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RESEARCH PAPERS

J Biomech Eng. 1994;116(4):377-383. doi:10.1115/1.2895787.

A nonlinear, three-dimensional finite element model of the ligamentous L4-SI segment was developed to analyze the dynamic response of the spine in the absence of damping. The effects of the upper body mass were simulated by including a mass of 40 kg on the L4 vertebral body. The modal analyses of the model indicated a resonant frequency of 17.5 Hz in axial mode and 3.8 Hz in flexion-extension mode. Accordingly, the predicted responses for the cyclic load of −400 ± 40 N applied at four different frequencies (5, 11, 16.5, and 25 Hz) were compared with the corresponding results for axial compressive static loads (−360, and −440 N). As compared to the static load cases, the predicted responses were higher for the cyclic loading. For example, the effect of cyclic load at 11 Hz was to produce significant changes (9.7 – 19.0 percent) in stresses, loads transmitted through the facets, intradiscal pressure (IDP), disk bulge, as compared to the static load predictions. The responses were found to be frequency dependent as well; supporting the in vivo observations of other investigators that the human spine has a resonant frequency. For example, the 11 Hz model (DYN11) compared to the DYN5 model showed an increase in majority of the predicted parameters. The parameters showed an increase with frequency until 17.5 Hz (resonant frequency of the model); thereafter a decrease at 25 Hz. A chronic change in these parameters, especially at the resonant frequency, beyond the “base” values may trigger the bone remodeling process leading to spinal degeneration/disorders associated with chronic vibration exposure. Future directions for extending the present model as a complement to the experimental investigations are also discussed.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1994;116(4):384-392. doi:10.1115/1.2895788.

We have constructed an electrokinetic surface probe capable of applying small sinusoidal currents to the surface of articular cartilage and measuring the resulting current-generated stress with a piezoelectric sensor. Using the probe, we have characterized the electromechanical response of excised discs of normal and chemically modified adult bovine femoropatellar groove cartilage. The measured stress amplitude was proportional to the applied current density and inversely proportional to the excitation frequency, consistent with a poroelastic model. As a function of bath pH, the stress amplitude exhibited a minimum in the range pH 2.4–2.8 and the phase underwent an abrupt 180° transition in the same range, consistent with an electrokinetic mechanism as the origin of the current-generated mechanical stress. Digestion of the tissue with trypsin resulted in a progressive loss of highly charged proteoglycan molecules from the tissue, with a concomitant decrease in the measured stress amplitude. These results support the feasibility of surface measurements as a means of assessing electromechanical transduction in cartilage and of detecting subtle molecular-level degradative changes in the extracellular matrix. This technique of surface spectroscopy provides a new means of nondestructively measuring the material properties of cartilage on intact joints and detecting degradative changes such as those seen in the earliest stages of osteoarthritis.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1994;116(4):393-400. doi:10.1115/1.2895789.

Bone atrophy caused by stress-shielding may cause serious complications for the long-term fixation of hip stems. In particular, uncemented total hip arthroplasty is threatened by this problem, because the stems are usually larger and, as a consequence, stiffer than those of cemented implants. In the present study, the effects of fit and bonding characteristics of femoral hip stems were investigated, using the (nonlinear) finite element method in combination with adaptive bone remodeling theory to predict the bone density distribution in a bone or bone/implant configuration. Unknown parameters used in the theory, such as a reference equilibrium loading stimulus and a threshold (dead) zone of this stimulus, were established (triggered) by using the method to predict the density distributions in the natural femur and around fully coated uncemented implants. The computer simulation method can provide long term predictions of remodeling patterns around various implant configurations. Several cases were analyzed, whereby the coating conditions (fully, partly, or noncoated) and the fit characteristics (press fitted or overreamed) were varied. The computer predictions showed that partly coating can only significantly reduce bone atrophy relative to fully coated stems, when the coating is applied at a small region at the utmost proximal part of the stem. For smooth press-fit stems the predicted amount of bone loss (35 percent in the proximal medial region) was less than for a one-third proximally coated or a fully coated stem (50 to 54 percent predicted bone loss in the proximal medial region). The results showed that overreaming the femoral canal in the press fit case can have important effects. Distal overreaming gave reduced proximal atrophy. Proximal overreaming (or undersizing) resulted in a distal jam of the stem, a proximal “stress-bypass,” and dramatic proximal bone loss (up to 90 percent).

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1994;116(4):401-407. doi:10.1115/1.2895790.

A 2-D finite element model of the human temporomandibular joint (TMJ) has been developed to investigate the stresses and reaction forces within the joint during normal sagittal jaw closure. The mechanical parameters analyzed were maximum principal and von Mises stresses in the disk, the contact stresses on the condylar and temporal surfaces, and the condylar reactions. The model bypassed the complexity of estimating muscle forces by using measured joint motion as input. The model was evaluated by several tests. The results demonstrated that the resultant condylar reaction force was directed toward the posterior side of the eminence. The contact stresses along the condylar and temporal surfaces were not evenly distributed. Separations were found at both upper and lower boundaries. High tensile stresses were found at the upper boundaries. High tensile stresses were found at the upper boundary of the middle portion of the disk.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1994;116(4):408-412. doi:10.1115/1.2895791.

A large deformation elasto-static finite element formulation is developed and used for the determination of the role of bone compliance in mechanics of a lumbar motion segment. This is done by simulating each vertebra as a deformable body with realistic material properties, as a deformable body with stiffer or softer mechanical properties, as a single rigid body, or finally as two rigid bodies attached by deformable beams. The single loadings of axial compression, flexion moment, extension moment, and axial torque are considered. The results indicate the marked effect of alteration in bone material properties on biomechanics of lumbar segments specially under larger loads. The biomechanical studies of the lumbar spine should, therefore, be performed and evaluated in the light of such dependency. A model for bony vertebrae is finally proposed that preserves both the accuracy and the cost-efficiency in nonlinear finite element analyses of spinal multi-motion segment systems.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1994;116(4):413-420. doi:10.1115/1.2895792.

In this paper, a lumped mass human model is used to minimize the energy absorption at the feet/hip level when the body is subjected to vertical vibration. The contact forces are assumed unknown. By coupling the dynamic response of the body with certain objective criteria, the optimum damping and stiffness coefficients of shoes/ chairs are sought. The optimization technique is based on the quasi-Newton and finite-difference gradient method and is used to seek optimum coefficients of the contact forces in the solution of the body’s response in the frequency domain. The criteria of acceleration, displacement and internal forces response area swept for a range of 0–15 Hz form the basis of our simulation study. In the seated/standing postures it is found that for each criteria the frequency response shifts the peak of resonance of each body segment response from 4.5/3.67 Hz to 2.5/2.255 Hz. In addition, the total energy reduces drastically when the contact conditions are optimum. The method presented in this paper is useful in modeling the medium of contacts and especially in controlling the effects of human body vibration.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1994;116(4):421-429. doi:10.1115/1.2895793.

A layer of skin and subcutaneous tissue on a bony substratum was modeled as a homogeneous layer of biphasic poroelastic material with uniform thickness. The epidermal surface and the bony interface were taken to be impervious. The soft tissue on the bony interface was assumed either fully adhered or completely free to slide on the bone. The cases for surface pressure loadings and displacement controlled indentations were simulated. The resultant biomechanical responses of the layer, including the transient tissue hydrostatic pressure and the tissue compaction, were presented. A new hypothesis is offered to interpret the threshold pressure-time curve for pressure sores in term of the time required for a particular area in the tissue layer to reach a critical compaction for a given level of applied pressure.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1994;116(4):430-445. doi:10.1115/1.2895794.

A new model is presented for the growth of cellular level macromolecular leakage spots in the arterial intima. The theoretical approach differs from the recent study by Yuan et al. [19] in that it directly models and calculates the intimal transport parameters based on Frank and Fogelman’s [22] ultrastructural observations of the extracellular subendothelial proteoglycan matrix that their rapid freeze etching technique preserves (see Addendum). Using a heterogeneous fiber matrix theory, which includes proteoglycan and collagen components, the model predicts that the Darcy permeability Kp and macromolecular diffusivity D of the subendothelial intima is two orders of magnitude larger than the corresponding values measured in the media, and supports the observations in Lark et al. [24] that the proteoglycan structure of the intima differs greatly from that of the media. Numerical results show that convection parallel to the endothelium is a very significant transport mechanism for macromolecules in the intima in a large region of roughly 200 μm diameter surrounding the leaky cleft. The predictions of the new model for the early-time spread of the advancing convective-diffusive front from the leakage spots in the intima are in close agreement with our experimental measurements for the growth of HRP spots in [20]. The regions of high concentration surrounding the leaky cell, however, are much more limited and cover an area that is typically equivalent to 20 cells. This prediction is consistent with the recent measurements of Truskey et al. for LDL spot size in rabbit aorta [21] and the hypothesis advanced in [19] that there is a colocalization of subendothelial liposome growth and cellular level leakage. Finally, comparison of predicted and experimentally-measured average LDL concentration in leakage spots strongly suggests that there is significant local molecular sieving at the interface between the fenestral openings in the internal elastic lamina and the media.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1994;116(4):446-451. doi:10.1115/1.2895795.

Atherosclerosis of the human arterial system produces major clinical symptoms when the plaque advances to create a high-grade stenosis. The hemodynamic shear rates produced in high-grade stenoses are important in the understanding of atheromatous plaque rupture and thrombosis. This study was designed to quantify the physiologic stress levels experienced by endothelial cells and platelets in the region of vascular stenoses. The steady hemodynamic flow field was solved for stenoses with percent area reductions of 50, 75, and 90 percent over a range of physiologic Reynolds numbers (100–400). The maximum wall shear rate in the throat region can be shown to vary by the square root of the Reynolds number. The shear rate results can be generalized to apply to a range of stenosis lengths and flow rates. Using dimensions typical for a human carotid or coronary artery, wall shear rates were found to vary from a maximum of 20,000 s−1 upstream of the throat to a minimum of −630 s−1 in the recirculation zone for a 90 percent stenosis. An example is given which illustrates how these values can be used to understand the relationship between hemodynamic shear and platelet deposition.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1994;116(4):452-459. doi:10.1115/1.2895796.

In this paper, an analysis of the dynamics in the closing phase of the occluder of a mechanical monoleaflet heart valve prosthesis is presented. The dynamic analysis of the fluid in the vicinity of the occluder was based on the control volume approach. The backflow velocity of the fluid was computed by applying the continuity and momentum equations in the unsteady state. By considering the fluid pressure and gravity as external forces acting on the occluder, the moment equilibrium on the occluder was employed to analyze the motion of the occluder during closing and the force of impact between the occluder and the guiding struts. The computed magnitudes of the occluder tip velocities, as well as the backflow of the fluid during the closing phase using this model, were in agreement with previously reported experimental measurements. The maximum impact force between the occluder and guiding struts of 140–280 N was determined to occur during the initial impact for a duration of 35–45 μus. The results of such model studies may be extended for the analysis of the endurance limit of the valve prostheses as well as to determine the mechanical stresses on the formed elements and the incipience of cavitation bubbles during the closing phase of the valve function.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1994;116(4):460-468. doi:10.1115/1.2895797.

A method for real-time in vitro observation of cavitation on a prosthetic heart valve has been developed. Cavitation of four blood analog fluids (distilled water, aqueous glycerin, aqueous polyacrylamide, and aqueous xanthan gum) has been documented for a Medtronic/Hall™ prosthetic heart valve. This method employed a Penn State Electrical Ventricular Assist Device in a mock circulatory loop that was operated in a partial filling mode associated with reduced atrial filling pressure. The observations were made on a valve that was located in the mitral position, with the cavitation occurring on the inlet side after valve closure on every cycle. Stroboscopic videography was used to document the cavity life cycle. Bubble cavitation was observed on the valve occluder face. Vortex cavitation was observed at two locations in the vicinity of the valve occluder and housing. For each fluid, cavity growth and collapse occurred in less than one millisecond, which provides strong evidence that the cavitation is vaporous rather than gaseous. The cavity duration time was found to decrease with increasing atrial pressure at constant aortic pressure and beat rate. The area of cavitation was found to decrease with increasing delay time at a constant aortic pressure, atrial pressure, and beat rate. Cavitation was found to occur in each of the fluids, with the most cavitation seen in the Newtonian fluids (distilled water and aqueous glycerin).

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1994;116(4):469-476. doi:10.1115/1.2895798.

This paper presents an extension of the previous analyses on the collapsible tubeflow problem using a simplified model based on a two-dimensional channel conveying a one-dimensional flow. The main objective of the paper is to exploit the static and dynamic behavior of the model, by comparing with available experimental data and examining the accuracy of calculated results obtained for different numerical resolutions. The main revision from the previous analyses is the incorporation of a universal “tube” law that is valid for a wide range of positive and negative transmural pressure. Most of the numerical results agree qualitatively with the experimental observations. Self-excited high-frequency oscillation with very small amplitude of the membrane wall is, however, predicted to occur in a flow range where the slope of the pressure drop curve is positive. It is seen that the high-frequency oscillation is associated with the motion of the separation point of the flow.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1994;116(4):477-487. doi:10.1115/1.2895799.

The presence of turbulence in the cardiovascular system is generally an indication of some type of abnormality. Most cardiologists agree that turbulence near a valve indicates either valvular stenosis or regurgitation, depending on the phase of its occurrence during the cardiac cycle. As no satisfying analytical solutions of the stability of turbulent pulsatile flow exist, accurate, unbiased flow stability criteria are needed for the identification of turbulence initiation. The traditional approach uses a stability diagram based upon the stability of a plane Stokes layer where a (the Womersley parameter) is defined by the fundamental heart rate. We suggest a modified approach that involves the decomposition of α into its frequency components, where α is derived from the preferred modes induced on the flow by interaction between flow pulsation and the valve. Transition to turbulence in pulsatile flow through heart values was investigated in a pulse duplicator system using three polymer aortic valve models representing a normal aortic valve, a 65 percent stenosed valve and a 90 percent severely stenosed valve, and two mitral valve models representing a normal mitral valve and a 65 percent stenosed valve. Valve characteristics were closely simulated as to mimic the conditions that alter flow stability and initiate turbulent flow conditions. Valvular velocity waveforms were measured by laser Doppler anemometry (LDA). Spectral analysis was performed on velocity signals at selected spatial and temporal points to produce the power density spectra, in which the preferred frequency modes were identified. The spectra obtained during the rapid closure stage of the valves were found to be governed by the stenosis geometry. A shift toward higher dominant frequencies was correlated with the severity of the stenosis. According to the modified approach, stability of the flow is represented by a cluster of points, each corresponding to a specific dominant mode apparent in the flow. In order to compare our results with those obtained by the traditional approach, the cluster of points was averaged to collapse into a single point that represents the flow stability. The comparison demonstrates the bias of the traditional stability diagram that leads to unreliable stability criteria. Our approach derives the stability information from measured flow phenomena known to initiate flow instabilities. It differentiates between stabilizing and destabilizing modes and depicts an unbiased and explicit stability diagram of the flow, thus offering a more reliable stability criteria.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1994;116(4):488-496. doi:10.1115/1.2895800.

Flow in a bifurcating tube system typifying a major bronchial bifurcation is studied experimentally with a two color, two velocity component laser Doppler anemometer. The flow loop is composed of a pumping station, flow stratifiers and a constant head pressure tank; it can accommodate steady, pulsatile or oscillatory flow. The test section is a symmetric bifurcation of constant cross sectional area and has a branching angle of 70 deg. The test section is a cast of clear silicon rubber in a plexiglass mold that was milled on a numerically controlled milling machine. The flow division ratio from the parent to daughter branches is about unity. Steady flow results that model the inspiratory phase at Reynolds numbers of 518, 1036 and 2089, corresponding to Dean numbers of 98, 196 and 395, show that in the bifurcation plane velocity profiles in the daughter branches are skewed toward the inner wall. In the transverse plane, “m” shaped velocity profiles are found with low velocity at the center. Secondary flow patterns, which are responsible for such phenomena, are first observed at the axial position where the flow begins to turn. Flow separation was not observed at any point in the bifurcation.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1994;116(4):497-501. doi:10.1115/1.2895801.

The flow of red blood cells (RBC) through a microvascular capillary bifurcation was modeled in a large scale system in which rigid circular tubes and bifurcations (diameter = .95 cm) simulated capillaries and capillary bifurcations, flexible disks (undeformed diameter = 0.75 cm) simulated RBC and glycerol simulated plasma. At low Reynolds numbers (0.01 to 0.1), pressure drop was measured in the tubes upstream and downstream from the bifurcation as well as across the bifurcation itself, for various flow splits at the bifurcation while the inflow in the upstream tube was held constant. Pressure gradient across the bifurcation is taken to be the average of the upstream and downstream pressure gradients if the additional pressure drop at the bifurcation due to the partitioning of flow and disks is negligible. For the case of glycerol alone, the ratio of pressure gradient (G) at the bifurcation to the one at the upstream region was always greater than expected and reached 1.14 when the flow in the side branch was zero. With introduction of flexible disks into the system, G at the bifurcation was as much as 10 times the G at the upstream region as disks came in contact with, or close to, the dividing line of the bifurcation and paused momentarily before they entered one or the other side of the bifurcation. The largest G was for even flow split at the bifurcation and the smallest G was for the case where the flow in the side branch was smallest. Therefore, for the range of tube hematocrits (0–30 percent) and flow splits tested here, a significant additional pressure drop at the bifurcation is observed.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1994;116(4):502-513. doi:10.1115/1.2895802.

The recent serial section electron microscopic studies by Adamson and Michel (1993) on microves gels of frog mesentery have revealed that the large pores in the junction strand of the interendothelial cleft are widely separated 150 nm wide orifice-like breaks whose gap height 20 nm is the same as the wide part of the cleft. In this paper a modified version of the model in Weinbaum et al. (1992) is first developed in which this orifice structure is explored in combination with a random or ordered fiber matrix layer that is at the luminal surface and/or occupies a fraction of the wide part of the cleft. This basic orifice model predicts that for the measured Lp to be achieved the fiber layer must be confined to a relatively narrow region at the entrance to the cleft where it serves as the primary molecular filter. The model provides a much better fit of the permeability P for intermediate size solutes between 1 and 2 nm radius than the previous model in Weinbaum et al., where the junction strand breaks were treated as finite depth circular or rectangular pores, but like the previous model significantly underestimates P for small ions. However, it is shown that if a small frequent pore of 1.5 nm radius with characteristic spacing comparable to the diameter of the junction proteins or a continuous narrow slit of approximately 1.5 to 2.3 nm gap height is also present in the continuous part of the junction strand, small ion permeability can also be satisfied. The 1.5 nm radius pore does not significantly change Lp , whereas the continuous narrow slit provides a contribution to Lp that is comparable to, or in the case of the 2.3 nm slit greater than, the widely spaced 150 nm orifices. Thus, for the narrow slit the contribution to Lp from the orifices can be as low as 1.0×10−7 cm/s/cm H2 O and it is also possible to satisfy the 2.5 fold increase in permeability that occurs when the matrix is enzymatically removed from the luminal side of the cleft, Adamson (1990). The likelihood of each of these cleft structures is discussed.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1994;116(4):514-520. doi:10.1115/1.2895803.

The use of pulsed blood flow in membrane plasmapheresis permits enhancement of plasma filtration yet may result in high levels of hemolysis due to large increases in instantaneous transmembrane pressure (TMP). This work investigates the occurrence of hemolysis as a function of TMP and wall shear rates (γw ) for both steady and pulsed blood flow conditions. Two types of hollow fiber filters with identical polypropylene membranes but different lengths and membrane areas (0.1 and 0.25 m2 ) were tested. Fresh citrated bovine blood was circulated through the fibers at various blood flowrates and TMP in a single pass circuit using a pulsation generator, made of a single roller peristaltic pump. The free hemoglobin concentration of the plasma, Hbm , was measured from permeate samples collected at each set of TMP and γw conditions. It was found that the net hemolysis generated by the filtration was proportional to the membrane area. This justified the introduction of an hemolysis index, IH , equal to the plasma hemoglobin per unit membrane area. The boundary for the occurrence of hemolysis was thus defined by setting IH = 30 mg/ dl.m2 . For both steady and pulsed flow conditions the hemolysis boundaries were found to be straight lines in the TMP-γw plane. They were identical for the two filters under steady flow but different for pulsed flow. At the same time mean wall shear rates hemolysis occurred at a lower time mean TMP under pulsed flow conditions than under steady flow conditions.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1994;116(4):521-527. doi:10.1115/1.2895804.

A new model of steady-state heat transport in perfused tissue is presented. The key elements of the model are as follows: (1) a physiologically-based algorithm for simulating the geometry of a realistic vascular tree containing all thermally significant vessels in a tissue; (2) a means of solving the conjugate heat transfer problem of convection by the blood coupled to three-dimensional conduction in the extravascular tissue, and (3) a statistical interpretation of the calculated temperature field. This formulation is radically different from the widely used Pennes and Weinbaum-Jiji bio-heat transfer equations that predict a loosely defined local average tissue temperature from a local perfusion rate and a minimal representation of the vascular geometry. Instead, a probability density function for the tissue temperature is predicted, which carries information on the most probable temperature at a point and uncertainty in that temperature due to the proximity of thermally significant blood vessels. A sample implementation illustrates the dependence of the temperature distribution on the flow rate of the blood and the vascular geometry. The results show that the Pennes formulation of the bio-heat transfer equation accurately predicts the mean tissue temperature except when the arteries and veins are in closely spaced pairs. The model is useful for fundamental studies of tissue heat transport, and should extend readily to other forms of tissue transport including oxygen, nutrient, and drug transport.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J Biomech Eng. 1994;116(4):528-531. doi:10.1115/1.2895805.

Dynamic programming techniques are useful in smoothing and differentiating noisy data signals according to an optimization criterion and the results are generally quite robust to noise spectra different from that assumed in the construction of the filter. If the noise properties are sufficiently different, however, the generalized cross-validation function used in the optimization can exhibit either multiple minima or no minima other than that corresponding to an insignificant amount of smoothing; in these cases, the smoothing parameter desired by the user typically does not lie at the global minimum of the generalized cross-validation function, but at some other point on the curve which can be identified heuristically. I present two cases to demonstrate this phenomenon and describe what measures one can take to ensure that the desired smoothing parameter is obtained.

Commentary by Dr. Valentin Fuster

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