J Biomech Eng. 2000;123(1):1-9. doi:10.1115/1.1338122.

Study of the behavior of trabecular bone at strains below 0.40 percent is of clinical and biomechanical importance. The goal of this work was to characterize, with respect to anatomic site, loading mode, and apparent density, the subtle concave downward stress–strain nonlinearity that has been observed recently for trabecular bone at these strains. Using protocols designed to minimize end-artifacts, 155 cylindrical cores from human vertebrae, proximal tibiae, proximal femora, and bovine proximal tibiae were mechanically tested to yield at 0.50 percent strain per second in tension or compression. The nonlinearity was quantified by the reduction in tangent modulus at 0.20 percent and 0.40 percent strain as compared to the initial modulus. For the pooled data, the mean±SD percentage reduction in tangent modulus at 0.20 percent strain was 9.07±3.24 percent in compression and 13.8±4.79 percent in tension. At 0.40 percent strain, these values were 23.5±5.71 and 35.7±7.10 percent, respectively. The magnitude of the nonlinearity depended on both anatomic site (p<0.001) and loading mode (p<0.001), and in tension was positively correlated with density. Calculated values of elastic modulus and yield properties depended on the strain range chosen to define modulus via a linear curve fit (p<0.005). Mean percent differences in 0.20 percent offset yield strains were as large as 10.65 percent for some human sites. These results establish that trabecular bone exhibits nonlinearity at low strains, and that this behavior can confound intersite comparisons of mechanical properties. A nonlinear characterization of the small strain behavior of trabecular bone was introduced to characterize the initial stress–strain behavior more thoroughly.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;123(1):10-17. doi:10.1115/1.1338123.

The role of osteocyte lacunar size and density on the apparent stiffness of bone matrix was predicted using a mechanical model from the literature. Lacunar size and lacunar density for different bones from different gender and age groups were used to predict the range of matrix apparent stiffness values for human cortical and cancellous tissue. The results suggest that bone matrix apparent stiffness depends on tissue type (cortical versus cancellous), age, and gender, the magnitudes of the effects being significant but small in all cases. Males had a higher predicted matrix apparent stiffness than females for vertebral cancellous bone p<10−7)and the difference increased with age (p=0.0007). In contrast, matrix apparent stiffness was not different between males and females for femoral cortical bone and increased with age in both males (p<0.0001) and females (p<0.0364). Osteocyte lacunar density and size may cause significant gender and age-related variations in bone matrix apparent stiffness. The magnitude of variations in matrix apparent stiffness was small within the physiological range of lacunar size and density for healthy bone, whereas the variations can be profound in certain pathological cases. It was proposed that the mechanical effects of osteocyte density be uncoupled from their biological effects by controlling lacunar size in normal bone.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;123(1):18-26. doi:10.1115/1.1339819.

Measurements of the sagittal profiles of the articular surfaces of 24 femoral condyles were performed using a laser range finder. An algebraic algorithm was developed to reconstruct the measured sagittal profiles with simple geometry. In particular, it has been shown that a two-circular-arc model provides a very accurate reconstruction of the actual profiles in the femorotibial contact region. The average sagittal profile was used for a femorotibial contact analysis of TKA implants. The contact analysis was performed by using a rigid-body-spring model extended to the case of nonlinear force-deformation behavior of the tibial polyethylene component.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;123(1):27-32. doi:10.1115/1.1336798.

This study quantified the relationships between local dynamic stability and variability during continuous overground and treadmill walking. Stride-to-stride standard deviations were computed from temporal and kinematic data. Maximum finite-time Lyapunov exponents were estimated to quantify local dynamic stability. Local stability of gait kinematics was shown to be achieved over multiple consecutive strides. Traditional measures of variability poorly predicted local stability. Treadmill walking was associated with significant changes in both variability and local stability. Thus, motorized treadmills may produce misleading or erroneous results in situations where changes in neuromuscular control are likely to affect the variability and/or stability of locomotion.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;123(1):33-39. doi:10.1115/1.1336799.

This paper deals with the analysis of experimental data obtained using an ergometer apparatus. A straightforward analysis method based on the power equation and the concept of generalized torques is presented. This method makes it possible to study the influence of the net muscle joint torques and gravity and inertia forces on the crank torque. The assumptions and limitations of the proposed method are discussed and this method is compared with the methods of analysis proposed by other researchers. In order to assess the validity of the method, some experimental data are elaborated. Results show that the method can highlight the effect of training and the pedaling technique of an athlete.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;123(1):40-46. doi:10.1115/1.1338121.

The inherent dynamics of bipedal, kneed mechanisms are studied with emphasis on the existence and stability of repetitive gait in a three-dimensional environment, in the absence of external, active control. The investigation is motivated by observations that sustained anthropomorphic locomotion is largely a consequence of geometric and inertial properties of the mechanism. While the modeling excludes active control, the energy dissipated in ground and knee collisions is continuously re-injected by considering gait down slight inclines. The paper describes the dependence of the resulting passive gait in vertically constrained and unconstrained mechanisms on model parameters, such as ground compliance and ground slope. We also show the possibility of achieving statically unstable gait with appropriate parameter choices.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;123(1):47-51. doi:10.1115/1.1339816.

A methodology was developed for determining the compressive properties of the supraspinatus tendon, based on finite element principles. Simplified three-dimensional models were created based on anatomical thickness measurements of unloaded supraspinatus tendons over 15 points. The tendon material was characterized as a composite structure of longitudinally arranged collagen fibers within an extrafibrillar matrix. The matrix was formulated as a hyperelastic material described by the Ogden form of the strain energy potential. The hyperelastic material parameters were parametrically manipulated until the analytical load-displacement results were similar to the results obtained from indentation testing. In the geometrically averaged tendon, the average ratio of experimental to theoretical maximum indentation displacement was 1.00 (SD: 0.01). The average normalization of residuals was 2.1g (SD: 0.9g). Therefore, the compressive material properties of the supraspinatus tendon extrafibrillar matrix were adequately derived with a first-order hyperelastic formulation. The initial compressive elastic modulus ranged from 0.024 to 0.090 MPa over the tendon surface and increased nonlinearly with additional compression. Using these material properties, the stresses induced during acromional impingement can be analyzed.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;123(1):52-57. doi:10.1115/1.1339817.

A biphasic, anisotropic elastic model of the aortic wall is developed and compared to literature values of experimental measurements of vessel wall radii, thickness, and hydraulic conductivity as a function of intraluminal pressure. The model gives good predictions using a constant wall modulus for pressures less than 60 mmHg, but requires a strain-dependent modulus for pressures greater than this. In both bovine and rabbit aorta, the tangential modulus is found to be approximately 20 times greater than the radial modulus. These moduli lead to predictions that, when perfused in a cylindrical geometry, the aortic volume and its specific hydraulic conductivity are relatively independent of perfusion pressure, in agreement with experimental measurements. M, the parameter that relates specific hydraulic conductivity to tissue dilation, is found to be a positive quantity correcting a previous error in the literature.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;123(1):58-65. doi:10.1115/1.1336143.

The topic of this study mainly concerns a representative model of the behavior of flexible ducts such as elastic tubes or veins. This model is based on a phenomenological approach of the inflation and collapse of the tube. It leads to a single “universal” analytical expression of the tube law, valid for a wide range of positive and negative transmural pressures, which presents a significant improvement compared to previous theoretical studies defined with different expressions on restricted ranges of pressure. Moreover, the theoretical approaches most often require simplifying hypotheses—no longitudinal tension, no surrounding tissues—which are quite unrealistic both in the physiological case and in the experimental setup. These theoretical models can therefore be expected only roughly to describe the actual behavior of such vessels. The representative model, on the contrary, allows one to account for the deformation—inflating as well as collapse—of elastic tubes or veins with better accuracy. The tube law is a function of six parameters chosen in order to fit the experimental data. A comparison between results obtained in our laboratory using silicone tubes and representative models is presented. The model is then applied to physiological data obtained in vivo on human leg veins.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;123(1):66-70. doi:10.1115/1.1336796.

Bone is a very dynamic tissue capable of modifying its composition, microstructure, and overall geometry in response to the changing biomechanical needs. Streaming potential has been hypothesized as a mechanotransduction mechanism that may allow osteocytes to sense their biomechanical environment. A correct understanding of the mechanism for streaming potential will illuminate our understanding of bone remodeling, such as the remodeling associated with exercise hypertrophy, disuse atrophy, and the bone remodeling around implants. In the current research, a numerical model based on the finite element discretization is proposed to simulate the fluid flows through the complicated hierarchical flow system and to calculate the concomitant stress generated potential (SGP) as a result of applied mechanical loading. The lacunae–canaliculi and the matrix microporosity are modeled together as discrete one-dimensional flow channels superposed in a biphasic poroelastic matrix. The cusplike electric potential distribution surrounding the Haversian canal that was experimentally observed and reported in the literature earlier was successfully reproduced by the current numerical calculation.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;123(1):71-79. doi:10.1115/1.1336144.

The fluid that resides within cranial and spinal cavities, cerebrospinal fluid (CSF), moves in a pulsatile fashion to and from the cranial cavity. This motion can be measured by magnetic resonance imaging (MRI) and may be of clinical importance in the diagnosis of several brain and spinal cord disorders such as hydrocephalus, Chiari malformation, and syringomyelia. In the present work, a geometric and hydrodynamic characterization of an anatomically relevant spinal canal model is presented. We found that inertial effects dominate the flow field under normal physiological flow rates. Along the length of the spinal canal, hydraulic diameter was found to vary significantly from 5 to 15 mm. The instantaneous Reynolds number at peak flow rate ranged from 150 to 450, and the Womersley number ranged from 5 to 17. Pulsatile flow calculations are presented for an idealized geometric representation of the spinal cavity. A linearized Navier–Stokes model of the pulsatile CSF flow was constructed based on MRI flow rate measurements taken on a healthy volunteer. The numerical model was employed to investigate effects of cross-sectional geometry and spinal cord motion on unsteady velocity, shear stress, and pressure gradient fields. The velocity field was shown to be blunt, due to the inertial character of the flow, with velocity peaks located near the boundaries of the spinal canal rather than at the midpoint between boundaries. The pressure gradient waveform was found to be almost exclusively dependent on the flow waveform and cross-sectional area. Characterization of the CSF dynamics in normal and diseased states may be important in understanding the pathophysiology of CSF related disorders. Flow models coupled with MRI flow measurements may become a noninvasive tool to explain the abnormal dynamics of CSF in related brain disorders as well as to determine concentration and local distribution of drugs delivered into the CSF space.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;123(1):80-87. doi:10.1115/1.1336145.

Various hemodynamic factors have been implicated in vascular graft intimal hyperplasia, the major mechanism contributing to chronic failure of small-diameter grafts. However, a thorough knowledge of the graft flow field is needed in order to determine the role of hemodynamics and how these factors affect the underlying biological processes. Computational fluid dynamics offers much more versatility and resolution than in vitro or in vivo methods, yet computations must be validated by careful comparison with experimental data. Whereas numerous numerical and in vitro simulations of arterial geometries have been reported, direct point-by-point comparisons of the two techniques are rare in the literature. We have conducted finite element computational analyses for a model of an end-to-side vascular graft and compared the results with experimental data obtained using laser-Doppler velocimetry. Agreement for velocity profiles is found to be good, with some clear differences near the recirculation zones during the deceleration and reverse-flow segments of the flow waveform. Wall shear stresses are determined from velocity gradients, whether by computational or experimental methods, and hence the agreement for this quantity, while still good, is less consistent than for velocity itself. From the wall shear stress numerical results, we computed four variables that have been cited in the development of intimal hyperplasia—the time-averaged wall shear stress, an oscillating shear index, and spatial and temporal wall shear stress gradients—in order to illustrate the versatility of numerical methods. We conclude that the computational approach is a valid alternative to the experimental approach for quantitative hemodynamic studies. Where differences in velocity were found by the two methods, it was generally attributed to the inability of the numerical method to model the fluid dynamics when flow conditions are destabilizing. Differences in wall shear, in the absence of destabilizing phenomena, were more likely to be caused by difficulties in calculating wall shear from relatively low resolution in vitro data.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;123(1):88-96. doi:10.1115/1.1339818.

Blood flow in arteries often shows a rich variety of vortical flows, which are dominated by the complex geometry of blood vessels, the dynamic pulsation of blood flow, and the complicated boundary conditions. With a two-dimensional model of unsteady flow in a stenosed channel, the pulsatile influence on such vortical fluid dynamics has been numerically studied in terms of waveform dependence on physiological pulsation. Results are presented for unsteady flows downstream of the stenosed portion with variation in the waveforms of systole and diastole. Overall, a train of propagating vortex waves is observed for all the cases, but it shows great sensitivity to the waveforms. The generation and development of the vortex waves may be linked to the presence of an adverse pressure gradient within a specific interval between two points of inflection of the systolic waveform. The adverse pressure gradient consists of a global pressure gradient that is found to be closely related to the dynamics of the pulsation, and a local pressure gradient, which is observed to be dominated by the nonlinear vortex dynamics.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;123(1):97-105. doi:10.1115/1.1338120.

This study examined the fluid dynamics of a textured blood-contacting surface using a computational fluid-dynamic modeling technique. The texture consisted of a regular array of microfibers of length 50 or 100 μm, spaced 100 μm apart, projecting perpendicularly to the surface. The results showed that the surface texture served as a flow-retarding solid boundary for a laminar viscous flow, resulting in a lowered wall shear stress on the base-plane surface. However, the maximum wall shear stress on the fibers was much higher than the shear stress on the nontextured base plane. At all fractions of fiber height down past 10 μm, the permeability of the textured region greatly exceeded the analytically predictable permeability of an equivalent array of infinite-height fibers. The lowered surface shear stress appears to explain in part the enhanced deposition of formed blood elements on the textured surface.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;123(1):106-113. doi:10.1115/1.1336146.

We have previously developed an adsorption-limited model to describe the exchange of lung surfactant and its fractions to and from an air–liquid interface in oscillatory surfactometers. Here we extend this model to allow for diffusion in the liquid phase. Use of the model in conjunction with experimental data in the literature shows that diffusion-limited transport is important for characterizing the transient period from the start of oscillations to the achievement of steady-state conditions. Matching previous data shows that upon high levels of film compression, large changes occur in adsorption rate, desorption rate, and diffusion constant, consistent with what one might expect if the subsurface region was greatly enriched in DPPC. Collapse of the surfactant film that occurs during compression leads to a significant elevation of surfactant concentration immediately beneath the interface, consistent with the subsurface depot of surfactant that has been postulated by other investigators. Modeling studies also uncovered a phenomenon of surfactant behavior in which the interfacial tension remains constant at its minimum equilibrium value while the film is compressed, but without collapse of the film. The phenomenon was due to desorption of surfactant from the interface and termed “pseudo-film collapse.” The new model also gave improved agreement with steady-state oscillatory cycling in a pulsating bubble surfactometer.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;123(1):114-120. doi:10.1115/1.1336147.

The Wissler human thermoregulation model was augmented to incorporate simulation of a space suit thermal control system that includes interaction with a liquid cooled garment (LCG) and ventilation gas flow through the suit. The model was utilized in the design process of an automatic controller intended to maintain thermal neutrality of an exercising subject wearing a liquid cooling garment. An experimental apparatus was designed and built to test the efficacy of specific physiological state measurements to provide feedback data for input to the automatic control algorithm. Control of the coolant inlet temperature to the LCG was based on evaluation of transient physiological parameters that describe the thermal state of the subject, including metabolic rate, skin temperatures, and core temperature. Experimental evaluation of the control algorithm function was accomplished in an environmental chamber under conditions that simulated the thermal environment of a space suit and transient metabolic work loads typical of astronaut extravehicular activity (EVA). The model was also applied to analyze experiments to evaluate performance of the automatic control system in maintaining thermal comfort during extensive transient metabolic profiles for a range of environmental temperatures. Finally, the model was used to predict the efficacy of the LCG thermal controller for providing thermal comfort for a variety of regimens that may be encountered in future space missions. Simulations with the Wissler model accurately predicted the thermal interaction between the subject and LCG for a wide range of metabolic profiles and environmental conditions and matched the function of the automatic temperature controller for inlet cooling water to the LCG.

Commentary by Dr. Valentin Fuster

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