J Biomech Eng. 1998;120(6):693-696. doi:10.1115/1.2834880.

The quasi-static and dynamic bending responses of the human mid-lower cervical spine were determined using cadaver intervertebral joints fixed at the base to a six-axis load cell. Flexion bending moment was applied to the superior end of the specimen using an electrohydraulic piston. Each specimen was tested under three cycles of quasi-static load-unload and one high-speed dynamic load. A total of five specimens were included in this study. The maximum intervertebral rotation ranged from 11.0 to 15.4 deg for quasi-static tests and from 22.9 to 34.4 deg for dynamic tests. The resulting peak moments at the center of the intervertebral joint ranged from 3.8 to 6.9 Nm for quasi-static tests and from 14.0 to 31.8 Nm for dynamic tests. The quasi-static stiffness ranged from 0.80 to 1.35 Nm/deg with a mean of 1.03 Nm/deg (±0.11 Nm/deg). The dynamic stiffness ranged from 1.08 to 2.00 Nm/deg with a mean of 1.50 Nm/deg (±0.17 Nm/deg). The differences between the two stiffnesses were statistically significant (p < 0.01). Exponential functions were derived to describe the quasi-static and dynamic moment-rotation responses. These results provide input data for lumped-parameter models and validation data for finite element models to better investigate the biomechanics of the human cervical spine.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(6):697-703. doi:10.1115/1.2834881.

The maximum pore fluid pressures due to uniaxial compression are determined for both the vascular porosity (Haversian and Volkmann’s canals) and the lacunar–canalicular porosity of live cortical bone. It is estimated that the peak pore water pressure will be 19 percent of the applied axial stress in the vascular porosity and 12 percent of the applied axial stress in the lacunar–canalicular porosity for an impulsive step loading. However, the estimated relaxation time for the vascular porosity (1.36 μs) is three orders of magnitude faster than that estimated for the lacunar–canalicular porosity (4.9 ms). Thus, under physiological loading, which has a stress rise time generally larger than 1 ms, pressures higher than the vascular pressure cannot be sustained in the vascular porosity due to the swift pressure relaxation in this porosity (unless the fluid drainage through the boundary is obstructed). The model also predicts a slight hydraulic stiffening of the bulk modulus due to longer draining time of the lacunar–canalicular porosity. The undrained bulk modulus is 6 percent higher than the drained bulk modulus in this case.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(6):704-709. doi:10.1115/1.2834882.

Chronic degeneration of articular cartilage and bone in a rabbit model of post-traumatic osteoarthrosis has been hypothesized to occur due to acute stresses that exceed a threshold for injury. In this study, we impacted the rabbit patellofemoral joint at low and high intensities. High-intensity impacts produced degenerative changes in the joint, such as softening of retropatellar cartilage, as measured by indentation, an increase in histopathology of the cartilage, and an increase in thickness of sub-chondral bone underlying the cartilage. Low-intensity impacts did not cause these progressive changes. These data suggest that low-intensity impacts produced acute tissue stresses below the injury threshold, while high-intensity impacts produced stresses that exceeded the threshold for disease pathogenesis. This study begins to identify “safe” and “unsafe” ranges of acute tissue stress, using the rabbit patella, which may have future utility in the design of injury prevention devices for the human.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(6):710-714. doi:10.1115/1.2834883.

Structural remodeling during acute myocardial infarction affects ventricular wall stress and strain. To see whether acute myocardial infarction alters residual stress and strain in the left ventricle (LV), we measured opening angles in rat hearts after 30 minutes of left coronary artery occlusion. The mean opening angle in 18 ischemic hearts (51 ± 20 deg) was significantly greater than in five sham-operated controls (29 ± 11 deg, P < 0.05). To determine whether these alterations in residual strain may be associated with strain softening caused by systolic overstretch of the noncontracting ischemic tissue, we also measured opening angles in isolated hearts that had been passively inflated to high LV pressures (120 mmHg). The mean opening angle of the strain-softened hearts was not significantly different from the sham-operated hearts (34 ± 27 deg, P = 0.74). Mean collagen area fractions in the myocardium were not significantly different between ischemic hearts (0.027 ± 0.014) and the nonischemic group (0.022 ± 0.011). Although there were significant differences in opening angles measured with ischemia, they do not appear to be a result of altered extracellular collagen content or softening associated with overstretch. Thus, there is a significant change in residual strain associated with acute ischemia that may be related to changes in collagen fiber structure, myocyte structure, or metabolic state.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(6):715-719. doi:10.1115/1.2834884.

Theoretical considerations and observations of residual stress suggest that geometric remodeling in the heart may also alter residual stress and strain. We investigated whether changes in left ventricular geometry during physiologic growth were associated with corresponding changes in myocardial residual strain. In anesthetized rats from eight age groups ranging from 2–25+ weeks, the heart was arrested and isolated, and equatorial slices were obtained. The geometry of the intact, unloaded state was recorded, as well as the “opening angle” of the stress-free configuration after radial resection of the tissue slice. The tissue was fixed and embedded for histological examination of collagen area fraction. Heart weight increased 10-fold with age and unloaded internal radius increased almost 4-fold. However, wall thickness increased only 66 percent, so that the ratio of wall thickness to internal radius decreased significantly from 2.22 ± 0.29 (mean ± SD) at 2 weeks to 0.81 ± 0.47 at 25 weeks. Opening angle of the stress-free slice decreased significantly from 87 ± 16 deg at 2 weeks to 51 ± 16 deg, and correlated linearly with wall thickness/radius ratio. Collagen area fraction increased with age. Hence physiologic ventricular remodeling in rats decreases myocardial residual strain in proportion to the relative reduction in wall thickness–radius ratio.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(6):720-726. doi:10.1115/1.2834885.

Thermal stresses were studied in freezing of biomaterials containing significant amounts of water. An apparent specific heat formulation of the energy equation and a viscoelastic model for the mechanics problem were used to analyze the transient axi-symmetric freezing of a long cylinder. Viscoelastic properties were measured in an Instron machine. Results show that, before phase change occurs at any location, both radial and circumferential stresses are tensile and keep increasing until phase change begins. The maximum principal tensile stress during phase change increases with a decrease in boundary temperature (faster cooling). This is consistent with experimentally observed fractures at a lower boundary temperature. Large volumetric expansion during water to ice transformation was shown to be the primary contributor to large stress development. For very rapid freezing, relaxation may not be significant, and an elastic model may be sufficient.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(6):727-736. doi:10.1115/1.2834886.

A finite difference heat transfer model has been developed to predict the Safe Touch Temperatures (STT) for plates made of different materials. SST can be defined as the highest temperature at which no pain is felt when the surface is touched for a long enough period to allow safe handling of the equipment. The criterion used to quantify damage is the “damage function” that was originally proposed by Henriques and Moritz. There are several uncertainties present in the physiological and thermal properties of the skin that give rise to a solution range rather than a single solution. Certain simplifying assumptions are made that tend to yield solutions for STT that are toward the lower or “safe” end of the solution range. The model developed is a two-dimensional axisymmetric model in cylindrical coordinates. A finite difference scheme that uses the Alternating Direction Implicit method is used to solve the problem. It is a second-order scheme in both space and time domains. A parametric analysis of the model is performed to isolate those factors that affect the STT to the greatest extent. Data are presented for a variety of cases, which cover commonly observed ranges in material and geometric properties. It is found that the material properties, namely thermal conductivity and volumetric heat capacity, and the plate thickness ratio are the three most important parameters. These three parameters account for a range of STT from 56°C–100°C with thick metals at the low end and thin metals and plastics in the high range. This method represents a significant improvement over existing standard practices.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(6):737-742. doi:10.1115/1.2834887.

A new theoretical approach was used to study the nonlinear response of a microvascular segment subjected to a pressure step at one end. The method is suitable for both large and small deformations of the vessel wall in the case of an elastic response of the segment. It is shown that the use of this simulation permits an indirect determination of the compliance of the vessel. The procedure is applied in two cases of major interest: first the in-vivo study of the intermittent blood flow in the microcirculation, and second, the analysis of experiments using micropipettes. The resulting values of the compliance agree with other values found in the previous studies. The theoretical method is particularly adapted to nonlinear equations.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(6):743-749. doi:10.1115/1.2834888.

A new method for deriving limb segment motion from markers placed on the skin is described. The method provides a basis for determining the artifact associated with nonrigid body movement of points placed on the skin. The method is based on a cluster of points uniformly distributed on the limb segment. Each point is assigned an arbitrary mass. The center of mass and the inertia tensor of this cluster of points are calculated. The eigenvalues and eigenvectors of the inertia tensor are used to define a coordinate system in the cluster as well as to provide a basis for evaluating non-rigid body movement. The eigenvalues of the inertia tensor remain invariant if the segment is behaving as a rigid body, thereby providing a basis for determining variations for nonrigid body movement. The method was tested in a simulation model where systematic and random errors were introduced into a fixed cluster of points. The simulation demonstrated that the error due to nonrigid body movement could be substantially reduced. The method was also evaluated in a group of ten normal subjects during walking. The results for knee rotation and translation obtained from the point cluster method compared favorably to results previously obtained from normal subjects with intra-cortical pins placed into the femur and tibia. The resulting methodology described in this paper provides a unique approach to the measurement of in vivo motion using skin-based marker systems.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(6):750-756. doi:10.1115/1.2834889.

The relationships between the lengths of the ligaments and kinematics of the knee and quadriceps load, for low to physiologic levels of quadriceps loads, have not previously been studied. We investigated the effects of increasing levels of quadriceps force, necessary to balance increasing levels of externally applied flexion moments, on the kinematics of the tibiofemoral joint and on the separation distances between insertions of selected fibers of the major ligaments of the knee in twelve cadavera. Static measurements were made using a six-degree-of-freedom digitizer for flexion angles ranging from 0 to 120 deg in 15 deg increments. Quadriceps generated extension of the knee was performed by applying loads to the quadriceps tendon to equilibrate each of four magnitudes of external flexion moments equivalent to 8.33, 16.67, 25.00, and 33.33 percent of values previously reported for maximum isometric extension moments. The magnitude of quadriceps force increased linearly (p < 0.0001) as external flexion moment increased throughout the entire range of flexion. Anterior translation, internal rotation, and abduction of the tibia increased linearly (p < 0.0001, p < 0.001, p < 0.001) as external flexion moment and, hence, quadriceps load increased. For the fibers studied, the anterior cruciate ligament (p < 0.0076), posterior cruciate ligament (p < 0.0001), and medial collateral ligament (p < 0.0383) lengthened linearly while the lateral collateral ligament (p < 0.0124) shortened linearly as quadriceps load increased. Based on these results for low to physiologic levels of quadriceps loads, it is reasonable to assume that the ligament lengths or knee kinematics expected with higher quadriceps loads can be extrapolated.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(6):757-763. doi:10.1115/1.2834890.

The objectives of this study were to determine the longitudinal and transverse material properties of the human medial collateral ligament (MCL) and to evaluate the ability of three existing constitutive models to describe the material behavior of MCL. Uniaxial test specimens were punched from ten human cadaveric MCLs and tensile tested along and transverse to the collagen fiber direction. Using load and optical strain analysis information, the tangent modulus, tensile strength and ultimate strain were determined. The material coefficients for each constitutive model were determined using nonlinear regression. All specimens failed within the substance of the tissue. Specimens tested along the collagen fiber direction exhibited the typical nonlinear behavior reported for ligaments. This behavior was absent from the stress–strain curves of the transverse specimens. The average tensile strength, ultimate strain, and tangent modulus for the longitudinal specimens was 38.6 ± 4.8 MPa, 17.1 ± 1.5 percent, and 332.2 ± 58.3 MPa, respectively. The average tensile strength, ultimate strain, and tangent modulus for the transverse specimens was 1.7 ± 0.5 MPa, 11.7 ± 0.9 percent, and 11.0 ± 3.6 MPa, respectively. All three constitutive models described the longitudinal behavior of the ligament equally well. However, the ability of the models to describe the transverse behavior of the ligament varied.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(6):764-769. doi:10.1115/1.2834891.

In-vivo tendon forces are commonly measured using transducers, which detect tension in the tendon fibers. A poorly understood source of measurement errors is the difference in stress distribution within the tendon between experimental and transducer calibration conditions. The objective of this study was to investigate this source of error, and to determine whether these errors could be minimized by proper selection of transducer size. The study was conducted using the infrapatellar ligament (patellar tendon) of New Zealand White rabbits. Tendon force was measured with two different size implantable force transducers (IFTs), one Wide and one Narrow, and by a strain gaged load cell in series with the tendon. Tests were conducted at five different loading conditions selected to produce five different stress distributions within the tendon. One loading condition corresponded to a typical post-experiment calibration, and the data from that condition were used to develop a calibration equation for the transducer. The errors that resulted from using this calibration were determined by comparing the tendon force measured by the in-series load cell with the force predicted from the IFT output using the calibration equation. Changes in stress distribution produced measurement errors up to 64 N with the Narrow IFT but only 24 N with the Wide IFT. We found the measurement error was dependent on sensor width. Our results support the hypothesis that measurement errors can be caused by differences in tendon stress distribution between calibration and experimental conditions. We further showed that these errors can be minimized by using an IFT, which samples the tension in a large percentage of the tendon fibers. Information from this study can be used for selection of an appropriately sized implantable force transducer for measuring tendon and ligament force.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(6):770-777. doi:10.1115/1.2834892.

Measurements on adherent cells have shown that spreading affects their mechanics. Highly spread cells are stiffer than less spread cells. The stiffness increases approximately linearly with increasing applied stress and more so in highly spread cells than in less spread cells. In this study, a six-strut tensegrity model of the cytoskeleton is used to analyze the effect of spreading on cellular mechanics. Two configurations are considered: a “round” configuration where a spherically shaped model is anchored to a flat rigid surface at three joints, and a “spread” configuration, where three additional joints of the model are attached to the surface. In both configurations a pulling force is applied at a free joint, distal from the anchoring surface, and the corresponding deformation is determined from equations of equilibrium. The model stiffness is obtained as the ratio of applied force to deformation. It is found that the stiffness changes with spreading consistently with the observations in cells. These findings suggest the possibility that the spreading-induced changes of the mechanical properties of the cell are the result of the concomitant changes in force distribution and microstructural geometry of the cytoskeleton.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(6):778-783. doi:10.1115/1.2834893.

Pitting wear is a dominant form of polyethylene surface damage in total knee replacements, and may originate from surface cracks that propagate under repeated tribological contact. In the present study, stress intensity factors, KI , and KII , were calculated for a surface crack in a polyethylene-CoCr-bone system in the presence of rolling or sliding contact pressures. Variations in crack length and load location were studied to determine probable crack propagation mechanisms and modes. The crack tip experienced a wide range of mixed-mode conditions that varied as a function of crack length, load location, and sliding friction. Positive KI values were observed for shorter cracks in rolling contact and for all crack lengths when the sliding load moved away from the crack. KII was greatest when the load was directly adjacent to the crack (g/a = ±1), where coincidental Mode I stresses were predominantly compressive. Sliding friction substantially increased both KI max and KII max . The effective Mode I stress intensity factors, Keff , were greatest at g/a = ±1, illustrating the significance of high shear stresses generated by loads adjacent to surface cracks. Keff trends suggest mechanisms for surface pitting by which surface cracks propagate along their original plane under repeated reciprocating rolling or sliding, and turn in the direction of sliding under unidirectional sliding contact.

Commentary by Dr. Valentin Fuster


J Biomech Eng. 1998;120(6):784-787. doi:10.1115/1.2834894.

Experimental techniques for measuring unsteady flow in a glass arterial bifurcation model have been developed to aid in quantifying three-dimensional wall shear fluctuations associated with arterial disease. The unique feature of the current technique is the use of a “curved” laser sheet, which was everywhere tangent to the inner wall of a daughter tube in an arterial bifurcation model. Surface tangent velocity vector field measurements were made to demonstrate the potential of this technique. Ensemble-averaged data showing weak secondary flows as well as statistical distributions of flow angles are presented. Measurements of this type may be used to estimate mean and instantaneous wall shear magnitude and direction, data that are necessary for understanding the importance of circumferential motions on arterial disease.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(6):787-791. doi:10.1115/1.2834895.
Topics: Transducers
Commentary by Dr. Valentin Fuster

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