in engineered tissue constructs: a multilevel finite element approach.

Abstract: A multilevel finite element approach is applied to predict local cell deformations in engineered tissue constructs. Cell deformations are predicted from detailed nonlinear FE analysis of the microstructure, consisting of an arrangement of cells embedded in matrix material. Effective macroscopic tissue behavior is derived by a computational homogenization procedure. To illustrate this approach, we simulated the compression of a skeletal muscle tissue construct and studied the influence of microstructural heterogeneity on local cell deformations. Results show that heterogeneity has a profound impact on local cell deformations, which highly exceed macroscopic deformations. Moreover, microstructural heterogeneity and the presence of neighboring cells leads to complex cell shapes and causes non-uniform deformations within a cell.

Experimental and biphasic FEM determinations of the material properties and hydraulic permeability of the meniscus in tension

Abstract: Tensile tests and biphasic finite element modeling were used to determine a set of transversely isotropic properties for the meniscus, including the hydraulic permeability coefficients and solid matrix properties. Stress-relaxation tests were conducted on planar samples of canine meniscus samples of different orientations, and the solid matrix properties were determined from equilibrium data. A 3-D linear biphasic and tranversely isotropic finite element model was developed to model the stress-relaxation behavior of the samples in tension, and optimization was used to determine the permeability coefficients, k1 and k2, governing fluid flow parallel and perpendicular to the collagen fibers, respectively. The collagen fibrillar orientation was observed to have an effect on the Young's moduli (E1=67.8 MPa, E2=11.1 MPa) and Poisson's ratios (v12=2.13, v21 =1.50, v23=1.02). However, a significant effect of anisotropy on permeability was not detected (k1 =0.09x10(-16) m4/Ns, k2=0.10x10(-16) m4/Ns). The low permeability values determined in this study provide insight into the extent of fluid pressurization in the meniscus and will impact modeling predictions of load support in the meniscus.

Noninvasive Measurement of Time-Varying Three-Dimensional Relative Pressure Fields Within the Human Heart

Abstract: Understanding cardiac blood flow patterns is important in the assessment of cardiovascular function. Three-dimensional flow and relative pressure fields within the human left ventricle are demonstrated by combining velocity measurements with computational fluid mechanics methods. The velocity field throughout the left atrium and ventricle of a normal human heart is measured using time-resolved three-dimensional phase-contrast MRI. Subsequently, the time-resolved three-dimensional relative pressure is calculated from this velocity field using the pressure Poisson equation. Noninvasive simultaneous assessment of cardiac pressure and flow phenomena is an important new tool for studying cardiac fluid dynamics.

The axial injury tolerance of the human foot/ankle complex and the effect of Achilles tension.

Abstract: Axial loading of the foot/ankle complex is an important injury mechanism in vehicular trauma that is responsible for severe injuries such as calcaneal and tibial pilon fractures. Axial loading may be applied to the leg externally, by the toepan and/or pedals, as well as internally, by active muscle tension applied through the Achilles tendon during pre-impact bracing. The objectives of this study were to investigate the effect of Achilles tension on fracture mode and to empirically model the axial loading tolerance of the foot/ankle complex. Blunt axial impact tests were performed on forty-three (43) isolated lower extremities with and without experimentally simulated Achilles tension. The primary fracture mode was calcaneal fracture in both groups. However, fracture initiated at the distal tibia more frequently with the addition of Achilles tension (p < 0.05). Acoustic sensors mounted to the bone demonstrated that fracture initiated at the time of peak local axial force. A survival analysis was performed on the injury data set using a Weibull regression model with specimen age, gender, body mass, and peak Achilles tension as predictor variables (R2 = 0.90). A closed-form survivor function was developed to predict the risk of fracture to the foot/ankle complex in terms of axial tibial force. The axial tibial force associated with a 50% risk of injury ranged from 3.7 kN for a 65 year-old 5th percentile female to 8.3 kN for a 45 year-old 50th percentile male, assuming no Achilles tension. The survivor function presented here may be used to estimate the risk of foot/ankle fracture that a blunt axial impact would pose to a human based on the peak tibial axial force measured by an anthropomorphic test device.

Fluid shear stress-induced alignment of cultured vascular smooth muscle cells.

Abstract: The study objectives were to quantify the time- and magnitude-dependence of flow-induced alignment in vascular smooth muscle cells (SMC) and to identify pathways related to the orientation process. Using an intensity gradient method, we demonstrated that SMC aligned in the direction perpendicular to applied shear stress, which contrasts with parallel alignment of endothelial cells under flow SMC alignment varied with the magnitude of and exposure time to shear stress and is a continuous process that is dependent on calcium and cycloskeleton based mechanisms. A clear understanding and control of flow-induced SMC alignment will have implications for vascular tissue engineering.

Direct Measurement of the Poisson’s Ratio of Human Patella Cartilage in Tension

Abstract: Articular cartilage has been shown to exhibit large transverse contractions when loaded in tension, suggesting the existence of large values for the Poisson's ratio. Previous studies have suggested that this effect is dependent on amplitude of applied strain, so that a single Poisson's ratio may not be sufficient to describe cartilage behavior. In this study, the Poisson's ratio (v), toe region modulus (Eo), and linear region modulus (E) of human patellar articular cartilage were calculated in simple tension tests from optical analysis of the two-dimensional strain fields at equilibrium. The Poisson's ratio was found to be independent of strain due to the absence of viscoelastic effects during testing. The Poisson's ratio was found to be significantly higher in the surface zone (1.87 +/- 1.11, p<0.01) than in the middle zone (0.62 +/- 0.23), with no significant correlation of v with age of the cartilage. In general, values for Poisson's ratio were greater than 0.5, suggesting cartilage behavior in tension deviates from isotropy. Reported values for the Poisson's ratio of cartilage in compression have been much lower than values measured here in tension, reflecting a mechanical contribution of the collagen fibers to anisotropy in tension but not compression. The toe-region modulus (Eo) was significantly higher in the surface zone (4.51 +/- 2.78 MPa, n=8) compared to the middle zone (2.51 +/- 1.93 MPa, n=10). In addition, the linear-region modulus (E) in the surface zone, but not middle zone (3.42 +/- 2.17 MPa, n=10), was found to correlate with age (R=0.97, p<0.02) with values of surface zone E equal to 23.92 +/- 12.29 MPa (n=5) for subjects under 70 yr of age, and 4.27 +/- 2.89 MPa (n=3) for subjects over 70 yr. Moduli values and trends with depth were consistent with previous studies of human and animal cartilage. From direct measures of two independent material properties, v and E, we calculated a shear modulus, G, which had not been previously reported for cartilage from tensile testing. Calculated values for surface zone G were 3.64 +/- 1.80 MPa for subjects under 70 yr old and 0.96 +/- 0.69 MPa for subjects over 70 yr old, and were significantly higher in the surface zone than in the middle zone (1.10 +/- 0.78 MPa). This study provides an intrinsic measure for the Poisson's ratio of articular cartilage and its dependence on depth which will be important in understanding the nonlinear tension-compression and anisotropic behaviors of articular cartilage.

Microdamage accumulation in bovine trabecular bone in uniaxial compression.

Abstract: In this study we investigated how microdamage accumulated with increasing compressive strain in bovine trabecular bone. We found that little damage is created in the linear elastic region, up to -0.4 percent strain. At an average strain of -0.76 percent +/-0.25 percent, the stress-strain curve became nonlinear, and peaked at -1.91 percent +/-0.55 percent strain. Microdamage increases rapidly during the peak of the stress-strain curve, and a localized band of damage formed. At strains beyond the ultimate strain, the damaged band widened and the density of damage within the band increased. Microdamage occurred as groupings of cracks; the majority of damage occurred as regions of cross-hatching. All microdamage parameters increased with increasing maximum compressive strain. We also observed exponential relationships between crack numerical density and damage (1(o) - (o)Esec/E0) and between crack length density and damage.

Relative contribution of wall shear stress and injury in experimental intimal thickening at PTFE end-to-side arterial anastomoses.

Abstract: Background Intimal hyperplastic thickening (IHT) is a frequent cause of prosthetic bypass graft failure. Induction and progression of IHT is thought to involve a number of mechanisms related to variation in the flow field, injury and the prosthetic nature of the conduit. This study was designed to examine the relative contribution of wall shear stress and injury to the induction of IHT at defined regions of experimental end-to-side prosthetic anastomoses. Methods and results The distribution of IHT was determined at the distal end-to-side anastomosis of seven canine Iliofemoral PTFE grafts after 12 weeks of implantation. An upscaled transparent model was constructed using the in vivo anastomotic geometry, and wall shear stress was determined at 24 axial locations from laser Doppler anemometry measurements of the near wall velocity under conditions of pulsatile flow similar to that present in vivo. The distribution of IHT at the end-to-side PTFE graft was determined using computer assisted morphometry. IHT involving the native artery ranged from 0.0+/-0.1 mm to 0.05+/-0.03 mm. A greater amount of IHT was found on the graft hood (PTFE) and ranged from 0.09+/-0.06 to 0.24+/-0.06 mm. Nonlinear multivariable logistic analysis was used to model IHT as a function of the reciprocal of wall shear stress, distance from the suture line, and vascular conduit type (i.e. PTFE versus host artery). Vascular conduit type and distance from the suture line independently contributed to IHT. An inverse correlation between wall shear stress and IHT was found only for those regions located on the juxta-anastomotic PTFE graft. Conclusions The data are consistent with a model of intimal thickening in which the intimal hyperplastic pannus migrating from the suture line was enhanced by reduced levels of wall shear stress at the PTFE graft/host artery interface. Such hemodynamic modulation of injury induced IHT was absent at the neighboring artery wall.

Confined Compression of a Tissue-Equivalent: Collagen Fibril and Cell Alignment in Response to Anisotropic Strain

Abstract: A method to impose and measure a one dimensional strain field via confined compression of a tissue-equivalent and measure the resulting cell and collagen fibril alignment was developed Strain was determined locally by the displacement of polystyrene beads dispersed and entrapped within the network of collagen fibrils along with the cells, and it was correlated to the spatial variation of collagen network birefringence and concentration. Alignment of fibroblasts and smooth muscle cells was determined based on the long axis of elongated cells. Cell and collagen network alignment were observed normal to the direction of compression after a step strain and increased monotonically up to 50% strain. These results were independent of time after straining over 24 hr despite continued cell motility after responding instantly to the step strain with a change in alignment by deforming/convecting with the strained network. Since the time course of cell alignment followed that of strain and not stress which, due to the viscoelastic fluid-like nature of the network relaxes completely within the observation period, these results imply cell alignment in a compacting tissue-equivalent is due to fibril alignment associated with anisotropic network strain. Estimation of a contact guidance sensitivity parameter indicates that both cell types align to a greater extent than the surrounding fibrils.

Non-linear characteristics in the dynamic responses of seated subjects exposed to vertical whole-body vibration.

Abstract: The effect of the magnitude of vertical vibration on the dynamic response of the seated human body has been investigated. Eight male subjects were exposed to random vibration in the 0.5 to 20 Hz frequency range at five magnitudes: 0.125, 0.25, 0.5, 1.0 and 2.0 ms(-2) r.m.s. The dynamic responses of the body were measured at eight locations: at the first, fifth, and tenth thoracic vertebrae (T1, T5, T10), at the first, third, and fifth lumbar vertebrae (L1, L3, L5) and at the pelvis (the posterior-superior iliac spine). At each location, the motions on the body surface were measured in the three orthogonal axes within the sagittal plane (i.e., the vertical, fore-and-aft, and pitch axes). The force at the seat surface was also measured. Frequency response functions (i.e., transmissibilities and apparent mass) were used to represent the responses of the body. Non-linear characteristics were observed in the apparent mass and in the transmissibilities to most measurement locations. Resonance frequencies in the frequency response functions decreased with increases in the vibration magnitude (e.g. for the vertical transmissibility to L3, a reduction from 6.25 to 4.75 Hz when the vibration magnitude increased from 0.125 to 2.0 ms(-2) r.m.s.). The transmission of vibration within the spine also showed some evidence of a non-linear characteristic. It can be concluded from this study that the dynamic responses of seated subjects are clearly non-linear with respect to vibration magnitude, whereas previous studies have reported inconsistent conclusions. More understanding of the dependence on vibration magnitude of both the dynamic responses of the soft tissues of the body and the muscle activity (voluntary and involuntary) is required to identify the causes of the non-linear characteristics observed in this study.

Simulation of progressive deformities in adolescent idiopathic scoliosis using a biomechanical model integrating vertebral growth modulation.

Abstract: While the etiology and pathogenesis of adolescent idiopathic scoliosis are still not well understood, it is generally recognized that it progresses within a biomechanical process involving asymmetrical loading of the spine and vertebral growth modulation. This study intends to develop a finite element model incorporating vertebral growth and growth modulation in order to represent the progression of scoliotic deformities. The biomechanical model was based on experimental and clinical observations, and was formulated with variables integrating a biomechanical stimulus of growth modulation along directions perpendicular (x) and parallel (y, z) to the growth plates, a sensitivity factor beta to that stimulus and time. It was integrated into a finite element model of the thoracic and lumbar spine, which was personalized to the geometry of a female subject without spinal deformity. An imbalance of 2 mm in the right direction at the 8th thoracic vertebra was imposed and two simulations were performed: one with only growth modulation perpendicular to growth plates (Sim1), and the other one with additional components in the transverse plane (Sim2). Semi-quantitative characterization of the scoliotic deformities at each growth cycle was made using regional scoliotic descriptors (thoracic Cobb angle and kyphosis) and local scoliotic descriptors (wedging angle and axial rotation of the thoracic apical vertebra). In all simulations, spinal profiles corresponded to clinically observable configurations. The Cobb angle increased non-linearly from 0.3 degree to 34 degrees (Sim1) and 20 degrees (Sim2) from the first to last growth cycle, adequately reproducing the amplifying thoracic scoliotic curve. The sagittal thoracic profile (kyphosis) remained quite constant. Similarly to clinical and experimental observations, vertebral wedging angle of the thoracic apex progressed from 2.6 degrees to 10.7 degrees (Sim1) and 7.8 degrees (Sim2) with curve progression. Concomitantly, vertebral rotation of the thoracic apex increased of 10 degrees (Sim1) and 6 degrees (Sim2) clockwise, adequately reproducing the evolution of axial rotation reported in several studies. Similar trends but of lesser magnitude (Sim2) suggests that growth modulation parallel to growth plates tend to counteract the growth modulation effects in longitudinal direction. Overall, the developed model adequately represents the self-sustaining progression of vertebral and spinal scoliotic deformities. This study demonstrates the feasibility of the modeling approach, and compared to other biomechanical studies of scoliosis it achieves a more complete representation of the scoliotic spine.

A three-dimensional finite element model for arterial clamping.

Abstract: Clamp induced injuries of the arterial wall may determine the outcome of surgical procedures. Thus, it is important to investigate the underlying mechanical effects. We present a three-dimensional finite element model, which allows the study of the mechanical response of an artery-treated as a two-layer tube-during arterial clamping. The important residual stresses, which are associated with the load-free configuration of the artery, are also considered. In particular, the finite element analysis of the deformation process of a clamped artery and the associated stress distribution is presented. Within the clamping area a zone of axial tensile peak-stresses was identified, which (may) cause intimal and medial injury. This is an additional injury mechanism, which clearly differs from the commonly assumed wall damage occurring due to compression between the jaws of the clamp. The proposed numerical model provides essential insights into the mechanics of the clamping procedure and the associated injury mechanisms. It allows detailed parameter studies on a virtual clamped artery, which can not be performed with other methodologies. This approach has the potential to identify the most appropriate clamps for certain types of arteries and to guide optimal clamp design.

Multiphase mechanics of capsule formation in tumors.

Abstract: The presence of a capsule around a tumor is known to be correlated with benign status, and the absence of a capsule often has negative implications for patient prognosis. A mechanical description is presented of the growth of a tumor and the resulting deformations of surrounding normal tissue. A mathematical model of the mechanics is analyzed using physical parameters measured in vivo and in vitro. The model has only three dimensionless parameters, and its results are very robust with respect to parameter variation. We show that the presence of contractility in the surrounding tissue, corresponding to a host defense, can make an existing capsule denser and constrain the tumor better, but cannot be responsible for the observed pressure gradients in encapsulated tumors. Some implications for treatment are discussed.

The mechanical advantage of local longitudinal shortening on peristaltic transport.

Abstract: Whereas bolus transport along the esophagus results from peristaltic contractions of the circular muscle layer, it has been suggested that local shortening of the longitudinal muscle layer concentrates circular muscle fibers in the region where the highest contractile pressures are required. Here we analyze the mechanical consequences of local longitudinal shortening (LLS) through a mathematical model based on lubrication theory. We find that local pressure and shear stress in the contraction zone are greatly reduced by the existence of LLS. In consequence, peak contractile pressure is reduced by nearly 2/3 at physiological LLS, and this reduction is greatest when peak in LLS is well aligned with peak contractile pressure. We conclude that a peristaltic wave of local longitudinal muscle contraction coordinated with the circular muscle contraction wave has both a great physiological advantage (concentrating circular muscle fibers), and a great mechanical advantage (reducing the level of contractile force required to transport the bolus), which combine to greatly reduce circular muscle tone during esophageal peristalsis.

An axisymmetric boundary integral model for assessing elastic cell properties in the micropipette aspiration contact problem.

Abstract: The micropipette aspiration technique has been used extensively in recent years to measure the mechanical properties of living cells. In the present study, a boundary integral formulation with quadratic elements is used to predict the elastic equilibrium response in the micropipette aspiration contact problem for a three-dimensional incompressible spherical continuum cell model (Young's modulus E). In contrast to the halfspace model, the spherical cell model accounts for nonlinearities in the cell response which result from a consideration of geometric factors including the finite cell dimension (radius R), curvature of the cell boundary, evolution of the cell-micropipette contact region and curvature of the edges of the micropipette (inner radius a, edge curvature radius epsilon). The efficiency of the boundary element method facilitates the quantification of cell response as a function of the scaled pressure p/E, for the range of parameters a/R = 0.4-0.7, epsilon/a = 0.02-0.08, in terms of two measures that can be quantified using video microscopy. These are the aspiration length, which measures projection of the cell into the micropipette, and a characteristic strain, which measures stretching along the symmetry axis. For both measures of cell response, the resistance to aspiration is found to decrease with increasing values of the aspect ratio a/R and curvature parameter epsilon/a, and the nonlinearities in the cell response are most pronounced in the earlier portion of the aspiration test. The aspiration length is found to exhibit less sensitivity to the aspect ratio a/R than to the curvature parameter epsilon/a, whereas the characteristic strain, which provides a more realistic measure of overall cell stiffness, exhibits sensitivity to the aspect ratio a/R. The resistance to aspiration in the spherical cell model is initially less than that of the half space model but eventually exceeds the halfspace prediction and the deviation between the two models increases as the parameter epsilon/a decreases. Adjustment factors for the Young's modulus E, as predicted by the halfspace model, are presented and the deviation from the spherical cell model is found to be as large as 35%, when measured locally on the response curve. In practice, the deviation will be less than the maximum figure but its precise value will depend on the number of data points available in the experiment and the specific curve-fitting procedure. The spherical cell model allows for efficient and more realistic simulations of the micropipette aspiration contact problem and quantifies two observable measures of cell response that, using video microscopy, can facilitate the determination of Young's modulus for various cell populations while, simultaneously, providing a means of evaluating the validity of continuum cell models. Furthermore, this numerical model may be readily extended to account for more complex geometries, inhomogeneities in cellular properties, or more complex constitutive descriptions of the cell.