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TECHNICAL PAPERS: Bone/Orthopedic

J Biomech Eng. 2004;127(2):213-219. doi:10.1115/1.1865188.

We present results on the growth of damage in 29 fatigue tests of human femoral cortical bone from four individuals, aged 53–79. In these tests we examine the interdependency of stress, cycles to failure, rate of creep strain, and rate of modulus loss. The behavior of creep rates has been reported recently for the same donors as an effect of stress and cycles (Cotton, J. R., Zioupos, P., Winwood, K., and Taylor, M., 2003, “Analysis of Creep Strain During Tensile Fatigue of Cortical Bone  ,” J. Biomech.36, pp. 943–949). In the present paper we first examine how the evolution of damage (drop in modulus per cycle) is associated with the stress level or the “normalized stress” level (stress divided by specimen modulus), and results show the rate of modulus loss fits better as a function of normalized stress. However, we find here that even better correlations can be established between either the cycles to failure or creep rates versus rates of damage than any of these three measures versus normalized stress. The data indicate that damage rates can be excellent predictors of fatigue life and creep strain rates in tensile fatigue of human cortical bone for use in practical problems and computer simulations.

Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS: Cell

J Biomech Eng. 2004;127(2):220-228. doi:10.1115/1.1865194.

Peptide modification of hydrogel-forming materials is being widely explored as a means to regulate the phenotype of cells immobilized within the gels. Alternatively, we hypothesized that the adhesive interactions between cells and peptides coupled to the gel-forming materials would also enhance the overall mechanical properties of the gels. To test this hypothesis, alginate polymers were modified with RGDSP-containing peptides and the resultant polymer was used to encapsulate C2C12 myoblasts. The mechanical properties of these gels were then assessed as a function of both peptide and cell density using compression and tensile tests. Overall, it was found that above a critical peptide and cell density, encapsulated myoblasts were able to provide additional mechanical integrity to hydrogels composed of peptide-modified alginate. This occurred presumably by means of cell-peptide cross-linking of the alginate polymers, in addition to the usual Ca++ cross-linking. These results are potentially applicable to other polymer systems and important for a range of tissue engineering applications.

Commentary by Dr. Valentin Fuster

Article

J Biomech Eng. 2004;127(2):229-236. doi:10.1115/1.1865197.

Highly curved cell membrane structures, such as plasmalemmal vesicles (caveolae) and clathrin-coated pits, facilitate many cell functions, including the clustering of membrane receptors and transport of specific extracellular macromolecules by endothelial cells. These structures are subject to large mechanical deformations when the plasma membrane is stretched and subject to a change of its curvature. To enhance our understanding of plasmalemmal vesicles we need to improve the understanding of the mechanics in regions of high membrane curvatures. We examine here, theoretically, the shapes of plasmalemmal vesicles assuming that they consist of three membrane domains: an inner domain with high curvature, an outer domain with moderate curvature, and an outermost flat domain, all in the unstressed state. We assume the membrane properties are the same in these domains with membrane bending elasticity as well as in-plane shear elasticity. Special emphasis is placed on the effects of membrane curvature and in-plane shear elasticity on the mechanics of vesicle during unfolding by application of membrane tension. The vesicle shapes were computed by minimization of bending and in-plane shear strain energy. Mechanically stable vesicles were identified with characteristic membrane necks. Upon stretch of the membrane, the vesicle necks disappeared relatively abruptly leading to membrane shapes that consist of curved indentations. While the resting shape of vesicles is predominantly affected by the membrane spontaneous curvatures, the membrane shear elasticity (for a range of values recorded in the red cell membrane) makes a significant contribution as the vesicle is subject to stretch and unfolding. The membrane tension required to unfold the vesicle is sensitive with respect to its shape, especially as the vesicle becomes fully unfolded and approaches a relative flat shape.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2004;127(2):237-243. doi:10.1115/1.1865198.

The viscoelastic properties of single, attached C2C12 myoblasts were measured using a recently developed cell loading device. The device allows global compression of an attached cell, while simultaneously measuring the associated forces. The viscoelastic properties were examined by performing a series of dynamic experiments over two frequency decades (0.110Hz) and at a range of axial strains (1040%). Confocal laser scanning microscopy was used to visualize the cell during these experiments. To analyze the experimentally obtained force-deformation curves, a nonlinear viscoelastic model was developed. The nonlinear viscoelastic model was able to describe the complete series of dynamic experiments using only a single set of parameters, yielding an elastic modulus of 2120±900Pa for the elastic spring, an elastic modulus of 1960±1350 for the nonlinear spring, and a relaxation time constant of 0.3±0.12s. To our knowledge, it is the first time that the global viscoelastic properties of attached cells have been quantified over such a wide range of strains. Furthermore, the experiments were performed under optimal environmental conditions and the results are, therefore, believed to reflect the viscoelastic mechanical behavior of cells, such as would be present in vivo.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2004;127(2):244-253. doi:10.1115/1.1865189.

Magnetically suspended left ventricular assist devices have only one moving part, the impeller. The impeller has absolutely no contact with any of the fixed parts, thus greatly reducing the regions of stagnant or high shear stress that surround a mechanical or fluid bearing. Measurements of the mean flow patterns as well as viscous and turbulent (Reynolds) stresses were made in a shaft-driven prototype of a magnetically suspended centrifugal blood pump at several constant flow rates (39Lmin) using particle image velocimetry (PIV). The chosen range of flow rates is representative of the range over which the pump may operate while implanted. Measurements on a three-dimensional measurement grid within several regions of the pump, including the inlet, blade passage, exit volute, and diffuser are reported. The measurements are used to identify regions of potential blood damage due to high shear stress and∕or stagnation of the blood, both of which have been associated with blood damage within artificial heart valves and diaphragm-type pumps. Levels of turbulence intensity and Reynolds stresses that are comparable to those in artificial heart valves are reported. At the design flow rate (6Lmin), the flow is generally well behaved (no recirculation or stagnant flow) and stress levels are below levels that would be expected to contribute to hemolysis or thrombosis. The flow at both high (9Lmin) and low (3Lmin) flow rates introduces anomalies into the flow, such as recirculation, stagnation, and high stress regions. Levels of viscous and Reynolds shear stresses everywhere within the pump are below reported threshold values for damage to red cells over the entire range of flow rates investigated; however, at both high and low flow rate conditions, the flow field may promote activation of the clotting cascade due to regions of elevated shear stress adjacent to separated or stagnant flow.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2004;127(2):254-263. doi:10.1115/1.1865190.

Measurements of the time-varying flow in a centrifugal blood pump operating as a left ventricular assist device (LVAD) are presented. This includes changes in both the pump flow rate as a function of the left ventricle contraction and the interaction of the rotating impeller and fixed exit volute. When operating with a pulsing ventricle, the flow rate through the LVAD varies from 011Lmin during each cycle of the heartbeat. Phase-averaged measurements of mean velocity and some turbulence statistics within several regions of the pump, including the inlet, blade passage, exit volute, and diffuser, are reported at 20 phases of the cardiac cycle. The transient flow fields are compared to the constant flow rate condition that was reported previously in order to investigate the transient effects within the pump. It is shown that the quasi-steady assumption is a fair treatment of the time varying flow field in all regions of this representative pump, which greatly simplifies the comprehension and modeling of this flow field. The measurements are further interpreted to identify the effects that the transient nature of the flow field will have on blood damage. Although regions of recirculation and stagnant flow exist at some phases of the cardiac cycle, there is no location where flow is stagnant during the entire heartbeat.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2004;127(2):264-269. doi:10.1115/1.1865191.

A computational fluid dynamics (CFD) model of the cerebrospinal fluid system was constructed based on a simplified geometry of the brain ventricles and their connecting pathways. The flow is driven by a prescribed sinusoidal motion of the third ventricle lateral walls, with all other boundaries being rigid. The pressure propagation between the third and lateral ventricles was examined and compared to data obtained from a similar geometry with a stenosed aqueduct. It could be shown that the pressure amplitude in the lateral ventricles increases in the presence of aqueduct stenosis. No difference in phase shift between the motion of the third ventricle walls and the pressure in the lateral ventricles because of the aqueduct stenosis could be observed. It is deduced that CFD can be used to analyze the pressure propagation and its phase shift relative to the ventricle wall motion. It is further deduced that only models that take into account the coupling between ventricles, which feature a representation of the original geometry that is as accurate as possible and which represent the ventricle boundary motion realistically, should be used to make quantitative statements on flow and pressure in the ventricular space.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2004;127(2):270-278. doi:10.1115/1.1865186.

Interstitium contains a matrix of fibrous molecules that creates considerable resistance to water and solutes in series with the microvessel wall. On the basis of our preliminary studies (Adamson, 1994, Microcirculation1(4), pp. 251–265; Fu, 1995Am. J. Physiol.269(38), pp. H2124–H2140), by using laser-scanning confocal microscopy and a theoretical model for interstitial transport, we determined both microvessel solute permeability (P) and solute tissue diffusion coefficient (Dt) of α-lactalbumin (Stokes radius 2.01nm) from the rate of tissue solute accumulation and the radial concentration gradient around individually perfused microvessel in frog mesentery. Pαlactalbumin is 1.7±0.7(SD)×106cms(n=6). DtDfree for α-lactalbumin is 27%±5%(SD)(n=6). This value of DtDfree is comparable to that for small solute sodium fluorescein (Stokes radius 0.45nm), while Pαlactalbumin is only 3.4% of Psodiumfluorescein. Our results suggest that frog mesenteric tissue is much less selective to solutes than the microvessel wall.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2004;127(2):279-294. doi:10.1115/1.1865193.

A comprehensive computational framework to simulate heat transfer during the freezing process in prostate cancer cryosurgery is presented. Tissues are treated as nonideal materials wherein phase transition occurs over a temperature range, thermophysical properties are temperature dependent and heating due to blood flow and metabolism are included. Boundary conditions were determined at the surfaces of the commercially available cryoprobes and urethral warmer by experimental study of temperature combined with a mathematical optimization process. For simulations, a suitable computational geometry was designed based on MRI imaging data of a real prostate. An enthalpy formulation-based numerical solution was performed for a prescribed surgical protocol to mimic a clinical freezing process. This computational framework allows for the individual planning of cryosurgical procedures and objective assessment of the effectiveness of prostate cryosurgery.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2004;127(2):295-300. doi:10.1115/1.1865213.

The effect of several cell-level parameters on the predicted optimal cooling rate Bopt of an arbitrary biological system has been studied using a well-defined water transport model. An extensive investigation of the water transport model revealed three key cell level parameters: reference permeability of the membrane to water Lpg, apparent activation energy ELp, and the ratio of the available surface area for water transport to the initial volume of intracellular water (SAWV). We defined Bopt as the “highest” cooling rate at which a predefined percent of the initial water volume is trapped inside the cell (values ranging from 5% to 80%) at a predefined end temperature (values ranging from 5°C to 40°C). Irrespective of the choice of the percent of initial water volume trapped and the end temperature, an exact and linear relationship exists between Lpg,SAWV, and Bopt. However, a nonlinear and inverse relationship is found between ELp and Bopt. Remarkably, for a variety of biological systems a comparison of the published experimentally determined values of Bopt agreed quite closely with numerically predicted Bopt values when the model assumed 5% of initial water is trapped inside the cell at a temperature of 15°C. This close agreement between the experimental and model predicted optimal cooling rates is used to develop a generic optimal cooling rate chart and a generic optimal cooling rate equation that greatly simplifies the prediction of the optimal rate of freezing of biological systems.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2004;127(2):301-310. doi:10.1115/1.1865192.

An understanding of the coordination of the leg muscles in recumbent pedaling would be useful to the design of rehabilitative pedaling exercises. The objectives of this work were to (i) determine whether patterns of muscle activity while pedaling in the recumbent and upright positions are similar when the different orientation in the gravity field is considered, (ii) compare the functional roles of the leg muscles while pedaling in the recumbent position to the upright position to the upright position and (iii) determine whether leg muscle onset and offset timing for recumbent and upright pedaling respond similarly to changes in pedaling rate. To fulfill these objectives, surface electromyograms were recorded from 10 muscles of 15 subjects who pedaled in both the recumbent and upright positions at 75, 90, and 105rpm and at a constant workrate of 250W. Patterns of muscle activation were compared over the crank cycle. Functional roles of muscles in recumbent and upright pedaling were compared using the percent of integrated activation in crank cycle regions determined previously for upright pedaling. Muscle onset and offset timing were also compared. When the crank cycle was adjusted for orientation in the gravity field, the activation patterns for the two positions were similar. Functional roles of the muscles in the two positions were similar as well. In recumbent pedaling, the uniarticular hip and knee extensors functioned primarily to produce power during the extension region of the crank cycle, whereas the biarticular muscles crossing the hip and knee functioned to propel the leg through the transition regions of the crank cycle. The adaptations of the muscles to changes in pedaling rate were also similar for the two body positions with the uniarticular power producing muscles of the hip and knee advancing their activity to earlier in the crank cycle as the pedaling rate increased. This information on the functional roles of the leg muscles provides a basis by which to form functional groups, such as power-producing muscles and transition muscles, to aid in the development of rehabilitative pedaling exercises and recumbent pedaling simulations to further our understanding of task-dependent muscle coordination.

Topics: Muscle , Cycles
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2004;127(2):311-317. doi:10.1115/1.1865195.

Kinematic interpolation is an important tool in biomechanics. The purpose of this work is to describe a method for interpolating three-dimensional kinematic data, minimizing error while maintaining ease of calculation. This method uses cubic quaternion and hermite interpolation to fill gaps between kinematic data points. Data sets with a small number of samples were extracted from a larger data set and used to validate the technique. Two additional types of interpolation were applied and then compared to the cubic quaternion interpolation. Displacement errors below 2% using the cubic quaternion method were achieved using 4% of the total samples, representing a decrease in error over the other algorithms.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2004;127(2):318-328. doi:10.1115/1.1865196.

Because thoroughbred racehorses have a high incidence of forelimb musculoskeletal injuries, a model was desired to screen potential risk factors for injuries. This paper describes the development of a musculoskeletal model of the thoroughbred forelimb and a dynamic simulation of the motion of the distal segments during the stance phase of high-speed (18ms) gallop. The musculoskeletal model is comprised of segment, joint, muscle-tendon, and ligament information. The dynamic simulation incorporates a proximal forward-driving force, a distal ground reaction force model, muscle activations, and initial positions and velocities. A simulation of the gallop after transection of an accessory ligament demonstrated increased soft tissue strains in the remaining support structures of the distal forelimb. These data were consistent with those previously reported from in vitro experimental data and supported usefulness of the model for the study of distal forelimb soft tissue mechanics during the stance phase of the gallop.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2004;127(2):329-336. doi:10.1115/1.1865187.

Living tissues show an adaptive response to mechanical loading by changing their internal structure and morphology. Understanding this response is essential for successful tissue engineering of load-bearing structures, such as the aortic valve. In this study, mechanically induced remodeling of the collagen architecture in the aortic valve was investigated. It was hypothesized that, in uniaxially loaded regions, the fibers aligned with the tensile principal stretch direction. For biaxial loading conditions, on the other hand, it was assumed that the collagen fibers aligned with directions situated between the principal stretch directions. This hypothesis has already been applied successfully to study collagen remodeling in arteries. The predicted fiber architecture represented a branching network and resembled the macroscopically visible collagen bundles in the native leaflet. In addition, the complex biaxial mechanical behavior of the native valve could be simulated qualitatively with the predicted fiber directions. The results of the present model might be used to gain further insight into the response of tissue engineered constructs during mechanical conditioning.

Topics: Fibers , Valves
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2004;127(2):337-344. doi:10.1115/1.1871194.

An analytical approach for the mechanical interaction of the self-expanding Cardiocoil stent with the stenosed artery is presented. The damage factor as the contact stress at the stent-artery interface is determined. The stent is considered as an elastic helical rod having a nonlinear pressure-displacement dependence, while the artery is modeled by an elastic cylindrical shell. An influence of a moderate relative thickness of the shell is estimated. The equations for both the stent and the artery are presented in the stent-associated helical coordinates. The computational efficiency of the model enabled to carry out a parametric study of the damage factor. Comparative examinations are conducted for the stents made of the helical rods with circular and rectangular cross sections. It was found, in particular, that, under same other conditions, the damage factor for the stent with a circular cross section may be two times larger than that for a rectangular one.

Topics: stents , Pressure
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2004;127(2):345-350. doi:10.1115/1.1865212.

The objective of this study was to develop a nonlinear and anisotropic three-dimensional mathematical model of tendon behavior in which the structural components of fibers, matrix, and fiber-matrix interactions are explicitly incorporated and to use this model to infer the contributions of these structures to tendon mechanical behavior. We hypothesized that this model would show that: (i) tendon mechanical behavior is not solely governed by the isotropic matrix and fiber stretch, but is also influenced by fiber-matrix interactions; and (ii) shear fiber-matrix interaction terms will better describe tendon mechanical behavior than bulk fiber-matrix interaction terms. Model versions that did and did not include fiber-matrix interaction terms were applied to experimental tendon stress-strain data in longitudinal and transverse orientations, and the R2 goodness-of-fit was evaluated. This study showed that models that included fiber-matrix interaction terms improved the fit to longitudinal data (RToe2=0.88,RLin2=0.94) over models that only included isotropic matrix and fiber stretch terms (RToe2=0.36,RLin2=0.84). Shear fiber-matrix interaction terms proved to be responsible for the best fit to data and to contribute to stress-strain nonlinearity. The mathematical model of tendon behavior developed in this study showed that fiber-matrix interactions are an important contributor to tendon behavior. The more complete characterization of mechanical behavior afforded by this mathematical model can lead to an improved understanding of structure-function relationships in soft tissues and, ultimately, to the development of tissue-engineered therapies for injury or degeneration.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2004;127(2):351-354. doi:10.1115/1.1871195.

This study was setup to investigate the design and performance of a shape memory alloy clip for colonic anastomosis. The thermomechanical properties of the shape memory alloy material were studied and the data were used to derive a nonlinear material model. This enabled the development of computer computer aided design models and finite element analysis of the clip and tissue compression. The maximum strain of the anastomosis clip was within the recoverable range, and it exerted parallel compression of the colonic walls with a uniform pressure distribution. The design of the anastomosis clip was optimized for safe, simple, and effective use in colon surgery.

Commentary by Dr. Valentin Fuster

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