0

IN THIS ISSUE

### Research Papers

J Biomech Eng. 2009;131(11):111001-111001-10. doi:10.1115/1.3148464.

A noninvasive method for estimating regional myocardial contractility in vivo would be of great value in the design and evaluation of new surgical and medical strategies to treat and/or prevent infarction-induced heart failure. As a first step toward developing such a method, an explicit finite element (FE) model-based formal optimization of regional myocardial contractility in a sheep with left ventricular (LV) aneurysm was performed using tagged magnetic resonance (MR) images and cardiac catheterization pressures. From the tagged MR images, three-dimensional (3D) myocardial strains, LV volumes, and geometry for the animal-specific 3D FE model of the LV were calculated, while the LV pressures provided physiological loading conditions. Active material parameters ($Tmax_B$ and $Tmax_R$) in the noninfarcted myocardium adjacent to the aneurysm (borderzone) and in the myocardium remote from the aneurysm were estimated by minimizing the errors between FE model-predicted and measured systolic strains and LV volumes using the successive response surface method for optimization. The significant depression in optimized $Tmax_B$ relative to $Tmax_R$ was confirmed by direct ex vivo force measurements from skinned fiber preparations. The optimized values of $Tmax_B$ and $Tmax_R$ were not overly sensitive to the passive material parameters specified. The computation time of less than 5 h associated with our proposed method for estimating regional myocardial contractility in vivo makes it a potentially very useful clinical tool.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(11):111002-111002-8. doi:10.1115/1.3128729.

Advanced solid freeform fabrication (SFF) techniques have been an interest for constructing tissue engineered polymeric scaffolds because of its repeatability and capability of high accuracy in fabrication resolution at the scaffold macro- and microscales. Among many important scaffold applications, hydrogel scaffolds have been utilized in tissue engineering as a technique to confide the desired proliferation of seeded cells in vitro and in vivo into its architecturally porous three-dimensional structures. Such fabrication techniques not only enable the reconstruction of scaffolds with accurate anatomical architectures but also enable the ability to incorporate bioactive species such as growth factors, proteins, and living cells. This paper presents a bioprinting system designed for the freeform fabrication of porous alginate scaffolds with encapsulated endothelial cells. The bioprinting fabrication system includes a multinozzle deposition system that utilizes SFF techniques and a computer-aided modeling system capable of creating heterogeneous tissue scaffolds. The manufacturing process is biologically compatible and is capable of functioning at room temperature and relatively low pressures to reduce the fluidic shear forces that could deteriorate biologically active species. The deposition system resolution is $10 μm$ in the three orthogonal directions $XYZ$ and has minimum velocity of $100 μm/s$. The ideal concentrations of sodium alginate and calcium chloride were investigated to determine a viable bioprinting process. The results indicated that the suitable fabrication parameters were 1.5% $(w/v)$ sodium alginate and 0.5% $(w/v)$ calcium chloride. Degradation studies via mechanical testing showed a decrease in the elastic modulus by 35% after 3 weeks. Cell viability studies were conducted on the cell encapsulated scaffolds for validating the bioprinting process and determining cell viability of 83%. This work exhibits the potential use of accurate cell placement for engineering complex tissue regeneration using computer-aided design systems.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(11):111003-111003-12. doi:10.1115/1.3212097.

Classical finite element (FE) models can estimate vertebral stiffness and strength with much lower computational costs than $μFE$ analyses, but the accuracy of these models rely on calibrated material properties that are not necessarily consistent with experimental results. In general, trabecular bone material properties are scaled with computer tomography (CT) density alone, without accounting for local variations in anisotropy or micro-architecture. Moreover, the cortex is often omitted or assigned with a constant thickness. In this work, voxel FE models, as well as surface-based homogenized FE models with topologically-conformed geometry and assigned with experimentally validated properties for bone, were developed from a series of 12 specimens tested up to failure. The effects of changing from a digital mesh to a smooth mesh, including a cortex of variable thickness and/or including heterogeneous trabecular fabric, were investigated. In each case, FE predictions of vertebral stiffness and strength were compared with the experimental gold-standard, and changes in elastic strain energy density and damage distributions were reported. The results showed that a smooth mesh effectively removed zones of artificial damage locations occurring in the ragged edges of the digital mesh. Adding an explicit cortex stiffened and strengthened the models, unloading the trabecular centrum while increasing the correlations to experimental stiffness and strength. Further addition of heterogeneous fabric improved the correlations to stiffness $(R2=0.72)$ and strength $(R2=0.89)$ and moved the damage locations closer to the vertebral endplates, following the local trabecular orientations. It was furthermore demonstrated that predictions of vertebral stiffness and strength of homogenized FE models with topologically-conformed cortical shell and heterogeneous trabecular fabric correlated well with experimental measurements, after assigning purely experimental data for bone without further calibration of material laws at the macroscale of bone. This study successfully demonstrated the limitations of current classical FE methods and provided valuable insights into the damage mechanisms of vertebral bodies.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(11):111004-111004-9. doi:10.1115/1.3212108.

This study utilizes a finite element model to characterize the transendothelial transport through overlapping endothelial cells in primary lymphatics during the uptake of interstitial fluid. The computational model is built upon the analytical model of these junctions created by Mendoza and Schmid-Schonbein (2003, “A Model for Mechanics of Primary Lymphatic Valves,” J. Biomed. Eng., 125, pp. 407–414). The goal of the present study is to investigate how adding more sophisticated and physiologically representative biomechanics affects the model’s prediction of fluid uptake. These changes include incorporating a porous domain to represent interstitial space, accounting for finite deformation of the deflecting endothelial cell, and utilizing an arbitrary Lagrangian–Eulerian algorithm to account for interacting and nonlinear mechanics of the junctions. First, the present model is compared with the analytical model in order to understand its effects on parameters such as cell deflection, pressure distribution, and velocity profile of the fluid entering the lumen. Without accounting for the porous nature of the interstitium, the computational model predicts greater cell deflection and consequently higher lymph velocities and flow rates than the analytical model. However, incorporating the porous domain attenuates the cell deflection and flow rate to values below that predicted by the analytical model for a given transmural pressure. Second, the present model incorporates recent experimental data for parameters such as lymph viscosity, transmural pressure measurements, and others to evaluate the ability of these junctions to act as unidirectional valves. The volume of flow through the valve is calculated to be $0.114 nL/μm$ per cycle for a transmural pressure varying between 8.0 mm Hg and −1.0 mm Hg at 0.4 Hz. Though experimental data for the absorption of lymph through these endothelial junctions are scarce, several measurements of lymph velocity and flow rates are cited to validate the present model.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(11):111005-111005-9. doi:10.1115/1.3212114.

We use an implicit large eddy simulation (ILES) method based on a finite volume approach to capture the turbulence in the anastomoses of a left ventricular assist device (LVAD) to the aorta. The order-of-accuracy of the numerical schemes is computed using a two-dimensional decaying Taylor–Green vortex. The ILES method is carefully validated by comparing to documented results for a fully developed turbulent channel flow at $Reτ=395$. Two different anastomotic flows (proximal and distal) are simulated for 50% and 100% LVAD supports and the results are compared with a healthy aortic flow. All the analyses are based on a planar aortic model under steady inflow conditions for simplification. Our results reveal that the outflow cannulae induce high exit jet flows in the aorta, resulting in turbulent flow. The distal configuration causes more turbulence in the aorta than the proximal configuration. The turbulence, however, may not cause any hemolysis due to low Reynolds stresses and relatively large Kolmogorov length scales compared with red blood cells. The LVAD support causes an acute increase in flow splitting in the major branch vessels for both anastomotic configurations, although its long-term effect on the flow splitting remains unknown. A large increase in wall shear stress is found near the cannulation sites during the LVAD support. This work builds a foundation for more physiologically realistic simulations under pulsatile flow conditions.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(11):111006-111006-6. doi:10.1115/1.4000081.

An infant less than 18 months of age with a skull fracture has a one in three chance of abuse. Injury biomechanics are often used in the investigation of these cases. In addition to case-based investigations, computer modeling, and test dummies, animal model studies can aid in these investigations. This study documents age effects on the mechanical properties of parietal bone and coronal suture in porcine infants and correlates the bending properties of the bone to existing human infant data. Three beam specimens were cut from porcine specimens aged 3 days, 7 days, 10 days, 14 days, 18 days, and 21 days: one across the coronal suture and two from the parietal bone, one parallel to and one perpendicular to the coronal suture. An actuator-mounted probe applied four-point bending in displacement control at 25 mm/s until failure. Bending stiffness of bone specimens increased with age; bone-suture-bone specimens showed no change up to 14 days but increased from 14 days to 18 days. All three specimen types showed decreases in ultimate stress with age. Ultimate strain for the bone-suture-bone specimens was significantly higher than that for the bone specimens up to 14 days with no differences thereafter. There was no change in the bending modulus with age for any specimen type. Bone-suture-bone bending modulus was lower than that of the bone specimens up to 14 days with no differences thereafter. There was no change in strain energy to failure with age for the bone specimens; bone-suture-bone specimens showed no change up to 14 days but decreased from 14 days to 18 days. There was an increase in specimen porosity with age. Correlation analysis revealed a weak $(−0.39)$ but significant and negative correlation between ultimate stress and porosity. While the mechanical properties of parietal bone and coronal suture did not change significantly with age, bone specimens showed an increase in bending stiffness with age. Bone-suture-bone specimens showed an increase in bending stiffness only between 14 days and 18 days of age. Correlation analyses using existing and new data to compute the bending rigidity of infant parietal bone specimens suggested that days of pig age may correlate with months of human age during the most common time frame of childhood abuse cases.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(11):111007-111007-7. doi:10.1115/1.3212104.

The highly organized structure and composition of the annulus fibrosus provides the tissue with mechanical behaviors that include anisotropy and nonlinearity. Mathematical models are necessary to interpret and elucidate the meaning of directly measured mechanical properties and to understand the structure-function relationships of the tissue components, namely, the fibers and extrafibrillar matrix. This study models the annulus fibrosus as a combination of strain energy functions describing the fibers, matrix, and their interactions. The objective was to quantify the behavior of both nondegenerate and degenerate annulus fibrosus tissue using uniaxial tensile experimental data. Mechanical testing was performed with samples oriented along the circumferential, axial, and radial directions. For samples oriented along the radial direction, the toe-region modulus was 2× stiffer with degeneration. However, no other differences in measured mechanical properties were observed with degeneration. The constitutive model fit well to samples oriented along the radial and circumferential directions $(R2≥0.97)$. The fibers supported the highest proportion of stress for circumferential loading at 60%. There was a 70% decrease in the matrix contribution to stress from the toe-region to the linear-region of both the nondegenerate and degenerate tissue. The shear fiber-matrix interaction (FMI) contribution increased by 80% with degeneration in the linear-region. Samples oriented along the radial and axial direction behaved similarly under uniaxial tension ($modulus=0.32 MPa$ versus 0.37 MPa), suggesting that uniaxial testing in the axial direction is not appropriate for quantifying the mechanics of a fiber reinforcement in the annulus. In conclusion, the structurally motivated nonlinear anisotropic hyperelastic constitutive model helps to further understand the effect of microstructural changes with degeneration, suggesting that remodeling in the subcomponents (i.e., the collagen fiber, matrix and FMI) may minimize the overall effects on mechanical function of the bulk material with degeneration.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(11):111008-111008-8. doi:10.1115/1.3212107.

There is still no agreement on the nature of tissues' viscoelasticity and on its reliable modeling. We speculate that disagreements between previous observations stem from difficulties of separating between viscoelastic and preconditioning effects, since both are manifested by similar response features. Here, this and related issues were studied in the tendon as a prototype for other soft tissues. Sheep digital tendons were preconditioned under strain that was higher by 1% than the one used in subsequent testing. Each specimen was then subjected to stress relaxation, and quick release or creep. A stochastic microstructural viscoelastic theory was developed based on the collagen fibers' properties and on their gradual recruitment with stretch. Model parameters were estimated from stress relaxation data and predictions were compared with the creep data. Following its validation, the new recruitment viscoelasticity (RVE) model was compared, both theoretically and experimentally, with the quasilinear viscoelastic (QLV) theory. The applied preconditioning protocol produced subsequent pure viscoelastic response. The proposed RVE model provided excellent fit to both stress relaxation and creep data. Both analytical and numerical comparisons showed that the new RVE theory and the popular QLV one are equivalent under deformation schemes at which no fibers buckle. Otherwise, the equivalence breaks down; QLV may predict negative stress, in contrast to data of the quick release tests, while RVE predicts no such negative stress. The results are consistent with the following conclusions: (1) fully preconditioned tendon exhibits pure viscoelastic response, (2) nonlinearity of the tendon viscoelasticity is induced by gradual recruitment of its fibers, (3) a new structure-based RVE theory is a reliable representation of the tendon viscoelastic properties under both stress relaxation and creep tests, and (4) the QLV theory is equivalent to the RVE one (and valid) only under deformations in which no fibers buckle. The results also suggest that the collagen fibers themselves are linear viscoelastic.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(11):111009-111009-9. doi:10.1115/1.4000116.

Computational fluid dynamics (CFD) is used to asses the hydrodynamic performance of a positive displacement left ventricular assist device. The computational model uses implicit large eddy simulation direct resolution of the chamber compression and modeled valve closure to reproduce the in vitro results. The computations are validated through comparisons with experimental particle image velocimetry (PIV) data. Qualitative comparisons of flow patterns, velocity fields, and wall-shear rates demonstrate a high level of agreement between the computations and experiments. Quantitatively, the PIV and CFD show similar probed velocity histories, closely matching jet velocities and comparable wall-strain rates. Overall, it has been shown that CFD can provide detailed flow field and wall-strain rate data, which is important in evaluating blood pump performance.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(11):111010-111010-5. doi:10.1115/1.4000079.

The compression behavior of spinal cord tissue is important for understanding spinal cord injury mechanics but has not yet been established. Characterizing compression behavior assumes precise specimen geometry; however, preparing test specimens of spinal cord tissue is complicated by the extreme compliance of the tissue. The objectives of this study were to determine the effect of flash freezing on both specimen preparation and mechanical response and to quantify the effect of small deviations in specimen geometry on mechanical behavior. Specimens of porcine spinal cord white matter were harvested immediately following sacrifice. The tissue was divided into two groups: partially frozen specimens were flash frozen (60 s at $−80°C$) prior to cutting, while fresh specimens were kept at room temperature. Specimens were tested in unconfined compression at strain rates of $0.05 s−1$ and $5.0 s−1$ to 40% strain. Parametric finite element analyses were used to investigate the effect of specimen face angle, cross section, and interface friction on the mechanical response. Flash freezing did not affect the mean mechanical behavior of the tissue but did reduce the variability in the response across specimens $(p<0.05)$. Freezing also reduced variability in the specimen geometry. Variations in specimen face angle (0–10 deg) resulted in a 34% coefficient of variation and a 60% underestimation of peak stress. The effect of geometry on variation and error was greater than that of interface friction. Taken together, these findings demonstrate the advantages of flash freezing in biomechanical studies of spine cord tissue.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(11):111011-111011-5. doi:10.1115/1.4000106.

The stress distribution in the vessel wall has an important bearing on vascular function in health and disease. We studied the relationship between the transmural stress distribution and the opening angle (OA) to determine the stress gradient. The simulation of wall stress was based on transmural measurements of strain and material properties of coronary arteries in reference to the zero-stress state. A one-layer model with material constants of the intact vessel was used to calculate the circumferential stress distribution. A sensitivity analysis using both one- and two-layer models (intima-media and adventitia layers) was carried out to study the effect of the OA on the circumferential stress distribution and average circumferential stress. A larger OA always shifts the circumferential stress from the intima-media to the adventitia layer. We report a new observation that the circumferential stress at the adventitia may exceed that at the intima at physiological loading due to the larger OA in the porcine coronary artery. This has important implications for growth and remodeling, where an increase in opening angle may shift excessive stress from the inner layer to the outer layer.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(11):111012-111012-5. doi:10.1115/1.4000111.

Mitral valve edge-to-edge repair (ETER) alters valve mechanics, which may impact efficacy and durability of the repair. The objective of this paper was to quantify stretches in the central region of the anterior leaflet of the mitral valve after ETER with a single suture and 6 mm suture. Sixteen markers, forming a $4×4$ array, were attached onto the central region of the mitral valve anterior leaflet. The mitral valve was subjected to ETER with a single suture and 6 mm suture, and mounted in an in vitro flow loop simulating physiological conditions. Images of the marker array were used to calculate marker displacement and stretch. A total of 9 mitral valves were tested. Two peak stretches were observed during a cardiac cycle, one in systole and the other in diastole under mitral valve edge-to-edge repair condition. The major principal (radial) stretch during systole was significantly greater than that during diastole. However, there was no significant difference between the minor principal (circumferential) stretch during diastole and that during systole. In addition, there were no significant differences in the radial and circumferential, or areal stretches and stretch rates during diastole between the single suture and 6 mm suture. The ETER subjects the mitral valve leaflets to double frequency of loading and unloading. Minor change in suture length may not result in a significant load difference in the central region of the anterior leaflet during diastole.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(11):111013-111013-9. doi:10.1115/1.4000112.

With the world’s aging population, it is expected that the number of people affected by glaucoma, the second most common cause of irreversible blindness, will increase considerably. Current knowledge on glaucoma progression relates elevation of the intraocular pressure (IOP) to optic nerve damage and hence visual impairment. For this reason, IOP measurement in tonometry has become an essential part of routine eye examinations needed for the diagnosis and management of the disease. The accuracy of the current reference standard in tonometry, the Goldmann applanation tonometer, is known to be affected by the natural variations in corneal thickness, curvature, and material properties. Earlier studies attempted to quantify these effects and produced correction factors that considered the variations in each one of these parameters separately, and no guidance was given as to how to combine the effects of variations in more than one parameter. The present research attempted to address this gap by conducting a multidimensional numerical study that considered variations in thickness, curvature, material properties, and IOP, and used the results to develop a single correction equation that considered these parameters simultaneously. The results of the analysis and the correction equation were validated successfully against the outcome of earlier clinical and mathematical studies on the effect of individual parameters, and the correction equation was presented in a simple form suitable for clinical application.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J Biomech Eng. 2009;131(11):114501-114501-5. doi:10.1115/1.4000109.

Inertial motion sensors (IMSs) combine three sensors to produce a reportedly stable and accurate orientation estimate in three dimensions. Although accuracy has been reported within the range of 2 deg of error by manufacturers, the sensors are rarely tested in the challenging motion present in human motion. Their accuracy was tested in static, quasistatic, and dynamic situations against gold-standard Vicon camera data. It was found that static and quasistatic rms error was even less than manufacturers’ technical specifications. Quasistatic rms error was minimal at 0.3 deg ($±0.15 deg$ SD) on the roll axis, 0.29 deg ($±0.20 deg$ SD) on the pitch axis, and 0.73 deg ($±0.81 deg$ SD) on the yaw axis. The dynamic rms error was between 1.9 deg and 3.5 deg on the main axes of motion but it increased considerably on off-axis during planar pendulum motion. Complex arm motion in the forward reaching plane proved to be a greater challenge for the sensors to track but results are arguably better than previously reported studies considering the large range of motion used.

Topics: Sensors , Motion , Errors , Pendulums , Yaw
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2009;131(11):114502-114502-3. doi:10.1115/1.4000085.

The stress distribution in the vessel wall has important bearing on vascular function including intima, media, and adventitia. The residual strain in the vessel wall has been thought to largely normalize the transmural stress distribution with slightly higher values at the intima. In hypertension, the compensatory increase in opening angle is thought to maintain a uniform stress distribution. We have recently shown that the circumferential stress at adventitia may exceed that at intima at physiological loading due to large opening angle $(OA)$ in normal porcine coronary arteries. The objective of this study was to show that increases in opening angle subsequent hypertension can further shift the stress from the intima to the adventitia. The change in stress distribution during acute hypertension was calculated using available data on the changes in vessel geometry, material property, and internal pressure during hypertension. It was found that the increase in $OA$ following acute hypertension off-loads the stress from intima to adventitia, therefore, relieving some of the stress increase in the intimal layer induced by the sudden pressure increase. This has important implications for hypertension where it may shift the excessive stress from the inner layer to the outer layer. This may be a protective mechanism for the intima layer in hypertension.

Commentary by Dr. Valentin Fuster

### Errata

J Biomech Eng. 2009;131(11):117001-117001-1. doi:10.1115/1.4000157.
FREE TO VIEW

There was an error in the original version of Fig. 9. Figure 9 has been corrected and is reprinted here.

Commentary by Dr. Valentin Fuster