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IN THIS ISSUE

### Research Papers

J Biomech Eng. 2018;140(5):051001-051001-18. doi:10.1115/1.4038779.

Simulations of soft tissues require accurate and robust constitutive models, whose form is derived from carefully designed experimental studies. For such investigations of membranes or thin specimens, planar biaxial systems have been used extensively. Yet, all such systems remain limited in their ability to: (1) fully prescribe in-plane deformation gradient tensor F2D, (2) ensure homogeneity of the applied deformation, and (3) be able to accommodate sufficiently small specimens to ensure a reasonable degree of material homogeneity. To address these issues, we have developed a novel planar biaxial testing device that overcomes these difficulties and is capable of full control of the in-plane deformation gradient tensor F2D and of testing specimens as small as ∼4 mm × ∼4 mm. Individual actuation of the specimen attachment points, combined with a robust real-time feedback control, enabled the device to enforce any arbitrary F2D with a high degree of accuracy and homogeneity. Results from extensive device validation trials and example tissues illustrated the ability of the device to perform as designed and gather data needed for developing and validating constitutive models. Examples included the murine aortic tissues, allowing for investigators to take advantage of the genetic manipulation of murine disease models. These capabilities highlight the potential of the device to serve as a platform for informing and verifying the results of inverse models and for conducting robust, controlled investigation into the biomechanics of very local behaviors of soft tissues and membrane biomaterials.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2018;140(5):051002-051002-8. doi:10.1115/1.4038745.

Rotator cuff disorders are one of the most common causes of shoulder pain and disability in the aging population but, unfortunately, the etiology is still unknown. One factor thought to contribute to the progression of disease is the external compression of the rotator cuff tendons, which can be significantly increased by age-related changes such as muscle weakness and poor posture. The objective of this study was to investigate the baseline compressive response of tendon and determine how this response is altered during maturation and aging. We did this by characterizing the compressive mechanical, viscoelastic, and poroelastic properties of young, mature, and aged mouse supraspinatus tendons using macroscale indentation testing and nanoscale high-frequency AFM-based rheology testing. Using these multiscale techniques, we found that aged tendons were stiffer than their mature counterparts and that both young and aged tendons exhibited increased hydraulic permeability and energy dissipation. We hypothesize that regional and age-related variations in collagen morphology and organization are likely responsible for changes in the multiscale compressive response as these structural parameters may affect fluid flow. Importantly, these results suggest a role for age-related changes in the progression of tendon degeneration, and we hypothesize that decreased ability to resist compressive loading via fluid pressurization may result in damage to the extracellular matrix (ECM) and ultimately tendon degeneration. These studies provide insight into the regional multiscale compressive response of tendons and indicate that altered compressive properties in aging tendons may be a major contributor to overall tendon degeneration.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2018;140(5):051003-051003-13. doi:10.1115/1.4037947.

Microstructural properties of extracellular matrix (ECM) promote cell and tissue homeostasis as well as contribute to the formation and progression of disease. In order to understand how microstructural properties influence the mechanical properties and traction force-induced remodeling of ECM, we developed an agent-based model that incorporates repetitively applied traction force within a discrete fiber network. An important difference between our model and similar finite element models is that by implementing more biologically realistic dynamic traction, we can explore a greater range of matrix remodeling. Here, we validated our model by reproducing qualitative trends observed in three sets of experimental data reported by others: tensile and shear testing of cell-free collagen gels, collagen remodeling around a single isolated cell, and collagen remodeling between pairs of cells. In response to tensile and shear strain, simulated acellular networks with straight fibrils exhibited biphasic stress–strain curves indicative of strain-stiffening. When fibril curvature was introduced, stress–strain curves shifted to the right, delaying the onset of strain-stiffening. Our data support the notion that strain-stiffening might occur as individual fibrils successively align along the axis of strain and become engaged in tension. In simulations with a single, contractile cell, peak collagen displacement occurred closest to the cell and decreased with increasing distance. In simulations with two cells, compaction of collagen between cells appeared inversely related to the initial distance between cells. These results for cell-populated collagen networks match in vitro findings. A demonstrable benefit of modeling is that it allows for further analysis not feasible with experimentation. Within two-cell simulations, strain energy within the collagen network measured from the final state was relatively uniform around the outer surface of cells separated by 250 μm, but became increasingly nonuniform as the distance between cells decreased. For cells separated by 75 and 100 μm, strain energy peaked in the direction toward the other cell in the region in which fibrils become highly aligned and reached a minimum adjacent to this region, not on the opposite side of the cell as might be expected. This pattern of strain energy was partly attributable to the pattern of collagen compaction, but was still present when mapping strain energy divided by collagen density. Findings like these are of interest because fibril alignment, density, and strain energy may each contribute to contact guidance during tissue morphogenesis.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2018;140(5):051004-051004-12. doi:10.1115/1.4038201.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2018;140(5):051005-051005-8. doi:10.1115/1.4039058.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2018;140(5):051006-051006-9. doi:10.1115/1.4039306.

One particular complexity of coronary artery is the natural tapering of the vessel with proximal segments having larger caliber and distal tapering as the vessel get smaller. The natural tapering of a coronary artery often leads to proximal incomplete stent apposition (ISA). ISA alters coronary hemodynamics and creates pathological path to develop complications such as in-stent restenosis, and more worryingly, stent thrombosis (ST). By employing state-of-the-art computer-aided design software, generic stent hoops were virtually deployed in an idealized tapered coronary artery with decreasing malapposition distance. Pulsatile blood flow simulations were carried out using computational fluid dynamics (CFD) on these computer-aided design models. CFD results reveal unprecedented details in both spatial and temporal development of microrecirculation environments throughout the cardiac cycle (CC). Arterial tapering also introduces secondary microrecirculation. These primary and secondary microrecirculations provoke significant fluctuations in arterial wall shear stress (WSS). There has been a direct correlation with changes in WSS and the development of atherosclerosis. Further, the presence of these microrecirculations influence strongly on the local levels of blood viscosity in the vicinity of the malapposed stent struts. The observation of secondary microrecirculations and changes in blood rheology is believed to complement the wall (-based) shear stress, perhaps providing additional physical explanations for tissue accumulation near ISA detected from high resolution optical coherence tomography (OCT).

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2018;140(5):051007-051007-10. doi:10.1115/1.4039175.

Increased arterial stiffness is associated with atherosclerosis in humans, but there have been limited animal studies investigating the relationship between these factors. We bred elastin wildtype (Eln+/+) and heterozygous (Eln+/−) mice to apolipoprotein E wildtype (Apoe+/+) and knockout (Apoe−/−) mice and fed them normal diet (ND) or Western diet (WD) for 12 weeks. Eln+/− mice have increased arterial stiffness. Apoe−/− mice develop atherosclerosis on ND that is accelerated by WD. It has been reported that Apoe−/− mice have increased arterial stiffness and that the increased stiffness may play a role in atherosclerotic plaque progression. We found that Eln+/+Apoe−/− arterial stiffness is similar to Eln+/+Apoe+/+ mice at physiologic pressures, suggesting that changes in stiffness do not play a role in atherosclerotic plaque progression in Apoe−/− mice. We found that Eln+/−Apoe−/− mice have increased structural arterial stiffness compared to Eln+/+Apoe−/− mice, but they only have increased amounts of ascending aortic plaque on ND, not WD. The results suggest a change in atherosclerosis progression but not end stage disease in Eln+/−Apoe−/− mice due to increased arterial stiffness. Possible contributing factors include increased blood pressure and changes in circulating levels of interleukin-6 (IL6) and transforming growth factor beta 1 (TGF-β1) that are also associated with Eln+/− genotype.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2018;140(5):051008-051008-10. doi:10.1115/1.4039176.

In modeling the mechanical behavior of soft tissues, the proper choice of an experiment for identifying material parameters is not an easy task. In this study, a finite element computational framework is used to virtually simulate and assess commonly used experimental setups: rotational rheometer tests, confined- and unconfined-compression tests, and indentation tests. Variance-based global sensitivity analysis is employed to identify which parameters in different experimental setups govern model prediction and are thus more likely to be determined through parameter identification processes. Therefore, a priori assessment of experimental setups provides a base for systematic and reliable parameter identification. It is found that in indentation tests and unconfined-compression tests, incompressibility of soft tissues (adipose tissue in this study) plays an important role at high strain rates. That means bulk stiffness constitutes the main part of the mechanism of tissue response; thus, these experimental setups may not be appropriate for identifying shear stiffness. Also, identified material parameters through loading–unloading shear tests at a certain rate might not be reliable for other rates, since adipose tissue shows highly strain rate dependent behavior. Frequency sweep tests at a wide-enough frequency range seem to be the best setup to capture the strain rate behavior. Moreover, analyzing the sensitivity of model parameters in the different experimental setups provides further insight about the model itself.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2018;140(5):051009-051009-14. doi:10.1115/1.4038896.
OPEN ACCESS

Computational models are useful for understanding respiratory physiology. Crucial to such models are the boundary conditions specifying the flow conditions at truncated airway branches (terminal flow rates). However, most studies make assumptions about these values, which are difficult to obtain in vivo. We developed a computational fluid dynamics (CFD) model of airflows for steady expiration to investigate how terminal flows affect airflow patterns in respiratory airways. First, we measured in vitro airflow patterns in a physical airway model, using particle image velocimetry (PIV). The measured and computed airflow patterns agreed well, validating our CFD model. Next, we used the lobar flow fractions from a healthy or chronic obstructive pulmonary disease (COPD) subject as constraints to derive different terminal flow rates (i.e., three healthy and one COPD) and computed the corresponding airflow patterns in the same geometry. To assess airflow sensitivity to the boundary conditions, we used the correlation coefficient of the shape similarity (R) and the root-mean-square of the velocity magnitude difference (Drms) between two velocity contours. Airflow patterns in the central airways were similar across healthy conditions (minimum R, 0.80) despite variations in terminal flow rates but markedly different for COPD (minimum R, 0.26; maximum Drms, ten times that of healthy cases). In contrast, those in the upper airway were similar for all cases. Our findings quantify how variability in terminal and lobar flows contributes to airflow patterns in respiratory airways. They highlight the importance of using lobar flow fractions to examine physiologically relevant airflow characteristics.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2018;140(5):051010-051010-10. doi:10.1115/1.4038746.
FREE TO VIEW

Systemic administration of drugs in tumors is a challenging task due to unorganized microvasculature and nonuniform extravasation. There is an imperative need to understand the transport behavior of drugs when administered intravenously. In this study, a transport model is developed to understand the therapeutic efficacy of a free drug and liposome-encapsulated drugs (LED), in heterogeneous vasculature of human brain tumors. Dynamic contrast enhanced-magnetic resonance imaging (DCE-MRI) data is employed to model the heterogeneity in tumor vasculature that is directly mapped onto the computational fluid dynamics (CFD) model. Results indicate that heterogeneous vasculature leads to preferential accumulation of drugs at the tumor position. Higher drug accumulation was found at location of higher interstitial volume, thereby facilitating more tumor cell killing at those areas. Liposome-released drug (LRD) remains inside the tumor for longer time as compared to free drug, which together with higher concentration enhances therapeutic efficacy. The interstitial as well as intracellular concentration of LRD is found to be 2–20 fold higher as compared to free drug, which are in line with experimental data reported in literature. Close agreement between the predicted and experimental data demonstrates the potential of the developed model in modeling the transport of LED and free drugs in heterogeneous vasculature of human tumors.

Topics: Drugs , Tumors
Commentary by Dr. Valentin Fuster

### Technical Brief

J Biomech Eng. 2018;140(5):054501-054501-6. doi:10.1115/1.4039165.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2018;140(5):054502-054502-5. doi:10.1115/1.4039378.

Atomic force microscopy (AFM) has been used to measure cellular stiffness at different osmolarities to investigate the effect of osmotic pressure on cells. However, substantial direct evidence is essential to clarify the phenomena derived from the experimental results. This study used both the single-point and force mapping methods to measure the effective Young's modulus of the cell by using temporal and spatial information. The single-point force measurements confirmed the positive correlation between cellular stiffness and osmolarity. The force mapping measurements provided local stiffness on the cellular surface and identified the cytoskeleton distribution underneath the plasma membrane. At hyper-osmolarity, the cytoskeleton was observed to cover most of the area underneath the plasma membrane, and the effective Young's modulus on the area with cytoskeleton support was determined to be higher than that at iso-osmolarity. The overall increase in cellular Young's modulus confirmed the occurrence of cytoskeleton compression at hyper-osmolarity. On the other hand, although the average Young's modulus at hypo-osmolarity was lower than that at iso-osmolarity, we observed that the local Young's modulus measured on the areas with cytoskeleton support remained similar from iso-osmolarity to hypo-osmolarity. The reduction of the average Young's modulus at hypo-osmolarity was attributed to reduced cytoskeleton coverage underneath the plasma membrane.

Commentary by Dr. Valentin Fuster

### Errata

J Biomech Eng. 2018;140(5):057001-057001-1. doi:10.1115/1.4038748.

On page 3, Eq. (1) should be modified to read

$E1=1−ν124R0.5d1.53F−1−ν22E2$

Commentary by Dr. Valentin Fuster