Research Papers

J Biomech Eng. 2011;133(8):081001-081001-10. doi:10.1115/1.4004492.

One way to restore physiological blood flow to occluded arteries involves the deformation of plaque using an intravascular balloon and preventing elastic recoil using a stent. Angioplasty and stent implantation cause unphysiological loading of the arterial tissue, which may lead to tissue in-growth and reblockage; termed “restenosis.” In this paper, a computational methodology for predicting the time-course of restenosis is presented. Stress-induced damage, computed using a remaining life approach, stimulates inflammation (production of matrix degrading factors and growth stimuli). This, in turn, induces a change in smooth muscle cell phenotype from contractile (as exists in the quiescent tissue) to synthetic (as exists in the growing tissue). In this paper, smooth muscle cell activity (migration, proliferation, and differentiation) is simulated in a lattice using a stochastic approach to model individual cell activity. The inflammation equations are examined under simplified loading cases. The mechanobiological parameters of the model were estimated by calibrating the model response to the results of a balloon angioplasty study in humans. The simulation method was then used to simulate restenosis in a two dimensional model of a stented artery. Cell activity predictions were similar to those observed during neointimal hyperplasia, culminating in the growth of restenosis. Similar to experiment, the amount of neointima produced increased with the degree of expansion of the stent, and this relationship was found to be highly dependant on the prescribed inflammatory response. It was found that the duration of inflammation affected the amount of restenosis produced, and that this effect was most pronounced with large stent expansions. In conclusion, the paper shows that the arterial tissue response to mechanical stimulation can be predicted using a stochastic cell modeling approach, and that the simulation captures features of restenosis development observed with real stents. The modeling approach is proposed for application in three dimensional models of cardiovascular stenting procedures.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(8):081002-081002-9. doi:10.1115/1.4004655.

Ejection from military aircraft exerts substantial loads on the lumbar spine. Fractures remain common, although the overall survivability of the event has considerably increased over recent decades. The present study was performed to develop and validate a biomechanically accurate experimental model for the high vertical acceleration loading to the lumbar spine that occurs during the catapult phase of aircraft ejection. The model consisted of a vertical drop tower with two horizontal platforms attached to a monorail using low friction linear bearings. A total of four human cadaveric spine specimens (T12-L5) were tested. Each lumbar column was attached to the lower platform through a load cell. Weights were added to the upper platform to match the thorax, head-neck, and upper extremity mass of a 50th percentile male. Both platforms were raised to the drop height and released in unison. Deceleration characteristics of the lower platform were modulated by foam at the bottom of the drop tower. The upper platform applied compressive inertial loads to the top of the specimen during deceleration. All specimens demonstrated complex bending during ejection simulations, with the pattern dependent upon the anterior-posterior location of load application. The model demonstrated adequate inter-specimen kinematic repeatability on a spinal level-by-level basis under different subfailure loading scenarios. One specimen was then exposed to additional tests of increasing acceleration to induce identifiable injury and validate the model as an injury-producing system. Multiple noncontiguous vertebral fractures were obtained at an acceleration of 21 g with 488 g/s rate of onset. This clinically relevant trauma consisted of burst fracture at L1 and wedge fracture at L4. Compression of the vertebral body approached 60% during the failure test, with -6,106 N axial force and 168 Nm flexion moment. Future applications of this model include developing a better understanding of the vertebral injury mechanism during pilot ejection and developing tolerance limits for injuries sustained under a variety of different vertical acceleration scenarios.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(8):081003-081003-11. doi:10.1115/1.4004532.

It is well known that blood vessels exhibit viscoelastic properties, which are modeled in the literature with different mathematical forms and experimental bases. The wide range of existing viscoelastic wall models may produce significantly different blood flow, pressure, and vessel deformation solutions in cardiovascular simulations. In this paper, we present a novel comparative study of two different viscoelastic wall models in nonlinear one-dimensional (1D) simulations of blood flow. The viscoelastic models are from papers by Holenstein in 1980 (model V1) and Valdez-Jasso in 2009 (model V2). The static elastic or zero-frequency responses of both models are chosen to be identical. The nonlinear 1D blood flow equations incorporating wall viscoelasticity are solved using a space-time finite element method and the implementation is verified with the Method of Manufactured Solutions. Simulation results using models V1, V2 and the common static elastic model are compared in three application examples: (i) wave propagation study in an idealized vessel with reflection-free outflow boundary condition; (ii) carotid artery model with nonperiodic boundary conditions; and (iii) subject-specific abdominal aorta model under rest and simulated lower limb exercise conditions. In the wave propagation study the damping and wave speed were largest for model V2 and lowest for the elastic model. In the carotid and abdominal aorta studies the most significant differences between wall models were observed in the hysteresis (pressure-area) loops, which were larger for V2 than V1, indicating that V2 is a more dissipative model. The cross-sectional area oscillations over the cardiac cycle were smaller for the viscoelastic models compared to the elastic model. In the abdominal aorta study, differences between constitutive models were more pronounced under exercise conditions than at rest. Inlet pressure pulse for model V1 was larger than the pulse for V2 and the elastic model in the exercise case. In this paper, we have successfully implemented and verified two viscoelastic wall models in a nonlinear 1D finite element blood flow solver and analyzed differences between these models in various idealized and physiological simulations, including exercise. The computational model of blood flow presented here can be utilized in further studies of the cardiovascular system incorporating viscoelastic wall properties.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(8):081004-081004-8. doi:10.1115/1.4004832.

A nonlinear biphasic fiber-reinforced porohyperviscoelastic (BFPHVE) model of articular cartilage incorporating fiber reorientation effects during applied load was used to predict the response of ovine articular cartilage at relatively high strains (20%). The constitutive material parameters were determined using a coupled finite element-optimization algorithm that utilized stress relaxation indentation tests at relatively high strains. The proposed model incorporates the strain-hardening, tension-compression, permeability, and finite deformation nonlinearities that inherently exist in cartilage, and accounts for effects associated with fiber dispersion and reorientation and intrinsic viscoelasticity at relatively high strains. A new optimization cost function was used to overcome problems associated with large peak-to-peak differences between the predicted finite element and experimental loads that were due to the large strain levels utilized in the experiments. The optimized material parameters were found to be insensitive to the initial guesses. Using experimental data from the literature, the model was also able to predict both the lateral displacement and reaction force in unconfined compression, and the reaction force in an indentation test with a single set of material parameters. Finally, it was demonstrated that neglecting the effects of fiber reorientation and dispersion resulted in poorer agreement with experiments than when they were considered. There was an indication that the proposed BFPHVE model, which includes the intrinsic viscoelasticity of the nonfibrillar matrix (proteoglycan), might be used to model the behavior of cartilage up to relatively high strains (20%). The maximum percentage error between the indentation force predicted by the FE model using the optimized material parameters and that measured experimentally was 3%.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(8):081005-081005-12. doi:10.1115/1.4004810.

Biological soft tissues and cells may be subjected to mechanical as well as chemical (osmotic) loading under their natural physiological environment or various experimental conditions. The interaction of mechanical and chemical effects may be very significant under some of these conditions, yet the highly nonlinear nature of the set of governing equations describing these mechanisms poses a challenge for the modeling of such phenomena. This study formulated and implemented a finite element algorithm for analyzing mechanochemical events in neutral deformable porous media under finite deformation. The algorithm employed the framework of mixture theory to model the porous permeable solid matrix and interstitial fluid, where the fluid consists of a mixture of solvent and solute. A special emphasis was placed on solute-solid matrix interactions, such as solute exclusion from a fraction of the matrix pore space (solubility) and frictional momentum exchange that produces solute hindrance and pumping under certain dynamic loading conditions. The finite element formulation implemented full coupling of mechanical and chemical effects, providing a framework where material properties and response functions may depend on solid matrix strain as well as solute concentration. The implementation was validated using selected canonical problems for which analytical or alternative numerical solutions exist. This finite element code includes a number of unique features that enhance the modeling of mechanochemical phenomena in biological tissues. The code is available in the public domain, open source finite element program FEBio (http://mrl.sci.utah.edu/software).

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(8):081006-081006-13. doi:10.1115/1.4004491.

Among the available tools for the early diagnosis of breast cancer, the elastographic technique based on ultrasounds has many advantages such as the noninvasive measure, the absence of ionizing effects, the high tolerability by patients, and the wide diffusion of the ecographic machines. However this diagnostic procedure is strongly affected by many subjective factors and is considered not reliable enough even to reduce the number of biopsies used to identify the nature of lesions. Therefore in the literature experimental and numerical simulations on physical and virtual phantoms are presented to test and validate procedures and algorithms and to interpret elastosonographic results. In this work, first a description of the elastographic technique and a review of the principal finite element (FE) models are provided and second diagnostic indexes employed to assess the nature of a lump mass are presented. As advances in FE simulations of elastosonography, axisymmetric phantom, and anthropomorphic models are described, which, with respect to the literature, include some features of breast mechanics. In particular deterministic analyses were used to compare the various details of virtual elastograms and also to investigate diagnostic indexes with respect to the regions where strains were considered. In order to improve the reliability of the elastosonographic procedure, univariate and multivariate sensitivity analyses, based on a probabilistic FE approach, were also performed to identify the parameters that mostly influence the deformation contrast between healthy and cancerous tissues. Moreover, synthetic indicators of the strain field, such as the strain contrast coefficient, were evaluated in different regions of interest in order to identify the most suitable for lesion type assessment. The deterministic analyses show that the malignant lesion is characterized by a uniform strain inside the inclusion due to the firmly bonding condition, while in the benign inclusion (loosely bonded) a strain gradient is observed independently from the elastic modulus contrast. The multivariate analyses reveal that the strain contrast depends linearly on the relative stiffness between the lesion and the healthy tissue and not linearly on the interface friction coefficient. The anthropomorphic model shows other interesting features, such as the layer or curvature effects, which introduce difficulties in selecting a reference region for strain assessment. The results show that a simple axisymmetric model with linear elastic material properties can be suitable to simulate the elastosonographic procedure although the breast curvature and layer distinction play a significant role in the strain assessment.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(8):081007-081007-6. doi:10.1115/1.4004864.

Many biological consequences of external mechanical loads applied to cells depend on localized cell deformations rather than on average whole-cell-body deformations. Such localized intracellular deformations are likely to depend, in turn, on the individual geometrical features of each cell, e.g., the local surface curvatures or the size of the nucleus, which always vary from one cell to another, even within the same culture. Our goal here was to characterize cell-to-cell variabilities in magnitudes and distribution patterns of localized tensile strains that develop in the plasma membrane (PM) and nuclear surface area (NSA) of compressed myoblasts, in order to identify resemblance or differences in mechanical performances across the cells. For this purpose, we utilized our previously developed confocal microscopy-based three-dimensional cell-specific finite element modeling methodology. Five different C2C12 undifferentiated cells belonging to the same culture were scanned confocally and modeled, and were then subjected to compression in the simulation setting. We calculated the average and peak tensile strains in the PM and NSA, the percentage of PM area subjected to tensile strains above certain thresholds and the coefficient of variation (COV) in average and peak strains. We found considerable COV values in tensile strains developing at the PM and NSA (up to ∼35%) but small external compressive deformations induced greater variabilities in intracellular strains across cells compared to large deformations. Interestingly, the external deformations needed to cause localized PM or NSA strains exceeding each threshold were very close across the different cells. Better understanding of variabilities in mechanical performances of cells—either of the same type or of different types—is important for interpreting experimental data in any experiments involving delivery of mechanical loads to cells.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(8):081008-081008-10. doi:10.1115/1.4004918.

Tissue scaffolds aim to provide a cell-friendly biomechanical environment for facilitating cell growth. Existing studies have shown significant demands for generating a certain level of wall shear stress (WSS) on scaffold microstructural surfaces for promoting cellular response and attachment efficacy. Recently, its role in shear-induced erosion of polymer scaffold has also drawn increasing attention. This paper proposes a bi-directional evolutionary structural optimization (BESO) approach for design of scaffold microstructure in terms of the WSS uniformity criterion, by downgrading highly-stressed solid elements into fluidic elements and/or upgrading lowly-stressed fluidic elements into solid elements. In addition to this, a computational model is presented to simulate shear-induced erosion process. The effective stiffness and permeability of initial and optimized scaffold microstructures are characterized by the finite element based homogenization technique to quantify the variations of mechanical properties of scaffold during erosion. The illustrative examples show that a uniform WSS is achieved within the optimized scaffold microstructures, and their architectural and biomechanical features are maintained for a longer lifetime during shear-induced erosion process. This study provides a mathematical means to the design optimization of cellular biomaterials in terms of the WSS criterion towards controllable shear-induced erosion.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(8):081009-081009-12. doi:10.1115/1.4004862.

The concept of semi-rigid fixation (SRF) has driven the development of spinal implants that utilize nonmetallic materials and novel rod geometries in an effort to promote fusion via a balance of stability, intra- and inter-level load sharing, and durability. The purpose of this study was to characterize the mechanical and biomechanical properties of a pedicle screw-based polyetheretherketone (PEEK) SRF system for the lumbar spine to compare its kinematic, structural, and durability performance profile against that of traditional lumbar fusion systems. Performance of the SRF system was characterized using a validated spectrum of experimental, computational, and in vitro testing. Finite element models were first used to optimize the size and shape of the polymeric rods and bound their performance parameters. Subsequently, benchtop tests determined the static and dynamic performance threshold of PEEK rods in relevant loading modes (flexion-extension (F/E), axial rotation (AR), and lateral bending (LB)). Numerical analyses evaluated the amount of anteroposterior column load sharing provided by both metallic and PEEK rods. Finally, a cadaveric spine simulator was used to determine the level of stability that PEEK rods provide. Under physiological loading conditions, a 6.35 mm nominal diameter oval PEEK rod construct unloads the bone-screw interface and increases anterior column load (approx. 75% anterior, 25% posterior) when compared to titanium (Ti) rod constructs. The PEEK construct’s stiffness demonstrated a value lower than that of all the metallic rod systems, regardless of diameter or metallic composition (78% < 5.5 mm Ti; 66% < 4.5 mm Ti; 38% < 3.6 mm Ti). The endurance limit of the PEEK construct was comparable to that of clinically successful metallic rod systems (135N at 5 × 106 cycles). Compared to the intact state, cadaveric spines implanted with PEEK constructs demonstrated a significant reduction of range of motion in all three loading directions (> 80% reduction in F/E, p < 0.001; > 70% reduction in LB, p < 0.001; > 54% reduction in AR, p < 0.001). There was no statistically significant difference in the stability provided by the PEEK rods and titanium rods in any mode (p = 0.769 for F/E; p = 0.085 for LB; p = 0.633 for AR). The CD HORIZON® LEGACY™ PEEK Rod System provided intervertebral stability comparable to currently marketed titanium lumbar fusion constructs. PEEK rods also more closely approximated the physiologic anteroposterior column load sharing compared to results with titanium rods. The durability, stability, strength, and biomechanical profile of PEEK rods were demonstrated and the potential advantages of SRF were highlighted.

Commentary by Dr. Valentin Fuster

Technical Briefs

J Biomech Eng. 2011;133(8):084501-084501-5. doi:10.1115/1.4004863.

Stenting of curved arteries is generally perceived to be more challenging than straight vessels. Conceptually implanting multiple shorter stents rather than a single longer stent into such a curved artery represents a promising concept, but little is known about the impact of such an approach. The objective of this study is to evaluate the effectiveness of using a multiple segment stent rather than a single long stent to dilate a curved artery using the finite element method. A double segment stent (DSS) and a single segment stent (SSS) were modeled. The stents were compared when expanded into a model of a curved artery. The model predicts that the DSS provides higher flexibility, more conformity, and lower recoil in comparison to the SSS. The volume of arterial tissue experiencing high levels of stress due to stent implantation is also reduced for the DSS. It is suggested that a multiple segment stenting system is a potential solution to the problem of higher rates of in-stent restenosis in curved arteries and mechanically challenging environments.

Topics: stents , Stress
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(8):084502-084502-6. doi:10.1115/1.4004915.

Extensive experimental work on the effects of penetrating annular injuries indicated that large injuries impact axial compressive properties of small animal intervertebral discs, yet there is some disagreement regarding the sensitivity of mechanical tests to small injury sizes. In order to understand the mechanism of injury size sensitivity, this study proposed a simple one dimensional model coupling elastic deformations in the annulus with fluid flow into and out of the nucleus through both porous boundaries and through a penetrating annular injury. The model was evaluated numerically in dynamic compression with parameters obtained by fitting the solution to experimental stress-relaxation data. The model predicted low sensitivity of mechanical changes to injury diameter at both small and large sizes (as measured by low and high ratios of injury diameter to annulus thickness), with a narrow range of high sensitivity in between. The size at which axial mechanics were most sensitive to injury size (i.e., critical injury size) increased with loading frequency. This study provides a quantitative hypothetical model of how penetrating annulus fibrosus injuries in discs with a gelatinous nucleus pulposus may alter disc mechanics by changing nucleus pulposus fluid pressurization through introduction of a new fluid transport pathway though the annulus. This model also explains how puncture-induced biomechanical changes depend on both injury size and test protocol.

Commentary by Dr. Valentin Fuster

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In