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TECHNICAL PAPERS

J Biomech Eng. 1996;118(4):433-439. doi:10.1115/1.2796028.

The collection and processing of data from mechanical tests of biological tissues usually follow classical principles appropriate for studying engineering materials. However, difficulties specific to biological tissues have generally kept such methods from producing quantitative results for statistically-oriented studies. This paper demonstrates a different approach linking testing and data reduction with modern statistical tools. Experimental design theory is used to minimize the detrimental effects of collinearity on the stability of the parameters in constitutive equations. The numerical effects of time-dependent biasing factors such as viscoelasticity are reduced by randomizing the order of collection of data points. Some of the parameters of the model are allowed to vary from specimen to specimen while the others are computed once from a database of designed experiments on several specimens. Finally, a new self-modeling algorithm based on principal component analysis is used to generate uncorrelated parameters for a model that is linear in its specimen-dependent parameters. The method, associated with a recently published complementary energy formulation for vascular mechanics, is illustrated with biaxial canine saphenous vein data. Results show that three specimen-dependent linear parameters are enough to characterize the experimental data and that they can be repeatedly estimated from different data sets. Independently collected biaxial inflation data can also be predicted reasonably well with this model.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(4):440-444. doi:10.1115/1.2796029.

Residual stress is observed in many parts of the cardiovascular system and is thought to reduce transmural stress gradients due to intravascular pressure. Its development is closely associated with normal growth and pathological remodeling, although there appear to be few previous reports of the relationship between aging and residual stress. We have estimated residual strain (an indicator of the magnitude of residual stress) at ten sites along the aorta of rats aged 2.5 to 56 weeks by measuring the degree to which rings of vessel spring open when cut (opening angle). At all ages the opening angle decreased along the aorta, reaching a minimum near the renal arteries and increasing toward the aorto-iliac bifurcation, a result that confirms previous studies. During growth, although the unloaded circumference of the aorta increased steadily, the wall thickness and medial surface area fell to a minimum at the age of 6 weeks before continuing a steady increase. Similarly, the opening angle decreased between the ages of 2.5 and 6 weeks, thereafter increasing with age. In the abdominal aorta, a strong correlation between opening angle and wall thickness relative to midwall radius (h/R) was seen; whereas in the thoracic segment, in which no increase in h/R with age occurred, no such relationship was found. These observations are in keeping with a recently proposed hypothesis that residual stress will change in response to growth-related changes in vessel geometry driven by a tendency to minimize the nonuniform stress distribution inevitably found in pressurized thick-walled cylinders.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(4):445-451. doi:10.1115/1.2796030.

This study illustrates how the highly nonlinear elastic behavior of artery wall material can cause unusual structural characteristics that do not occur with a linear-elastic material. An example mathematical model of an end-to-end anastomosis successfully predicts the experimentally observed area of elevated elastic compliance, called the “Para-anastomotic Hypercompliant Zone” (PHZ). The elastic hypercompliance is shown to occur because the anastomosis locally restricts the arterial diameter, thus forcing the adjacent material to remain in a lower strain, and correspondingly a lower stiffness, part of its non-linear stress-strain curve. Elevated elastic compliance can be avoided by locally matching both the arterial diameter and the elastic compliance within the physiological pressure range.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(4):452-463. doi:10.1115/1.2796031.

A three-dimensional Galerkin finite element method was developed for large deformations of ventricular myocardium and other incompressible, nonlinear elastic, anisotropic materials. Cylindrical and spherical elements were used to solve axisymmetric problems with r.m.s. errors typically less than 2 percent. Isochoric interpolation and pressure boundary constraint equations enhanced low-order curvilinear elements under special circumstances (69 percent savings in degrees of freedom, 78 percent savings in solution time for inflation of a thick-walled cylinder). Generalized tensor products of linear Lagrange and cubic Hermite polynomials permitted custom elements with improved performance, including 52 percent savings in degrees of freedom and 66 percent savings in solution time for compression of a circular disk. Such computational efficiencies become significant for large scale problems such as modeling the heart.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(4):464-472. doi:10.1115/1.2796032.

A three-dimensional finite element method for nonlinear finite elasticity is presented using prolate spheroidal coordinates. For a thick-walled ellipsoidal model of passive anisotropic left ventricle, a high-order (cubic Hermite) mesh with 3 elements gave accurate continuous stresses and strains, with a 69 percent savings in degrees of freedom (dof) versus a 70-element standard low-order model. A custom mixed-order model offered 55 percent savings in dof and 39 percent savings in solution time compared with the low-order model. A nonsymmetric 3D model of the passive canine LV was solved using 16 high-order elements. Continuous nonhomogeneous stresses and strains were obtained within 1 hour on a laboratory workstation, with an estimated solution time of less than 4 hours to model end-systole. This method represents the first practical opportunity to solve large-scale anatomically detailed models for cardiac stress analysis.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(4):473-481. doi:10.1115/1.2796033.

Membrane inflation tests were performed on fresh, intact human corneas using a fiber optic displacement probe to measure the apical displacements. Finite element models of each test were used to identify the material properties for four different constitutive laws commonly used to model corneal refractive surgery. Finite element models of radial keratotomy using the different best-fit constitutive laws were then compared. The results suggest that the nonlinearity in the response of the cornea is material rather than geometric, and that material nonlinearity is important for modeling refractive surgery. It was also found that linear transverse isotropy is incapable of representing the anisotropy that has been experimentally measured by others, and that a hyperelastic law is not suitable for modeling the stiffening response of the cornea.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(4):482-488. doi:10.1115/1.2796034.

Hotani has studied, by means of dark-field light microscopy, morphological transformations which unilamellar liposomes undergo when their interior volume decreases steadily with time as a consequence of osmosis. In a previous paper, we made a theoretical study of the initial buckling of an originally spherical vesicle into the observed oblate spheroidal shape; and we argued that some in-plane shear elastic stiffness is required—in addition to the well-known flexural stiffness of the lipid bilayer—in order to explain the observed phenomena. In the present paper, we consider a later stage in the chain of morphological transitions observed by Hotani, when a series of cudgel-shaped lobes have sprung out of a previously axisymmetric, biconcave-shaped vesicle. Specifically, we compare the observed shapes of such lobes with half of a series of “peanut”-shaped vesicles that are an equilibrium conformation of an initially spherical liposome under reduced internal volume. We find that the shapes do not match well. On the other hand, the observed lobe forms do match satisfactorily portions of “undulating tube” shapes which evolve from a hypothetical cylindrical vesicle, according to some simple calculations. In view of this agreement, we are led to propose that the formation of cudgel-shaped lobes requires some sliding of one lipid monolayer over another. This conflicts, of course, with the Love-Kirchhoff hypothesis which is normally invoked at the outset of analyses of lipid vesicles by means of classical thin-shell theory; but it is in accord with previous suggestions in the context of more obviously severe distortion of the lipid bilayer.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(4):489-497. doi:10.1115/1.2796035.

The influence of passive vasomotion on the pressure drop-flow (ΔP-Q) characteristics of a partially compliant stenosis was studied in an in vitro model of the coronary circulation. Twelve stenosis models of different severities (50 to 90 percent area reduction) and degrees of flexible wall (0 to 1/2 of the wall circumference) were inserted into thin-walled latex tubing and pressure and flow data were collected during simulated cardiac cycles. In general, the pressure drop increased with increasing fraction of flexible wall for a given flow rate and stenosis severity. The magnitude of this effect was directly dependent upon the underlying stenosis severity. The diastolic ΔP-Q relationship of severe, compliant models exhibited features of partial collapse with an increase in pressure drop at a decreasing flow rate. It is concluded that passive vasomotion of a normal wall segment at an eccentric stenosis in response to periodic changes in intraluminal pressure causes dimensional changes in the residual lumen area which can strongly affect the hemodynamic characteristics of the stenosis during the cardiac cycle. This mechanism may have important implications for the onset of plaque fracture and the prediction of the functional significance of a coronary stenosis based on quantitative angiogram analysis.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(4):498-505. doi:10.1115/1.2796036.

Mitral and tricuspid regurgitation create turbulent jets within the atria. Clinically, for the purpose of estimating regurgitant severity, jet size is assumed to be proportional to peak jet flow rate and regurgitant volume. Unfortunately, the relationship is more complex because the determinants of jet size include interactions between jet pulsatility, jet momentum, atrial width, and the velocity of ambient atrial counterftows. These effects on fluorescent jet penetration were measured using an in vitro simulation. Both steady and pulsatile jets were driven into an opposing counterflow velocity field peak jet length (Ljp ) measurements made as a function of (1) peak orifice velocity (Ujp ), (2) the time required for the jet to accelerate from zero to peak velocity and begin to decelerate (Tjp ), (3) jet orifice diameter (Dj ), (4) counterflow velocity (Uc ), and (5) counterflow tube diameter (Dc ). A compact mathematical description was developed using dimensional analysis. Results showed that peak jet length was a function of the counterflow tube diameter, the ratio of peak jet to counterflow momentum, (Mjp /Mc ) = (Ujp 2 Dj 2 )/(Uc 2 Dc 2 ), and a previously undescribed jet pulsatility parameter, the pulsatility index (PI), PI = Dc 2 /(Tjp Ujp Dj ). For the same jet orifice flow conditions, jet penetration decreased as chamber diameter decreased, as the jet PI increased, and as the momentum ratio decreased. These interactions provide insight into why regurgitant jet size is not always a good estimate of regurgitant severity.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(4):506-510. doi:10.1115/1.2796037.

Employing a validated finite volume code, a computer-aided design of the distal end of a femoral graft-artery junction has been considered to simulate transient three-dimensional blood flow for various flow input waveforms. The study relies on the hypothesis that large sustained wall shear stress gradients play a major role in the rapid recurrence of intimal hyperplasia plus atheroma after bypass surgery, leading to early graft failure. Two new dimensionless parameters have been introduced to correlate flow waveform characteristics with the severity of nonuniform hemodynamics and hence the potential risk for restenosis. The transient and, more importantly, the time-averaged wall shear stress gradient distributions shown, map out the junction areas which are still susceptible to restenosis, especially the toe region. Future geometric modifications will further reduce disturbed flow patterns and hence the probability of graft failure.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(4):511-519. doi:10.1115/1.2796038.

Albumin transport in a stenosed artery configuration is analyzed numerically under steady and pulsatile flow conditions. The flow dynamics is described applying the incompressible Navier-Stokes equations for Newtonian fluids, the mass transport is modelled using the convection diffusion equation. The boundary conditions describing the solute wall flux take into account the concept of endothelial resistance to albumin flux by means of a shear dependent permeability model based on experimental data. The study concentrates on the influence of steady and pulsatile flow patterns and of regional variations in vascular geometry on the solute wall flux and on the ratio of endothelial resistance to concentration boundary layer resistance. The numerical solution of the Navier-Stokes equations and of the transport equation applies the finite element method where stability of the convection dominated transport process is achieved by using an upwind procedure and a special subelement technique. Numerical simulations are carried out for albumin transport in a stenosed artery segment with 75 percent area reduction representing a late stage in the progression of an atherosclerotic disease. It is shown that albumin wall flux varies significantly along the arterial section, is strongly dependent upon the different flow regimes and varies considerably during a cardiac cycle. The comparison of steady results and pulsatile results shows differences up to 30 percent between time-averaged flux and steady flux in the separated flow region downstream the stenosis.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(4):520-528. doi:10.1115/1.2796039.

The bidirectional cavopulmonary anastomosis (BCPA or bidirectional Glenn) is an operation to treat congenital heart diseases of the right heart by diverting the systemic venous return from the superior vena cava to both lungs. The main goal is to provide the correct perfusion to both lungs avoiding an excessive increase in systemic venous pressure. One of the factors which can affect the clinical outcome of the surgically reconstructed circulation is the amount of pulsatile blood flow coming from the main pulmonary artery. The purpose of this work is to analyse the influence of this factor on the BCPA hemodynamics. A 3-D finite element model of the BCPA has been developed to reproduce the flow of the surgically reconstructed district. Geometry and hemodynamic data have been taken from angiocardiogram and catheterization reports, respectively. On the basis of the developed 3-D model, four simulations have been performed with increasing pulsatile blood flow rate from the main pulmonary artery. The results show that hemodynamics in the pulmonary arteries are greatly influenced by the amount of flow through the native main pulmonary artery and that the flow from the superior vena cava allows to have a similar distribution of the blood to both lungs, with a little predilection for the left side, in agreement with clinical postoperative data.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(4):529-537. doi:10.1115/1.2796040.

The dynamics of intraventricular blood flow, i.e. its rapid evolution, implies the rise of intraventricular pressure gradients (IPGs) characteristic of the inertia-driven events as experimentally observed by Pasipoularides (1987, 1990) and by Falsetti et al. (1986). The IPG time course is determined by the wall contraction which, in turn, depends on the load applied, namely the intraventricular pressure which is the sum of the aortic pressure (i.e., the systemic net response) and the IPG. Hence the IPGs account, at least in part, for the wall movement. These considerations suggest the necessity of a comprehensive analysis of the ventricular mechanics involving both ventricular wall mechanics and intraventricular fluid dynamics as each domain determines the boundary conditions of the other. This paper presents a computational approach to ventricular ejection mechanics based on a fluid-structure interaction calculation for the evaluation of the IPG time course. An axisymmetric model of the left ventricle is utilized. The intraventricular fluid is assumed to be Newtonian. The ventricle wall is thin and is composed of two sets of counter-rotating fibres which behave according to the modified version of Wong’s sarcomere model proposed by Montevecchi and Pietrabissa and Pietrabissa et al. (1987, 1991). The full Navier-Stokes equations describing the fluid domain are solved using Galerkin’s weighted residual approach in conjunction with finite element approximation (FIDAP). The wall displacement is solved using the multiplane quasi-Newton method proposed by Buzzi Ferraris and Tronconi (1985). The interaction procedure is performed by means of an external macro which compares the flow fields and the wall displacement and appropriately modifies the boundary conditions to reach the simultaneous and congruous convergence of the two problems. The results refer to a simulation of the ventricular ejection with a heart rate of 72 bpm. In this phase the ventricle ejects 61 cm3 (ejection fraction equal to 54 percent) and the ventricular pressure varies from 78 mmHg to 140 mmHg. The IPG show an oscillating behaviour with two major peaks at the beginning (11.09 mmHg) and at the end (4.32) of the ejection phase, when the flow rate hardly changes, according to the experimental data. Furthermore the wall displacement, the wall stress and strain, the pressure and velocity fields are calculated and reported.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(4):538-544. doi:10.1115/1.2796041.

Red blood cells undergo continual deformation when traversing microvessels in living tissues. This may contribute to higher resistance to blood flow observed in living microvessels, compared with that in corresponding uniform glass tubes. We use a theoretical model to simulate single-file motion of red cells though capillaries with variable cross-sections, assuming axisymmetric geometry. Effects of cell membrane shear viscosity and elasticity are included, but bending resistance is neglected. Lubrication theory is used to describe the flow of surrounding plasma. When a red cell encounters a region of capillary narrowing, additional energy is dissipated, due to membrane viscosity, and due to narrowing of the lubrication layer, increasing the flow resistance. Predicted resistance to cell motion in a vessel with periodic constrictions (diameter varying between 5 μm and 4 μm) is roughly twice that in a uniform vessel with diameter 4.5 μm. Effects of transient red cell deformations may contribute significantly to blood flow resistance in living microvessels.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(4):545-556. doi:10.1115/1.2796042.

Crack formation and propagation is a significant element of the degeneration process in articular cartilage. In order to understand this process, and separate the relative importance of structural overload and material failure, methods for measuring the fracture toughness of cartilage are needed. In this paper, two such methods are described and used to measure fracture properties of cartilage from the canine patella. A modified single edge notch (MSEN) specimen was used to measure J , and a trouser tear test was used to measure T , both measures of fracture toughness with units of kN/m. A pseudo-elastic modulus was also obtained from the MSEN test. Several potential error sources were examined, and results for the MSEN test compared with another method for measuring the fracture parameter for urethane rubber. Good agreement was found. The two test methods were used to measure properties of cartilage from the patellae of 12 canines: 4–9 specimens from each of 12 patellae, with 5 right-left pairs were tested. Values of J ranged from 0.14–1.2 kN/m. J values correlated with T and were an average of 1.7 times larger than T . A variety of failure responses was seen in the MSEN tests, consequently a grade of 0 to 3 was assigned to each test, where 0 represented a brittle-like crack with minimal opening and 3 represented plastic flow with no crack formation. The initial cracks in 12/82 specimens did not propagate and were assigned to grade 3. The method for reducing data in the MSEN test assumed pseudo-elastic response and could not be used for the grade 3 specimens. Stiffness did not correlate with J . Neither J nor T was statistically different between right-left pairs, but varied between animals. The test methods appear useful for providing a quantitative measure of fracture toughness for cartilage and other soft materials.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(4):557-564. doi:10.1115/1.2796043.

A series of experiments was performed to determine the effect of diabetes on the viscoelastic properties of knee joint ligaments. The experimental model was collateral ligaments from spontaneously diabetic, hyperglycemic (BBZDP/Wor) rats, and various controls including nondiabetic littermates, insulin treated diabetic rats, and alloxan treated rats. Material properties were measured using a dynamic, uniaxial loading paradigm. Ligaments were subjected to load controlled, sinusoidal tensile testing, using frequencies from 0.1 to 2.0 Hz. The resulting data were used to determine the storage and loss compliances of the ligaments Storage compliance, which reflects tissue elastic properties, did not differ between groups Loss compliance, which reflects the viscous component of the tissue response, was increased in the hyperglycemic animals. Thus, hyperglycemic diabetes affects tissue mechanical properties through the viscous rather than the elastic component of the response to dynamic loading. Rats treated with alloxan to induce diabetes did not show an increase in loss compliance.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(4):565-574. doi:10.1115/1.2796044.

The purpose of this study was to critically evaluate the modeling potential of proposed optimization cost functions for predicting muscle forces during isometric loading. Models of the muscles about the elbow (eleven muscles) and wrist (five muscles) were constructed. The models accounted for muscle moment arms, physiological cross-sectional area, specific tension, and percent fiber type. Five nonlinear optimization cost functions, a representative sample of those proposed to date, were analyzed: minimizing the sums of muscle force2 , stress2 , stress3 , (normalized force)2 , and minimizing fatigue. Several different protocols were implemented, including elbow models which balanced combinations of flexion-extension, supination-pronation, and varus-valgus loads. Theoretical predictions were compared with EMG data of muscle activation changes as a function of load direction and muscle coactivation relationships. Results indicate a strong dependence of muscle coordination predictions on the number of degrees of freedom balanced. The choice of cost function had little influence on the results. The cost functions examined were not able to reliably estimate muscle activation as a function of load direction. Furthermore, specific synergic relationships between muscle pairs could not be accurately represented. An error analysis indicated that the discrepancies between predicted values and actual values could not be explained by errors in physiological measurements, as the differences between these two were relatively insensitive to changes in the anatomical parameters. In short, no particular cost function was found to adequately represent actual muscle activity at the elbow, although predictions at the wrist were more favorable due to differences in the degrees of freedom at the joints.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(4):575-578. doi:10.1115/1.2796045.

In an attempt to test the hypothesis of spontaneous hip fracture, seven pairs of femurs, with ages ranging from 59 to 90, were tested under two loading conditions designed to simulate muscular contraction. Simulated iliopsoas contraction produced femoral neck fractures at an average normalized ultimate load of 5.2 ± 0.8 times body weight. Simulated gluteus medius contraction produced sub-/inter-trochanteric fractures at an average normalized ultimate load of 4.1 ± 0.6 times body weight. The average ultimate load for all specimens was 3040 ± 720 N. Fracture patterns produced by both loading conditions were clinically relevant. The results from this study suggest that abnormal contraction produced by major rotator muscles could induce hip fracture.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(4):579-585. doi:10.1115/1.2796047.

Clinical follow-up studies of joint replacements indicate that debonding of the implant from the bone-cement is the first mechanical event of loosening. Debonding can occur due to unsustainable interface stresses, usually initiated from defects along the interface. Such defects, or flaws, are inevitably introduced during the surgical procedure and from polymerisation shrinkage. Debonding leads to increased stresses within the cement mantle. This study is concerned with modelling the propagation of a crack from the debonded region on the cement/implant interface under physiological loading conditions for different implant materials and prosthesis designs. Using the theory of linear fracture mechanics for bimaterial interfaces, the behaviour of a crack along an interface between implant materials, under various states of stress, is studied. Specifically, a model is developed to determine the conditions under which a debonded region, along an otherwise bonded interface, will either propagate along the interface or will “kink” into the cement mantle. The relationship between the stress state and the crack propagation direction at the interface is then predicted for different interface materials, and it is shown that different crack directions exist for different materials, even when the stress state is the same. Furthermore, the crack behavior is shown to be dependent on the ratio of normal stress to shear stress at the interface and this may be important for the design optimisation of load-bearing cemented prostheses. Finally, the likelihood that an interface crack will propagate into the cement mantle is explored using a suitable fracture criterion.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(4):586-594. doi:10.1115/1.2796048.

A mechanical linkage with electro-magnetic sensors (a displacement transducer) is described, which may be used to measure accurately the relative motion at a bony junction such as a fracture. The linkage may be fixed to bone screws of externally-fixated fractures during routine patient activity, to measure three-dimensional inter fragmentary displacements arising from dynamic loading. Movements of the linkage are monitored by six Hall Effect devices for the six degrees of freedom (three orthogonal translations and three rotations about the translating axes). Measurements are made within error bounds of ±0.025 mm and ±0.025 deg over a range of 5 mm for the two orthogonal transverse translations, 8 mm for axial translation and 8 deg for the three rotations. Movements at the linkage, remote from the fracture, are then translated mathematically to the fracture site, assuming rigid screw contact with the bone. Displacements of the distal fragment in relation to the proximal, at the fracture center, can then be expressed anatomically through anterior, medial, and distal translations, and rotations in the sagittal, coronal, or transverse planes.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(4):597-600. doi:10.1115/1.2796050.

An intermittent cervical traction modality with closed-loop traction force control based on EMG biofeedback was developed and used for clinical study. This system consists of a EMG scanner, on-line self-adjusted traction force controller, audio/video alarm system, real time therapeutic status display, computer interface hardware, and control software. Twenty-four subjects with diagnosed cervical radiculopathy and muscle spasm symptom who were randomly divided into two groups served as subjects in this study. The control and experimental groups were treated with conventional open loop and new EMG biofeedback closed loop traction control protocols respectively. The results of this study indicate that the average reductions in paraspinal EMG signal during traction after 7 weeks treatment for experimental and control groups were 71 and 50 percent, respectively (p < 0.001). These results not only support the clinical use of intermittent, sitting traction to produce cervical paraspinal muscle relaxation, but also revealed that the average myoelectric activity of cervical paraspinal muscle during traction was reduced as traction force increased over the 7-week duration of traction treatment. Through EMG biofeedback traction force control, muscle injury, neck soreness, or pain after traction may be avoided.

Commentary by Dr. Valentin Fuster

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