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TECHNICAL PAPERS

J Biomech Eng. 1997;119(1):1-5. doi:10.1115/1.2796059.

The experimental and analytical methods presented in the companion paper [1] are used here to study the effects of cryopreservation on the in vitro biaxial random-elastic mechanical properties of canine saphenous veins. The properties of specimens tested in their physiological range of loadings immediately after thawing were not significantly different from their properties before cryopreservation. However, they stiffened significantly in the few hours following thawing. This effect was not observed for aging fresh specimens, nor for cyanide-poisoned specimens, indicating that the static tone of the venous smooth muscle may be affected by cryopreservation and thawing, but the elastin and collagen fibers are most likely unaffected.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(1):6-12. doi:10.1115/1.2796067.

We investigated whether strain softening (or the Mullins effect) may explain the reduced left ventricular stiffness previously associated with the strain-history-dependent preconditioning phenomenon. Passive pressure–volume relations were measured in the isolated, arrested rat heart during LV balloon inflation and deflation cycles. With inflation to a new higher maximum pressure, the pressure–volume relation became less stiff, particularly in the low (diastolic) pressure range, without a significant change in unloaded ventricular volume. In five different loading protocols in which the maximum passive cycle pressure ranged from 10 to 120 mmHg, we measured increases at 10 mmHg in LV volume up to 350 percent of unloaded volume that depended significantly on the history (p < 0.05) and magnitude (p < 0.01) of maximum previous pressure. Although a quasi-linear viscoelastic model based on the pressure-relaxation response could produce a nonlinear pressure–volume relation with hysteresis, it was unable to show any significant change in ventricular stiffness with new maximum pressure. We incorporated a strain softening theory proposed by Johnson and Beatty (1992) into the model by modifying the elastic response with a volume-amplification factor that depended on the maximum previous pressure. This model more accurately reproduced the experimentally observed behavior. Thus, the preconditioning behavior of the myocardium is better explained by strain softening rather than viscoelasticity and may be due to damage to elastic components, rather than the effects of viscous tissue components.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(1):13-19. doi:10.1115/1.2796058.

Flow patterns generated during ventricular filling have been investigated for three different combinations of flow rate and injection volume. The numerical solutions from a commercially available computational fluid dynamics package were compared with observations made under identical flow conditions in a physical model for the purpose of code validation. Particle pathlines were generated from the numerical velocity data and compared with corresponding flow-visualization pictures. A vortex formed at the inlet to the ventricle in both cases: During the filling phase, the vortex expanded and traveled toward the apex of the ventricle until, at the end of filling, the vortex occupied the full radial extent of the ventricle; the vortex continued to travel once the filling process had ended. The vortices in vitro were more circular in shape and occupied a smaller volume than those generated by the numerical model. Nevertheless, comparison of the trajectories of the vortex centres showed that there was good agreement for the three conditions studied. Postprocessing of velocity data from the numerical solution yielded wall shear-stress measurements and particle pathlines that clearly illustrate the mass-transport qualities of the traveling vortex structure. For the cases considered here, the vortex transit produced a time-dependent shear stress distribution that had a peak value of 20 dynes cm−2 , with substantially lower levels of shear stress in those regions not reached by the traveling vortex. We suggest that vortex formation and travel could reduce the residence time of fluid within a skeletal muscle ventricle, provided that the vortex travels the complete length of the ventricle before fluid is ejected at the start of the next cycle.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(1):20-29. doi:10.1115/1.2796060.

This paper investigates mathematical relations between models of calcium activation kinetics and Huxley-type models of cross-bridge dynamics in muscle. It is found that different calcium-activation schemes lead to the same form of generalized Huxley rate equation with calcium activation

(∂n/∂t) − v (∂n/∂x) = rf(α − n) − gn
if it is assumed that calcium–troponin interaction rates are fast compared to the rates of transition associated with force-generating cross-bridge states. Calcium affects cross-bridge dynamics by modifying the bonding rate f, but does not affect the number of interacting cross bridges α or the unbonding rate g; this occurs through the appearance in the equation of an activation factor, r, which is a pure function of sarcoplasmic free calcium concentration. In particular, it is shown that both the “tight-coupling” and “loose-coupling” calcium-activation schemes introduced by Zahalak and Ma [1] lead to the same rate equation with the same activation factor; the difference between them appears in the calcium mass-balance equation. While both of these activation models can be made to fit simple twitch and force-velocity data equally well, experimentally observed load-dependent shifts in the free calcium concentration are compatible with the tight-coupling scheme, but not with loose coupling.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(1):30-38. doi:10.1115/1.2796061.

In-vivo velocity profiles were recorded with a 20 MHz, 80-channel pulsed Doppler ultrasound velocimeter in canine end-to-side ilio-femoral anastomotic grafts. The geometries were obtained from casts of the anastomotic region, and flow rates were measured with electromagnetic flow probes. Three cases reported here include a “standard” geometry, which was similar to previously studied in vitro models, a stenosed geometry, and a case with below average flow rate. Observed flow features include separation at the hood and toe, movement of the floor stagnation point, and skewed profiles in the proximal outflow segment. Out-of-plane curvature and lateral displacement of the anastomosis inlet appear to have a strong effect on the flow fields. In addition, compliance affects the instantaneous flow rates within the proximal and distal branches.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(1):39-44. doi:10.1115/1.2796062.

The flow (Q) through regurgitant valves may be quantified by multiplying the area of an isovelocity contour (isovel) by its velocity. This was tested computationally and experimentally (using MRI), Q = 14 to 141 ml/s, using flat and conical orifice plates. Plotting Q versus isovelocity radius, a plateau was found which, for low flow, corresponded to the true Q. At higher flow or large confinement, Q was overestimated. For conical plates, angle correction worked at low Q but not at higher values due to the formation of separation regions. These converted the cone plate into a flat plate. MRI produced similar results at 57 ml/s in that Q was correct with no angle correction. At low flow, MRI was too noisy to produce a clear plateau consistently.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(1):45-51. doi:10.1115/1.2796063.

Laminar vortical flow around a fully opened Björk–Shiley valve in an aorta is obtained by solving the three-dimensional incompressible Navier–Stokes equations. Used is a noniterative implicit finite-element Navier–Stokes code developed by the authors, which makes use of the well-known finite difference algorithm PISO. The code utilizes segregated formulation and efficient iterative matrix solvers such as PCGS and ICCG. Computational results show that the three-dimensional vortical flow is recirculating with large shear in the sinus region of the valve chamber. Passing through the valve, the flow is split into major upper and lower jet flows. The spiral vortices generated by the disk are advected in the wake and attenuated rapidly downstream by diffusion. It is shown also that the shear stress becomes maximum near the leading edge of the disk valve.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(1):52-58. doi:10.1115/1.2796064.

Steady inspiratory and expiratory flow in a symmetrically bifurcating airway model was studied numerically using the finite element method (FIDAP). Flows of Reynolds number of 500 and 1000 during inspiration and a flow of Reynolds number of 500 during expiration were analyzed. Since the geometry of the bifurcation model used in this study is exactly the same as the model used in the experimental studies, the computed results were compared to the experimental findings. Results show that most of the important flow features that were observed in the experiment, such as the skewed velocity profiles in the daughter branches during inspiration and velocity peak in the parent tube during expiration, were captured in the numerical simulation. Quantitatively, the computed velocity profiles are in good agreement with the measured profiles. This comparison validates the computational simulations.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(1):59-65. doi:10.1115/1.2796065.

Two-dimensional steady inspiratory airflow through a three-generation model of the human central airways is numerically investigated, with dimensions corresponding to those encountered in the fifth to seventh generations of the Weibel’s model. Wall curvatures are added at the outer walls of the junctions for physiological purposes. Computations are carried out for Reynolds numbers in the mother branch ranging from 200 to 1200, which correspond to mouth air breathing at flow rates ranging from 0.27 to 1.63 liters per second. The difficulty of generating grids in a so complex configuration is overcome using a nonoverlapping multiblock technique. Simulations demonstrate the existence of separation regions whose number, location, and size strongly depend on the Reynolds number. Consequently, four different flow configurations are detected. Velocity profiles downstream of the bifurcations are shown to be highly skewed, thus leading to an important unbalance in the flow distribution between the medial and lateral branches of the model. These results confirm the observations of Snyder et al. and Tsuda et al. and suggest that a resistance model of flow partitioning based on Kirchhoff’s laws is inadequate to simulate the flow behavior accurately within the airways. When plotted in a Moody diagram, airway resistance throughout the model is shown to fit with a linear relation of slope −0.61. This is qualitatively in good agreement with the experimental investigations of Pedley et al. and Slutsky et al.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(1):66-76. doi:10.1115/1.2796066.

A model for the coupled problem of wall deformation and fluid flow, based on thin-shell and lubrication theories, and driven by a propagating wave of smooth muscle activation, is proposed for peristaltic pumping in the ureter. The model makes use of the available experimental data on the mechanical properties of smooth muscle and accounts for the soft material between the muscle layer and the vessel lumen. The main input is the activation wave of muscular contraction. Equations for the time-dependent problem in tubes of arbitrary length are derived and applied to the particular case of periodic activation waves in an infinite tube. Mathematical (small amplitude) and numerical analyses of this case are presented. Predictions on phase-lag in wall constriction with respect to peak activation wave, lumen occlusion due to thickening lumen material with contracting smooth muscle, and the general bolus shape are in qualitative agreement with observation. Some modifications to the mechanical, elastic, and hydrodynamic properties of the ureter that will make peristalsis less efficient, due for example to disease, are identified. In particular, the flow rate-pressure rise relationship is linear for weak to moderate activation waves, but as the lumen is squeezed shut, it is seen to be nonlinear in a way that increases pumping efficiency. In every case a ureter whose lumen can theoretically be squeezed shut is the one for which pumping is most efficient.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(1):77-80. doi:10.1115/1.2796068.

Design criteria for implantable, heat-generating devices such as the total artificial heart require the determination of safe thresholds for chronic heating. This involves in-vivo experiments in which tissue temperature distributions are obtained in response to known heat sources. Prior to experimental studies, simulation using a mathematical model can help optimize the design of experiments. In this paper, a theoretical analysis of heat transfer is presented that describes the dynamic, one-dimensional distribution of temperature from a heated surface. Loss of heat by perfusion is represented by temperature-independent and temperature-dependent terms that can reflect changes in local control of blood flow. Model simulations using physiologically appropriate parameter values indicate that the temperature elevation profile caused by a heated surface adjacent to tissue may extend several centimeters into the tissue. Furthermore, sensitivity analysis indicates the conditions under which temperature profiles are sensitive to changes in thermal diffusivity and perfusion parameters. This information provides the basis for estimation of model parameters in different tissues and for prediction of the thermal responses of these tissues.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(1):81-86. doi:10.1115/1.2796069.

A theoretical boundary friction model is proposed for predicting the frictional behavior of articular cartilage, including its time-dependent, velocity-dependent, and load-dependent responses. This theoretical model uses the framework of the biphasic theory for articular cartilage, and provides a mathematical formulation for the principle that interstitial fluid pressurization contributes significantly to reduction of the effective friction coefficient. Several examples of the application of this theory are provided, which demonstrate that a variety of experimentally observed cartilage frictional behaviors can now be theoretically predicted.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(1):87-92. doi:10.1115/1.2796070.

In this study, a three-dimensional finite element model of the human lower cervical spine (C4-C6) was constructed. The mathematical model was based on close-up CT scans from a young human cadaver. Cortical shell, cancellous core, endplates, and posterior elements including the lateral masses, pedicle, lamina, and transverse and spinous processes, and the intervertebral disks, were simulated. Using the material properties from literature, the 10,371-element model was exercised under an axial compressive mode of loading. The finite element model response agreed with literature. As a logical step, a parametric study was conducted by evaluating the biomechanical response secondary to changes in the elastic moduli of the intervertebral disk and the endplates. In the stress analysis, the minimum principal compressive stress was used for the cancellous core of the vertebral body and von Mises stress was used for the endplate component. The model output indicated that an increase in the elastic modulii of the disk resulted in an increase in the endplate stresses at all the three spinal levels. In addition, the inferior endplate of the middle vertebral body responded with the highest mean compressive stress followed by its superior counterpart. Furthermore, the middle vertebral body produced the highest compressive stresses compared to its counterparts. These findings appear to correlate with experimental results as well as common clinical experience wherein cervical fractures are induced due to external compressive forces. As a first step, this model will lead to more advanced simulations as additional data become available.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(1):93-102. doi:10.1115/1.2796071.

A simplified model of the mechanical properties of muscle and of the musculoskeletal geometry was used to predict torques at the shoulder and elbow during arm movements in the sagittal plane. Subjects made movements to 20 targets spaced on the diameter of a circle centered on the initial location of the hand. Movement kinematics and the electromyographic (EMG) activity of nine shoulder and elbow muscles were recorded. Muscle force was predicted using rectified EMG activity as an input to a Hill-type model of muscle dynamics. The model also made simplifying assumptions about muscle geometry. Muscle force was then converted to torque and the individual muscle torques were weighted to provide the best fit to the joint torque computed from the kinematic data. The overall fit of the model was reasonably good, but the goodness of fit was not uniform over all movement directions. The results suggest that the assumptions about the musculo-skeletal geometry, the model of muscle dynamics, and muscles not included in the analysis all contributed to the error.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(1):103-108. doi:10.1115/1.2796051.

The role that intertrabecular contents and their boundary conditions have on the dynamic mechanical response of canine femoral heads was investigated in vivo. Femoral heads from paired intact hind limbs of canine specimens were subjected to a sinusoidal strain excitation, at physiologic frequencies, in the cranio-caudal direction. The fluid boundary conditions for the contralateral limbs were changed by predrilling through the lateral femoral cortex and into the femoral neck. The drilling procedure did not invade the head itself. This femoral head fluid boundary alteration reduced the stiffness by 19 percent for testing at 1 Hz. The results of this study demonstrate that fluid stiffening occurs in vivo as previously observed ex vivo.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(1):109-114. doi:10.1115/1.2796052.

Rapid transients were applied to the outstretched human index finger tip, which resulted in motion primarily at the metacarpophalangeal (MCP) joint in extension and in abduction. A second-order linear model was fit to approximately 20 milliseconds of the force and displacement data to determine the effective mechanical impedance at the finger tip. Ranges of mass, damping, and stiffness parameters were estimated over a range of mean finger tip force (2–20 N for extension, 2–8 N for abduction). Effective translational finger tip mass for each subject was relatively constant for force levels greater than 6 N for extension, and constant throughout the abduction trials. Stiffness increased linearly with muscle activation. The estimated damping ratio for extension trials was about 1.7 times the ratio for abduction.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(1):115-123. doi:10.1115/1.2796053.

This research had two main objectives: to identify and quantify the multiple reaction parameters of human footfall load histories for 24 subjects; and to seek statistical correlations of the reaction parameters with two gaits: fitness walking and running, with two footfall surfaces: rigid and mat, and with two subject attributes: gender and arch index. These reaction parameters, measured with a force plate, include the subjects’ foot reaction forces in the three orthogonal directions and the particular features of these forces such as their duration, average values, peak values, and rates of loading. An automated data retrieval-software system evaluated these reaction parameters. The statistical correlations were made using principal component analysis (PCA), a method that projected the 13 identified footfall reaction parameters onto subsets of three or four parameters called principal components that contained most of the variance of the original thirteen. The results, among others, show couplings between the vertical and the peak medial load, but an uncoupling of the posterior–anterior loads with the loads in the other two directions.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J Biomech Eng. 1997;119(1):124-127. doi:10.1115/1.2796054.

Advances in tissue engineering have led to the development of artificially grown dermal tissues for use in burn and ulcer treatments. An example of such an engineered tissue is Dermagraft™, which is grown using human neonatal fibroblasts on rectangular sheets of biodegradable mesh. Using small angle light scattering (SALS), we quantified the collagen fiber architecture of Dermagraft with the mesh scaffold contributions removed through the use of a structurally based optical model. Dermagraft collagen fibers were found to have a preferred direction nearly parallel to the long dimension of the kiteshaped mesh opening with small spatial variations over the mesh. This study demonstrated the utility of SALS as a rapid and inexpensive technique for the evaluation of gross collagen fiber architecture in engineered tissues.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(1):127-129. doi:10.1115/1.2796055.

Arrays of two or more parallel blood vessels in a tissue matrix have been studied extensively in the context of bioheat transfer. The average vessel Nusselt number (based on the difference between the mixed-mean blood temperature and the average vessel surface temperature) is a crucial parameter in such studies. Various workers have noted that in particular cases the average Nusselt number is identical to that for fully developed flow in a single vessel in an infinite medium. In other words, the Nusselt number is unaffected by the presence of other vessels. It is proven here that this surprising result holds true for arbitrary number, size, flow direction, and velocity profile in the blood vessels, and for very general boundary conditions on the outer tissue boundary. A useful corollary is that the average wall temperature in a particular vessel may be found by evaluating the temperature fields due to the other vessels and the tissue boundaries at a single point, the center of the vessel in question.

Commentary by Dr. Valentin Fuster

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