J Biomech Eng. 1998;120(3):313-320. doi:10.1115/1.2797996.

Blood vessels are subject to tensile stress and associated strain which may influence the structure and organization of smooth muscle cells (SMCs) during physiological development and pathological remodeling. This study focused on the influence of the major tensile strain on the SMC orientation in the blood vessel wall. Several blood vessels, including the aorta, the mesenteric artery and vein, and the jugular vein of the rat were used to observe the normal distribution of tensile strains and SMC orientation; and a vein graft model was used to observe the influence of altered strain direction on the SMC orientation. The circumferential and longitudinal strains in these blood vessels were measured by using a biomechanical technique, and the SMC orientation was examined by fluorescent microscopy at times of 10, 20, and 30 days. Results showed that the SMCs were mainly oriented in the circumferential direction of straight blood vessels with an average angle of ~85 deg between the SMC axis and the vessel axis in all observed cases. The SMC orientation coincided with the principal direction of the circumferential strain, a major tensile strain, in the blood vessel wall. In vein grafts, the major tensile strain direction changed from the circumferential to the longitudinal direction at observation times of 10, 20, and 30 days after graft surgery. This change was associated with a decrease in the angle between the axis of newly proliferated SMCs and that of the vessel at all observation times (43 ± 11 deg, 42 ± 10 deg, and 41 ± 10 deg for days 10, 20, and 30, respectively), indicating a shift of the SMC orientation from the circumferential toward the longitudinal direction. These results suggested that the major tensile strain might play a role in the regulation of SMC orientation during the development of normal blood vessels as well as during remodeling of vein grafts.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(3):321-326. doi:10.1115/1.2797997.

The velocity of longitudinal stress waves in an elastic body is given by the square root of the ratio of its elastic modulus to its density. In tendinous and ligamentous tissue, the elastic modulus increases with strain and with strain rate. Therefore, it was postulated that stress wave velocity would also increase with increasing strain and strain rate. The purpose of this study was to determine the velocity of stress waves in tendinous tissue as a function of strain and to compare these values to those predicted using the elastic modulus derived from quasi-static testing. Five bovine patellar tendons were harvested and potted as bone–tendon–bone specimens. Quasi-static mechanical properties were determined in tension at a deformation rate of 100 mm/s. Impact loading was employed to determine wave velocity at various strain levels, achieved by preloading the tendon. Following impact, there was a measurable delay in force transmission across the specimen and this delay decreased with increasing tendon strain. The wave velocities at tendon strains of 0.0075, 0.015, and 0.0225 were determined to be 260 ± 52 m/s, 360 ± 71 m/s, and 461 ± 94 m/s, respectively. These velocities were significantly (p < 0.01) faster than those predicted using elastic moduli derived from the quasi-static tests by 52, 45, and 41 percent, respectively. This study has documented that stress wave velocity in patellar tendon increases with increasing strain and is underestimated with a modulus estimated from quasi-static testing.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(3):327-333. doi:10.1115/1.2797998.

The goal of this study was to develop a new implantable transducer for measuring anterior cruciate ligament (ACL) graft tension postoperatively in patients who have undergone ACL reconstructive surgery. A unique approach was taken of integrating the transducer into a femoral fixation device. To devise a practical in vivo calibration protocol for the fixation device transducer (FDT), several hypotheses were investigated: (1) The use of a cable versus the actual graft as the means for applying load to the FDT during calibration has no significant effect on the accuracy of the FDT tension measurements; (2) the number of flexion angles at which the device is calibrated has no significant effect on the accuracy of the FDT measurements; (3) the friction between the graft and femoral tunnel has no significant effect on measurement accuracy. To provide data for testing these hypotheses, the FDT was first calibrated with both a cable and a graft over the full range of flexion. Then graft tension was measured simultaneously with both the FDT on the femoral side and load cells, which were connected to the graft on the tibial side, as five cadaver knees were loaded externally. Measurements were made with both standard and overdrilled tunnels. The error in the FDT tension measurements was the difference between the graft tension measured by the FDT and the load cells. Results of the statistical analyses showed that neither the means of applying the calibration load, the number of flexion angles used for calibration, nor the tunnel size had a significant effect on the accuracy of the FDT. Thus a cable may be used instead of the graft to transmit loads to the FDT during calibration, thus simplifying the procedure. Accurate calibration requires data from just three flexion angles of 0, 45, and 90 deg and a curve fit to obtain a calibration curve over a continuous range of flexion within the limits of this angle group. Since friction did not adversely affect the measurement accuracy of the FDT, the femoral tunnel can be drilled to match the diameter of the graft and does not need to be overdrilled. Following these procedures, the error in measuring graft tension with the FDT averages less than 10 percent relative to a full-scale load of 257 N.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(3):334-341. doi:10.1115/1.2797999.

The objectives of this study were twofold. The first was to develop a forward dynamic model of cycling and an optimization framework to simulate pedaling during submaximal steady-state cycling conditions. The second was to use the model and framework to identify the kinetic, kinematic, and muscle timing quantities that should be included in a performance criterion to reproduce natural pedaling mechanics best during these pedaling conditions. To make this identification, kinetic and kinematic data were collected from 6 subjects who pedaled at 90 rpm and 225 W. Intersegmental joint moments were computed using an inverse dynamics technique and the muscle excitation onset and offset were taken from electromyographic (EMG) data collected previously (Neptune et al., 1997). Average cycles and their standard deviations for the various quantities were used to describe normal pedaling mechanics. The model of the bicycle-rider system was driven by 15 muscle actuators per leg. The optimization framework determined both the timing and magnitude of the muscle excitations to simulate pedaling at 90 rpm and 225 W. Using the model and optimization framework, seven performance criteria were evaluated. The criterion that included all of the kinematic and kinetic quantities combined with the EMG timing was the most successful in replicating the experimental data. The close agreement between the simulation results and the experimentally collected kinetic, kinematic, and EMG data gives confidence in the model to investigate individual muscle coordination during submaximal steady-state pedaling conditions from a theoretical perspective, which to date has only been performed experimentally.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(3):342-347. doi:10.1115/1.2798000.

Residual stress and strain in living tissues have been investigated from the viewpoint of mechanical optimality maintained by adaptive remodeling. In this study, the residual stresses in the cortical-cancellous bone complex of bovine coccygeal vertebrae were examined. Biaxial strain gages were bonded onto the cortical surface, so that the gage axes were aligned in the cephalocaudal and circumferential directions. Strains induced by removal of the end-plate and the cancellous bone were recorded sequentially. The results revealed the existence of compressive residual stress in the cortical bone and tensile residual stress in the cancellous bone in both the cephalocaudal and the circumferential direction. The observed strains were examined on the basis of the uniform stress hypothesis using a three-bar model for the cephalocaudal direction and a three-layered cylinder model for the circumferential direction. In this model study, the magnitude of effective stresses, which is defined as the macroscopic stress divided by the area fraction of bone material, was found not to differ significantly between cephalocaudal and circumferential directions, although they were evaluated using independent models. These results demonstrate that the uniform stress state of the cortical-cancellous bone structure is consistent with results obtained in the cutting experiment when the existence of residual stress is taken into account.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(3):348-354. doi:10.1115/1.2798001.

Stress-modulated growth in the aorta is studied using a theoretical model. The model is a thick-walled tube composed of two pseudoelastic, orthotropic layers representing the intima/media and the adventitia. Both layers are assumed to follow a growth law in which the time rates of change of the growth stretch ratios depend linearly on the local smooth muscle fiber stress and on the shear stress due to blood flow on the endothelium. Using finite elasticity theory modified to include volumetric growth, we computed temporal changes in stress, geometry, and opening angle (residual strain) during development and following the onset of sudden hypertension. For appropriate values of the coefficients in the growth law, the model yields results in reasonable agreement with published data for global and local growth of the rat aorta.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(3):355-361. doi:10.1115/1.2798002.

A new experimental method was developed to quantify parameters of swelling-induced shape change in articular cartilage. Full-thickness strips of cartilage were studied in free-swelling tests and the swelling-induced stretch, curvature, and areal change were measured. In general, swelling-induced stretch and curvature were found to increase in cartilage with decreasing ion concentration, reflecting an increasing tendency to swell and “curl” at higher swelling pressures. An exception was observed at the articular surface, which was inextensible for all ionic conditions. The swelling-induced residual strain at physiological ionic conditions was estimated from the swelling-induced stretch and found to be tensile and from 3–15 percent. Parameters of swelling were found to vary with sample orientation, reflecting a role for matrix anisotropy in controlling the swelling-induced residual strains. In addition, the surface zone was found to be a structurally important element, which greatly limits swelling of the entire cartilage layer. The findings of this study provide the first quantitative measures of swelling-induced residual strain in cartilage ex situ, and may be readily adapted to studies of cartilage swelling in situ.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(3):362-369. doi:10.1115/1.2798003.

A hydrogel with potential applications in the role of a cushion form replacement joint bearing surface material has been investigated. The material properties are required for further development and design studies and have not previously been quantified. Creep indentation experiments were therefore performed on samples of the hydrogel. The biphasic model developed by Mow and co-workers (Mak et al., 1987; Mow et al., 1989a) was used to curve-fit the experimental data to theoretical solutions in order to extract the three intrinsic biphasic material properties of the hydrogel (aggregate modulus, HA , Poisson’s ratio, νs , and permeability, k). Ranges of material properties were determined: aggregate modulus was calculated to be between 18.4 and 27.5 MPa, Poisson’s ratio 0.0–0.307, and permeability 0.012–7.27 × 10−17 m4 /Ns. The hydrogel thus had a higher aggregate modulus than values published for natural normal articular cartilage, the Poisson’s ratios were similar to articular cartilage, and finally the hydrogel was found to be less permeable than articular cartilage. The determination of these values will facilitate further numerical analysis of the stress distribution in a cushion form replacement joint.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(3):370-381. doi:10.1115/1.2798004.

Physiological studies strongly support the view that hydration control in the cornea is dependent on active ion transport at the corneal endothelium. However, the mechanism by which endothelial ion transport regulates corneal thickness has not been elaborated in detail. In this study, the corneal stroma is modeled as a triphasic material under steady-state conditions. An ion flux boundary condition is developed to represent active transport at the endothelium. The equations are solved in cylindrical coordinates for confined compression and in spherical coordinates to represent an intact cornea. The model provides a mechanism by which active ion transport at the endothelium regulates corneal hydration and provides a basis for explaining the origin of the “imbibition pressure” and stromal “swelling pressure.” The model encapsulates the Donnan view of corneal swelling as well as the “pump-leak hypothesis.”

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(3):382-388. doi:10.1115/1.2798005.

We present data from isothermal, isotonic-shrinkage tests wherein bovine chordae tendineae were subjected to well-defined constant temperatures (from 65 to 90°C), durations of heating (from 180 to 3600 s), and isotonic uniaxial stresses during heating (from 100 to 650 kPa). Tissue response during heating and “recovery” at 37°C following heating was evaluated in terms of the axial shrinkage, a gross indicator of underlying heat-induced denaturation. There were three key findings. First, scaling the heating time via temperature and load-dependent characteristic times for the denaturation process collapsed all shrinkage data to a single curve, and thereby revealed a time-temperature-load equivalency. Second, the characteristic times exhibited an Arrhenius-type behavior with temperature wherein the slopes were nearly independent of applied load—this suggested that applied loads during heating affect the activation entropy, not energy. Third, all specimens exhibited a time-dependent, partial recovery when returned to 37°C following heating, but the degree of recovery decreased with increases in the load imposed during heating. These new findings on heat-induced changes in tissue behavior will aid in the design of improved clinical heating protocols and provide guidance for the requisite constitutive formulations.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(3):389-394. doi:10.1115/1.2798006.

The thermal response of fingers exposed to cold weather conditions has been simulated. Energy balance equations were formulated, in a former study, for the tissue layers and the arterial, venous, and capillary blood vessels. The equations were solved by a finite difference scheme using the Thomas algorithm and the method of alternating directions. At this stage of development the model does not include any autonomic control functions. Model simulations assumed an electrical heating element to be embedded in the glove layers applied on the finger. A 1.3 W power input was calculated for maintaining finger temperatures at their pre-cold exposure level in a 0°C environment. Alternate assumptions of nutritional (low) and basal (high) blood flows in the finger demonstrated the dominance of this factor in maintaining finger temperatures at comfortable levels. Simulated exposures to still and windy air, at 4.17 m/s (15 km/h), indicated the profound chilling effects of wind on fingers in cold environments. Finally, the effects of variable blood flow in the finger, known as “cold-induced vasodilatation,” were also investigated. Blood flow variations were assumed to be represented by periodic, symmetric triangular waves allowing for gradual opening-closing cycles of blood supply to the tip of the finger. Results of this part of the simulation were compared with measured records of bare finger temperatures. Good conformity was obtained for a plausible pattern of change in blood flow, which was assumed to be provided in its entirety to the tip of the finger alone.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(3):395-404. doi:10.1115/1.2798007.

A new equation for calculating temperatures in living tissues, the tissue convective energy balance equation (TCEBE), is derived using only a few assumptions. The resulting equation is basic, general and applicable to any tissue. The (unsolved) TCEBE is used: (a) to relate both Pennes’ BHTE perfusion-related parameter (W) and the effective thermal conductivity equation’s perfusion-related parameter (keff ) to the true capillary perfusion Ṗcap , and (b) to show that both W and keff are defined, nonphysiological variables, which are only related to Ṗcap in a problem-dependent manner. Finally, the derivation of the relationship between W and Ṗcap provides a complete derivation of Pennes’ BHTE, something that has not been previously done.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(3):405-415. doi:10.1115/1.2798008.

The efficiency of axial gas dispersion during ventilation with high-frequency oscillation (HFO) is improved by manipulating the oscillatory flow waveform such that intermittent oscillatory flow occurs. We therefore measured the velocity profiles and effective axial gas diffusivity during intermittent oscillatory flow in a straight tube to verify the intermittency augmentation effect on axial gas transfer. The effective diffusivity was dependent on the flow patterns and significantly increased with an increase in the duration of the stationary phase. It was also found that the ratio of effective diffusivity to molecular diffusivity is two times greater than that in sinusoidal oscillatory flow. Moreover, turbulence during deceleration or at the beginning of the stationary phase further augments axial dispersion, with the effective diffusivity being over three times as large, thereby proving that the use of intermittent oscillatory flow effectively augments axial dispersion for ventilation with HFO.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(3):416-422. doi:10.1115/1.2798009.

A three-dimensional numerical modeling of airflow in the human pharynx using an anatomically accurate model was conducted. The pharynx walls were assumed to be passive and rigid. The results showed that the pressure drop in the pharynx lies in the range 200-500 Pa. The onset of turbulence was found to increase the pressure drop by 40 percent. A wide range of pharynx geometries covering three sleep apnea treatment therapies (CPAP, mandibular repositioning devices, and surgery) were modeled and the resulting flow characteristics were investigated and compared. The results confirmed that the airflow in the pharynx lies in the laminar-to-turbulence transitional flow regime and thus, a subtle change in the morphology caused by these treatment therapies can significantly affect the airflow characteristics.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1998;120(3):423-430. doi:10.1115/1.2798010.

A computational analysis of confined nonimpinging jet flow in a blind tube is performed as an initial investigation of the underlying fluid and mass transport mechanics of tracheal gas insufflation. A two-dimensional axisymmetric model of a laminar steady jet flow into a concentric blind-end tube is put forth and the governing continuity, momentum, and convection-diffusion equations are solved with a finite element code. The effects of the jet diameter based Reynolds number (Rej ), the ratio of the jet-to-outer tube diameters (ε), and the Schmidt number (Sc) are evaluated with the determined velocity and contaminant concentration fields. The normalized penetration depth of the jet is found to increase linearly with increasing Rej for ε = O(0.I). For a given ε, a ring vortex that develops is observed to be displaced downstream and radially outward from the jet tip for increasing Rej . The axial shear stress profile along the inside wall of the outer tube possesses regions of fixed shear stress in addition to a local minimum and maximum in the vicinity of the jet tip. Corresponding regions of axial shear stress gradients exist between the fixed shear stress regions and the local extrema. Contaminant concentration gradients develop across the ring vortex indicating the inward diffusion of contaminant into the jet flow. For fixed ε and Sc and Rej ~ 900, normalized contaminant flow rate is observed to be approximately twice that of simple diffusion. This model predicts modest net axial contaminant transport enhancement due to convection-diffusion interaction in the region of the ring vortex.

Commentary by Dr. Valentin Fuster


J Biomech Eng. 1998;120(3):431-435. doi:10.1115/1.2798011.

Recent technical improvements and cost reductions in electromagnetic motion tracking systems invite their application to motion axis determination in the surgical setting. After evaluation of the accuracy of a state-of-the-art D. C. electromagnetic tracking system, which generates complete three-dimensional kinematic outputs from just a single receiver, we calculated screw displacement axes (SDA’s) from its source data. The accuracy of SDA determination from such source data was evaluated for various rotational increment sizes around a revolute joint. A novel smoothing procedure, customized for this type of source data, was developed, enabling SDA detection from incremental rotations of less than 1 deg, at an accuracy appropriate for intra-operative measurement of human joint motion. Examples of SDA determination are given for motion tracking of a ball joint and of the elbow articulation.

Commentary by Dr. Valentin Fuster

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