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TECHNICAL PAPERS

J Biomech Eng. 1995;117(1):1-7. doi:10.1115/1.2792266.

Determination of ligament forces is an integral part of understanding their contribution during motion and external loading of an intact joint. While almost all previous investigations have reported only the magnitude of tension, this alone cannot adequately describe the function of a particular ligament. An alternative approach to determine the in-situ forces in ligaments has been developed which utilizes a universal force-moment sensor in conjunction with a force transformation scheme. In addition to providing the magnitude of ligament force, the direction and point of application of this in-situ force can also be determined. Further, the approach does not require mechanical contact with the ligament. Application of this new methodology is demonstrated for the human anterior cruciate ligament in the present study (n = 7) although it may be similarly applied to other ligaments at the knee or in other synovial joints of the human body.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1995;117(1):8-14. doi:10.1115/1.2792275.

Results of the direct in vitro measurement of the full three-dimensional representation of the patellofemoral contact force and the point of application on the patella of the resultant contact force for eleven normal knees are presented. The applied knee moment versus flexion angle pattern was similar to that experienced when rising from a chair. There was a wide variability of the details of the patellofemoral force interaction among the specimens tested. The magnitude of the resultant contact force increased approximately linearly with flexion angle for some knees while in others the force leveled off or decreased at higher flexion angles. The change in direction of the resultant contact force with respect to the patella was relatively small compared to the angular rotation of the patella. The medial-lateral component of the contact force exhibited substantial variability among knees. The direction of this force (medially or laterally directed) varied among knees and, in some knees, changed direction as a function of flexion angle. The point of application on the patella of the resultant contact force migrated superiorly from 20 to 90 deg flexion. Above 90 deg flexion this point tended to migrate inferiorly. The only significant and consistent effect of varying the direction of the quadriceps extension force was a change in the medial-lateral component of the contact force. In all cases, the tendency to sublux laterally increased when the extensor force was rotated 10 deg laterally and decreased when the extensor force was rotated 10 deg medially.

Topics: Force , Knee , Rotation
Commentary by Dr. Valentin Fuster
J Biomech Eng. 1995;117(1):15-26. doi:10.1115/1.2792265.

To understand how humans perform non-ballistic movements, we have developed an optimal control model to simulate rising from a chair. The human body was modeled as a three-segment, articulated, planar linkage, with adjacent links joined together by frictionless revolutes. The skeleton was actuated by eight musculotendinous units with each muscle modeled as a three-element entity in series with tendon. Because rising from a chair presents a relatively ambiguous performance criterion, we chose to evaluate a number of different performance criteria, each based upon a fundamental dynamical property of movement: muscle force. Through a quantitative comparison of model and experiment, we found that neither a minimum-impulse nor a minimum-energy criterion is able to reproduce the major features of standing up. Instead, we introduce a performance criterion based upon an important and previously overlooked dynamical property of muscle: the time derivative of force. Our motivation for incorporating such a quantity into a mathematical description of the goal of a motor task is founded upon the belief that non-ballistic movements are controlled by gradual increases in muscle force rather than by rapid changes in force over time. By computing the optimal control solution for rising from a static squatting position, we show that minimizing the integral of a quantity which depends upon the time derivative of muscle force meets an important physiological requirement: it minimizes the peak forces developed by muscles throughout the movement. Furthermore, by computing the optimal control solution for rising from a chair, we demonstrate that multi-joint coordination is dictated not only by the choice of a performance criterion but by the presence of a motion constraint as well.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1995;117(1):27-40. doi:10.1115/1.2792267.

A measurement technique is presented for recording positions of the bones of the shoulder mechanism, i.e., thorax, clavicula, scapula and humerus, in 3-D space, based on palpating and recording positions of bony landmarks. The palpation technique implies that only static positions can be measured. Accuracy of retrieving bony landmarks is checked on-line using rigid body assumptions. The measurement error is calculated afterwards and is comparable with cinegraphic methods. Axial rotation of the clavicula is estimated by minimizing rotations in the acromioclavicular joint. A number of motion definitions is compared by means of interindividual variation and subjective interpretability. Two useful definitions are proposed for describing motions of the shoulder mechanism. Four conditions have been recorded: abduction and anteflexion of the humerus both with and without additional weight in the hand. Abduction and anteflexion result in large differences in scapular and clavicular motions. The effect of additional weight in the hand on the position of the shoulder girdle is negligible.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1995;117(1):41-47. doi:10.1115/1.2792268.

In order to study the effect of intra-operative tensioning on the laxity and strength of healing ligament grafts in an animal model, a method of quantifying graft tension was needed. In this study a sensitive ligament tensioning device was developed to measure accurately the prefixation loads in the rabbit medial collateral ligament (MCL) graft. To verify that reproducible changes in ligament tension could be created with the tensioning device, a group of animals had their MCL grafts replaced at one of three different graft loads (tight, anatomic, or loose). The tensioning device consists of two posts which move relative to one another by means of an axial screw. The movable post, which is inserted into the tibial bone island of the MCL graft has a series of strain gauges which can measure the tension applied to the graft. The stationary post attaches to the tibial shaft, permitting the ligament graft to be tensioned relative to this fixed point. After graft tensioning and fixation, the animals were euthanized immediately postoperatively and their ligament load-deformation behavior was measured using an Instron materials testing machine. Specific measures of low load behavior was taken to quantify ligament laxity. Our results demonstrate that the tensioning device was capable of reproducibly altering prefixation graft load intra-operatively as well as MCL laxity immediately postoperatively. A baseline of laxity values was thus developed to follow changes in this laxity measure for future studies of MCL graft healing in this model.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1995;117(1):48-52. doi:10.1115/1.2792269.

The objective of the present study was to measure dynamic chest deformations and compute chest velocity and viscous criterion during real world frontal impacts conducted on a horizontal sled. Four unembalmed human cadavers were restrained using a three-point belt restraint in the driver seat of a sled buck. Two chest bands (each with a 24 gauge capability) were placed on the thorax to record the temporal deformation patterns during impact. All tests were conducted at a velocity of approximately 50 kph. Biomechanical data were gathered digitally at a sampling rate of 12,500 Hz. Multiple rib fractures were identified in all specimens at autopsy. Analysis of approximately 800 temporal deformation contours of the thorax demonstrated regional differences. The overall mean maximum normalized chest deflections, maximum chest compression velocities, and peak viscous response variables ranged from 0.15 to 0.51, 1.79 to 4.87 m/s, and 0.15 to 1.95 m/s, respectively. These findings clearly illustrate the potential use of the chest band output to correlate injury with biomechanical variables and establish thoracic impact tolerance.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1995;117(1):53-58. doi:10.1115/1.2792270.

Compression (or crushing) is used to induce nerve injury in test rats to study nerve degeneration and regeneration. The compression forces could be applied using a variety of techniques developed by several investigators. The lack of precise control of the applied compression may be the source of significant variations among observations. In this study, a Mosquito and dressing forceps were used. The Mosquito forceps was calibrated to determine the tip load corresponding to the clamping position. The dressing forceps was modified, instrumented with strain gauges and calibrated to directly measure the force applied at its tip. These two forceps were used to induce known and controlled nerve compression in 75 male Wistar rats (280–300g). The applied forces were of the order of 40N and 20N, for the Mosquito and dressing forceps, respectively.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1995;117(1):59-63. doi:10.1115/1.2792271.

Cryosurgery of the skin is a common treatment for both benign and malignant skin cancers. Monitoring the depth of the frozen lesion during cryosurgery, either by estimation based on the lateral spread of freeze at the skin surface or via thermocouples, may be inaccurate because of the heterogeneous nature of tissue. We describe an integrated cryosurgical probe and magnitude resonance imaging probe which we use to obtain high resolution MR images of skin, subcutaneous muscle and the frozen lesion during cryosurgery.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1995;117(1):64-73. doi:10.1115/1.2792272.

Two-dimensional microvascular tissue preparations have been extensively used to study blood flow in the microcirculation, and, most recently, the mechanism of thermal equilibration between thermally significant countercurrent artery-vein pairs. In this paper, an approximate three-dimensional solution for the heat transfer from a periodic array of blood vessels in a tissue preparation of uniform thickness with surface convection is constructed using a newly derived fundamental solution for a Green’s function for this flow geometry. This approximate solution is exact when the ratio K′ of the blood to tissue conductivity is unity and a highly accurate approximation when K′ ≠ 1. This basic solution is applied to develop a model for the heat transfer from a countercurrent artery-vein pair in an exteriorized rat cremaster muscle preparation. The numerical results provide important new insight into the design of microvascular experiments in which the axial variation of the thermal equilibration in microvessels can be measured for the first time. The solutions also provide new insight into the design of fluted fins and microchips that are convectively cooled by internal pores.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1995;117(1):74-85. doi:10.1115/1.2792273.

A thermal method has been developed to quantify continuous perfusion changes with self-calibration. A dynamic, one-dimensional bio-heat transfer model of the thermal probe and tissue describes the system response to either continuous or transient heating. A nonlinear least-squares fit of the model to experimental data yields estimates of the baseline perfusion and other model parameters. With a partial analytical solution of the model, the optimal estimation procedure is two orders of magnitude more efficient than with a total numerical solution of the model system. Experimental data is used to estimate the operating relations between perfusion and the temperature measurement. A new procedure has also been presented to obtain the dynamic response of the system for continuous measurement of perfusion.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1995;117(1):86-93. doi:10.1115/1.2792274.

We performed in vitro pressure-diameter and axial force-length experiments on nondiseased, passive bovine coronary arteries subjected to bath temperatures from 21 to 80° C for 90 s to 4 hr. Over the strain ranges studied, we found that: (a) vessel behavior remained the same over 20 min of testing at 21 to 55° C, (b) vessels stiffened multiaxially after 5 min of exposure to 60° C and continued to stiffen over 20 min of testing, (c) dramatic multiaxial vessel stiffening and shrinkage occurred after 90 s of exposure to 70 and 80° C, and (d) heat-induced changes at 70° C depended on the intraluminal pressure during heating. Thus, passive bovine coronary arteries exhibit a complex thermomechanical behavior that depends on the temperature, duration of thermal exposure, and the mechanical loads applied during heating.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1995;117(1):94-102. doi:10.1115/1.2792276.

Systolic anterior motion of the mitral valve leaflets (SAM) is a disease of the left ventricle which results from an abnormal force balance on the mitral valve. The mechanism by which is initiated is poorly understood, and a complete understanding of this mechanism is required for effective treatment of SAM. There are currently two theories for the initiation mechanism of SAM, the Venturi hypothesis and the altered papillary muscle-mitral valve geometry theory (PM-MV). The Venturi hypothesis states that abnormally high ejection velocities create Venturi forces which initiate SAM. The PM-MV theory asserts that SAM is the result of abnormally distributed chordal forces which are incapable of preventing SAM. To investigate the initiation mechanism of SAM, a computer model of early systolic flow in an anatomically-correct human left ventricle was developed using Peskin’s immersed boundary algorithm. The computer model was used to determine the effect of chordal force distribution and septal thickness of the intraventricular flow field. The results show that the degree of SAM is inversely proportional to the amount of chordal restraint applied to the central portion of the leaflets. Also, the results support the PM-MV theory and indicate the following: (i) fluid forces capable of initiating SAM as always present in a normal human ventricle; (ii) SAM does not occur normally because of the presence of chordal forces on the central portion of the mitral leaflet; (Hi) SAM will occur when these central chordal forces are sufficiently low; (iv) the extent of SAM is inversely proportional to these central chordal forces; and (v) Venturi forces alone can not cause SAM.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1995;117(1):103-106. doi:10.1115/1.2792257.

Ultrasound heart catheters are used to measure the velocity in coronary arteries. However, the act of introducing a catheter into the vessel disturbs the very flow being measured. We used laser Doppler anemometry to measure the velocity distribution in an axially symmetric model, both with and without a catheter inserted. The catheter reduced the center-line velocity by as much as 60 percent at a distance of 2 mm downstream from the catheter, and by as much as 25 percent at a distance of 10 mm. This means the velocity measured with an ultrasound catheter does not show the maximum velocity of the undisturbed flow in the tube center. In the constriction, however, the measured velocities with the LDA and ultrasound catheter are almost the same. Thus, catheter measurements in the stenosis achieve accurate results. The velocity profile in the stenosed areas is flattened over nearly the whole cross section. The velocity is extremely reduced only close to the wall. The measurements outside of the stenosis lead to large differences which need to be studied carefully in the future. The disturbed flow finally disappeared 15 mm downstream of the catheter. The measurements were done at steady flow using a glycerine water solution with a dynamic viscosity of 4.35m Pas. In future studies, these experiments will be repeated for pulsatile flow conditions using non-Newtonian blood-like fluids.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1995;117(1):107-116. doi:10.1115/1.2792258.

A mathematical model of the arm tissue mechanical behavior under the effect of external pressure loads is presented. The model has been used to study stress and strain distribution across the tissue, and pressure transmission to the brachial artery, when the arm is compressed by two adjacent cuffs independently inflated. Using this configuration, the tissue elastic parameters (Young modulus and Poisson ratio) can be individually identified using a simple and noninvasive experimental procedure. Model validation has been achieved by comparing its results with data obtained experimentally on 10 subjects. These comparisons demonstrate that the proposed model may constitute a simple but valid new tool able to describe tissue behavior, subjected to external pressures, with sufficient accuracy. Joined with a model of brachial hemodynamics, it might contribute to improve our understanding of noninvasive blood pressure estimation techniques.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1995;117(1):117-126. doi:10.1115/1.2792259.

The main biomechanical factors which may affect the accuracy of the oscillometric method for indirect blood pressure measurement are analyzed using a new model of brachial hemodynamics. In a first stage of this work, the model has been used to reproduce some well-known responses of collapsing arteries, such as the sharp increase in compliance, and the nonlinear pressure-flow characteristic with negative dynamic resistance. In a second stage the model has been linked to the arm tissue mechanics description presented in a previous work. The final model so obtained has then been employed to analyze the pattern of the main hemodynamic quantities (pressure pulsations in the cuffs, blood volume changes, blood flow upstream and downstream of the cuffs) during deflation manoeuvres. The simulation results agree with those found in the recent literature quite well. Results indicate that the cuff pressure value for maximum pulsations exhibits a large plateau, located approximately around the mean arterial pressure. However, stiffness of wall artery, or stretching of the cuff internal surface, may significantly alter the obtained results causing a phenomena of “pseudohypertension.”

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1995;117(1):127-135. doi:10.1115/1.2792260.

Oscillatory flow of a Newtonian fluid in an elastic tube, which is a model of blood flow in arteries, is analyzed in this paper. For a rigid tube, the steady flow field can be described by Poiseuille’s law and the unsteady flow field by Womersley’s solution. These are the linearized solutions for flow in elastic tubes. To evaluate the importance of nonlinear effects, a perturbation solution is developed realizing that the amplitude of arterial wall movement is small (typically 5–10 percent of the diameter). The nonlinear effects on the amplitude of the wall shear rate, on the amplitude of the pressure gradient, and on the mean velocity profile have been considered. Nonlinear effects on the oscillatory components depend on Womersley’s unsteadiness parameter (α), the ratio between the mean and amplitude of the flow rate, the diameter variation, and the phase difference between the diameter variation and the flow rate (φ) which is indicative of the degree of wave reflection. On the other hand, the mean velocity profile is found to be dependent on the steady-streaming Reynolds number, R s . When R s is small, the mean velocity profile is parabolic (1 − ξ2 ); however, when R s is large, the velocity profile is distorted by the nonlinear effect and can be described by sin(πξ2 ). The increase of the amplitude and reduction of the mean of wall shear rate as π changes from 0 to −90 deg suggests an indirect mechanism for the role of hypertension in arterial disease: hypertension → increased wave reflection → wall shear stress is reduced and more oscillatory.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1995;117(1):136-145. doi:10.1115/1.2792261.

In order to determine the stress-strain relationship of the inner (intima and media) and outer (adventitia) layers of blood vessels in the neighborhood of the zero-stress state, bending experiments were performed on aortic strips of rats. In the experiments, one end of a strip was clamped, and a force was applied on the other end. The deflection curves of the strips were measured. By regarding the aortic strip as a curved beam, the classical beam theory was employed to analyze the strain distribution from the experimental data. A computer program dealing with nonlinear equations and nonlinear least squares optimization was developed. Strains were referred to the zero-stress state. The load-deflection relationship was then used to determine the stress-strain relationship. Certain forms of the stress-strain laws were assumed. The linear laws fit the experimental data accurately, probably because the strains during bending are quite small, although the rotations are large. The Young’s modulus of the inner layer, which consists of endothelial and smooth muscle cells and elastic lamina, was found to be three to four times larger than that of the outer layer which consists of collagen with a small amount of fibroblasts and elastin. The residual stresses and strains at the no-load state were calculated from the deduced stress-strain relationship. It is shown that large errors (up to 50 percent) in the values of the residual strains will occur if the wall material was treated as homogeneous, i.e., if the layered constitution was ignored.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1995;117(1):146-152. doi:10.1115/1.2792262.

A mechanical model of the human trachea is investigated experimentally. A modified version of an earlier model, it consists of a square sectioned rigid tube in which part of one wall is removed, and replaced by a prestretched flat latex membrane. Air is drawn from atmosphere through an inlet into the rigid upstream tube; it then flows through the flexible section and finally through a rigid section Into a plenum chamber where suction is applied. As the membrane collapses in response to flow, the transmural pressure and deflection are measured at the mid-point. These values are used in conjunction with a finite deformation membrane wall theory to determine the elastic constant in a nonlinear material constitutive equation. This equation is used to predict the tube law. Results show that the flow limits at the long wave speed predicted by this law. Thus it behaves as a conventional collapsible tube while having the advantage of a rational wall model.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J Biomech Eng. 1995;117(1):153-155. doi:10.1115/1.2792263.
Abstract
Commentary by Dr. Valentin Fuster
J Biomech Eng. 1995;117(1):155-157. doi:10.1115/1.2792264.

We have examined the feasibility of using massively-parallel and vector-processing supercomputers to solve large-scale optimization problems for human movement. Specifically, we compared the computational expense of determining the optimal controls for the single support phase of gait using a conventional serial machine (SGI Iris 4D25), a MIMD parallel machine (Intel iPSC/860), and a parallel-vector-processing machine (Cray Y-MP 8/864). With the human body modeled as a 14 degree-of-freedom linkage actuated by 46 musculotendinous units, computation of the optimal controls for gait could take up to 3 months of CPU time on the Iris. Both the Cray and the Intel are able to reduce this time to practical levels. The optimal solution for gait can be found with about 77 hours of CPU on the Cray and with about 88 hours of CPU on the Intel. Although the overall speeds of the Cray and the Intel were found to be similar, the unique capabilities of each machine are better suited to different portions of the computational algorithm used. The Intel was best suited to computing the derivatives of the performance criterion and the constraints whereas the Cray was best suited to parameter optimization of the controls. These results suggest that the ideal computer architecture for solving very large-scale optimal control problems is a hybrid system in which a vector-processing machine is integrated into the communication network of a MIMD parallel machine.

Commentary by Dr. Valentin Fuster

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