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TECHNICAL PAPERS

J Biomech Eng. 1996;118(2):145-151. doi:10.1115/1.2795952.

The pressure dependent or myogenic contraction of arterioles is one of the most fundamental control mechanisms of microvascular perfusion. While many experimental observations have been obtained on the myogenic response, no generally accepted biomechanical model has been formulated. A novel biomechanical theory is proposed based on two fundamental assumptions: the arteriolar wall exhibits viscoelastic properties before and during myogenic contractions, and the contraction is achieved by a pressure dependent change of reference length. The formulation of the model and its application to different experimental procedures on microvascular smooth muscle in the literature is presented. The model describes closely a broad spectrum of steady and unsteady pressure dependent diameter variations of arterioles under a pressure dependent stimulus.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(2):152-157. doi:10.1115/1.2795953.

In order to test experimentally a novel model for myogenic contraction of the arterioles, presented in Part I of this series, a sequence of in-vivo studies was performed on arterioles of rat cremaster muscle using a modified “Box Method.” The tissue was enclosed in a sealed chamber in which the extravascular pressure could be changed as a means of stimulating the myogenic response. The microvascular pressures were measured using an improved cremaster preparation with intact distal feeder. The experiment consists of measurements of a static myogenic response and the response to a step extravascular pressure, as well as passive viscoelastic properties of the arteriole. These measurements served to determine the parameters involved in the theoretical model. The model prediction were then compared with in-vivo observations during a ramp and during oscillatory extravascular pressure changes in the same arterioles. The results indicate that the model is capable of quantitatively predicting time dependent in-vivo changes in response to transmural pressure. The measured model parameters suggest an increase in myogenic activity from proximal arcade arterioles to more distal transverse arterioles in cremaster muscle of Wistar rats.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(2):158-164. doi:10.1115/1.2795954.

The quantification of particle (platelet) residence times in arterial geometries is relevant to the pathogenesis of several arterial diseases. In this manuscript, the concept of “volumetric residence time” (VRT) is introduced. The VRT takes into account where particles accumulate and how long they remain there, and is wellsuited to characterizing particle distributions in the complex geometries typical of the cardiovascular system. A technique for the calculation of volumetric residence time is described, which assumes that platelets are neutrally buoyant passive tracer particles, and which tracks small Lagrangian fluid elements containing a uniform concentration of platelets. This approach is used to quantify particle (platelet) residence times in the region of a modeled stenosis with a 45 percent area reduction. Residence time distributions are computed for a representative population of platelets, and for a subpopulation assumed to be “activated” by exposure to shear stresses above a threshold value. For activated platelets, high particle residence times were observed just distal to the apex of the stenosis throat, which can be explained by the presence of high shear stresses and low velocities in the throat immediately adjacent to the vessel wall. Interestingly, the separation zone distal to the stenosis showed only modestly elevated residence times, due to its highly mobile and transient nature. This calculation demonstrates the utility of the VRT concept for cardiovascular studies, particularly if a subpopulation of all particles is to be tracked. We conclude that the volumetric residence time is a useful tool.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(2):165-171. doi:10.1115/1.2795955.

Flow visualization and pressure measurements were carried out in a single valve saphenous vein casting which was made from a saphenous vein segment obtained from a bypass patient at Cedars Sinai Medical Center. Dye was injected to understand the flow around the valve. The dye showed very complex flow patterns around the valve and in the valve sinus, and the cavity formed by a ligated branch. For steady flow, pressure drops across the valve were 0.72, 2.0 and 6.3 mmHg for the physiological flow rates of 45, 84, and 169 ml/min, respectively. Overall pressure drop across the casting (compared to Poiseuille flow for a straight tube) increased with the flow rate, being 130 to 290 percent higher over this flow rate range. In the case of pulsatile flow, pressure drops across the valve were 0.95 and 3.0 mmHg for the flow rates of 47 and 87 ml/min which were 26 and 43 percent higher than those of steady flow. Overall pressure drop was 220 and 360 percent higher for those flow rates compared to Poiseuille flow. The measured spatial pressure distributions along the casting and flow visualization indicated the global nature of the flow field with the accelerated flow through the valve separating and reattaching downstream along the wall in the pressure recovery region. Atherosclerosis may be prone to occur in the lower shear region along the wall beyond the valve tip in the reattachment region, as we have observed in vivo in rabbit experiments.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(2):172-179. doi:10.1115/1.2795956.

Intimal hyperplasia and atherosclerosis have a predominant role in the failure of coronary artery bypass procedures. Theoretical studies and in vivo observations have shown that these pathologies are much more likely to occur in the proximity of end-to-side anastomosis, thus indicating that fluid dynamic conditions may be included in the pathogenic causes of the initiation, progression and complication of intimal hyperplasia. In order to study the fluid dynamics at the anastomosis of an aorto-coronary bypass, a three-dimensional mathematical model based on a FEM approach was developed. Steady-state simulations were studied in two different geometrical models of anastomosis which differ in their insertion angles (45 and 60 degree). Flow fields with three-dimensional helical patterns, secondary flows, and shear stresses were also investigated. The results show the presence of low shear stresses on the top wall just beyond the toe of the anastomosis and in the region of the coronary artery before the junction. A high wall shear stress region is present on the lateral wall of the coronary artery immediately downstream from the anastomosis. The influence of flow rate distribution on the secondary flows is also illustrated. These results confirm the sensitivity of flow behavior to the model’s geometrical parameters and enhance the importance of reproducing the anastomosis junction as closely as possible in order to evaluate the effective shear stress distribution.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(2):180-186. doi:10.1115/1.2795957.

We measured the velocity profiles of pulsatile entrance flow in a strongly curved tube using a laser-Doppler anemometer in order to simulate blood flow in the aortic arch under various conditions, i.e., a ratio of tube to curvature radius of 1/3, Womersley parameters of 12 and 18, and peak Dean number up to 1200. Axial isovelocity contours of the cross-section showed the potential vortex to be near the entrance, and with the maximum velocity there being skewed towards the inner wall; thereafter shifting towards the outer wall. During the deceleration phase, reverse axial flow occurred near the inner wall, and a region of this flow extended downstream. The large curvature contributes to the enhancement of the secondary flow and flow reversal, which elevates the wall-shear stress oscillations. The location of elevated wall-shear oscillations corresponds to the vessel wall region where atherosclerotic formation frequently occurs; thereby indicating that both the large curvature and pulsatility play key roles in formation of localized atherosclerotic lesions.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(2):187-192. doi:10.1115/1.2795958.

A mechanical filter developed to improve the performances of an artificial heart whose electrical motor has a reciprocating motion is presented. The filter phases the mechanical load strongly reducing its inertial component (which is of the same order of magnitude as the useful load). The analysis reported for a prototype developed by us shows that when its rate is equal to the first resonant frequency of the filter, a reduction of about 50 percent for the maximum value of the torque due to inertial and friction forces is obtained.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(2):193-200. doi:10.1115/1.2795959.

An electron paramagnetic resonance (EPR) technique, potentially suitable for in vivo temperature measurements, has been developed based on the temperature response of nitroxide stable free radicals. The response has been substantially enhanced by encapsulating the nitroxide in a medium of a fatty acid mixture inside a proteinaceous microsphere. The mixture underwent a phase transition in the temperature range required by the application. The phase change dramatically altered the shape of the EPR spectrum, providing a highly temperature sensitive signal. Using the nitroxide dissolved in a cholesterol and a long-chain fatty acid ester, we developed a mixture which provides a peakheight ratio change from 3.32 to 2.11, with a standard deviation of 0.04, for a temperature change typical in biological and medical applications, from 38 to 48°C. This translated to an average temperature resolution of 0.2°C for our experimental system. The average diameter of the nitroxide mixture-filled microspheres was ≈2 μm. Therefore, they are compatible with in vivo studies where the microspheres could be injected into the microvasculature having a minimum vessel diameter of the order of 8 μm. This temperature measuring method has various potential clinical applications, especially in monitoring and optimizing the treatment of cancer with hyperthermia. However, several problems regarding temperature and spatial resolution need to be resolved before this technique can be successfully used to monitor temperatures in vivo.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(2):201-209. doi:10.1115/1.2795960.

We present numerical computations of the deformation of an oil-droplet under the influence of a surface tension gradient generated by the surfactant released at the poles (the Greenspan experiment). We find this deformation to be very small under the pure surface tension gradient. To explain the large deformation of oil droplets observed in Greenspan’s experiments, we propose the existence of a phoretic force generated by the concentration gradient of the surfactant. We show that this hypothesis successfully explains the available experimental data and we propose some further tests.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(2):210-215. doi:10.1115/1.2795961.

A computational method is proposed for the construction of a three-dimensional space-filling model of an acinar ventilatory unit. Its geometry consists of truncated octahedra arranged in a cuboidal block. The ducts and alveoli are formed by opening specific common faces between polyhedra. The branching structure is automatically computed using algorithms solely to maximise the number of alveoli and minimise the average path lengths; it is not formed with reference to published experimental data. Properties of the model such as the total alveolar and ductal volumes, the distribution of individual path lengths to the alveolar sacs, and the average number of ducts per generation are calculated. The predicted morphology of the model compares well with published data for rat lungs.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(2):216-220. doi:10.1115/1.2795962.

We studied the effects of restressing on the mechanical properties and morphology of stress-shielded rabbit patellar tendons. After completely unloading the patellar tendon for 1 to 3 weeks, tension was again applied to the tendon for the subsequent 3 to 12 weeks. Although the stress shielding markedly decreased the tangent modulus and tensile strength of the tendon, restressing significantly increased them. However, the mechanical properties of the tendon were not completely recovered even after a prolonged period of restressing. The microstructure of the tendon was also restored by although the recovery was incomplete. These results indicate that the mechanical properties and morphology of tendinous tissue change in response to mechanical demands.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(2):221-226. doi:10.1115/1.2795963.

A general continuum model for the nonlinear viscoelastic behavior of soft biological tissues was formulated. This single integral finite strain (SIFS) model describes finite deformation of a nonlinearly viscoelastic material within the context of a three-dimensional model. The specific form describing uniaxial extension was obtained, and the idea of conversion from one material to another (at a microscopic level) was then introduced to model the nonlinear behavior of ligaments and tendons. Conversion allowed different constitutive equations to be used for describing a single ligament or tendon at different strain levels. The model was applied to data from uniaxial extension of younger and older human patellar tendons and canine medial collateral ligaments. Model parameters were determined from curve-fitting stress-strain and stress-relaxation data and used to predict the time-dependent stress generated by cyclic extensions.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(2):227-239. doi:10.1115/1.2795965.

In this investigation the complex multi-bundle structure of the cruciate ligaments and their interaction with the tibiofemoral joint was modeled analytically by representing the different regions of the cruciates with ligament elements. A sensitivity analysis was then performed to describe the effect that variations of the model input parameters had on the model variables (outputs). The effect that the cruciate ligament bundles had in controlling joint kinematics was dependent on knee flexion angle, and the load applied to the tibiofemoral joint. For passive range of knee motion with the thigh in the horizontal plane (a common rehabilitation activity), all cruciate ligament bundles were strained with the joint positioned between 0 and 10 deg of knee flexion, between 10 and 50 deg only the anterior bundle of the posterior cruciate ligament A-PCL was strained, and from 50 to 90 deg both the anteromedial portion of the anterior cruciate ligament A-ACL and the A-PCL were strained. This finding indicates that a strain distribution about a transverse cross section of the cruciates exists, and demonstrates the importance of differentiating between the strained and unstrained (unloaded) states of these ligaments. The strain value of a cruciate ligament bundle was an indication of how the bundle controls joint kinematics, while the unstrained values describe how much the ligament bundle must deform before it becomes strained and a restraint to tibiofemoral joint motion. In response to anterior and posterior directed loads, applied parallel to the tibial plateau, the respective ACL and PCL load values were larger in magnitude. The sensitivity of the model outputs to the input parameters was highly dependent on knee flexion angle. The geometrical input parameters of the model (including the ligament insertion site locations and articular surface geometry) had the most pronounced effect on the model output quantities, while the stiffness and initial strain conditions of the ligament bundles had less of an effect on the model outputs. When loaded, the strain values of the ligament bundles were sensitive to the ligament insertion site position. The greatest sensitivity of the model outputs was the femoral insertion of the ACL; supporting clinical impressions and previous experimental findings. Changes in the anterior-posterior dimension of the femoral articular surface did not produce a substantial effect on the model outputs, while changes in the proximal-distal dimension created a large effect; similar results were found for the tibial surface dimensions. These findings indicate that rigid body contact between the articular surfaces may not be a realistic assumption particularly with application to the prediction of tibiofemoral compressive loading and the force/strain values of the cruciate ligament elements. This also has important implications for the design and clinical application of total knee replacements (that function as rigid bodies), particularly those that spare the PCL.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(2):240-246. doi:10.1115/1.2795966.

Damage accumulation in living tissues occurs when the rate of damage formation is greater than the rate of damage repair. For very large increases in the loading rate of bones, this can result in “stress fractures” due to the growth and coalescence of fatigue related microdamage. At lower increases of loading rates, the damage accumulation process is halted because there is time for adaptive bone-remodeling to occur in response to the new load. However, it is not known if there is a relationship between microdamage and bone remodeling per se. One hypothesis for the control of bone remodeling is that osteocytes sense strains and mediate osteoblastic and osteoclastic activity. The purpose of this study was to investigate whether damage generates strains which may trigger bone remodeling. If this were true, then accumulative damage would cause adaptive bone remodeling. This study applies the methods of finite element analysis to determine the effect of observed damage mechanisms on the proposed sensors of remodeling in Haversian bone. Individual lamellae are modeled and osteocyte-lacunae are included in a generalized plane strain geometric representation. It is predicted that microdamage alters the local deformation behavior around lacunae, and that the changes increase as microdamage accumulates. Hence, if damage accumulates in a bone, it could be sensed as a change in strain at a microstructural level. The results give theoretical support to the experimental studies that have shown a correlation between microdamage and the initiation of resorption as a first step in bone remodeling.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(2):247-252. doi:10.1115/1.2795967.

Three-dimensional configuration of the scoliotic spine was mathematically expressed by a spatial curve passing through each vertebral centroid (“vertebral body line”). Three-dimensional location of the vertebral centroid was determined from digitization on the frontal and sagittal roentgenograms. Cobb angle, which is clinically used for measuring scoliosis curvature, was calculated in space to evaluate scoliosis deformity three-dimensionally. In forty-five scoliotic spines, regardless of curvature and curve patterns, the spinal configurations were excellently approximated by vertebral body lines. Vertebral body lines swerved from the sagittal plane at the end vertebrae, but aligned on a certain plane within the scoliosis region. Three-dimensional Cobb angle, which was larger than that in the frontal plane, can be utilized to evaluate the scoliosis deformity.

Topics: Scoliosis
Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1996;118(2):258-261. doi:10.1115/1.2795970.

The purpose of this study was to find an effective way for in vivo measurement of joint motion and give the normal knee motion according to this method. The joint model proposed by Grood and Suntay (1983) was chosen; the origin of the tibia was modified for the convenience of in vivo test. A computerized 6 degree-of-freedom electrogoniometer (EGM) was used in the measurement. Repeated tests on one subject were performed to establish the reliability of the method. Knee motions obtained from 42 males during level walking were expressed as flexion-extension, abduction-adduction, external-internal rotation, lateral-medial translation, anterior-posterior translation, and superior-inferior translation. The results showed that, with the proper choice of the origin of the tibia, the EGM could depend much less on external landmarks and be more effective for the joint measurement.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

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