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TECHNICAL PAPERS

J Biomech Eng. 2000;122(6):553-569. doi:10.1115/1.1324665.

Tissues change in many ways in the period that they are part of a living organism. They are created in fairly repeatable structural patterns, and we know that the patterns are due to both the genes and the (mechanical) environment, but we do not know exactly what part or percentage of a particular pattern to consider the genes, or the environment, responsible for. We do not know much about the beginning of tissue construction (morphogenesis) and we do not know the methods of tissue construction. When the tissue structure is altered to accommodate a new loading, we do not know how the decision is made for the structural reconstruction. We do know that tissues grow or reconstruct themselves without ceasing to continue with their structural function, but we do not understand the processes that permit them to accomplish this. Tissues change their structures to altered mechanical environments, but we are not sure how. Tissues heal themselves and we understand little of the structural mechanics of the process. With the objective of describing the interesting unsolved mechanics problems associated with these biological processes, some aspects of the formation, growth, and adaptation of living tissues are reviewed. The emphasis is on ideas and models. Beyond the objective is the hope that the work will stimulate new ideas and new observations in the mechanical and chemical aspects of developmental biology. [S0148-0731(00)00106-0]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;122(6):570-575. doi:10.1115/1.1318906.

“Tissue engineering” uses implanted cells, scaffolds, DNA, protein, and/or protein fragments to replace or repair injured or diseased tissues and organs. Despite its early success, tissue engineers have faced challenges in repairing or replacing tissues that serve a predominantly biomechanical function. An evolving discipline called “functional tissue engineering” (FTE) seeks to address these challenges. In this paper, the authors present principles of functional tissue engineering that should be addressed when engineering repairs and replacements for load-bearing structures. First, in vivo stress/strain histories need to be measured for a variety of activities. These in vivo data provide mechanical thresholds that tissue repairs/replacements will likely encounter after surgery. Second, the mechanical properties of the native tissues must be established for subfailure and failure conditions. These “baseline data” provide parameters within the expected thresholds for different in vivo activities and beyond these levels if safety factors are to be incorporated. Third, a subset of these mechanical properties must be selected and prioritized. This subset is important, given that the mechanical properties of the designs are not expected to completely duplicate the properties of the native tissues. Fourth, standards must be set when evaluating the repairs/replacements after surgery so as to determine, “how good is good enough?” Some aspects of the repair outcome may be inferior, but other mechanical characteristics of the repairs and replacements might be suitable. New and improved methods must also be developed for assessing the function of engineered tissues. Fifth, the effects of physical factors on cellular activity must be determined in engineered tissues. Knowing these signals may shorten the iterations required to replace a tissue successfully and direct cellular activity and phenotype toward a desired end goal. Finally, to effect a better repair outcome, cell-matrix implants may benefit from being mechanically stimulated using in vitro “bioreactors” prior to implantation. Increasing evidence suggests that mechanical stress, as well as other physical factors, may significantly increase the biosynthetic activity of cells in bioartificial matrices. Incorporating each of these principles of functional tissue engineering should result in safer and more efficacious repairs and replacements for the surgeon and patient. [S0148-0731(00)00206-5]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;122(6):576-586. doi:10.1115/1.1324669.

A biphasic mixture model is developed that can account for the observed tension-compression nonlinearity of cartilage by employing the continuum-based Conewise Linear Elasticity (CLE) model of Curnier et al. (J. Elasticity, 37 , 1–38, 1995) to describe the solid phase of the mixture. In this first investigation, the orthotropic octantwise linear elasticity model was reduced to the more specialized case of cubic symmetry, to reduce the number of elastic constants from twelve to four. Confined and unconfined compression stress-relaxation, and torsional shear testing were performed on each of nine bovine humeral head articular cartilage cylindrical plugs from 6 month old calves. Using the CLE model with cubic symmetry, the aggregate modulus in compression and axial permeability were obtained from confined compression (H−A=0.64±0.22 MPa, kz=3.62±0.97×10−16 m4/N⋅s,r2=0.95±0.03), the tensile modulus, compressive Poisson ratio, and radial permeability were obtained from unconfined compression (E+Y=12.75±1.56 MPa, v=0.03±0.01,kr=6.06±2.10×10−16 m4/N⋅s,r2=0.99±0.00), and the shear modulus was obtained from torsional shear (μ=0.17±0.06 MPa). The model was also employed to predict the interstitial fluid pressure successfully at the center of the cartilage plug in unconfined compression (r2=0.98±0.01). The results of this study demonstrate that the integration of the CLE model with the biphasic mixture theory can provide a model of cartilage that can successfully curve-fit three distinct testing configurations while producing material parameters consistent with previous reports in the literature. [S0148-0731(00)00306-X]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;122(6):587-593. doi:10.1115/1.1319658.

We hypothesize that a direction-dependent flow resistance exists in the intervertebral disc due to constriction flow in the cartilage endplates. A comparison of the hydrostatic pressure in the nucleus of the healthy intervertebral disc during daily loading with the relatively low osmotic swelling pressure during rest, suggests the necessity of such directiondependent flow resistance to ensure that all the fluid exuded from the disc during loading is recovered during rest. A physical model demonstrating the direction-dependent resistance of constriction flow in a poroelastic solid is presented. A finite element model was developed and validated against this physical model. The finite element model showed that decrease of the constriction hole area not only increases the resistance to fluid flow, but also causes the direction-dependency of flow resistance to decrease. Through this mechanism, endplate sclerosis could affect normal daily fluid exchange in the intervertebral disc, resulting in decreased mass transport and/or dehydration of the disc. [S0148-0731(00)00406-4]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;122(6):594-599. doi:10.1115/1.1319659.

This study was performed to determine the contribution of extrinsic cell infiltration and revascularization into the patellar tendon in alteration of the mechanical properties of the patellar tendon after intrinsic fibroblast necrosis using 77 rabbits. In Group I, after the patellar tendon underwent the in situ freeze-thaw treatment, a wrapping treatment was performed to inhibit any extrinsic cell infiltration into the tendon. In Group II, the patellar tendon underwent the freeze-thaw treatment without any of the wrapping treatment. In Group III, the patellar tendon underwent the same wrapping treatment but without any freeze-thaw treatment. The cell culture study demonstrated that the in situ freeze-thaw treatment killed from 97 to 100 percent of the cells in the patellar tendon. Histologically, no cells were found in the midsubstance of the patellar tendon in Group I at 1, 3, and 6 weeks. In Group II, a number of cells and some vessels were found scattered in the tendon at 3 and 6 weeks. Mechanically, the elastic modulus and the tensile strength of the patellar tendon of Group II were significantly lower than those of Groups I and III at 3 and 6 weeks. These facts suggest that extrinsic cell infiltration and revascularization from the surrounding tissues accelerate the deterioration of the mechanical properties of the patellar tendon matrix after intrinsic fibroblast necrosis. [S0148-0731(00)00506-9]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;122(6):600-603. doi:10.1115/1.1324007.

To determine which exercises do not overload the graft-fixation complex during intensive rehabilitation from reconstructive surgery of the anterior cruciate ligament (ACL), it would be useful to measure ACL graft loads during rehabilitative activities in vivo in humans. A previous paper by Ventura et al. (1998) reported on the design of an implantable transducer integrated into a femoral fixation device and demonstrated that the transducer could be calibrated to measure graft loads to better than 10 percent full-scale error in cadaveric knees. By measuring both the static and fatigue strengths of the transducer, the purpose of the present study was to determine whether the transducer could be safely implanted in humans without risk of structural failure. Eight devices were loaded to failure statically. Additionally, seven devices were tested using the up-and-down method to estimate the median fatigue strength at a life of 225,000 cycles. The average ultimate strength was 1856±74 N and the median fatigue strength was 441 N at a life of 225,000 cycles. The maximum graft load during normal daily activities is estimated to be 500 N and the 225,000 cycle life corresponds to that of the average healthy individual during a 12-week period. Considering that patients who have had an ACL reconstruction are less ambulatory than normal immediately following surgery and that biologic incorporation of the graft should be well developed by 12 weeks thus decreasing the load transmitted to the fixation device, the FDT can be safely implanted in humans without undue risk of structural failure. [S0148-0731(00)00606-3]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;122(6):604-607. doi:10.1115/1.1324668.

The technique of surgical repair for zone two flexor tendon injuries has been debated extensively throughout the years, yet adhesion formation, suture rupture, and suture locking on the pulley edge remain possible consequences of a poor repair. The partially lacerated tendon is especially challenging to treat since there can be justification for not intervening surgically. In a partial laceration canine model we measured failure load and suture gap formation for tendons repaired with the Lee, modified four-strand Savage, Kessler, modified Kessler, and Augmented Becker core suture techniques and with a simple running peripheral suture. The modified Kessler (106.3 N, SD 18.8 N) and modified Savage (108.2 N, SD 19.9 N) repair techniques had a significantly higher failure load than the Lee (85.0 N, SD 20.6 N) suture method (p<0.05), while there were no differences among the other techniques. There were no significant differences in resistance to gap formation among the repair techniques, with the mean values ranging from 38.9 N/mm (SD 15.7 N/mm) using the simple running suture to 53.2 N/mm (SD 25.8 N/mm) with the Kessler repair. The mean load to produce a 1.5 mm repair site gap ranged from 71.1 N (SD 21.5 N) in the Lee repair to 91.3 N (SD 22.2 N) in the Augmented Becker repair although there were no significant differences among repair methods. All repair methods were much weaker than tendons left unrepaired (184.7 N, SD 41.3 N). [S0148-0731(00)00706-8]

Topics: Maintenance , Tendons , Stress
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;122(6):608-614. doi:10.1115/1.1319660.

With the aim of studying mechanisms of the remodeling of tendons and ligaments, the effects of stress shielding on the rabbit patellar tendon were studied by performing tensile and stress relaxation tests in the transverse direction. The tangent modulus, tensile strength, and strain at failure of non-treated, control patellar tendons in the transverse direction were 1272 kPa, 370 kPa, and 40.5 percent, respectively, whereas those of the tendons stress-shielded for 1 week were 299 kPa, 108 kPa, and 40.4 percent, respectively. Stress shielding markedly decreased tangent modulus and tensile strength in the transverse direction, and the decreases were larger than those in the longitudinal direction, which were determined in our previous study. For example, tensile strength in the transverse and longitudinal direction decreased to 29 and 50 percent of each control value, respectively, after 1 week stress shielding. In addition, the stress relaxation in the transverse direction of stress-shielded patellar tendons was much larger than that of non-treated, control ones. In contrast to longitudinal tensile tests for the behavior of collagen, transverse tests reflect the contributions of ground substances such as proteoglycans and mechanical interactions between collagen fibers. Ground substances provide lubrication and spacing between fibers, and also confer viscoelastic properties. Therefore, the results obtained from the present study suggest that ground substance matrix, and interfiber and fiber–matrix interactions have important roles in the remodeling response of tendons to stress. [S0148-0731(00)00806-2]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;122(6):615-622. doi:10.1115/1.1324667.

In vivo, tissue-level, mechanical thresholds for axonal injury were determined by comparing morphological injury and electrophysiological impairment to estimated tissue strain in an in vivo model of axonal injury. Axonal injury was produced by dynamically stretching the right optic nerve of an adult male guinea pig to one of seven levels of ocular displacement (Nlevel=10;Ntotal=70). Morphological injury was detected with neurofilament immunohistochemical staining (NF68, SMI32). Simultaneously, functional injury was determined by the magnitude of the latency shift of the N35 peak of the visual evoked potentials (VEPs) recorded before and after stretch. A companion set of in situ experiments (Nlevel=5) was used to determine the empirical relationship between the applied ocular displacement and the magnitude of optic nerve stretch. Logistic regression analysis, combined with sensitivity and specificity measures and receiver operating characteristic (ROC) curves were used to predict strain thresholds for axonal injury. From this analysis, we determined three Lagrangian strain-based thresholds for morphological damage to white matter. The liberal threshold, intended to minimize the detection of false positives, was a strain of 0.34, and the conservative threshold strain that minimized the false negative rate was 0.14. The optimal threshold strain criterion that balanced the specificity and sensitivity measures was 0.21. Similar comparisons for electrophysiological impairment produced liberal, conservative, and optimal strain thresholds of 0.28, 0.13, and 0.18, respectively. With these threshold data, it is now possible to predict more accurately the conditions that cause axonal injury in human white matter. [S0148-0731(00)00906-7]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;122(6):623-629. doi:10.1115/1.1322034.

This study characterized the geometry and mechanical properties of the cervical ligaments from C2–T1 levels. The lengths and cross-sectional areas of the anterior longitudinal ligament, posterior longitudinal ligament, joint capsules, ligamentum flavum, and interspinous ligament were determined from eight human cadavers using cryomicrotomy images. The geometry was defined based on spinal anatomy and its potential use in complex mathematical models. The biomechanical force-deflection, stiffness, energy, stress, and strain data were obtained from 25 cadavers using in situ axial tensile tests. Data were grouped into middle (C2–C5) and lower (C5–T1) cervical levels. Both the geometric length and area of cross section, and the biomechanical properties including the stiffness, stress, strain, energy, and Young’s modulus, were presented for each of the five ligaments. In both groups, joint capsules and ligamentum flavum exhibited the highest cross-sectional area (p<0.005), while the longitudinal ligaments had the highest length measurements. Although not reaching statistical significance, for all ligaments, cross-sectional areas were higher in the C5–T1 than in the C2–C5 group; and lengths were higher in the C2–C5 than in the C5–T1 group with the exception of the flavum (Table 1 in the main text). Force-deflection characteristics (plots) are provided for all ligaments in both groups. Failure strains were higher for the ligaments of the posterior (interspinous ligament, joint capsules, and ligamentum flavum) than the anterior complex (anterior and posterior longitudinal ligaments) in both groups. In contrast, the failure stress and Young’s modulus were higher for the anterior and posterior longitudinal ligaments compared to the ligaments of the posterior complex in the two groups. However, similar tendencies in the structural responses (stiffness, energy) were not found in both groups. Researchers attempting to incorporate these data into stress-analysis models can choose the specific parameter(s) based on the complexity of the model used to study the biomechanical behavior of the human cervical spine. [S0148-0731(00)01006-2]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;122(6):630-639. doi:10.1115/1.1318904.

A novel three-dimensional numerical model of the foot, incorporating, for the first time in the literature, realistic geometric and material properties of both skeletal and soft tissue components of the foot, was developed for biomechanical analysis of its structural behavior during gait. A system of experimental methods, integrating the optical Contact Pressure Display (CPD) method for plantar pressure measurements and a Digital Radiographic Fluoroscopy (DRF) instrument for acquisition of skeletal motion during gait, was also developed in this study and subsequently used to build the foot model and validate its predictions. Using a Finite Element solver, the stress distribution within the foot structure was obtained and regions of elevated stresses for six subphases of the stance (initial-contact, heel-strike, midstance, forefoot-contact, push-off, and toe-off) were located. For each of these subphases, the model was adapted according to the corresponding fluoroscopic data, skeletal dynamics, and active muscle force loading. Validation of the stress state was achieved by comparing model predictions of contact stress distribution with respective CPD measurements. The presently developed measurement and numerical analysis tools open new approaches for clinical applications, from simulation of the development mechanisms of common foot disorders to pre- and post-interventional evaluation of their treatment. [S0148-0731(00)01106-7]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;122(6):640-646. doi:10.1115/1.1318905.

The chin bar of a motorcycle helmet protects the rider from facial and head injuries. To evaluate the protective performance of chin bars against head injuries from facial impacts, an explicit finite element method was used to simulate the Snell Memorial Foundation test and a proposed drop test. The maximum acceleration and Head Injury Criterion (HIC) were employed to assess the impact-absorbing capability of the chin bar. The results showed that the proposed approach should be more practical than the Snell test, and provided more information for improving the chin bar design to protect against head injuries. The shell stiffness was important in determining the protective ability of the chin bar, but a chin bar with only an outer shell and comfort foam offered inadequate protection. An energy-absorbing liner was essential to increase the protective performance of the chin bar and the liner density should be denser than that used in the cranial portion of the helmet. For the chin bar with energy-absorbing liner, a shell design that is less stiff would provide better protection. [S0148-0731(00)01206-1]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;122(6):647-651. doi:10.1115/1.1322035.

A clamped cantilever beam test was developed to determine the fatigue crack propagation rate of the CoCr alloy/PMMA cement interface at high crack tip phase angles. A combination of finite element and experimental methods was used to determine the fatigue crack growth rates of two different CoCr alloy/PMMA cement surfaces. A crack tip phase angle of 69 deg was found, indicating that loading at the crack tip was mixed-mode with a large degree of in-plane shear loading. The energy required to propagate a crack at the interface was much greater for the plasma-sprayed CoCr surface when compared to the PMMA-precoated satin finish (p<0.001). Both interface surfaces could be modeled using a Paris fatigue crack growth law over crack propagation rates of 10−4 to 10−9 m/cycle.[S0148-0731(00)01306-6]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;122(6):652-660. doi:10.1115/1.1322036.

The study was aimed to test the hypothesis that in the knee extension range 100 to 30 deg, the patellar “out-of-plane” tracking pattern is controlled by the passive restraint provided by the topographic interaction of the patellofemoral contacting surfaces. The out-of-plane tracking pattern, i.e., the pattern of patellar displacements not in the plane of knee extension/flexion, consists of translation in the medial–lateral direction, and rotations about the anterior–posterior axis (spin) and the proximal–distal axis (tilt). Using 15 fresh-frozen knees subjected to extensor moment magnitudes comparable to those in the “static-lifting” activity (foot-ground reaction=334 N), the patellar displacements were measured using a calibrated six-degree-of-freedom electromechanical goniometer. The topographies of the trochlear and retropatellar surfaces were then measured using a calibrated traveling dial-gage arrangement and the same coordinate system used for the displacement measurements. Three indices were defined to quantify particular natural features of the three-dimensional topographies that are expected to control the patellar displacements. Correlation of the indices with their corresponding displacements showed that topographic interaction was significant in the control of all three displacements. However, for patellar spin, unlike for the other two displacements, the direction of the active quadriceps tension vector was also a significant controlling factor. Patellar medial–lateral translation was found to be controlled dominantly by the trochlear topography, while retropatellar topography also had a significant role in the control of the other two displacements. [S0148-0731(00)01406-0]

Topics: Particle spin , Tension , Knee
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;122(6):661-666. doi:10.1115/1.1318907.

Maximal wall shear stress (MWSS) in the convergent part of a stenosis is calculated by the interactive boundary-layer theory. A dimensional analysis of the problem shows that MWSS depends only on a few measurable parameters. A simple relationship between MWSS and these parameters is obtained, validated, and used to calculate the magnitude of MWSS in a carotid stenosis, as a function of the patency of the circle of Willis and the stenotic pattern. This demonstrates the huge effect of collateral pathways. Elevated MWSS are observed even in moderate stenoses, provided they are associated with a contralateral occlusion, a large anterior, and narrow posterior communicating arteries, suggesting a potential risk of embolus release in this configuration. [S0148-0731(00)01506-5]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;122(6):667-674. doi:10.1115/1.1318941.

A two-dimensional axisymmetric computer model is developed for the simulation of the filling flow in the left ventricle (LV). The computed results show that vortices are formed during the acceleration phases of the filling waves. During the deceleration phases these are amplified and convected into the ventricle. The ratio of the maximal blood velocity at the mitral valve (peak E velocity) to the flow wave propagation velocity (WPV) of the filling wave is larger than 1. This hemodynamic behavior is also observed in experiments in vitro (Steen and Steen, 1994, Cardiovasc. Res., 28 , pp. 1821–1827) and in measurements in vivo with color M-mode Doppler echocardiography (Stugaard et al., 1994, J. Am. Coll. Cardiol., 24 , 663–670). Computed intraventricular pressure profiles are similar to observed profiles in a dog heart (Courtois et al., 1988, Circulation, 78 , pp. 661–671). The long-term goal of the computer model is to study the predictive value of noninvasive parameters (e.g., velocities measured with Doppler echocardiography) on invasive parameters (e.g., pressures, stiffness of cardiac wall, time constant of relaxation). Here, we show that higher LV stiffness results in a smaller WPV for a given peak E velocity. This result may indicate an inverse relationship between WPV and LV stiffness, suggesting that WPV may be an important noninvasive index to assess LV diastolic stiffness, LV diastolic pressure and thus atrial pressure (preload). [S0148-0731(00)01606-X]

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J Biomech Eng. 2000;122(6):675-677. doi:10.1115/1.1319661.

Coronary flow estimates were made for a spiral coronary artery segment (identified from a post-mortem replica casting) by using a modified Dean number based on the approximate coil radius of curvature, as suggested earlier. The estimates were found to correlate experimental pressure drop data for helical coiled tubes. Over a physiological range of mean Reynolds numbers from 100 to 400 for blood flow through main coronary arteries, estimates of the flow resistance increase relative to a straight lumen segment ranged from about 20 to 80 percent, and were of similar magnitude to those found in a flow study in a sinuous coronary vessel segment with no spiral. [S0148-0731(00)01706-4]

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2000;122(6):677-680. doi:10.1115/1.1318942.

Bone remodeling is widely viewed as a dynamic process—maintaining bone structure through a balance between the opposed activities of osteoblast and osteoclast cells—in which the stability problem is often pointed out. By an analytical approach, we present a bone remodeling model applied to n unit-elements in order to analyze the stationary states and the condition of their stability. In addition, this theory has been simulated in a computer model using the Finite Element Method (FEM) to show a relationship between the bone remodeling process and the stability analysis. [S0148-0731(00)01806-9]

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