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IN THIS ISSUE

### Guest Editorial

J Biomech Eng. 2015;137(7):070301-070301-2. doi:10.1115/1.4030529.
Commentary by Dr. Valentin Fuster

### Research Papers

J Biomech Eng. 2015;137(7):071001-071001-9. doi:10.1115/1.4030070.

Transport of solutes through diffusion is an important metabolic mechanism for the avascular cartilage tissue. Three types of interconnected physical phenomena, namely mechanical, electrical, and chemical, are all involved in the physics of transport in cartilage. In this study, we use a carefully designed experimental-computational setup to separate the effects of mechanical and chemical factors from those of electrical charges. Axial diffusion of a neutral solute (Iodixanol) into cartilage was monitored using calibrated microcomputed tomography (micro-CT) images for up to 48 hr. A biphasic-solute computational model was fitted to the experimental data to determine the diffusion coefficients of cartilage. Cartilage was modeled either using one single diffusion coefficient (single-zone model) or using three diffusion coefficients corresponding to superficial, middle, and deep cartilage zones (multizone model). It was observed that the single-zone model cannot capture the entire concentration-time curve and under-predicts the near-equilibrium concentration values, whereas the multizone model could very well match the experimental data. The diffusion coefficient of the superficial zone was found to be at least one order of magnitude larger than that of the middle zone. Since neutral solutes were used, glycosaminoglycan (GAG) content cannot be the primary reason behind such large differences between the diffusion coefficients of the different cartilage zones. It is therefore concluded that other features of the different cartilage zones such as water content and the organization (orientation) of collagen fibers may be enough to cause large differences in diffusion coefficients through the cartilage thickness.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(7):071002-071002-7. doi:10.1115/1.4030173.

We compare experimental and computational results for the actions of the cardioactive drugs Lidocaine, Verapamil, Veratridine, and Bay K 8644 on a tissue monolayer consisting of mainly fibroblasts and human-induced pluripotent stem cell-derived cardiomyocytes (hiPSc-CM). The choice of the computational models is justified and literature data is collected to model drug action as accurately as possible. The focus of this work is to evaluate the validity and capability of existing models for native human cells with respect to the simulation of pharmaceutical treatment of monolayers and hiPSc-CM. From the comparison of experimental and computational results, we derive suggestions for model improvements which are intended to computationally support the interpretation of experimental results obtained for hiPSc-CM.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(7):071003-071003-10. doi:10.1115/1.4030176.

A continuum mathematical model with sharp interface is proposed for describing the occurrence of patterns in initially circular and homogeneous bacterial colonies. The mathematical model encapsulates the evolution of the chemical field characterized by a Monod-like uptake term, the chemotactic response of bacteria, the viscous interaction between the colony and the underlying culture medium and the effects of the surface tension at the boundary. The analytical analysis demonstrates that the front of the colony is linearly unstable for a proper choice of the parameters. The simulation of the model in the nonlinear regime confirms the development of fingers with typical wavelength controlled by the size parameters of the problem, whilst the emergence of branches is favored if the diffusion is dominant on the chemotaxis or for high values of the friction parameter. Such results provide new insights on pattern selection in bacterial colonies and may be applied for designing engineered patterns.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(7):071004-071004-8. doi:10.1115/1.4030310.

Hydrated soft tissues, such as articular cartilage, are often modeled as biphasic systems with individually incompressible solid and fluid phases, and biphasic models are employed to fit experimental data in order to determine the mechanical and hydraulic properties of the tissues. Two of the most common experimental setups are confined and unconfined compression. Analytical solutions exist for the unconfined case with the linear, isotropic, homogeneous model of articular cartilage, and for the confined case with the non-linear, isotropic, homogeneous model. The aim of this contribution is to provide an easily implementable numerical tool to determine a solution to the governing differential equations of (homogeneous and isotropic) unconfined and (inhomogeneous and isotropic) confined compression under large deformations. The large-deformation governing equations are reduced to equivalent diffusive equations, which are then solved by means of finite difference (FD) methods. The solution strategy proposed here could be used to generate benchmark tests for validating complex user-defined material models within finite element (FE) implementations, and for determining the tissue's mechanical and hydraulic properties from experimental data.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(7):071005-071005-8. doi:10.1115/1.4030175.

In this paper, a quantitative interpretation for atomic force microscopy-based dynamic nanoindentation (AFM-DN) tests on the superficial layers of bovine articular cartilage (AC) is provided. The relevant constitutive parameters of the tissue are estimated by fitting experimental results with a finite element model in the frequency domain. Such model comprises a poroelastic stress–strain relationship for a fibril reinforced tissue constitution, assuming a continuous distribution of the collagen network orientations. The identification procedure was first validated using a simplified transversely isotropic constitutive relationship; then, the experimental data were manually fitted by using the continuous distribution fibril model. Tissue permeability is derived from the maximum value of the phase shift between the input harmonic loading and the harmonic tissue response. Tissue parameters related to the stiffness are obtained from the frequency response of the experimental storage modulus and phase shift. With this procedure, an axial to transverse stiffness ratio (anisotropy ratio) of about 0.15 is estimated.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(7):071006-071006-14. doi:10.1115/1.4030174.

Different digital volume correlation (DVC) approaches are currently available or under development for bone tissue micromechanics. The aim of this study was to compare accuracy and precision errors of three DVC approaches for a particular three-dimensional (3D) zero-strain condition. Trabecular and cortical bone specimens were repeatedly scanned with a micro-computed tomography (CT). The errors affecting computed displacements and strains were extracted for a known virtual translation, as well as for repeated scans. Three DVC strategies were tested: two local approaches, based on fast-Fourier-transform (DaVis-FFT) or direct-correlation (DaVis-DC), and a global approach based on elastic registration and a finite element (FE) solver (ShIRT-FE). Different computation subvolume sizes were tested. Much larger errors were found for the repeated scans than for the virtual translation test. For each algorithm, errors decreased asymptotically for larger subvolume sizes in the range explored. Considering this particular set of images, ShIRT-FE showed an overall better accuracy and precision (a few hundreds microstrain for a subvolume of 50 voxels). When the largest subvolume (50–52 voxels) was applied to cortical bone, the accuracy error obtained for repeated scans with ShIRT-FE was approximately half of that for the best local approach (DaVis-DC). The difference was lower (250 microstrain) in the case of trabecular bone. In terms of precision, the errors shown by DaVis-DC were closer to the ones computed by ShIRT-FE (differences of 131 microstrain and 157 microstrain for cortical and trabecular bone, respectively). The multipass computation available for DaVis software improved the accuracy and precision only for the DaVis-FFT in the virtual translation, particularly for trabecular bone. The better accuracy and precision of ShIRT-FE, followed by DaVis-DC, were obtained with a higher computational cost when compared to DaVis-FFT. The results underline the importance of performing a quantitative comparison of DVC methods on the same set of samples by using also repeated scans, other than virtual translation tests only. ShIRT-FE provides the most accurate and precise results for this set of images. However, both DaVis approaches show reasonable results for large nodal spacing, particularly for trabecular bone. Finally, this study highlights the importance of using sufficiently large subvolumes, in order to achieve better accuracy and precision.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(7):071007-071007-10. doi:10.1115/1.4029986.

The effects of diabetes on the collagen structure and material properties of the sclera are unknown but may be important to elucidate whether diabetes is a risk factor for major ocular diseases such as glaucoma. This study provides a quantitative assessment of the changes in scleral stiffness and collagen fiber alignment associated with diabetes. Posterior scleral shells from five diabetic donors and seven non-diabetic donors were pressurized to 30 mm Hg. Three-dimensional surface displacements were calculated during inflation testing using digital image correlation (DIC). After testing, each specimen was subjected to wide-angle X-ray scattering (WAXS) measurements of its collagen organization. Specimen-specific finite element models of the posterior scleras were generated from the experimentally measured geometry. An inverse finite element analysis was developed to determine the material properties of the specimens, i.e., matrix and fiber stiffness, by matching DIC-measured and finite element predicted displacement fields. Effects of age and diabetes on the degree of fiber alignment, matrix and collagen fiber stiffness, and mechanical anisotropy were estimated using mixed effects models accounting for spatial autocorrelation. Older age was associated with a lower degree of fiber alignment and larger matrix stiffness for both diabetic and non-diabetic scleras. However, the age-related increase in matrix stiffness was 87% larger in diabetic specimens compared to non-diabetic controls and diabetic scleras had a significantly larger matrix stiffness (p = 0.01). Older age was associated with a nearly significant increase in collagen fiber stiffness for diabetic specimens only (p = 0.06), as well as a decrease in mechanical anisotropy for non-diabetic scleras only (p = 0.04). The interaction between age and diabetes was not significant for all outcomes. This study suggests that the age-related increase in scleral stiffness is accelerated in eyes with diabetes, which may have important implications in glaucoma.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(7):071008-071008-11. doi:10.1115/1.4029746.

Closure of the left atrioventricular orifice is achieved when the anterior and posterior leaflets of the mitral valve press together to form a coaptation zone along the free edge of the leaflets. This coaptation zone is critical to valve competency and is maintained by the support of the mitral annulus, chordae tendinae, and papillary muscles. Myocardial ischemia can lead to an altered performance of this mitral complex generating suboptimal mitral leaflet coaptation and a resultant regurgitant orifice. This paper reports on a two-part experiment undertaken to measure the dependence of coaptation force distribution on papillary muscle position in normal and functional regurgitant porcine mitral heart valves. Using a novel load sensor, the local coaptation force was measured in vitro at three locations (A1–P1, A2–P2, and A3–P3) along the coaptation zone. In part 1, the coaptation force was measured under static conditions in ten whole hearts. In part 2, the coaptation force was measured in four explanted mitral valves operating in a flow loop under physiological flow conditions. Here, two series of tests were undertaken corresponding to the normal and functional regurgitant state as determined by the position of the papillary muscles relative to the mitral valve annulus. The functional regurgitant state corresponded to grade 1. The static tests in part 1 revealed that the local force was directly proportional to the transmitral pressure and was nonuniformly distributed across the coaptation zone, been strongest at A1–P1. In part 2, tests of the valve in a normal state showed that the local force was again directly proportional to the transmitral pressure and was again nonuniform across the coaptation zone, been strongest at A1–P1 and weakest at A2–P2. Further tests performed on the same valves in a functional regurgitant state showed that the local force measured in the coaptation zone was directly proportional to the transmitral pressure. However, the force was now observed to be weakest at A1–P1 and strongest at A2–P2. Movement of the anterolateral papillary muscle (APM) away from both the annular and anterior–posterior (AP) planes was seen to contribute significantly to the altered force distribution in the coaptation zone. It was concluded that papillary muscle displacement typical of myocardial ischemia changes the coaptation force locally within the coaptation zone.

Topics: Valves , Muscle , Displacement
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(7):071009-071009-8. doi:10.1115/1.4028967.

This work studies a model for milk transport through lactating human breast ducts and describes mathematically the mass transfer from alveolar sacs through the mammary ducts to the nipple. In this model, both the phenomena of diffusion in the sacs and conventional flow in ducts have been considered. The ensuing analysis reveals that there is an optimal range of bifurcation numbers leading to the easiest milk flow based on the minimum flow resistance. This model formulates certain difficult-to-measure values like diameter of the alveolar sacs and the total length of the milk path as a function of easy-to-measure properties such as milk fluid properties and macroscopic measurements of the breast. Alveolar dimensions from breast tissues of six lactating women are measured and reported in this paper. The theoretically calculated alveoli diameters for optimum milk flow (as a function of bifurcation numbers) show excellent match with our biological data on alveolar dimensions. Also, the mathematical model indicates that for minimum milk flow resistance the glandular tissue must be within a short distance from the base of the nipple, an observation that matches well with the latest anatomical and physiological research.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(7):071010-071010-8. doi:10.1115/1.4030404.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(7):071011-071011-6. doi:10.1115/1.4030532.

In the past years, there have been several experimental studies that aimed at quantifying the material properties of articular ligaments such as tangent modulus, tensile strength, and ultimate strain. Little has been done to describe their response to mechanical stimuli that lead to damage. The purpose of this experimental study was to characterize strain-induced damage in medial collateral ligaments (MCLs). Displacement-controlled tensile tests were performed on 30 MCLs harvested from Sprague Dawley rats. Each ligament was monotonically pulled to several increasing levels of displacement until complete failure occurred. The stress–strain data collected from the mechanical tests were analyzed to determine the onset of damage and its evolution. Unrecoverable changes such as increase in ligament's elongation at preload and decrease in the tangent modulus of the linear region of the stress–strain curves indicated the occurrence of damage. Interestingly, these changes were found to appear at two significantly different threshold strains ($P<0.05$). The mean threshold strain that determined the increase in ligament's elongation at preload was found to be 2.84% (standard deviation (SD) = 1.29%) and the mean threshold strain that caused the decrease in the tangent modulus of the linear region was computed to be 5.51% (SD = 2.10%), respectively. The findings of this study suggest that the damage mechanisms associated with the increase in ligament's elongation at preload and decrease in the tangent modulus of the linear region in the stress–strain curves in MCLs are likely different.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(7):071012-071012-8. doi:10.1115/1.4029984.

Accurate and reliable “individualized” low back erector spinae muscle (ESM) data are of importance to estimate its force producing capacity. Knowing the force producing capacity, along with spinal loading, enhances the understanding of low back injury mechanisms. The objective of this study was to build regression models to estimate the ESM cross-sectional area (CSA). Measurements were taken from axial-oblique magnetic resonance imaging (MRI) scans of a large historical population [54 females and 53 males at L3/L4, 50 females and 44 males at L4/L5, and 41 females and 35 males at L5/S1 levels]. Results suggest that an individual's ESM CSA can be accurately estimated based on his/her gender, height, and weight. Results further show that there is no significant difference between the measured and estimated ESM CSAs, and expected absolute error is less than 15%.

Commentary by Dr. Valentin Fuster

### Technical Brief

J Biomech Eng. 2015;137(7):074501-074501-5. doi:10.1115/1.4030405.

Accurate quantification of subtle wrist motion changes resulting from ligament injuries is crucial for diagnosis and prescription of the most effective interventions for preventing progression to osteoarthritis. Current imaging techniques are unable to detect injuries reliably and are static in nature, thereby capturing bone position information rather than motion which is indicative of ligament injury. A recently developed technique, 4D (three dimensions + time) computed tomography (CT) enables three-dimensional volume sequences to be obtained during wrist motion. The next step in successful clinical implementation of the tool is quantification and validation of imaging biomarkers obtained from the four-dimensional computed tomography (4DCT) image sequences. Measures of bone motion and joint proximities are obtained by: segmenting bone volumes in each frame of the dynamic sequence, registering their positions relative to a known static posture, and generating surface polygonal meshes from which minimum distance (proximity) measures can be quantified. Method accuracy was assessed during in vitro simulated wrist movement by comparing a fiducial bead-based determination of bone orientation to a bone-based approach. The reported errors for the 4DCT technique were: 0.00–0.68 deg in rotation; 0.02–0.30 mm in translation. Results are on the order of the reported accuracy of other image-based kinematic techniques.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(7):074502-074502-6. doi:10.1115/1.4030406.

The ranges of angular motion measured using multisegmented spinal column models are typically small, meaning that minor experimental errors can potentially affect the reliability of these measures. This study aimed to investigate the sensitivity of the 3D intersegmental angles, measured using a multisegmented spinal column model, to errors due to marker misplacement. Eleven healthy subjects performed trunk bending in five directions. Six cameras recorded the trajectory of 22 markers, representing seven spinal column segments. Misplacement error for each marker was modeled as a Gaussian function with a standard deviation of 6 mm, and constrained to a maximum value of 12 mm in each coordinate across the skin. The sensitivity of 3D intersegmental angles to these marker misplacement errors, added to the measured data, was evaluated. The errors in sagittal plane motions resulting from marker misplacement were small (RMS error less than 3.2 deg and relative error in the angular range less than 15%) during the five trunk bending direction. The errors in the frontal and transverse plane motions, induced by marker misplacement, however, were large (RMS error up to 10.2 deg and relative error in the range up to 58%), especially during trunk bending in anterior, anterior-left, and anterior-right directions, and were often comparable in size to the intersubject variability for those motions. The induced errors in the frontal and transverse plane motions tended to be the greatest at the intersegmental levels in the lower lumbar region. These observations questioned reliability of angle measures in the frontal and transverse planes particularly in the lower lumbar region during trunk bending in anterior direction, and thus did not recommend interpreting these measures for clinical evaluation and decision-making.

Topics: Errors , Human spine
Commentary by Dr. Valentin Fuster