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### Research Papers

J Biomech Eng. 2016;138(6):061001-061001-8. doi:10.1115/1.4033178.

Styrene-based block copolymers are promising materials for the development of a polymeric heart valve prosthesis (PHV), and the mechanical properties of these polymers can be tuned via the manufacturing process, orienting the cylindrical domains to achieve material anisotropy. The aim of this work is the development of a computational tool for the optimization of the material microstructure in a new PHV intended for aortic valve replacement to enhance the mechanical performance of the device. An iterative procedure was implemented to orient the cylinders along the maximum principal stress direction of the leaflet. A numerical model of the leaflet was developed, and the polymer mechanical behavior was described by a hyperelastic anisotropic constitutive law. A custom routine was implemented to align the cylinders with the maximum principal stress direction in the leaflet for each iteration. The study was focused on valve closure, since during this phase the fibrous structure of the leaflets must bear the greatest load. The optimal microstructure obtained by our procedure is characterized by mainly circumferential orientation of the cylinders within the valve leaflet. An increase in the radial strain and a decrease in the circumferential strain due to the microstructure optimization were observed. Also, a decrease in the maximum value of the strain energy density was found in the case of optimized orientation; since the strain energy density is a widely used criterion to predict elastomer's lifetime, this result suggests a possible increase of the device durability if the polymer microstructure is optimized. The present method represents a valuable tool for the design of a new anisotropic PHV, allowing the investigation of different designs, materials, and loading conditions.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;138(6):061002-061002-10. doi:10.1115/1.4033179.

Age-associated alterations in cardiovascular structure and function induce cardiovascular disease in elderly subjects. To investigate the effects of normal vascular aging (NVA) and early vascular aging (EVA) on hemodynamic characteristics in the circle of Willis (CoW), a closed-loop one-dimensional computational model was developed based on fluid mechanics in the vascular system. The numerical simulations revealed that higher central pulse pressure and augmentation index (AIx) appear in the EVA subjects due to early arrival of reflected waves, resulted in the increase of cardiac afterload compared with the NVA subjects. Moreover, the hemodynamic characteristics in the CoW show that the EVA subjects in an older age display a higher blood pressure than that of the NVA with a complete CoW. Herein, the increased blood pressure and flow rate coexist in the subjects with an incomplete CoW. In conclusion, the hemodynamic characteristics in the aortic tree and CoW related to aging appear to play an important role in causing cardiovascular and intravascular disease.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;138(6):061003-061003-9. doi:10.1115/1.4033300.

There is a significant need for fixed biological tissues with desired structural and material constituents for tissue engineering applications. Here, we introduce the lung ligament as a fixed biological material that may have clinical utility for tissue engineering. To characterize the lung tissue for potential clinical applications, we studied glutaraldehyde-treated porcine pulmonary ligament (n = 11) with multiphoton microscopy (MPM) and conducted biaxial planar experiments to characterize the mechanical property of the tissue. The MPM imaging revealed that there are generally two families of collagen fibers distributed in two distinct layers: The first family largely aligns along the longitudinal direction with a mean angle of θ = 10.7 ± 9.3 deg, while the second one exhibits a random distribution with a mean θ = 36.6 ± 27.4. Elastin fibers appear in some intermediate sublayers with a random orientation distribution with a mean θ = 39.6 ± 23 deg. Based on the microstructural observation, a microstructure-based constitutive law was proposed to model the elastic property of the tissue. The material parameters were identified by fitting the model to the biaxial stress–strain data of specimens, and good fitting quality was achieved. The parameter $e0$ (which denotes the strain beyond which the collagen can withstand tension) of glutaraldehyde-treated tissues demonstrated low variability implying a relatively consistent collagen undulation in different samples, while the stiffness parameters for elastin and collagen fibers showed relatively greater variability. The fixed tissues presented a smaller $e0$ than that of fresh specimen, confirming that glutaraldehyde crosslinking increases the mechanical strength of collagen-based biomaterials. The present study sheds light on the biomechanics of glutaraldehyde-treated porcine pulmonary ligament that may be a candidate for tissue engineering.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;138(6):061004-061004-15. doi:10.1115/1.4033177.

A number of robotic exoskeletons are being developed to provide rehabilitation interventions for those with movement disabilities. We present a systematic framework that allows for virtual prototyping (i.e., design, control, and experimentation (i.e. design, control, and experimentation) of robotic exoskeletons. The framework merges computational musculoskeletal analyses with simulation-based design techniques which allows for exoskeleton design and control algorithm optimization. We introduce biomechanical, morphological, and controller measures to optimize the exoskeleton performance. A major advantage of the framework is that it provides a platform for carrying out hypothesis-driven virtual experiments to quantify device performance and rehabilitation progress. To illustrate the efficacy of the framework, we present a case study wherein the design and analysis of an index finger exoskeleton is carried out using the proposed framework.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;138(6):061005-061005-9. doi:10.1115/1.4032966.

Mathematical cervical spine models allow for studying of impact loading that can cause whiplash associated disorders (WAD). However, existing models only cover the male anthropometry, despite the female population being at a higher risk of sustaining WAD in automotive rear-end impacts. The aim of this study is to develop and validate a ligamentous cervical spine intended for biomechanical research on the effect of automotive impacts. A female model has the potential to aid the design of better protection systems as well as improve understanding of injury mechanisms causing WAD. A finite element (FE) mesh was created from surface data of the cervical vertebrae of a 26-year old female (stature 167 cm, weight 59 kg). Soft tissues were generated from the skeletal geometry and anatomical literature descriptions. Ligaments were modeled with nonlinear elastic orthotropic membrane elements, intervertebral disks as composites of nonlinear elastic bulk elements, and orthotropic anulus fibrosus fiber layers, while cortical and trabecular bones were modeled as isotropic plastic–elastic. The model has geometrical features representative of the female cervical spine—the largest average difference compared with published anthropometric female data was the vertebral body depth being 3.4% shorter for the model. The majority the cervical segments compare well with respect to biomechanical data at physiological loads, with the best match for flexion–extension loads and less biofidelity for axial rotation. An average female FE ligamentous cervical spine model was developed and validated with respect to physiological loading. In flexion–extension simulations with the developed female model and an existing average male cervical spine model, a greater range of motion (ROM) was found in the female model.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;138(6):061006-061006-5. doi:10.1115/1.4033437.

Availability of material as well as biological properties of native tissues is critical for biomaterial design and synthesis for regenerative engineering. Until recently, selection of biomaterials and biomolecule carriers for dental pulp regeneration has been done randomly or based on experience mainly due to the absence of benchmark data for dental pulp tissue. This study, for the first time, characterizes the linear viscoelastic material functions and compressive properties of human dental pulp tissue harvested from wisdom teeth, under oscillatory shear and compression. The results revealed a gel-like behavior of the pulp tissue over the frequency range of 0.1–100 rps. Uniaxial compression tests generated peak normal stress and compressive modulus values of 39.1±20.4 kPa and 5.5±2.8 kPa, respectively. Taken collectively, the linear viscoelastic and uniaxial compressive properties of the human dental pulp tissue reported here should enable the better tailoring of biomaterials or biomolecule carriers to be employed in dental pulp regeneration.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;138(6):061007-061007-7. doi:10.1115/1.4033476.

A direct method to express the center of pressure (CoP) measured by an insole pressure sensor system (IPSS) into a known coordinate system measured by motion tracking equipment is presented. A custom probe was constructed with reflective markers to allow its tip to be precisely tracked with motion tracking equipment. This probe was utilized to activate individual sensors on an IPSS that was placed in a shoe fitted with reflective markers used to establish a local shoe coordinate system. When pressed onto the IPSS the location of the probe's tip was coincident with the CoP measured by the IPSS (IPSS-CoP). Two separate pushes (i.e., data points) were used to develop vectors in each respective coordinate system. Simple vector mathematics determined the rotational and translational components of the transformation matrix needed to express the IPSS-CoP into the local shoe coordinate system. Validation was performed by comparing IPSS-CoP with an embedded force plate measured CoP (FP-CoP) from data gathered during kinematic trials. Six male subjects stood on an embedded FP and performed anterior/posterior (AP) sway, internal rotation, and external rotation of the body relative to a firmly planted foot. The IPSS-CoP was highly correlated with the FP-CoP for all motions, root mean square errors (RMSRRs) were comparable to other research, and there were no statistical differences between the displacement of the IPSS-CoP and FP-CoP for both the AP and medial/lateral (ML) axes, respectively. The results demonstrated that this methodology could be utilized to determine the transformation variables need to express IPSS-CoP into a known coordinate system measured by motion tracking equipment and that these variables can be determined outside the laboratory anywhere motion tracking equipment is available.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;138(6):061008-061008-10. doi:10.1115/1.4033475.

One limitation of forced spirometry is that it integrates the contribution of the complex and dynamic behavior of all of the airways and tissue of the lung into a single exhaling unit, hence, it is not clear how spirometric measures are affected by local changes to the airways or tissue such as the presence of “ventilation defects.” Here, we adapt a wave-speed limitation model to a spatially distributed and anatomically based airway tree that is embedded within a deformable parenchyma, to simulate forced expiration in 1 s (FEV1). This provides a model that can be used to assess the consequence of imposed constrictions on FEV1. We first show how the model can be parameterized to represent imaging and forced spirometry data from nonasthmatic healthy young adults. We then compare the effect of homogeneous and clustered bronchoconstriction on FEV1 in six subject-specific models (three male and three female). The model highlights potential sources of normal subject variability in response to agonist challenge, including the interaction between sites of airway constriction and sites of flow limitation at baseline. The results support earlier studies which proposed that the significant constriction of nondefect airways must be present in order to match to clinical measurements of lung function.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;138(6):061009-061009-11. doi:10.1115/1.4033477.

Recent high-resolution computational fluid dynamics (CFD) studies have detected persistent flow instability in intracranial aneurysms (IAs) that was not observed in previous in silico studies. These flow fluctuations have shown incidental association with rupture in a small aneurysm dataset. The aims of this study are to explore the capabilities and limitations of a commercial cfd solver in capturing such velocity fluctuations, whether fluctuation kinetic energy (fKE) as a marker to quantify such instability could be a potential parameter to predict aneurysm rupture, and what geometric parameters might be associated with such fluctuations. First, we confirmed that the second-order discretization schemes and high spatial and temporal resolutions are required to capture these aneurysmal flow fluctuations. Next, we analyzed 56 patient-specific middle cerebral artery (MCA) aneurysms (12 ruptured) by transient, high-resolution CFD simulations with a cycle-averaged, constant inflow boundary condition. Finally, to explore the mechanism by which such flow instabilities might arise, we investigated correlations between fKE and several aneurysm geometrical parameters. Our results show that flow instabilities were present in 8 of 56 MCA aneurysms, all of which were unruptured bifurcation aneurysms. Statistical analysis revealed that fKE could not differentiate ruptured from unruptured aneurysms. Thus, our study does not lend support to these flow instabilities (based on a cycle-averaged constant inflow as opposed to peak velocity) being a marker for rupture. We found a positive correlation between fKE and aneurysm size as well as size ratio. This suggests that the intrinsic flow instability may be associated with the breakdown of an inflow jet penetrating the aneurysm space.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;138(6):061010-061010-8. doi:10.1115/1.4033480.

Several approaches have been used to devise a model of the human tibiofemoral joint for embedment in lower limb musculoskeletal models. However, no study has considered the use of cadaveric 6 × 6 compliance (or stiffness) matrices to model the tibiofemoral joint under normal or pathological conditions. The aim of this paper is to present a method to determine the compliance matrix of an ex vivo tibiofemoral joint for any given equilibrium pose. Experiments were carried out on a single ex vivo knee, first intact and, then, with the anterior cruciate ligament (ACL) transected. Controlled linear and angular displacements were imposed in single degree-of-freedom (DoF) tests to the specimen, and the resulting forces and moments were measured using an instrumented robotic arm. This was done starting from seven equilibrium poses characterized by the following flexion angles: 0 deg, 15 deg, 30 deg, 45 deg, 60 deg, 75 deg, and 90 deg. A compliance matrix for each of the selected equilibrium poses and for both the intact and ACL-deficient specimen was calculated. The matrix, embedding the experimental load–displacement relationship of the examined DoFs, was calculated using a linear least squares inversion based on a QR decomposition, assuming symmetric and positive-defined matrices. Single compliance matrix terms were in agreement with the literature. Results showed an overall increase of the compliance matrix terms due to the ACL transection (2.6 ratio for rotational terms at full extension) confirming its role in the joint stabilization. Validation experiments were carried out by performing a Lachman test (the tibia is pulled forward) under load control on both the intact and ACL-deficient knee and assessing the difference (error) between measured linear and angular displacements and those estimated using the appropriate compliance matrix. This error increased nonlinearly with respect to the values of the load. In particular, when an incremental posterior–anterior force up to 6 N was applied to the tibia of the intact specimen, the errors on the estimated linear and angular displacements were up to 0.6 mm and 1.5 deg, while for a force up to 18 N, the errors were 1.5 mm and 10.5 deg, respectively. In conclusion, the method used in this study may be a viable alternative to characterize the tibiofemoral load-dependent behavior in several applications.

Commentary by Dr. Valentin Fuster

### Technical Brief

J Biomech Eng. 2016;138(6):064501-064501-4. doi:10.1115/1.4033546.