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Research Papers

J Biomech Eng. 2013;135(11):111001-111001-11. doi:10.1115/1.4024823.

Computational tools are often needed to model the complex behavior of biological tissues and cells when they are represented as mixtures of multiple neutral or charged constituents. This study presents the formulation of a finite element modeling framework for describing multiphasic materials in the open-source finite element software febio.1 Multiphasic materials may consist of a charged porous solid matrix, a solvent, and any number of neutral or charged solutes. This formulation proposes novel approaches for addressing several challenges posed by the finite element analysis of such complex materials: The exclusion of solutes from a fraction of the pore space due to steric volume and short-range electrostatic effects is modeled by a solubility factor, whose dependence on solid matrix deformation and solute concentrations may be described by user-defined constitutive relations. These solute exclusion mechanisms combine with long-range electrostatic interactions into a partition coefficient for each solute whose value is dependent upon the evaluation of the electric potential from the electroneutrality condition. It is shown that this electroneutrality condition reduces to a polynomial equation with only one valid root for the electric potential, regardless of the number and valence of charged solutes in the mixture. The equation of charge conservation is enforced as a constraint within the equation of mass balance for each solute, producing a natural boundary condition for solute fluxes that facilitates the prescription of electric current density on a boundary. It is also shown that electrical grounding is necessary to produce numerical stability in analyses where all the boundaries of a multiphasic material are impermeable to ions. Several verification problems are presented that demonstrate the ability of the code to reproduce known or newly derived solutions: (1) the Kedem–Katchalsky model for osmotic loading of a cell; (2) Donnan osmotic swelling of a charged hydrated tissue; and (3) current flow in an electrolyte. Furthermore, the code is used to generate novel theoretical predictions of known experimental findings in biological tissues: (1) current-generated stress in articular cartilage and (2) the influence of salt cation charge number on the cartilage creep response. This generalized finite element framework for multiphasic materials makes it possible to model the mechanoelectrochemical behavior of biological tissues and cells and sets the stage for the future analysis of reactive mixtures to account for growth and remodeling.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(11):111002-111002-15. doi:10.1115/1.4025101.

This study is aimed to develop a high quality, extensively validated finite element (FE) human head model for enhanced head injury prediction and prevention. The geometry of the model was based on computed tomography (CT) and magnetic resonance imaging scans of an adult male who has the average height and weight of an American. A feature-based multiblock technique was adopted to develop hexahedral brain meshes including the cerebrum, cerebellum, brainstem, corpus callosum, ventricles, and thalamus. Conventional meshing methods were used to create the bridging veins, cerebrospinal fluid, skull, facial bones, flesh, skin, and membranes—including falx, tentorium, pia, arachnoid, and dura. The head model has 270,552 elements in total. Thirty five loading cases were selected from a range of experimental head impacts to check the robustness of the model predictions based on responses including the brain pressure, relative skull-brain motion, skull response, and facial response. The brain pressure was validated against intracranial pressure data reported by Nahum et al. (1977, “Intracranial Pressure Dynamics During Head Impact,” Proc. 21st Stapp Car Crash Conference, SAE Technical Paper No. 770922) and Trosseille et al. (1992, “Development of a F.E.M. of the Human Head According to a Specific Test Protocol,” Proc. 36th Stapp Car Crash Conference, SAE Technical Paper No. 922527). The brain motion was validated against brain displacements under sagittal, coronal, and horizontal blunt impacts performed by Hardy et al. (2001, “Investigation of Head Injury Mechanisms Using Neutral Density Technology and High-Speed Biplanar X-Ray,” Stapp Car Crash Journal, 45, pp. 337–368; and 2007, “A Study of the Response of the Human Cadaver Head to Impact,” Stapp Car Crash Journal, 51, pp. 17–80). The facial bone responses were validated under nasal impact (Nyquist et al. 1986, “Facial Impact Tolerance and Response,” Proc. 30th Stapp Car Crash Conference, SAE Technical Paper No. 861896), zygoma and maxilla impact (Allsop et al. 1988, “Facial Impact Response – A Comparison of the Hybrid III Dummy and Human Cadaver,” Proc. 32nd Stapp Car Crash Conference, SAE Technical Paper No. 881719)]. The skull bones were validated under frontal angled impact, vertical impact, and occipital impact (Yoganandan et al. 1995, “Biomechanics of Skull Fracture,” J Neurotrauma, 12(4), pp. 659–668) and frontal horizontal impact (Hodgson et al. 1970, “Fracture Behavior of the Skull Frontal Bone Against Cylindrical Surfaces,” 14th Stapp Car Crash Conference, SAE International, Warrendale, PA). The FE head model was further used to study injury mechanisms and tolerances for brain contusion (Nahum et al. 1976, “An Experimental Model for Closed Head Impact Injury,” 20th Stapp Car Crash Conference, SAE International, Warrendale, PA). Studies from 35 loading cases demonstrated that the FE head model could predict head responses which were comparable to experimental measurements in terms of pattern, peak values, or time histories. Furthermore, tissue-level injury tolerances were proposed. A maximum principal strain of 0.42% was adopted for skull cortical layer fracture and maximum principal stress of 20 MPa was used for skull diploë layer fracture. Additionally, a plastic strain threshold of 1.2% was used for facial bone fracture. For brain contusion, 277 kPa of brain pressure was calculated from reconstruction of one contusion case.

Topics: Pressure , Brain
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(11):111003-111003-11. doi:10.1115/1.4024822.

Current understanding of the biomechanics of cervical spine injuries in head-first impact is based on decades of epidemiology, mathematical models, and in vitro experimental studies. Recent mathematical modeling suggests that muscle activation and muscle forces influence injury risk and mechanics in head-first impact. It is also known that muscle forces are central to the overall physiologic stability of the cervical spine. Despite this knowledge, the vast majority of in vitro head-first impact models do not incorporate musculature. We hypothesize that the simulation of the stabilizing mechanisms of musculature during head-first osteoligamentous cervical spine experiments will influence the resulting kinematics and injury mechanisms. Therefore, the objective of this study was to document differences in the kinematics, kinetics, and injuries of ex vivo osteoligamentous human cervical spine and surrogate head complexes that were instrumented with simulated musculature relative to specimens that were not instrumented with musculature. We simulated a head-first impact (3 m/s impact speed) using cervical spines and surrogate head specimens (n = 12). Six spines were instrumented with a follower load to simulate in vivo compressive muscle forces, while six were not. The principal finding was that the axial coupling of the cervical column between the head and the base of the cervical spine (T1) was increased in specimens with follower load. Increased axial coupling was indicated by a significantly reduced time between head impact and peak neck reaction force (p = 0.004) (and time to injury (p = 0.009)) in complexes with follower load relative to complexes without follower load. Kinematic reconstruction of vertebral motions indicated that all specimens experienced hyperextension and the spectrum of injuries in all specimens were consistent with a primary hyperextension injury mechanism. These preliminary results suggest that simulating follower load that may be similar to in vivo muscle forces results in significantly different impact kinetics than in similar biomechanical tests where musculature is not simulated.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(11):111004-111004-9. doi:10.1115/1.4025111.

Computational hemodynamic models of the cardiovascular system are often limited to finite segments of the system and therefore need well-controlled inlet and outlet boundary conditions. Classical boundary conditions are measured total pressure or flow rate imposed at the inlet and impedances of RLR, RLC, or LR filters at the outlet. We present a new approach based on an unidirectional propagative approach (UPA) to model the inlet/outlet boundary conditions on the axisymmetric Navier–Stokes equations. This condition is equivalent to a nonreflecting boundary condition in a fluid–structure interaction model of an axisymmetric artery. First we compare the UPA to the best impedance filter (RLC). Second, we apply this approach to a physiological situation, i.e., the presence of a stented segment into a coronary artery. In that case a reflection index is defined which quantifies the amount of pressure waves reflected upon the singularity.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(11):111005-111005-10. doi:10.1115/1.4025325.

The reverse shoulder replacement, recommended for the treatment of several shoulder pathologies such as cuff tear arthropathy and fractures in elderly people, changes the biomechanics of the shoulder when compared to the normal anatomy. Although several musculoskeletal models of the upper limb have been presented to study the shoulder joint, only a few of them focus on the biomechanics of the reverse shoulder. This work presents a biomechanical model of the upper limb, including a reverse shoulder prosthesis, to evaluate the impact of the variation of the joint geometry and position on the biomechanical function of the shoulder. The biomechanical model of the reverse shoulder is based on a musculoskeletal model of the upper limb, which is modified to account for the properties of the DELTA® reverse prosthesis. Considering two biomechanical models, which simulate the anatomical and reverse shoulder joints, the changes in muscle lengths, muscle moment arms, and muscle and joint reaction forces are evaluated. The muscle force sharing problem is solved for motions of unloaded abduction in the coronal plane and unloaded anterior flexion in the sagittal plane, acquired using video-imaging, through the minimization of an objective function related to muscle metabolic energy consumption. After the replacement of the shoulder joint, significant changes in the length of the pectoralis major, latissimus dorsi, deltoid, teres major, teres minor, coracobrachialis, and biceps brachii muscles are observed for a reference position considered for the upper limb. The shortening of the teres major and teres minor is the most critical since they become unable to produce active force in this position. Substantial changes of muscle moment arms are also observed, which are consistent with the literature. As expected, there is a significant increase of the deltoid moment arms and more fibers are able to elevate the arm. The solutions to the muscle force sharing problem support the biomechanical advantages attributed to the reverse shoulder design and show an increase in activity from the deltoid, teres minor, and coracobrachialis muscles. The glenohumeral joint reaction forces estimated for the reverse shoulder are up to 15% lower than those in the normal shoulder anatomy. The data presented here complements previous publications, which, all together, allow researchers to build a biomechanical model of the upper limb including a reverse shoulder prosthesis.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(11):111006-111006-7. doi:10.1115/1.4025326.

A 1D fluid model is implemented for the purpose of fluid-structure interaction (FSI) simulations in complex and completely collapsible geometries, particularly targeting the case of obstructive sleep apnea (OSA). The fluid mechanics are solved separately from any solid mechanics, making possible the use of a highly complex and/or black-box solver for the solid mechanics. The fluid model is temporally discretized with a second-order scheme and spatially discretized with an asymmetrical fourth-order scheme that is robust in highly uneven geometries. A completely collapsing and reopening geometry is handled smoothly using a modified area function. The numerical implementation is tested with two driven-geometry cases: (1) an inviscid analytical solution and (2) a completely closing geometry with viscous flow. Three-dimensional fluid simulations in static geometries are performed to examine the assumptions of the 1D model, and with a well-defined pressure-recovery constant the 1D model agrees well with 3D models. The model is very fast computationally, is robust, and is recommended for OSA simulations where the bulk flow pressure is primarily of interest.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(11):111007-111007-9. doi:10.1115/1.4025329.

While a number of studies have quantified overall ribcage morphology (breadth, depth, kyphosis/lordosis) and rib cross-sectional geometry in humans, few studies have characterized the centroidal geometry of individual ribs. In this study, a novel model is introduced to describe the centroidal path of a rib (i.e., the sequence of centroids connecting adjacent cross-sections) in terms of several physically-meaningful and intuitive geometric parameters. Surface reconstructions of rib levels 2–10 from 16 adult male cadavers (aged 31–75 years) were first extracted from CT scans, and the centroidal path was calculated in 3D for each rib using a custom numerical method. The projection of the centroidal path onto the plane of best fit (i.e., the “in-plane” centroidal path) was then modeled using two geometric primitives (a circle and a semiellipse) connected to give C1 continuity. Two additional parameters were used to describe the deviation of the centroidal path from this plane; further, the radius of curvature was calculated at various points along the rib length. This model was fit to each of the 144 extracted ribs, and average trends in rib size and shape with rib level were reported. In general, upper ribs (levels 2–5) had centroidal paths which were closer to circular, while lower ribs (levels 6–10) tended to be more elliptical; further the centroidal curvature at the posterior extremity was less pronounced for lower ribs. Lower ribs also tended to exhibit larger deviations from the best-fit plane. The rib dimensions and trends with subject stature were found to be consistent with findings previously reported in the literature. This model addresses a critical need in the biomechanics literature for the accurate characterization of rib geometry, and can be extended to a larger population as a simple and accurate way to represent the centroidal shape of human ribs.

Topics: Geometry , Shapes , Dimensions
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(11):111008-111008-8. doi:10.1115/1.4025330.

Human vocal folds experience flow-induced vibrations during phonation. In previous computational models, the vocal fold dynamics has been treated with linear elasticity theory in which both the strain and the displacement of the tissue are assumed to be infinitesimal (referred to as model I). The effect of the nonlinear strain, or geometric nonlinearity, caused by finite displacements is yet not clear. In this work, a two-dimensional model is used to study the effect of geometric nonlinearity (referred to as model II) on the vocal fold and the airflow. The result shows that even though the deformation is under 1 mm, i.e., less than 10% of the size of the vocal fold, the geometric nonlinear effect is still significant. Specifically, model I underpredicts the gap width, the flow rate, and the impact stress on the medial surfaces as compared to model II. The study further shows that the differences are caused by the contact mechanics and, more importantly, the fluid-structure interaction that magnifies the error from the small-displacement assumption. The results suggest that using the large-displacement formulation in a computational model would be more appropriate for accurate simulations of the vocal fold dynamics.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(11):111009-111009-9. doi:10.1115/1.4025334.

Irreversible electroporation (IRE) is a new technology for ablating aberrant tissue that utilizes pulsed electric fields (PEFs) to kill cells by destabilizing their plasma membrane. When treatments are planned correctly, the pulse parameters and location of the electrodes for delivering the pulses are selected to permit destruction of the target tissue without causing thermal damage to the surrounding structures. This allows for the treatment of surgically inoperable masses that are located near major blood vessels and nerves. In select cases of high-dose IRE, where a large ablation volume is desired without increasing the number of electrode insertions, it can become challenging to design a pulse protocol that is inherently nonthermal. To solve this problem we have developed a new electrosurgical device that requires no external equipment or protocol modifications. The design incorporates a phase change material (PCM) into the electrode core that melts during treatment and absorbs heat out of the surrounding tissue. Here, this idea is reduced to practice by testing hollow electrodes filled with gallium on tissue phantoms and monitoring temperature in real time. Additionally, the experimental data generated are used to validate a numerical model of the heat transfer problem, which is then applied to investigate the cooling performance of other classes of PCMs. The results indicate that metallic PCMs, such as gallium, are better suited than organics or salt hydrates for thermal management, because their comparatively higher thermal conductivity aids in heat dissipation. However, the melting point of the metallic PCM must be properly adjusted to ensure that the phase transition is not completed before the end of treatment. When translated clinically, phase change electrodes have the potential to continue to allow IRE to be performed safely near critical structures, even in high-dose cases.

Commentary by Dr. Valentin Fuster

Technical Briefs

J Biomech Eng. 2013;135(11):114501-114501-8. doi:10.1115/1.4025103.

Application of low-magnitude strains to cells on small-thickness scaffolds, such as those for rodent calvarial defect models, is problematic, because general translation systems have limitations in terms of generating low-magnitude smooth signals. To overcome this limitation, we developed a cyclic strain generator using a customized, flexure-based, translational nanoactuator that enabled generation of low-magnitude smooth strains at the subnano- to micrometer scale to cells on small-thickness scaffolds. The cyclic strain generator we developed showed predictable operational characteristics by generating a sinusoidal signal of a few micrometers (4.5 μm) without any distortion. Three-dimensional scaffolds fitting the critical-size rat calvarial defect model were fabricated using poly(caprolactone), poly(lactic-co-glycolic acid), and tricalcium phosphate. Stimulation of human adipose–derived stem cells (ASCs) on these fabricated scaffolds using the cyclic strain generator we developed resulted in upregulated osteogenic marker expression compared to the nonstimulated group. These preliminary in vitro results suggest that the cyclic strain generator successfully provided mechanical stimulation to cells on small-thickness scaffolds, which influenced the osteogenic differentiation of ASCs.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(11):114502-114502-14. doi:10.1115/1.4025105.

The purpose of this study is to investigate the effects of preconditioning on the deformation response of planar tissues measured by inflation tests. The inflation response of test specimens, including the bovine cornea, bovine and porcine sclera, and human skin, exhibited a negligible evolving deformation response when subjected to repeated pressure loading with recovery periods between cycles. Tissues obtained complete recovery to the reference state, and strain contours across the entire specimen were nearly identical at the maximum pressure of each load cycle. This repeatability was obtained regardless of strain history. These results suggest that negligible permanent change was induced in the microstructure by inflation testing. Additionally, we present data illustrating that a lack of a recovery period can result in an evolving deformation response to repeated loading that is commonly attributed to preconditioning. These results suggest that the commonly observed effects of preconditioning may be avoided by experimental design for planar tissues characterized by long collagen fibers arranged in the plane of the tissue. Specifically, if the test is designed to fully fix the specimen boundary during loading, adequate recovery periods are allowed after each load cycle, and loads are limited to avoid damage, preconditioning effects may be avoided for planar tissues.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(11):114503-114503-6. doi:10.1115/1.4025107.

Steady flow simulations of blood flow in an axisymmetric stenosed artery, subjected to a static magnetic field, are performed to investigate the influence of artery size, magnetic field strength, and non-Newtonian behavior on artery wall shear stress and pressure drop in the stenosed section. It is found that wall shear stress and pressure drop increase by decreasing artery size, assuming non-Newtonian fluid, and increasing magnetic field strength. In the computations, the shear thinning behavior of blood is accounted for by the Carreau–Yasuda model. Computational results are compared and found to be inline with available experimental data.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(11):114504-114504-4. doi:10.1115/1.4025327.

In studies of the biomechanics of joints, the representation of moments using the joint coordinate system has been discussed by several authors. The primary purpose of this technical brief is to emphasize that there are two distinct, albeit related, representations for moment vectors using the joint coordinate system. These distinct representations are illuminated by exploring connections between the Euler and dual Euler bases, the “nonorthogonal projections” presented in a recent paper by Desroches et al. (2010, “Expression of Joint Moment in the Joint Coordinate System,” ASME J. Biomech. Eng., 132(11), p. 11450) and seminal works by Grood and Suntay (Grood and Suntay, 1983, “A Joint Coordinate System for the Clinical Description of Three-Dimensional Motions: Application to the Knee,” ASME J. Biomech. Eng., 105(2), pp. 136–144) and Fujie et al. (1996, “Forces and Moment in Six-DOF at the Human Knee Joint: Mathematical Description for Control,” Journal of Biomechanics, 29(12), pp. 1577–1585) on the knee joint. It is also shown how the representation using the dual Euler basis leads to straightforward definition of joint stiffnesses.

Topics: Knee , Rotation
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(11):114505-114505-5. doi:10.1115/1.4025328.

It is well known that arteries are subject to residual stress. In earlier studies, the residual stress in the arterial ring relieved by a radial cut was considered in stress analysis. However, it has been found that axial strips sectioned from arteries also curled into arcs, showing that the axial residual stresses were relieved from the arterial walls. The combined relief of circumferential and axial residual stresses must be considered to accurately analyze stress and strain distributions under physiological loading conditions. In the present study, a mathematical model of a stress-free configuration of artery was proposed using Riemannian geometry. Stress analysis for arterial walls under unloaded and physiologically loaded conditions was performed using exponential strain energy functions for porcine and human common carotid arteries. In the porcine artery, the circumferential stress distribution under physiological loading became uniform compared with that without axial residual strain, whereas a gradient of axial stress distribution increased through the wall thickness. This behavior showed almost the same pattern that was observed in a recent study in which approximate analysis accounting for circumferential and axial residual strains was performed, whereas the circumferential and axial stresses increased from the inner surface to the outer surface under a physiological condition in the human common carotid artery of a two-layer model based on data of other recent studies. In both analyses, Riemannian geometry was appropriate to define the stress-free configurations of the arterial walls with both circumferential and axial residual strains.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(11):114506-114506-11. doi:10.1115/1.4025323.

Design excellence (DEX) tools have been widely used for years in some industries for their potential to facilitate new product development. The medical sector, targeted by cost pressures, has therefore started adopting them. Numerous tools are available; however only appropriate deployment during the new product development stages can optimize the overall process. The primary study objectives were to describe generic tools and illustrate their implementation and management during the development of new orthopaedic implants, and compile a reference package. Secondary objectives were to present the DEX tool investment costs and savings, since the method can require significant resources for which companies must carefully plan. The publicly available DEX method “Define Measure Analyze Design Verify Validate” was adopted and implemented during the development of a new spinal implant. Several tools proved most successful at developing the correct product, addressing clinical needs, and increasing market penetration potential, while reducing design iterations and manufacturing validations. Cost analysis and Pugh Matrix coupled with multi generation planning enabled developing a strong rationale to activate the project, set the vision and goals. improved risk management and product map established a robust technical verification-validation program. Design of experiments and process quantification facilitated design for manufacturing of critical features, as early as the concept phase. Biomechanical testing with analysis of variance provided a validation model with a recognized statistical performance baseline. Within those tools, only certain ones required minimum resources (i.e., business case, multi generational plan, project value proposition, Pugh Matrix, critical To quality process validation techniques), while others required significant investments (i.e., voice of customer, product usage map, improved risk management, design of experiments, biomechanical testing techniques). All used techniques provided savings exceeding investment costs. Some other tools were considered and found less relevant. A matrix summarized the investment costs and generated estimated savings. Globally, all companies can benefit from using DEX by smartly selecting and estimating those tools with best return on investment at the start of the project. For this, a good understanding of the available company resources, background and development strategy are needed. In conclusion, it was possible to illustrate that appropriate management of design excellence tools can greatly facilitate the development of new orthopaedic implant systems.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(11):114507-114507-5. doi:10.1115/1.4025386.

This technical brief serves as an update to our previous work characterizing the region-dependence of viscoelastic mechanical properties of the P17 and adult rat brain in the coronal plane (Elkin et al., 2011, “A Detailed Viscoelastic Characterization of the P17 and Adult Rat Brain,” J. Neurotrauma, 28, pp. 2235–2244.). Here, modifications to the microindentation device provided for the reliable measurement of load during the ramp portion of load relaxation microindentation tests. In addition, a correction factor for finite sample thickness was incorporated to more accurately assess the intrinsic mechanical properties of the tissue.The shear relaxation modulus was significantly dependent on the anatomic region and developmental age, with a general increase in stiffness with age and increased stiffness in the hippocampal and cortical regions compared with the white matter and cerebellar regions of the brain. The shear modulus ranged from ∼0.2 kPa to ∼2.6 kPa depending on region, age, and time scale. Best-fit Prony series parameters from least squares fitting to the indentation data from each region are reported, which describe the shear relaxation behavior for each anatomic region within each age group at both short (<10 ms) and long (∼20 s) time scales. These data will be useful for improving the biofidelity of finite element models of rat brain deformation at short time scales, such as models of traumatic brain injury.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(11):114508-114508-4. doi:10.1115/1.4025331.

Impact testing of pedestrian headforms is usually conducted at one velocity and with one mass of headform, but real impacts occur at a range of velocities and masses. A method is proposed to predict the Head Injury Criterion (HIC) and similar quantities at other velocities from their values observed under test conditions. A specific assumption is made about acceleration during the impact as related to displacement, its differential (instantaneous velocity), mass of headform, and initial velocity: namely, that it is the product of a power function of displacement (representing a possibly nonlinear spring) and a term that includes a type of damping. This equation is not solved, but some properties of the solution are obtained: HIC, maximum acceleration, and maximum displacement are found to be power functions of mass of headform and initial velocity. Expressions for the exponents are obtained in terms of the nonlinearity parameter of the spring. Simple formulae are obtained for the dependence of HIC, maximum acceleration, and maximum displacement on velocity and mass. These are relevant to many types of impact.

Commentary by Dr. Valentin Fuster

Errata

J Biomech Eng. 2013;135(11):117001-117001-1. doi:10.1115/1.4025336.
FREE TO VIEW

After additional review and consideration of our recent publication, “Confocal Image-Based Computational Modeling of Nitric Oxide Transport in a Rat Mesenteric Lymphatic Vessel,” published in Volume 135 issue 5 of Journal of Biomechanical Engineering on April 24, 2013, the authors feel further clarification is needed to identify the meaning and origin of the results shown in Fig. 10Fig. 10

Comparison of steady versus unsteady normalized WSS and NO wall concentrations as a function of axial position along the line indicated in the lower figure. Data at three time points (A, B, and C; refer to Fig. 3 of the original manuscript) are shown, with time point C corresponding to peak reverse flow. Steady simulations were run at corresponding instantaneous flow rates, and wall shear stresses are normalized with respect to the instantaneous Poiseuille flow value. With forward flow (A and B), the steady and unsteady results agree to within 0.4% and 1.4% rms, respectively (sampled from the entire lymphangion surface). When flow is reversed, the differences are as much as 23% at specific locations, amounting to a 6.7% rms difference overall.

Grahic Jump LocationComparison of steady versus unsteady normalized WSS and NO wall concentrations as a function of axial position along the line indicated in the lower figure. Data at three time points (A, B, and C; refer to Fig. 3 of the original manuscript) are shown, with time point C corresponding to peak reverse flow. Steady simulations were run at corresponding instantaneous flow rates, and wall shear stresses are normalized with respect to the instantaneous Poiseuille flow value. With forward flow (A and B), the steady and unsteady results agree to within 0.4% and 1.4% rms, respectively (sampled from the entire lymphangion surface). When flow is reversed, the differences are as much as 23% at specific locations, amounting to a 6.7% rms difference overall.

. A revised figure with a new legend is attached. In the published manuscript, exact details of the location from which the data came were unfortunately excluded.

Commentary by Dr. Valentin Fuster

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