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RESEARCH PAPERS

J Biomech Eng. 1993;115(4A):335-343. doi:10.1115/1.2895495.

A new implantable transducer has been developed for in situ evaluation of ligament and tendon forces. Unlike previous devices, this sensor is placed within the specimen, minimizing measurement errors due to impingement on surrounding soft tissues and bone. In this study, we present the sensor design details as well as test results from initial in vitro trials in the goat patellar tendon model. Device performance and influence of the device on the specimen were evaluated under several loading conditions. In all cases, device output had a strong correlation with induced tissue load. Significant variations in device performance were only noted at high tissue deformation rates. More extensive investigations will be conducted to assess how changes in transducer design might alter performance characteristics.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(4A):344-349. doi:10.1115/1.2895496.

The selection of an appropriate and/or standardized method for representing 3-D joint attitude and motion is a topic of popular debate in the field of biomechanics. The joint coordinate system (JCS) is one method that has seen considerable use in the literature. The JCS consists of an axis fixed in the proximal segment, an axis fixed in the distal segment, and a “floating” axis. There has not been general agreement in the literature on how to select the body fixed axes of the JCS. The purpose of this paper is to propose a single definition of the body fixed axes of the JCS. The two most commonly used sets of body fixed axes are compared and the differences between them quantified. These differences are shown to be relevant in terms of practical applications of the JCS. Argumentation is provided to support a proposal for a standardized selection of body fixed axes of the JCS consisting of the axis ê1 embedded in the proximal segment and chosen to represent flexion-extension, the “floating” axis ê2 chosen to represent ad-abduction, and the axis ê3 embedded in the distal segment and chosen to represent axial rotation of that segment. The algorithms for the JCS are then documented using generalized terminology.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(4A):350-356. doi:10.1115/1.2895497.

In this paper, a two-dimensional, three-body segment dynamic model of the human knee is introduced. The model includes tibio-femoral and patello-femoral articulations, and anterior cruciate, posterior cruciate, medial collateral, lateral collateral, and patellar ligaments. It enables one to obtain dynamic response of the knee joint to any one or combination of quadriceps femoris, hamstrings, and gastrocnemius muscle actions, as well as any externally applied forces on the lower leg. A specially developed human knee animation program is utilized in order to fine tune some model parameters. Numerical results are presented for knee extension under the impulsive action of the quadriceps femoris muscle group to simulate a vigorous lower limb activity such as kicking. The model shows that the patella can be subjected to very large transient patello-femoral contact force during a strenuous lower limb activity even under conditions of small knee-flexion angles. The results are discussed and compared with limited data reported in the literature.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(4A):357-365. doi:10.1115/1.2895498.

The objective of this study is to develop a two-dimensional dynamic model of the knee joint to simulate its response under sudden impact. The knee joint is modeled as two rigid bodies, representing a fixed femur and a moving tibia, connected by 10 nonlinear springs representing the different fibers of the anterior and posterior cruciate ligaments, the medial and lateral collateral ligaments, and the posterior part of the capsule. In the analysis, the joint profiles were represented by polynomials. Model equations include three nonlinear differential equations of motion and three nonlinear algebraic equations representing the geometric constraints. A single point contact was assumed to exist at all times. Numerical solutions were obtained by applying Newmark constant-average-acceleration scheme of differential approximation to transform the motion equations into a set of nonlinear simultaneous algebraic equations. The equations reduced thus to six nonlinear algebraic equations in six unknowns. The Newton-Raphson iteration technique was then used to obtain the solution. Knee response was determined under sudden rectangular pulsing posterior forces applied to the tibia and having different amplitudes and durations. The results indicate that increasing pulse amplitude and/or duration produced a decrease in the magnitude of the tibio-femoral contact force, indicating thus a reduction in the joint stiffness. It was found that the anterior fibers of the posterior cruciate and the medial collateral ligaments are the primary restraints for a posterior forcing pulse in the range of 20 to 90 degrees of knee flexion; this explains why most isolated posterior cruciate ligament injuries and combined injuries to the posterior cruciate ligament and the medial collateral results from a posterior impact on a flexed knee.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(4A):366-373. doi:10.1115/1.2895499.

The B-spline least-squares surface-fitting method is employed to create geometric models of diarthrodial joint articular surfaces. This method provides a smooth higher-order surface approximation from experimental three-dimensional surface data that have been obtained with any suitable measurement technique. Akima’s method for surface interpolation is used to provide complete support to the B-spline surface. The surface-fitting method is successfully tested on a known analytical surface, and is applied to the human distal femur. Applications to other articular surfaces are also shown. Results show that this method is precise, highly flexible, and can be successfully applied to a large variety of articular surface shapes.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(4A):374-379. doi:10.1115/1.2895500.

A finite element code was developed for the analysis of the temperature field around two adjacent cylindrical cryo-probes. The two-phase, two-dimensional Stefan problem is solved using a moving boundary approach and space-time finite elements. Solution of one-cryo-probe problem compared well with an existing analytic solution. The two-cryo-probes problem yielded reasonable results. The program simulated the nonsymmetric activation of two probes and the merging of the two freezing fronts in the case of symmetric activation.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(4A):380-388. doi:10.1115/1.2895501.

Subsets of data from spatially sampled temperatures measured in each of nine experimental heatings of normal canine thighs were used to test the feasibility of using a state and parameter estimation (SPE) technique to predict the complete measured data set in each heating. Temperature measurements were made at between seventy-two and ninety-six stationary thermocouple locations within the thigh, and measurements from as few as thirteen of these locations were used as inputs to the estimation algorithm. The remaining (non “input”) measurements were compared to the predicted temperatures for the corresponding “unmeasured” locations to judge the ability of the estimation algorithm to accurately reconstruct the complete experimental data set. The results show that the predictions of the “unmeasured” steady-state temperatures are quite accurate in general (average errors usually < 0.5°C; and small variances about those averages) and that this reconstruction procedure can yield improved descriptors of the steady-state temperature distribution. The accuracy of the reconstructed temperature distribution was not strongly affected by either the number of perfusion zones or by the number of input sensors used by the algorithm. One situation extensively considered in this study modeled the thigh with twenty-seven independent regions of perfusion. For this situation, measurements from ninety-six to thirteen sensors were used as input to the estimation algorithm. The average error for all of these cases ranged from −0.55°C to +0.75°C, respectively, and was not strongly related to the number of sensors used as input to the estimation algorithm. For these same cases the maximum prediction error (the maximum absolute difference between the measured temperature and the predicted temperature determined by a search over all locations) ranged from 0.92°C to 5.08°C, respectively. To attempt to explain the magnitude of the maximum error, several possible sources of model mismatch and of experimental uncertainty were considered. For this study, a significant source of error appears to arise from differences between the true power deposition field, the power deposition model predictions, and the experimentally measured powers. In summary, while large errors can be present for a few isolated locations in the predicted temperature fields, the SPE algorithm can accurately predict the average characteristics of the temperature field. This predictive ability should be clinically useful.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(4A):389-395. doi:10.1115/1.2895502.

In this paper, fluttering behavior of a mechanical monoleaflet tilting disk heart valve prostheses during the opening phase was analyzed. The impact between the occluder and the guiding strut at the fully open position was included in the analysis with a Bjork-Shiley monoleaflet aortic valve. The motion of the valve occluder was modeled as a rotating system, and equations were derived by employing the moment equilibrium principle. Forces due to lift, drag, gravity, and buoyancy were considered as external forces acting on the occluder. The 4th-order Runge-Kutta method was used to solve the governing equations. The results demonstrated that the occluder reaches the steady equilibrium position only after damped vibration. Fluttering frequency varies as a function of time after opening and is in the range of 8–84 Hz. Valve opening appears to be affected by the orientation of the valve relative to gravitational force. The opening velocities are in the range of 0.56–1.37 m/sec and the dynamic loads by impact of the occluder and the strut are in the range of 60–190 N.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(4A):396-403. doi:10.1115/1.2895503.

The purpose of this study was to develop a method to accurately determine mean velocities and Reynolds stresses in pulsatile flows. The pulsatile flow used to develop this method was produced within a transparent model of a left ventricular assist device (LVAD). Velocity measurements were taken at locations within the LVAD using a two-component laser Doppler anemometry (LDA) system. At each measurement location, as many as 4096 realizations of two coincident orthogonal velocity components were collected during preselected time windows over the pump cycle. The number of realizations was varied to determine how the number of data points collected affects the accuracy of the results. The duration of the time windows was varied to determine the maximum window size consistent with an assumption of pseudostationary flow. Erroneous velocity realizations were discarded from individual data sets by implementing successive elliptical filters on the velocity components. The mean velocities and principal Reynolds stresses were determined for each of the filtered data sets. The filtering technique, while eliminating less than 5 percent of the original data points, significantly reduced the computed Reynolds stresses. The results indicate that, with proper filtering, reasonable accuracy can be achieved using a velocity data set of 250 points, provided the time window is small enough to ensure pseudostationary flow (typically 20 to 40 ms). The results also reveal that the time window which is required to assume pseudostationary flow varies with location and cycle time and can range from 100 ms to less than 20 ms. Rotation of the coordinate system to the principal stress axes can lead to large variations in the computed Reynolds stresses, up to 2440 dynes/cm2 for the normal stress and 7620 dynes/cm2 for the shear stress.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(4A):404-411. doi:10.1115/1.2895504.

The study of pulsatile flows is relevant to many areas of applications. Typical applications include aerodynamics, biofluid mechanics, wind flows, and gas transport. Transition to turbulence during pulsatile flow is physiologically and clinically important. It has been suggested as a possible mechanism to enhance the transport of gases during high-frequency ventilation, may be related to valvular regurgitation and heart murmurs and to post stenotic dilatation and aneurysms. Measurements in a pulsatile pipe flow with a superimposed mean flow are reported. Data were taken in a water flow with mean Reynolds numbers in the range of 0 < Rem < 3000, oscillating Reynolds numbers of 0 < Reω < 4000, and Stokes parameter 7 < λ < 15. Velocity profiles of various phases of the flow, condition for flow reversal, and pressure losses were measured. The adequacy of a quasi-steady-state model is discussed. Condition for transition is determined by visually inspecting velocity signals at the centerline.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(4A):412-417. doi:10.1115/1.2895505.

An experiment on the fully developed sinusoidal pulsatile flow at transitional Reynolds numbers was performed to evaluate the basic characteristics of the wall shear stress. In this experiment, the wall shear stress was calculated from the measured section averaged axial velocity and the pressure gradient by using the section averaged Navier-Stokes equation. The experimental results showed that the ratio of the amplitude of the wall shear stress to the amplitude of the pressure gradient had the maximum value when the time averaged Reynolds number was about 4000 and the Womersley number was about 10. As this condition is close to the blood flow condition in the human aorta, it is suggested that the parameter of the aorta has an effect to increase the amplitude of the wall shear stress acting on the arterial wall.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(4A):418-423. doi:10.1115/1.2895506.

Steady flow in abdominal aortic aneurysm models has been examined for four aneurysm sizes over Reynolds numbers from 500 to 2600. The Reynolds number is based on entrance tube diameter, and the inlet condition is fully developed flow. Experimental and numerical methods have been used to determine: (i) the overall features of the flow, (ii) the stresses on the aneurysm walls in laminar flow, and (iii) the onset and characteristics of turbulent flow. The laminar flow field is characterized by a jet of fluid (passing directly through the aneurysm) surrounded by a recirculating vortex. The wall shear stress magnitude in the recirculation zone is about ten times less than in the entrance tube. Both wall shear stress and wall normal stress profiles exhibit large magnitude peaks near the reattachment point at the distal end of the aneurysm. The onset of turbulence in the model is intermittent for 2000 < Re < 2500. The results demonstrate that a slug of turbulence in the entrance tube grows much more rapidly in the aneurysm than in a corresponding length of uniform cross section pipe. When turbulence is present in the aneurysm the recirculation zone breaks down and the wall shear stress returns to a magnitude comparable to that in the entrance tube.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(4A):424-431. doi:10.1115/1.2895507.

Dispersion of a bolus contaminant in a straight tube with oscillatory flows and conductive walls is solved by using a derivative-expansion method. Using asymptotic methods when small conductance exists, the axial dispersion, as measured by the time-averaged effective diffusivity, increases over the insulated case, as long as the dimensionless frequency (Womersley parameter), α, is smaller than a critical value. When α exceeds this value, axial dispersion is diminished by wall conductance. The functional dependence of this critical α on the system parameters is investigated. We examine the radial wall transport both for total mass and localized flux, which is found to be independent of velocity field, and compute the time-dependent total mass of wall transport and asymptotic Sherwood number for large times as a function of the wall conductance.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(4A):432-440. doi:10.1115/1.2895508.

The topic of this study concerns principally representative models of some elliptical thin-walled anatomic vessels and polymeric tubes under uniform negative transmural pressure p (internal pressure minus external pressure). The ellipse’s ellipticity ko , defined as the major-to-minor axis ratio, varies from 1 up to 10. As p decreases from zero, at first the cross-section becomes somewhat oval, then the opposite sides touch in one point at the first-contact pressure p c . If p is lowered beneath p c , the curvature of the cross-section at the point of contact decreases until it becomes zero at the osculation pressure or the first line-contact pressure p1 . For p <p1 , the contact occurs along a straight-line segment, the length of which increases as p decreases. The pressures pc and p1 are determined numerically for various values of the wall thickness of the tubes. The nature of contact is especially described. The solution of the related nonlinear, two-boundary-values problem is compared with previous experimental results which give the luminal cross-sectional area (from two tubes), and the area of the mid-cross-section (from a third tube).

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(4A):441-446. doi:10.1115/1.2895509.

Finite difference time domain (FDTD) techniques have been developed to calculate the specific absorption rates (SAR) in hyperthermia models. The University of Utah Hyperthermia Research Group has extended these numerical techniques for developing a percutaneous transluminal microwave angioplasty applicator, calculating the SARs produced by a high energy electromagnetic field to remove atherosclerotic plaques in blood vessels. The objective of this research was to derive a method for calculating the bioheat transfer in biological tissue surrounding a microwave angioplasty applicator. A hypothetical model was developed and observations are discussed based on the numerical results of this study. A limited analysis on the thermal effects of microwave pulsing was also completed. Preliminary numerical calculations yielded reasonable results. Experimental laboratory tests are required to validate the accuracy of the numerical results found in this study. Further development of this thermal analysis method may greatly assist in future studies of new applicator configurations to ensure safe atherosclerotic plaque removal and to predict the resulting thermal environments.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J Biomech Eng. 1993;115(4A):447-449. doi:10.1115/1.2895510.

The effects of bone water content during dehydration and rehydration on the flexural properties of whole mouse femora were evaluated using three-point bending. The elastic and plastic flexural properties of the bones were determined on a dry mass normalized basis over dehydration times ranging from 0.25 to 48.0 hr; and (following complete dehydration) rehydration times ranging from 0.08 to 12.0 hr. Bones stored in physiological saline for times <1 hr served as the control group. As expected, dehydration produced increased stiffness and strength along with decreased ductility. Upon rehydration, a statistically significant linear dependence of mechanical properties on recovered free water was obtained for all parameters except the maximum load. Elastic mechanical properties comparable to the controls were regained at differing rates and levels of recovered water content; however, after 3 hr of rehydration there were no statistically significant differences with respect to the control values. The results of this study indicate that the original flexural properties of whole mouse femora are preserved by air dehydration and can be recovered using appropriate saline rehydration intervals.

Commentary by Dr. Valentin Fuster

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