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EDITORIAL

J Biomech Eng. 1997;119(4):369. doi:10.1115/1.2798279.
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Abstract
Commentary by Dr. Valentin Fuster

IN MEMORIAM

J Biomech Eng. 1997;119(4):370-371. doi:10.1115/1.2798280.
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Abstract
Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS

J Biomech Eng. 1997;119(4):372-378. doi:10.1115/1.2798281.

We present data from isothermal free-shrinkage tests (i.e., performed in the absence of mechanical loads) wherein bovine chordae tendineae were subjected to temperatures from 65 to 85°C for 120 to 1200 s. These data reveal four new insights into heat-induced denaturation of a collagenous tissue. First, a characteristic time for the free shrinkage appears to exhibit an Arrhenius-type relationship with temperature. Second, scaling the actual heating time via the characteristic time results in a single correlation between free shrinkage and the duration of heating; this correlation suggests a time-temperature equivalence. Third, it is the cumulative, not current, heating time that governs the free shrinkage. And fourth, heat-induced free shrinkage is partially recovered when the tissue is returned to 37°C, this recovery also being time-dependent. Although these findings will help guide future experimentation and constitutive modeling, as well as the design of new heat-based clinical therapies, there is a pressing need to collect additional isothermal data, particularly in the presence of well-defined mechanical loads.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(4):379-385. doi:10.1115/1.2798282.

This study was conducted to validate a new in vitro method to expose the medial compartment of the knee to be used in subsequent studies aimed at examining the load bearing capabilities of medial meniscal allografts. The new method involves an osteotomy and reattachment of the medial femoral condyle. The primary hypothesis was that the new method does not alter tibio-femoral contact pressure and area. To validate this method, the baseline contact pressure of the intact medial compartment was measured using a new nondestructive procedure for inserting pressure measurement film into the intact medial hemijoint. A secondary and related hypothesis was that incising the coronary ligament, a destructive method used by previous investigators to position pressure measurement film, alters the normal tibio-femoral contact pressure. To test these hypotheses, Fuji Prescale pressure-sensitive film was used to measure both tibio-femoral contact pressure and area within the medial compartment of the (1) intact knee, (2) the knee after osteotomizing and reattaching the medial femoral condyle, and (3) the osteotomized knee with an incised coronary ligament, using seven cadaver specimens. Measurements were taken at a compressive load of approximately two times body weight with the knee in 0, 15, 30, 45 deg of flexion. No significant differences between the intact and osteotomized knee were detected. Likewise, no significant differences were observed between the osteotomized knee and the osteotomized knee with an incised coronary ligament. These results confirm the utility of the new method in exposing the medial compartment for manipulation and placement of medial meniscal allografts in future studies examining the load-bearing characteristics of meniscal allografts.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(4):386-391. doi:10.1115/1.2798283.

Sarcomere length was measured intraoperatively in five patients undergoing tendon transfer of the flexor carpi ulnaris (FCU) to the extensor carpi radialis longus (ECRL) for radial nerve palsy. All measurements were made with the elbow in 20 deg of flexion. Prior to tendon transfer, FCU sarcomere length ranged from 2.84 ±. 12 μm (mean ± SEM) with the wrist flexed to 4.16 ± .15 μm with the wrist extended. After transfer into the ECRL tendon, sarcomere length ranged from 4.82 ± .11 μm with the wrist flexed (the new longest position of the FCU) to 3.20 ± .09 μm with the wrist extended, resulting in a shift in the sarcomere length operating range to significantly longer sarcomere lengths (p < 0.001). At these longer sarcomere lengths, the FCU muscle was predicted to develop high active tension only when the wrist was highly extended. A biomechanical model of this tendon transfer was generated using normative values obtained from previous studies of muscle architectural properties, tendon compliance, and joint moment arms. Predicted sarcomere lengths pre- and post-tendon transfer agreed well with intraoperative experimental measurements. The theoretical wrist extension moment-wrist joint angle relationship was also calculated for a variety of values of FCU muscle length. These different lengths represented the different conditions under which the FCU could be sutured into the ECRL tendon. Variation in FCU muscle length over the range 200 mm to 260 mm resulted in large changes in absolute peak moment produced as well as the angular dependence of peak moment. This was due to the change in the region of FCU operation on its sarcomere length-tension curve relative to the magnitude of the ECRL moment arm. These data demonstrate the sensitivity of a short-fibered muscle such as the FCU to affect the functional outcome of surgery. In addition, we demonstrated that intraoperative sarcomere length measurements, combined with biomechanical modeling provide the surgeon with a powerful method for predicting the functional effect of tendon transfer surgery.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(4):392-399. doi:10.1115/1.2798284.

We propose a mechanical model for tendon or ligament stress–stretch behavior that includes both microstructural and tissue level aspects of the structural hierarchy in its formulation. At the microstructural scale, a constitutive law for collagen fibers is derived based on a strain-energy formulation. The three-dimensional orientation and deformation of the collagen fibrils that aggregate to form fibers are taken into consideration. Fibril orientation is represented by a probability distribution function that is axisymmetric with respect to the fiber. Fiber deformation is assumed to be incompressible and axisymmetric. The matrix is assumed to contribute to stress only through a constant hydrostatic pressure term. At the tissue level, an average stress versus stretch relation is computed by assuming a statistical distribution for fiber straightening during tissue loading. Fiber straightening stretch is assumed to be distributed according to a Weibull probability distribution function. The resulting comprehensive stress–stretch law includes seven parameters, which represent structural and microstructural organization, fibril elasticity, as well as a failure criterion. The failure criterion is stretch based. It is applied at the fibril level for disorganized tissues but can be applied more simply at a fiber level for well-organized tissues with effectively parallel fibrils. The influence of these seven parameters on tissue stress–stretch response is discussed and a simplified form of the model is shown to characterize the nonlinear experimentally determined response of healing medial collateral ligaments. In addition, microstructural fibril organizational data (Frank et al., 1991, 1992) are used to demonstrate how fibril organization affects material stiffness according to the formulation. A simplified form, assuming a linearly elastic fiber stress versus stretch relationship, is shown to be useful for quantifying experimentally determined nonlinear toe-in and failure behavior of tendons and ligaments. We believe this ligament and tendon stress–stretch law can be useful in the elucidation of the complex relationships between collagen structure, fibril elasticity, and mechanical response.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(4):400-405. doi:10.1115/1.2798285.

Experimental evidence suggests that the tensile behavior of tendons and ligaments is in part a function of tissue hydration. The models currently available do not offer a means by which the hydration effects might be explicitly explored. To study these effects, a finite element model of a collagen sub-fascicle, a substructure of tendon and ligament, was formulated. The model was microstructurally based, and simulated oriented collagen fibrils with elastic-orthotropic continuum elements. Poroelastic elements were used to model the interfibrillar matrix. The collagen fiber morphology reflected in the model interacted with the interfibrillar matrix to produce behaviors similar to those seen in tendon and ligament during tensile, cyclic, and relaxation experiments conducted by others. Various states of hydration and permeability were parametrically investigated, demonstrating their influence on the tensile response of the model.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(4):406-408. doi:10.1115/1.2798286.
Abstract
Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(4):409-416. doi:10.1115/1.2798287.

This work addresses a method for improving vertical whole body vibration isolation through optimal seat suspension design. The primary thrusts of this investigation are: (1) the development of a simple model that captures the essential dynamics of a seated human exposed to vertical vibration, (2) the selection and evaluation of several standards for assessing human sensitivity to vertical vibration, and (3) the determination of the seat suspension parameters that minimize these standards to yield optimal vibration isolation. Results show that the optimal seat and cushion damping coefficients depend very much on the selection of the vibration sensitivity standard and on the lower bound of the stiffnesses used in the constrained optimization procedure. In all cases, however, the optimal seat damping obtained here is significantly larger (by than a factor of 10) than that obtained using existing seat suspension design methods or from previous optimal suspension studies. This research also indicates that the existing means of assessing vibration in suspension design (ISO 7096) requires modification.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(4):417-422. doi:10.1115/1.2798288.

Previous attempts to use inverse dynamics solutions in direct dynamics simulations have failed to replicate the input data of the inverse dynamics problem. Measurement and derivative estimation error, different inverse dynamics and direct dynamics models, and numerical integration error have all been suggested as possible causes of inverse dynamics simulation failure. However, using a biomechanical model of the type typically used in gait analysis applications for inverse dynamics calculations of joint moments, we produce a direct dynamics simulation that exactly matches the measured movement pattern used as input to the inverse dynamic problem. This example of successful inverse dynamics simulation demonstrates that although different inverse dynamics and direct dynamics models may lead to inverse dynamics simulation failure, measurement and derivative estimation error do not. In addition, inverse dynamics simulation failure due to numerical integration errors can be avoided. Further, we demonstrate that insufficient control signal dimensionality (i.e., freedom of the control signals to take on different “shapes”), a previously unrecognized cause of inverse dynamics simulation failure, will cause inverse dynamics simulation failure even with a perfect model and perfect data, regardless of sampling frequency.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(4):423-432. doi:10.1115/1.2798289.

The objective of this study was to determine a relationship between shear stress and strain for human brain tissue by performing transient, single-pulse, high-rate, shear displacement tests. A constant velocity, parallel plate shear test device was designed and fabricated. This equipment generated constant rate shear strains in cylindrical tissue samples mounted between the shear plates. The transverse reaction force at the upper end of the sample was measured during the event with a sensitive quartz piezoelectric force transducer, thus obtaining the force associated with the displacement versus time ramp. Shear tests were performed on 125 tissue samples taken from twelve fresh cadaver brain specimens. The average true shear stress and finite strain were calculated. A nonlinear, viscoelastic, standard solid model was fit to the constant rate test data and the material constants were determined.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(4):433-437. doi:10.1115/1.2798290.

Recent epidemiological, clinical, and biomechanical studies have implicated axial impact to the plantar surface of the foot to be a cause of lower extremity trauma in vehicular crashes. The present study was conducted to evaluate the biomechanics of the human foot–ankle complex under axial impact. Nine tests were conducted on human cadaver below knee–foot–ankle complexes. All specimens were oriented in a consistent anatomical position on a mini-sled and the impact load was delivered using a pendulum. Specimens underwent radiography and gross dissection following the test. The pathology included intra-articular fractures of the calcaneus and/or the distal tibia complex with extensions into the anatomic joints. Impactor load cell forces consistently exceeded the tibial loads for all tests. The mean dynamic forces at the plantar surface of the foot were 7.7 kN (SD = 4.3) and 15.1 kN (SD = 2.7) for the nonfracture and fracture tests, respectively. In contrast, the mean dynamic forces at the proximal tibial end of the preparation were 5.2 kN (SD = 3.1) in the nonfracture group, and 10.2 kN (SD = 1.5) in the fracture group. The foot and tibial end forces were statistically significantly different between these two groups (p < 0.01). The present investigation provides fundamental data to the understanding of the biomechanics of human foot–ankle trauma. Quantifying the effects of other factors such as gender and bone quality on the injury thresholds is necessary to understand foot–ankle tolerance fully.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(4):438-444. doi:10.1115/1.2798291.

Arterial wall stresses are thought to be a major determinant of vascular remodeling both during normal growth and throughout the development of occlusive vascular disease. A completely physiologic mechanical model of the arterial wall should account not only for its residual strains but also for its structural nonhomogeneity. It is known that each layer of the artery wall possesses different mechanical properties, but the distribution of residual strain among the different mechanical components, and thus the true zero stress state, remain unknown. In this study, two different sets of experiments were carried out in order to determine the distribution of residual strains in artery walls, and thus the true zero stress state. In the first, collagen and elastin were selectively eliminated by chemical methods and smooth muscle cells were destroyed by freezing. Dissolving elastin provoked a decrease in the opening angle, while dissolving collagen and destroying smooth muscle cells had no effect. In the second, different wall layers of bovine carotid arteries were removed from the exterior or luminal surfaces by lathing or drilling frozen specimens, and then allowing the frozen material to thaw before measuring residual strain. Lathing material away from the outer surface caused the opening angle of the remaining inner layers to increase. Drilling material from the inside caused the opening angle of the remaining outer layers to decrease. Mechanical nonhomogeneity, including the distribution of residual strains, should thus be considered as an important factor in determining the distribution of stress in the artery wall and the configuration of the true zero stress state.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(4):445-451. doi:10.1115/1.2798292.

The first stress–strain measurements on embryonic cardiovascular tissue are described here, obtained from cyclic uniaxial loading of the primitive Ventricle. An excised ventricular segment from Hamburger/Hamilton stage-16 or stage-18 chicks (2-1/2 and 3 days of a 21-day incubation period) was mounted longitudinally between two small wires in oxygenated Krebs–Henseleit cardioplegia solution. One wire was attached to an ultrasensitive force transducer and the other to a Huxley micromanipulator controlled by remote motor drive. A real-time video tracking system calculated three myocardial surface strains based on the positions of three surface markers while the heart was deformed in a triangular wave pattern. Force transducer output was filtered, digitally sampled, and stored with strains and time. Results were plotted as strain (longitudinal, circumferential, shear, and principal) versus time, stress versus time, and stress versus longitudinal strain. The stress–strain curves were nonlinear, even at low strain levels. The hysteresis loops were large; mean hysteresis energy as a proportion of total cycle stored strain energy was 36 percent (stage 16) and 41 percent (stage 18). We created a finite element model of the ventricle and fit the model behavior to the experimental behavior to determine parameters for a stage-18 pseudoelastic strain-energy function of exponential form. The calculated exponential parameter is significantly lower than that found in corresponding uniaxial studies of mature myocardium, possibly indicating the lower fiber content of the immature tissue. The results of this study are the first step in characterizing material properties for comparisons with later developmental stages and with impaired and altered myocardium. The long-term goal is to aid in identifying the biomechanical factors regulating growth and morphogenesis.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(4):452-460. doi:10.1115/1.2798293.

Computational fluid dynamics (CFD) has become an indispensable part of aerospace research and design. The solution procedure for incompressible Navier–Stokes equations can be used for biofluid mechanics research. The computational approach provides detailed knowledge of the flowfield complementary to that obtained by experimental measurements. This paper illustrates the extension of CFD techniques to artificial heart flow simulation. Unsteady incompressible Navier–Stokes equations written in three-dimensional generalized curvilinear coordinates are solved iteratively at each physical time step until the incompressibility condition is satisfied. The solution method is based on the pseudocompressibility approach. It uses an implicit upwind-differencing scheme together with the Gauss–Seidel line-relaxation method. The efficiency and robustness of the time-accurate formulation of the numerical algorithm are tested by computing the flow through model geometries. A channel flow with a moving indentation is computed and validated by experimental measurements and other numerical solutions. In order to handle the geometric complexity and the moving boundary problems, a zonal method and an overlapped grid embedding scheme are employed, respectively. Steady-state solutions for the flow through a tilting-disk heart valve are compared with experimental measurements. Good agreement is obtained. Aided by experimental data, the flow through an entire Penn State artificial heart model is computed.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(4):461-468. doi:10.1115/1.2798294.

This study was undertaken to gain a better understanding of the countercurrent heat exchange of thermally significant blood vessels in skeletal muscle by measuring the vascular structure and flow in an exteriorized rat spinotrapezius muscle and estimating the enhancement in the effective thermal conductivity of the muscle. Detailed anatomic measurements of the number density and length of countercurrent vessel pairs between 45 and 165 μm diameter were obtained. Moreover, diameter and blood flow in the 1A to 3A vessels were measured for muscles in which pharmacological vasoactive agents were introduced, allowing one to vary the local blood flow Peclet number from 1 to 18 in the major feeding arteries. These combined measurements have been used to estimate the range of possible enhancement in the effective thermal conductivity of the tissue. The newly derived conduction shape factor in Zhu et al. [23] for countercurrent vessels in two-dimensional tissue preparations was used in this analysis. Our experimental data indicated that the value of this conduction shape factor was about one-third to two-thirds the value for two countercurrent vessels of the same size and spacing in an infinite medium. The experiment also revealed that the Weinbaum–Jiji expression for keff was valid for the spinotrapezius muscle when the largest vessels were less than 195 μm diameter. A fivefold increase in keff was predicted for 195 μm diameter vessels. Vasoregulation was also shown to have a dramatic effect on keff . A tissue that exhibits only small increases in keff due to countercurrent convection in its vasoconstricted state can exhibit a more than fivefold increase in Keff in its vasodilated state.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(4):469-475. doi:10.1115/1.2798295.

The purpose of this study was to model the transport of oxygen in large arteries, including the physiologically important effects of oxygen transport by hemoglobin, coupling of transport between oxygen in the blood and in wall tissue, and metabolic consumption of oxygen by the wall. Numerical calculations were carried out in an 89 percent area reduction axisymmetric stenosis model for several wall thicknesses. The effects of different boundary conditions, different schemes for linearizing the oxyhemoglobin saturation curve, and different Schmidt numbers were all examined by comparing results against a reference solution obtained from solving the full nonlinear governing equations with physiologic values of Schmidt number. Our results showed that for parameters typical of oxygen mass transfer in the large arteries, oxygen transport was primarily determined by wall-side effects, specifically oxygen consumption by wall tissue and wall-side mass transfer resistance. Hemodynamic factors played a secondary role, producing maximum local variations in intimal oxygen tension on the order of only 5–6 mmHg. For purposes of modeling blood-side oxygen transport only, accurate results were obtained through use of a computationally efficient linearized form of the convection-diffusion equation, so long as blood-side oxygen tensions remained in the physiologic range for large arteries. Neglect of oxygen binding by hemoglobin led to large errors, while arbitrary reduction of the Schmidt number led to more modest errors. We conclude that further studies of oxygen transport in large arteries must couple blood-side oxygen mass transport to transport in the wall, and accurately model local oxygen consumption within the wall.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(4):476-482. doi:10.1115/1.2798296.

This paper presents measurements of the geometric shape, perimeter, and cross-sectional area of the human oral passage (from oral entrance to midtrachea) and relates them through dimensionless parameters to the depositional mass transfer of ultrafine particles. Studies were performed in two identical replicate oral passage models, one of which was cut orthogonal to the airflow direction into 3 mm elements for measurement, the other used intact for experimental measurements of ultrafine aerosol deposition. Dimensional data were combined with deposition measurements in two sections of the oral passage (the horizontal oral cavity and the vertical laryngeal–tracheal airway) to calculate the dimensionless mass transfer Sherwood number (Sh). Mass transfer theory suggests that Sh should be expressible as a function of the Reynolds numper (Re) and the Schmidt number (Sc). For inhalation and exhalation through the oral cavity (O-C), an empirical relationship was obtained for flow rates from 7.5–30.0 1 min−1 :

Sh = 15.3 Re0.812 Sc−0.986
An empirical relationship was likewise obtained for the laryngeal–tracheal (L-T) region over the same range of flow rates:
Sh = 25.9 Re0.861 Sc−1.37
These relationships were compared to heat transfer in the human upper airways through the well-known analogy between heat and mass transfer. The Reynolds number dependence for both the O-C and L-T relationships was in good agreement with that for heat transfer. The mass transfer coefficients were compared to extrathoracic uptake of gases and vapors and showed similar flow rate dependence. For gases and vapors that conform to the zero concentration boundary condition, the empirical relationships are applicable when diffusion coefficients are taken into consideration.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(4):483-488. doi:10.1115/1.2798297.

Peristaltic transport of two-layered power-law fluids in axisymmetric tubes is studied. Use of the power-law fluid model permits independent choice of shear thinning, shear thickening, or Newtonian fluids for the core and the peripheral layer. The interface between the two layers is determined from a transcendental equation in the core radius. The variation of the time-mean flow Q̄ with the pressure rise or drop over one wavelength Δp is studied. It is observed that a negative time-mean flow is achieved under free pumping (Δp = 0) for the wave forms considered here if one of the peripheral layer and core fluids is non-Newtonian. The rheology of the peripheral layer fluid is a dominant factor in producing a negative or positive mean flow. It is noticed that a sinusoidal wave always yields a positive mean flow for powerlaw fluids. The trapped bolus volume for sinusoidal peristaltic wave is observed to decrease with an increase in the rate of shear thinning of the core and the peripheral layer fluids.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(4):489-495. doi:10.1115/1.2798298.

A Monte Carlo model is described for modeling photo propagation in a scattering medium. The fraction of locally absorbed photons is proportional to the local rate of heat generation in laser-irradiated tissue and the associated distribution of light (fluence rate) is obtained by dividing the rate of heat generation by the local absorption coefficient. Examples of computed distributions of the rate of heat generation are presented for situations where light scattering in tissue is important. The method is applied to analyze treatment of Port Wine Stain and the selection of laser wave-lengths for cyclophotocoagulation.

Commentary by Dr. Valentin Fuster

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