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IN THIS ISSUE

### Research Papers

J Biomech Eng. 2019;141(4):041001-041001-7. doi:10.1115/1.4042433.

Current shoulder clinical range of motion (ROM) assessments (e.g., goniometric ROM) may not adequately represent shoulder function beyond controlled clinical settings. Relative inertial measurement unit (IMU) motion quantifies ROM precisely and can be used outside of clinic settings capturing “real-world” shoulder function. A novel IMU-based shoulder elevation quantification method was developed via IMUs affixed to the sternum/humerus, respectively. This system was then compared to in-laboratory motion capture (MOCAP) during prescribed motions (flexion, abduction, scaption, and internal/external rotation). MOCAP/IMU elevation were equivalent during flexion (R2 = 0.96, μError = 1.7 deg), abduction (R2 = 0.96, μError = 2.9 deg), scaption (R2 = 0.98, μError = −0.3 deg), and internal/external rotation (R2 = 0.90, μError = 0.4 deg). When combined across movements, MOCAP/IMU elevation were equal (R2 = 0.98, μError = 1.4 deg). Following validation, the IMU-based system was deployed prospectively capturing continuous shoulder elevation in 10 healthy individuals (4 M, 69 ± 20 years) without shoulder pathology for seven consecutive days (13.5 ± 2.9 h/day). Elevation was calculated continuously daily and outcome metrics included percent spent in discrete ROM (e.g., 0–5 deg and 5–10 deg), repeated maximum elevation (i.e., >10 occurrences), and maximum/average elevation. Average elevation was 40 ± 6 deg. Maximum with >10 occurrences and maximum were on average 145–150 deg and 169 ± 8 deg, respectively. Subjects spent the vast majority of the day (97%) below 90 deg of elevation, with the most time spent in the 25–30 deg range (9.7%). This study demonstrates that individuals have the ability to achieve large ROMs but do not frequently do so. These results are consistent with the previously established lab-based measures. Moreover, they further inform how healthy individuals utilize their shoulders and may provide clinicians a reference for postsurgical ROM.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2019;141(4):041002-041002-11. doi:10.1115/1.4042439.

A multiscale model for mineralized collagen fibril (MCF) is proposed by taking into account the uncertainties associated with the geometrical properties of the mineral phase and its distribution in the organic matrix. The asymptotic homogenization approach along with periodic boundary conditions has been used to derive the effective elastic moduli of bone's nanostructure at two hierarchical length scales, namely: microfibril (MF) and MCF. The uncertainties associated with the mineral plates have been directly included in the finite element mesh by randomly varying their sizes and structural arrangements. A total of 100 realizations for the MCF model with random distribution have been generated using an in-house MATLAB code, and Monte Carlo type of simulations have been performed under tension load to obtain the statistical equivalent modulus. The deformation response has been studied in both small ($≤$10%) and large ($≥$10%) strain regimes. The stress transformation mechanism has also been explored in MF which showed stress relaxation in the organic phase upon different stages of mineralization. The elastic moduli for MF under small and large strains have been obtained as 1.88 and 6.102 GPa, respectively, and have been used as an input for the upper scale homogenization procedure. Finally, the characteristic longitudinal moduli of the MCF in the small and large strain regimes are obtained as 4.08 $±$ 0.062 and 12.93 $±$ 0.148 GPa, respectively. All the results are in good agreement to those obtained from previous experiments and molecular dynamics (MD) simulations in the literature with a significant reduction in the computational cost.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2019;141(4):041003-041003-9. doi:10.1115/1.4042437.

Vaginal tears are very common and can lead to severe complications such as hemorrhaging, fecal incontinence, urinary incontinence, and dyspareunia. Despite the implications of vaginal tears on women's health, there are currently no experimental studies on the tear behavior of vaginal tissue. In this study, planar equi-biaxial tests on square specimens of vaginal tissue, with sides oriented along the longitudinal direction (LD) and circumferential direction (CD), were conducted using swine as animal model. Three groups of specimens were mechanically tested: the NT group (n =9), which had no pre-imposed tear, the longitudinal tear (LT) group (n =9), and the circumferential tear (CT) group (n =9), which had central pre-imposed elliptically shaped tears with major axes oriented in the LD and the CD, respectively. Through video recording during testing, axial strains were measured for the NT group using the digital image correlation (DIC) technique and axial displacements of hook clamps were measured for the NT, LT, and CT groups in the LD and CD. The swine vaginal tissue was found to be highly nonlinear and somewhat anisotropic. Up to normalized axial hook displacements of 1.15, no tears were observed to propagate, suggesting that the vagina has a high resistance to further tearing once a tear has occurred. However, in response to biaxial loading, the size of the tears for the CT group increased significantly more than the size of the tears for the LT group (p =0.003). The microstructural organization of the vagina is likely the culprit for its tear resistance and orientation-dependent tear behavior. Further knowledge on the structure–function relationship of the vagina is needed to guide the development of new methods for preventing the severe complications of tearing.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2019;141(4):041004-041004-12. doi:10.1115/1.4042601.

Cardiovascular diseases (CVDs) are the number one cause of death globally. Arterial endothelial cell (EC) dysfunction plays a key role in many of these CVDs, such as atherosclerosis. Blood flow-induced wall shear stress (WSS), among many other pathophysiological factors, is known to significantly contribute to EC dysfunction. The present study reports an in vitro investigation of the effect of quantified WSS on ECs, analyzing the EC morphometric parameters and cytoskeletal remodeling. The effects of four different flow cases (low steady laminar (LSL), medium steady laminar (MSL), nonzero-mean sinusoidal laminar (NZMSL), and laminar carotid (LCRD) waveforms) on the EC area, perimeter, shape index (SI), angle of orientation, F-actin bundle remodeling, and platelet endothelial cell adhesion molecule-1 (PECAM-1) localization were studied. For the first time, a flow facility was fully quantified for the uniformity of flow over ECs and for WSS determination (as opposed to relying on analytical equations). The SI and angle of orientation were found to be the most flow-sensitive morphometric parameters. A two-dimensional fast Fourier transform (2D FFT) based image processing technique was applied to analyze the F-actin directionality, and an alignment index (AI) was defined accordingly. Also, a significant peripheral loss of PECAM-1 in ECs subjected to atheroprone cases (LSL and NZMSL) with a high cell surface/cytoplasm stain of this protein is reported, which may shed light on of the mechanosensory role of PECAM-1 in mechanotransduction.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2019;141(4):041005-041005-9. doi:10.1115/1.4042680.

The high-resolution peripheral quantitative computed tomography (HR-pQCT) provides unprecedented visualization of bone microstructure and the basis for constructing patient-specific microfinite element (μFE) models. Based on HR-pQCT images, we have developed a plate-and-rod μFE (PR μFE) method for whole bone segments using individual trabecula segmentation (ITS) and an adaptive cortical meshing technique. In contrast to the conventional voxel approach, the complex microarchitecture of the trabecular compartment is simplified into shell and beam elements based on the trabecular plate-and-rod configuration. In comparison to voxel-based μFE models of μCT and measurements from mechanical testing, the computational and experimental gold standards, nonlinear analyses of stiffness and yield strength using the HR-pQCT-based PR μFE models demonstrated high correlation and accuracy. These results indicated that the combination of segmented trabecular plate-rod morphology and adjusted cortical mesh adequately captures mechanics of the whole bone segment. Meanwhile, the PR μFE modeling approach reduced model size by nearly 300-fold and shortened computation time for nonlinear analysis from days to within hours, permitting broader clinical application of HR-pQCT-based nonlinear μFE modeling. Furthermore, the presented approach was tested using a subset of radius and tibia HR-pQCT scans of patients with prior vertebral fracture in a previously published study. Results indicated that yield strength for radius and tibia whole bone segments predicted by the PR μFE model was effective in discriminating vertebral fracture subjects from nonfractured controls. In conclusion, the PR μFE model of HR-pQCT images accurately predicted mechanics for whole bone segments and can serve as a valuable clinical tool to evaluate musculoskeletal diseases.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2019;141(4):041006-041006-10. doi:10.1115/1.4042684.

The control of joint stiffness is a fundamental mechanism used to control human movements. While many studies have observed how stiffness is modulated for tasks involving shoulder and elbow motion, a limited amount of knowledge is available for wrist movements, though the wrist plays a crucial role in manipulation. We have developed a computational framework based on a realistic musculoskeletal model, which allows one to calculate the passive and active components of the wrist joint stiffness. We first used the framework to validate the musculoskeletal model against experimental measurements of the wrist joint stiffness, and then to study the contribution of different muscle groups to the passive joint stiffness. We finally used the framework to study the effect of muscle cocontraction on the active joint stiffness. The results show that thumb and finger muscles play a crucial role in determining the passive wrist joint stiffness: in the neutral posture, the direction of maximum stiffness aligns with the experimental measurements, and the magnitude increases by 113% when they are included. Moreover, the analysis of the controllability of joint stiffness showed that muscle cocontraction positively correlates with the stiffness magnitude and negatively correlates with the variability of the stiffness orientation (p < 0.01 in both cases). Finally, an exhaustive search showed that with appropriate selection of a muscle activation strategy, the joint stiffness orientation can be arbitrarily modulated. This observation suggests the absence of biomechanical constraints on the controllability of the orientation of the wrist joint stiffness.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2019;141(4):041007-041007-12. doi:10.1115/1.4042765.

In this study, coupled hemodynamic–acoustic simulations are employed to study the generation and propagation of murmurs associated with aortic stenoses where the aorta with a stenosed aortic valve is modeled as a curved pipe with a constriction near the inlet. The hemodynamics of the poststenotic flow is investigated in detail in our previous numerical study (Zhu et al., 2018, “Computational Modelling and Analysis of Haemodynamics in a Simple Model of Aortic Stenosis,” J. Fluid Mech., 851, pp. 23–49). The temporal history of the pressure on the aortic lumen is recorded during the hemodynamic study and used as the murmur source in the acoustic simulations. The thorax is modeled as an elliptic cylinder and the thoracic tissue is assumed to be homogeneous, linear and viscoelastic. A previously developed high-order numerical method that is capable of dealing with immersed bodies is applied in the acoustic simulations. To mimic the clinical practice of auscultation, the sound signals from the epidermal surface are collected. The simulations show that the source of the aortic stenosis murmur is located at the proximal end of the aortic arch and that the sound intensity pattern on the epidermal surface can predict the source location of the murmurs reasonably well. Spectral analysis of the murmur reveals the disconnect between the break frequency obtained from the flow and from the murmur signal. Finally, it is also demonstrated that the source locations can also be predicted by solving an inverse problem using the free-space Green's function. The implications of these results for cardiac auscultation are discussed.

Commentary by Dr. Valentin Fuster

### Technical Brief

J Biomech Eng. 2019;141(4):044501-044501-5. doi:10.1115/1.4042600.

Predicting the mechanical behavior of the intervertebral disk (IVD) in health and in disease requires accurate spatial mapping of its compressive mechanical properties. Previous studies confirmed that residual strains in the annulus fibrosus (AF) of the IVD, which result from nonuniform extracellular matrix deposition in response to in vivo loads, vary by anatomical regions (anterior, posterior, and lateral) and zones (inner, middle, and outer). We hypothesized that as the AF is composed of a nonlinear, anisotropic, viscoelastic material, the state of residual strain in the transverse plane would influence the apparent values of axial compressive properties. To test this hypothesis, axial creep indentation tests were performed, using a 1.6 mm spherical probe, at nine different anatomical locations on bovine caudal AFs in both the intact (residual strain present) and strain relieved states. The results showed a shift toward increased spatial homogeneity in all measured parameters, particularly instantaneous strain. This shift was not observed in control AFs, which were tested twice in the intact state. Our results confirm that time-dependent axial compressive properties of the AF are sensitive to the state of residual strain in the transverse plane, to a degree that is likely to affect whole disk behavior.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2019;141(4):044502-044502-7. doi:10.1115/1.4042683.

This study aims to estimate the control law employed by the central nervous system (CNS) to keep a person in balance after a sudden disturbance. For this aim, several experiments were carried out, in which the subjects were perturbed sagittally by using a single-axis tilt-platform and their motions were recorded with appropriate sensors. The analysis of the experimental results leads to the contribution of this paper as a conjecture that the CNS commands the muscular actuators of the joints according to an adaptive proportional-derivative (PD) control law such that its gains and set points are updated continuously. This conjecture is accompanied with an assumption that the CNS is able to acquire perfect and almost instantaneous position and velocity feedback by means of a fusion of the signals coming from the proprioceptive, somatosensory, and vestibular systems. In order to verify the conjectured control law, an approximate biomechanical model was developed and several simulations were carried out to imitate the experimentally observed motions. The time variations of the set points and the control gains were estimated out of the experimental data. The simulated motions were observed to be considerably close to the experimental motions. Thus, the conjectured control law is validated. However, the experiments also indicate that the mentioned adaptation scheme is quite variable even for the same subject tested repeatedly with the same perturbation. In other words, this experimental study also leads to the implication that the way the CNS updates the control parameters is not quite predictable.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2019;141(4):044503-044503-7. doi:10.1115/1.4042769.

Total wrist arthroplasty (TWA) for improving the functionality of severe wrist joint pathology has not had the same success, in parameters such as motion restoration and implant survival, as hip, knee, and shoulder arthroplasty. These other arthroplasties have been studied extensively, including the use of biplane videoradiography (BVR) that has allowed investigators to study the in vivo motion of the total joint replacement during dynamic activities. The wrist has not been a previous focus, and utilization of BVR for wrist arthroplasty presents unique challenges due to the design characteristics of TWAs. Accordingly, the aims of this study were (1) to develop a methodology for generating TWA component models for use in BVR and (2) to evaluate the accuracy of model-image registration in a single cadaveric model. A model of the carpal component was constructed from a computed tomography (CT) scan, and a model of the radial component was generated from a surface scanner. BVR was acquired for three anatomical tasks from a cadaver specimen. Optical motion capture (OMC) was used as the gold standard. BVR's bias in flexion/extension, radial/ulnar deviation, and pronosupination was less than 0.3 deg, 0.5 deg, and 0.6 deg. Translation bias was less than 0.2 mm with a standard deviation of less than 0.4 mm. This BVR technique achieved a kinematic accuracy comparable to the previous studies on other total joint replacements. BVR's application to the study of TWA function in patients could advance the understanding of TWA, and thus, the implant's success.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2019;141(4):044504-044504-4. doi:10.1115/1.4042766.

Allometric scaling laws relate physiologic parameters to body weight. Genetically modified mice allow investigation of allometric scaling laws when fundamental cardiovascular components are altered. Elastin haploinsufficient (Eln+/−) mice have reduced elastin amounts, and fibulin-5 knockout (Fbln5−/−) mice have compromised elastic fiber integrity in the large arteries which may alter cardiovascular scaling laws. Previously published echocardiography data used to investigate aortic and left ventricular function in Eln+/− and Fbln5−/− mice throughout postnatal development and early adulthood were reanalyzed to determine cardiovascular scaling laws. Aortic diameter, heart weight, stroke volume, and cardiac output have scaling exponents within 1–32% of the predicted theoretical range, indicating that the scaling laws apply to maturing mice. For aortic diameter, Eln+/− and Eln+/+ mice have similar scaling exponents, but different scaling constants, suggesting a shift in starting diameter, but no changes in aortic growth with body weight. In contrast, the scaling exponent for aortic diameter in Fbln5−/− mice is lower than Fbln5+/+ mice, but the scaling constant is similar, suggesting that aortic growth with body weight is compromised in Fbln5−/− mice. For both Eln+/− and Fbln5−/− groups, the scaling constant for heart weight is increased compared to the respective control group, suggesting an increase in starting heart weight, but no change in the increase with body weight during maturation. The scaling exponents and constants for stroke volume and cardiac output are not significantly affected by reduced elastin amounts or compromised elastic fiber integrity in the large arteries, highlighting a robust cardiac adaptation despite arterial defects.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2019;141(4):044505-044505-6. doi:10.1115/1.4042767.

Posterior fixation with contoured rods is an established methodology for the treatment of spinal deformities. Both uniform industrial preforming and intraoperative contouring introduce tensile and compressive plastic deformations, respectively, at the concave and at the convex sides of the rod. The purpose of this study is to develop a validated numerical framework capable of predicting how the fatigue behavior of contoured spinal rods is affected by residual stresses when loaded in lordotic and kyphotic configurations. Established finite element models (FEM) describing static contouring were implemented as a preliminary simulation step and were followed by subsequent cyclical loading steps. The equivalent Sines stress distribution predicted in each configuration was compared to that in straight rods (SR) and related to the corresponding experimental number of cycles to failure. In the straight configuration, the maximum equivalent stress (441 MPa) exceeds the limit curve, as confirmed by experimental rod breakage after around 1.9 × 105 loading cycles. The stresses further increased in the lordotic configuration, where failure was reached within 2.4 × 104 cycles. The maximum equivalent stress was below the limit curve for the kyphotic configuration (640 MPa), for which a run-out of 106 cycles was reached. Microscopy inspection confirmed agreement between numerical predictions and experimental fatigue crack location. The contouring technique (uniform contouring (UC) or French bender (FB)) was not related to any statistically significant difference. Our study demonstrates the key role of residual stresses in altering the mean stress component, superposing to the tensile cyclic load, potentially explaining the higher failure rate of lordotic rods compared to kyphotic ones.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2019;141(4):044506-044506-5. doi:10.1115/1.4042900.

We experimentally determined the tensile stress–strain response of human muscle along fiber direction and compressive stress–strain response transverse to fiber direction at intermediate strain rates (100–102/s). A hydraulically driven material testing system with a dynamic testing mode was used to perform the tensile and compressive experiments on human muscle tissue. Experiments at quasi-static strain rates (below 100/s) were also conducted to investigate the strain-rate effects over a wider range. The experimental results show that, at intermediate strain rates, both the human muscle's tensile and compressive stress–strain responses are nonlinear and strain-rate sensitive. Human muscle also exhibits a stiffer and stronger tensile mechanical behavior along fiber direction than its compressive mechanical behavior along the direction transverse to fiber direction. An Ogden model with two material constants was adopted to describe the nonlinear tensile and compressive behaviors of human muscle.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2019;141(4):044507-044507-5. doi:10.1115/1.4042901.

Bone is a complex material that exhibits an amount of plasticity before bone fracture takes place, where the nonlinear relationship between stress and strain is of importance to understand the mechanism behind the fracture. This brief presents our study on the examination of the stress–strain relationship of bovine femoral cortical bone and the relationship representation by employing the Ramberg–Osgood (R–O) equation. Samples were taken and prepared from different locations (upper, middle, and lower) of bone diaphysis and were then subjected to the uniaxial tensile tests under longitudinal and transverse loading conditions, respectively. The stress–strain curves obtained from tests were analyzed via linear regression analysis based on the R–O equation. Our results illustrated that the R–O equation is appropriate to describe the nonlinear stress–strain behavior of cortical bone, while the values of equation parameters vary with the sample locations (upper, middle, and lower) and loading conditions (longitudinal and transverse).

Commentary by Dr. Valentin Fuster

### Errata

J Biomech Eng. 2019;141(4):047001-047001-1. doi:10.1115/1.4042685.

In the paper “The Mechanical Role of the Radial Fibers Network Within the Annulus Fibrosus of the Lumbar Intervertebral Disc: A Finite Elements Study,” the affiliation of Fabio Galbusera was incorrect. The correct affiliation is “IRCCS Istituto Ortopedico Galeazzi, Milan, Italy.”

Commentary by Dr. Valentin Fuster