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IN THIS ISSUE

### Editorial

J Biomech Eng. 2011;133(4):040201-040201-1. doi:10.1115/1.4003694.
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I am pleased to present in this issue the first of a series of specially invited review articles that seek to present the state of the art of their chosen biomechanical topic. The inaugural article is entitled “The specific growth rates of tissues: A review and a reevaluation” by Dr. Stephen C. Cowin of the Department of Biomedical Engineering, CUNY. In this article, Dr. Cowin presents a brief history of efforts to mathematically model the growth of tissues. He then continues to present a case for the reevaluation of current approaches and several novel ideas. It is one of the most thought-provoking, expansive articles I have read in recent years on the very exciting topic of tissue growth and remodeling. I hope you all enjoy it as much as I have.

Commentary by Dr. Valentin Fuster

### Research Papers

J Biomech Eng. 2011;133(4):041001-041001-20. doi:10.1115/1.4003341.

The first objective of this review and re-evaluation is to present a brief history of efforts to mathematically model the growth of tissues. The second objective is to place this historical material in a current perspective where it may be of help in future research. The overall objective is to look backward in order to see ways forward. It is noted that two distinct methods of imaging or modeling the growth of an organism were inspired over 70 years ago by Thompson’s (1915, “XXVII Morphology and Mathematics,” Trans. - R. Soc. Edinbrgh, 50, pp. 857–895; 1942, On Growth and Form, Cambridge University Press, Cambridge, UK) method of coordinate transformations to study the growth and form of organisms. One is based on the solid mechanics concept of the deformation of an object, and the other is based on the fluid mechanics concept of the velocity field of a fluid. The solid mechanics model is called the distributed continuous growth (DCG) model by Skalak (1981, “Growth as a Finite Displacement Field,” Proceedings of the IUTAM Symposium on Finite Elasticity, D. E. Carlson and R. T. Shield, eds., Nijhoff, The Hague, pp. 348–355) and Skalak (1982, “Analytical Description of Growth,” J. Theor. Biol., 94, pp. 555–577), and the fluid mechanics model is called the graphical growth velocity field representation (GVFR) by Cowin (2010, “Continuum Kinematical Modeling of Mass Increasing Biological Growth,” Int. J. Eng. Sci., 48, pp. 1137–1145). The GVFR is a minimum or simple model based only on the assumption that a velocity field may be used effectively to illustrate experimental results concerning the temporal evolution of the size and shape of the organism that reveals the centers of growth and growth gradients first described by Huxley (1924, “Constant Differential Growth-Ratios and Their Significance,” Nature (London), 114, pp. 895–896; 1972, Problems of Relative Growth, 2nd ed., L. MacVeagh, ed., Dover, New York). It is the method with an independent future that some earlier writers considered as an aspect of the DCG model. The development of the DCG hypothesis and the mixture theory models into models for the predicted growth of an organism is taking longer because these models are complicated and the development and refinement of the basic concepts are slower.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(4):041002-041002-14. doi:10.1115/1.4003440.

This study is part of a FDA-sponsored project to evaluate the use and limitations of computational fluid dynamics (CFD) in assessing blood flow parameters related to medical device safety. In an interlaboratory study, fluid velocities and pressures were measured in a nozzle model to provide experimental validation for a companion round-robin CFD study. The simple benchmark nozzle model, which mimicked the flow fields in several medical devices, consisted of a gradual flow constriction, a narrow throat region, and a sudden expansion region where a fluid jet exited the center of the nozzle with recirculation zones near the model walls. Measurements of mean velocity and turbulent flow quantities were made in the benchmark device at three independent laboratories using particle image velocimetry (PIV). Flow measurements were performed over a range of nozzle throat Reynolds numbers $(Rethroat)$ from 500 to 6500, covering the laminar, transitional, and turbulent flow regimes. A standard operating procedure was developed for performing experiments under controlled temperature and flow conditions and for minimizing systematic errors during PIV image acquisition and processing. For laminar $(Rethroat=500)$ and turbulent flow conditions $(Rethroat≥3500)$, the velocities measured by the three laboratories were similar with an interlaboratory uncertainty of $∼10%$ at most of the locations. However, for the transitional flow case $(Rethroat=2000)$, the uncertainty in the size and the velocity of the jet at the nozzle exit increased to $∼60%$ and was very sensitive to the flow conditions. An error analysis showed that by minimizing the variability in the experimental parameters such as flow rate and fluid viscosity to less than 5% and by matching the inlet turbulence level between the laboratories, the uncertainties in the velocities of the transitional flow case could be reduced to $∼15%$. The experimental procedure and flow results from this interlaboratory study (available at http://fdacfd.nci.nih.gov) will be useful in validating CFD simulations of the benchmark nozzle model and in performing PIV studies on other medical device models.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(4):041003-041003-11. doi:10.1115/1.4003526.

The purpose of this study is to validate numerical simulations of flow and pressure in an abdominal aortic aneurysm (AAA) using phase-contrast magnetic resonance imaging (PCMRI) and an in vitro phantom under physiological flow and pressure conditions. We constructed a two-outlet physical flow phantom based on patient imaging data of an AAA and developed a physical Windkessel model to use as outlet boundary conditions. We then acquired PCMRI data in the phantom while it operated under conditions mimicking a resting and a light exercise physiological state. Next, we performed in silico numerical simulations and compared experimentally measured velocities, flows, and pressures in the in vitro phantom to those computed in the in silico simulations. There was a high degree of agreement in all of the pressure and flow waveform shapes and magnitudes between the experimental measurements and simulated results. The average pressures and flow split difference between experiment and simulation were all within 2%. Velocity patterns showed good agreement between experimental measurements and simulated results, especially in the case of whole-cycle averaged comparisons. We demonstrated methods to perform in vitro phantom experiments with physiological flows and pressures, showing good agreement between numerically simulated and experimentally measured velocity fields and pressure waveforms in a complex patient-specific AAA geometry.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(4):041004-041004-12. doi:10.1115/1.4003524.

In this paper, a method is presented to analyze the mechanical stress distribution in a pacing lead based on a sequence of paired 2D angiographic images. The 3D positions and geometrical shapes of an implanted pacemaker lead throughout the cardiac cycle were generated using a previously validated 3D modeling technique. Based on the Frenet–Serret formulas, the kinematic property of the lead was derived and characterized. The distribution of curvature and twist angle per unit length in the pacing lead was calculated from a finite difference method, which enabled a rapid and effective computation of the mechanical stress in the pacing lead. The analytical solution of the helix deformation geometry was used to evaluate the accuracy of the proposed numerical method, and an excellent agreement in curvature, twist angle, and stresses was achieved. As demonstrated in the example, the proposed technique can be used to analyze the complex movement and deformation of the implanted pacing lead in vivo. The information can facilitate the future development of pacing leads.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(4):041005-041005-11. doi:10.1115/1.4003525.

Conventional gait rehabilitation treatment does not provide quantitative information on abnormal gait kinematics, and the match of the intervention strategy to the underlying clinical presentation may be limited by clinical expertise and experience. Also the effect of rehabilitation treatment may be reduced as the rehabilitation treatment is achieved only in a clinical setting. In this paper, a mobile gait monitoring system (MGMS) is proposed for the diagnosis of abnormal gait and rehabilitation. The proposed MGMS consists of Smart Shoes and a microsignal processor with a touch screen display. It monitors patients’ gait by observing the ground reaction force (GRF) and the center of GRF, and analyzes the gait abnormality. Since visual feedback about patients’ GRFs and normal GRF patterns are provided by the MGMS, patients can practice the rehabilitation treatment by trying to follow the normal GRF patterns without restriction of time and place. The gait abnormality proposed in this paper is defined by the deviation between the patient’s GRFs and normal GRF patterns, which are constructed as GRF bands. The effectiveness of the proposed gait analysis methods with the MGMS has been verified by preliminary trials with patients suffering from gait disorders.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(4):041006-041006-11. doi:10.1115/1.4003620.

We describe a modeling methodology intended as a preliminary step in the identification of appropriate constitutive frameworks for the time-dependent response of biological tissues. The modeling approach comprises a customizable rheological network of viscous and elastic elements governed by user-defined 1D constitutive relationships. The model parameters are identified by iterative nonlinear optimization, minimizing the error between experimental and model-predicted structural (load-displacement) tissue response under a specific mode of deformation. We demonstrate the use of this methodology by determining the minimal rheological arrangement, constitutive relationships, and model parameters for the structural response of various soft tissues, including ex vivo perfused porcine liver in indentation, ex vivo porcine brain cortical tissue in indentation, and ex vivo human cervical tissue in unconfined compression. Our results indicate that the identified rheological configurations provide good agreement with experimental data, including multiple constant strain rate load/unload tests and stress relaxation tests. Our experience suggests that the described modeling framework is an efficient tool for exploring a wide array of constitutive relationships and rheological arrangements, which can subsequently serve as a basis for 3D constitutive model development and finite-element implementations. The proposed approach can also be employed as a self-contained tool to obtain simplified 1D phenomenological models of the structural response of biological tissue to single-axis manipulations for applications in haptic technologies.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(4):041007-041007-5. doi:10.1115/1.4003621.

The external knee adduction moment (KAM) measured during gait is an indicator of tibiofemoral joint osteoarthritis progression and various strategies have been proposed to lower it. Gait retraining has been shown to be an effective, noninvasive approach for lowering the KAM. We present a new gait retraining approach in which the KAM is fed back to subjects in real-time during ambulation. A study was conducted in which 16 healthy subjects learned to alter gait patterns to lower the KAM through visual or tactile (vibration) feedback. Participants converged on a comfortable gait in just a few minutes by using the feedback to iterate on various kinematic modifications. All subjects adopted altered gait patterns with lower KAM compared with normal ambulation (average reduction of 20.7%). Tactile and visual feedbacks were equally effective for real-time training, although subjects using tactile feedback took longer to converge on an acceptable gait. This study shows that real-time feedback of the KAM can greatly increase the effectiveness and efficiency of subject-specific gait retraining compared with conventional methods.

Topics: Feedback , Knee , Vibration
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(4):041008-041008-10. doi:10.1115/1.4003622.

We report a study of the role of hemodynamic shear stress in the remodeling and failure of a peripheral artery bypass graft. Three separate scans of a femoral to popliteal above-knee bypass graft were taken over the course of a 16 month period following a revision of the graft. The morphology of the lumen is reconstructed from data obtained by a custom 3D ultrasound system. Numerical simulations are performed with the patient-specific geometries and physiologically realistic flow rates. The ultrasound reconstructions reveal two significant areas of remodeling: a stenosis with over 85% reduction in area, which ultimately caused graft failure, and a poststenotic dilatation or widening of the lumen. Likewise, the simulations reveal a complicated hemodynamic environment within the graft. Preliminary comparisons with in vivo velocimetry also showed qualitative agreement with the flow dynamics observed in the simulations. Two distinct flow features are discerned and are hypothesized to directly initiate the observed in vivo remodeling. First, a flow separation occurs at the stenosis. A low shear recirculation region subsequently develops distal to the stenosis. The low shear region is thought to be conducive to smooth muscle cell proliferation and intimal growth. A poststenotic jet issues from the stenosis and subsequently impinges onto the lumen wall. The lumen dilation is thought to be a direct result of the high shear stress and high frequency pressure fluctuations associated with the jet impingement.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(4):041009-041009-8. doi:10.1115/1.4003673.

In this work, we examine the dynamics of fluid flow in a mechanical heart valve when the solid inertia and leaflet compliance are important. The fluid is incompressible and Newtonian, and the leaflet is an incompressible neo-Hookean material. In the case of an inertialess leaflet, we find that the maximum valve opening angle and the time that the valve remains closed increase as the shear modulus of the leaflet decreases. More importantly, the regurgitant volume decreases with decreasing shear modulus. When we examined the forces exerted on the leaflet, we found that the downward motion of the leaflet is initiated by a vertical force exerted on its right side and, later on, by a vertical force exerted on the top side of the leaflet. In the case of solid inertia, we find that the maximum valve opening angle and the regurgitant volume are larger than in the case of an inertialess leaflet. These results highlight the importance of solid compliance in the dynamics of blood flow in a mechanical heart valve. More importantly, they indicate that mechanical heart valves with compliant leaflets may have smaller regurgitant volumes and smaller shear stresses than the ones with rigid leaflets.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(4):041010-041010-12. doi:10.1115/1.4003314.

Mechanically induced cell deformations have been shown to influence chondrocyte response in 3D culture. However, the relationship between the mechanical stimulation and cell response is not yet fully understood. In this study a finite element model was developed to investigate cell-matrix interactions under unconfined compression conditions, using a tissue engineered encapsulating hydrogel seeded with chondrocytes. Model predictions of stress and strain distributions within the cell and on the cell boundary were shown to exhibit space-dependent responses that varied with scaffold mechanical properties, the presence of a pericellular matrix (PCM), and the cell size. The simulations predicted that when the cells were initially encapsulated into the hydrogel scaffolds, the cell size hardly affected the magnitude of the stresses and strains that were reaching the encapsulated cells. However, with the inclusion of a PCM layer, larger cells experienced enhanced stresses and strains resulting from the mechanical stimulation. It was also noted that the PCM had a stress shielding effect on the cells in that the peak stresses experienced within the cells during loading were significantly reduced. On the other hand, the PCM caused the stresses at the cell-matrix interface to increase. Based on the model predictions, the PCM modified the spatial stress distribution within and around the encapsulated cells by redirecting the maximum stresses from the periphery of the cells to the cell nucleus. In a tissue engineered cartilage exposed to mechanical loading, the formation of a neo-PCM by encapsulated chondrocytes appears to protect them from initially excessive mechanical loading. Predictive models can thus shed important insight into how chondrocytes remodel their local environment in order to redistribute mechanical signals in tissue engineered constructs.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J Biomech Eng. 2011;133(4):044501-044501-6. doi:10.1115/1.4003438.

Recently, a noninvasive method for determining regional myocardial contractility, using an animal-specific finite element (FE) model-based optimization, was developed to study a sheep with anteroapical infarction (Sun, 2009, “A Computationally Efficient Formal Optimization of Regional Myocardial Contractility in a Sheep With Left Ventricular Aneurysm,” ASME J. Biomech. Eng., 131(11), p. 111001). Using the methodology developed in the previous study (Sun, 2009, “A Computationally Efficient Formal Optimization of Regional Myocardial Contractility in a Sheep With Left Ventricular Aneurysm,” ASME J. Biomech. Eng., 131(11), p. 111001), which incorporates tagged magnetic resonance images, three-dimensional myocardial strains, left ventricular (LV) volumes, and LV cardiac catheterization pressures, the regional myocardial contractility and stress distribution of a sheep with posterobasal infarction were investigated. Active material parameters in the noninfarcted border zone (BZ) myocardium adjacent to the infarct $(Tmax_B)$, in the myocardium remote from the infarct $(Tmax_R)$, and in the infarct $(Tmax_I)$ were estimated by minimizing the errors between FE model-predicted and experimentally measured systolic strains and LV volumes using the previously developed optimization scheme. The optimized $Tmax_B$ was found to be significantly depressed relative to $Tmax_R$, while $Tmax_I$ was found to be zero. The myofiber stress in the BZ was found to be elevated, relative to the remote region. This could cause further damage to the contracting myocytes, leading to heart failure.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(4):044502-044502-7. doi:10.1115/1.4003489.

Finite element models (FEMs) including characteristic large deformations in highly nonlinear materials (hyperelasticity and coupled diffusive/convective transport of neutral mobile species) will allow quantitative study of in vivo tissues. Such FEMs will provide basic understanding of normal and pathological tissue responses and lead to optimization of local drug delivery strategies. We present a coupled porohyperelastic mass transport (PHEXPT) finite element approach developed using a commercially available ABAQUS finite element software. The PHEXPT transient simulations are based on sequential solution of the porohyperelastic (PHE) and mass transport (XPT) problems where an Eulerian PHE FEM is coupled to a Lagrangian XPT FEM using a custom-written FORTRAN program. The PHEXPT theoretical background is derived in the context of porous media transport theory and extended to ABAQUS finite element formulations. The essential assumptions needed in order to use ABAQUS are clearly identified in the derivation. Representative benchmark finite element simulations are provided along with analytical solutions (when appropriate). These simulations demonstrate the differences in transient and steady state responses including finite deformations, total stress, fluid pressure, relative fluid, and mobile species flux. A detailed description of important model considerations (e.g., material property functions and jump discontinuities at material interfaces) is also presented in the context of finite deformations. The ABAQUS -based PHEXPT approach enables the use of the available ABAQUS capabilities (interactive FEM mesh generation, finite element libraries, nonlinear material laws, pre- and postprocessing, etc.). PHEXPT FEMs can be used to simulate the transport of a relatively large neutral species (negligible osmotic fluid flux) in highly deformable hydrated soft tissues and tissue-engineered materials.

Commentary by Dr. Valentin Fuster

### Errata

J Biomech Eng. 2011;133(4):047001-047001-1. doi:10.1115/1.4003527.
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The percentage reduction in Ef due to 12 days of refrigeration at $4°C$ is reported incorrectly in the text of both the Abstract and the Results (Sec. 3.2) (1). The published text states that Ef is reduced to $3.1±41.3%$ of control values: “…Ef (to $3.1±41.3%$ of control values, $p=0.046$)…” (p. 064502-1), and “By day 12, Ef decreased to $3.1±41.3%$ ($mean±95%$ CI)” (p. 064502-3). Please note that the decimal point is incorrectly placed, and Ef was in fact reduced to $31.3±41.3%$ of control values. This percentage is consistent with the reduction in Ef illustrated in Fig. 3(c) (1).

Commentary by Dr. Valentin Fuster