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IN THIS ISSUE

### Research Papers

J Biomech Eng. 2015;137(12):121001-121001-9. doi:10.1115/1.4031766.

The high stiffness of conventional intramedullary (IM) nails may result in stress shielding and subsequent bone loss following healing in long bone fractures. It can also delay union by reducing compressive loads at the fracture site, thereby inhibiting secondary bone healing. This paper introduces a new approach for the optimization of a fiber-reinforced composite nail made of carbon fiber (CF)/epoxy based on a combination of the classical laminate theory, beam theory, finite-element (FE) method, and bone remodeling model using irreversible thermodynamics. The optimization began by altering the composite stacking sequence and thickness to minimize axial stiffness, while maximizing torsional stiffness for a given range of bending stiffnesses. The selected candidates for the seven intervals of bending stiffness were then examined in an experimentally validated FE model to evaluate their mechanical performance in transverse and oblique femoral shaft fractures. It was found that the composite nail having an axial stiffness of 3.70 MN and bending and torsional stiffnesses of 70.3 and 70.9 $N⋅m2$, respectively, showed an overall superiority compared to the other configurations. It increased compression at the fracture site by 344.9 N (31%) on average, while maintaining fracture stability through an average increase of only 0.6 mm (49%) in fracture shear movement in transverse and oblique fractures when compared to a conventional titanium-alloy nail. The long-term results obtained from the bone remodeling model suggest that the proposed composite IM nail reduces bone loss in the femoral shaft from 7.9% to 3.5% when compared to a conventional titanium-alloy nail. This study proposes a number of practical guidelines for the design of composite IM nails.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(12):121002-121002-7. doi:10.1115/1.4031570.

It is well known that the organization of the fibers constituting a collagenous tissue can affect its failure behavior. Less clear is how that effect can be described computationally so as to predict the failure of a native or engineered tissue under the complex loading conditions that can occur in vivo. Toward the goal of a general predictive strategy, we applied our multiscale model of collagen gel mechanics to the failure of a double-notched gel under tension, comparing the results for aligned and isotropic samples. In both computational and laboratory experiments, we found that the aligned gels were more likely to fail by connecting the two notches than the isotropic gels. For example, when the initial notches were 30% of the sample width (normalized tip-to-edge distance = 0.7), the normalized tip-to-tip distance at which the transition occurred from between-notch failure to across-sample failure shifted from 0.6 to 1.0. When the model predictions for the type of failure event (between the two notches versus across the sample width) were compared to the experimental results, the two were found to be strongly covariant by Fisher’s exact test (p < 0.05) for both the aligned and isotropic gels with no fitting parameters. Although the double-notch system is idealized, and the collagen gel system is simpler than a true tissue, it presents a simple model system for studying failure of anisotropic tissues in a controlled setting. The success of the computational model suggests that the multiscale approach, in which the structural complexity is incorporated via changes in the model networks rather than via changes to a constitutive equation, has the potential to predict tissue failure under a wide range of conditions.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(12):121003-121003-7. doi:10.1115/1.4031821.

Screw loosening is a common complication in spinal fixation using pedicle screws which may lead to loss of correction and revision surgery. The mechanisms of pedicle screw loosening are not well understood. The purpose of this study was to compare the pedicle screw pullout force and stiffness subsequent or not to multidirectional cyclic bending load (toggling). Pedicle screws inserted into porcine lumbar vertebrae underwent toggling in craniocaudal (CC), mediolateral (ML) directions, and no toggling (NT) before pullout. This study suggests that toggling and in particular CC toggling should be included in biomechanical evaluation of pedicle screw fixation strength.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(12):121004-121004-9. doi:10.1115/1.4031846.

A miniaturized version of the double cantilever beam (DCB) test is used to determine the fracture energy in human cortical bone under pure mode I loading. An equivalent crack length based data-reduction scheme is used with remarkable advantages relative to classical methods. Digital image correlation (DIC) technique is employed to determine crack opening displacement at the crack tip being correlated with the evolution of fracture energy. A method is presented to obtain the cohesive law (trapezoidal bilinear softening) mimicking the mechanical behavior observed in bone. Cohesive zone modeling (CZM) (finite-element method) was performed to validate the procedure showing excellent agreement.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(12):121005-121005-8. doi:10.1115/1.4031795.

Prevention of muscle atrophy caused by reduced mechanical loading in microgravity conditions remains a challenge for long-duration spaceflight. To combat leg muscle atrophy, astronauts on the International Space Station (ISS) often perform squat exercise using the Advanced Resistive Exercise Device (ARED). While the ARED is effective at building muscle strength and volume on Earth, NASA researchers do not know how closely ARED squat exercise on the ISS replicates Earth-level squat muscle moments, or how small variations in exercise form affect muscle loading. This study used dynamic simulations of ARED squat exercise on the ISS to address these two questions. A multibody dynamic model of the complete astronaut-ARED system was constructed in OpenSim. With the ARED base locked to ground and gravity set to 9.81 m/s2, we validated the model by reproducing muscle moments, ground reaction forces, and foot center of pressure (CoP) positions for ARED squat exercise on Earth. With the ARED base free to move relative to the ISS and gravity set to zero, we then used the validated model to simulate ARED squat exercise on the ISS for a reference squat motion and eight altered squat motions involving changes in anterior–posterior (AP) foot or CoP position on the ARED footplate. The reference squat motion closely reproduced Earth-level muscle moments for all joints except the ankle. For the altered squat motions, changing the foot position was more effective at altering muscle moments than was changing the CoP position. All CoP adjustments introduced an undesirable shear foot reaction force that could cause the feet to slip on the ARED footplate, while some foot and CoP adjustments introduced an undesirable sagittal plane foot reaction moment that would cause the astronaut to rotate off the ARED footplate without the use of some type of foot fixation. Our results provide potentially useful information for achieving desired increases or decreases in specific muscle moments during ARED squat exercise performed on the ISS.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(12):121006-121006-7. doi:10.1115/1.4031851.

The Arrhenius formulation for single-step irreversible unimolecular reactions has been used for many decades to describe the thermal damage and cell death processes. Arrhenius predictions are acceptably accurate for structural proteins, for some cell death assays, and for cell death at higher temperatures in most cell lines, above about 55 °C. However, in many cases—and particularly at hyperthermic temperatures, between about 43 and 55 °C—the particular intrinsic cell death or damage process under study exhibits a significant “shoulder” region that constant-rate Arrhenius models are unable to represent with acceptable accuracy. The primary limitation is that Arrhenius calculations always overestimate the cell death fraction, which leads to severely overoptimistic predictions of heating effectiveness in tumor treatment. Several more sophisticated mathematical model approaches have been suggested and show much-improved performance. But simpler models that have adequate accuracy would provide useful and practical alternatives to intricate biochemical analyses. Typical transient intrinsic cell death processes at hyperthermic temperatures consist of a slowly developing shoulder region followed by an essentially constant-rate region. The shoulder regions have been demonstrated to arise chiefly from complex functional protein signaling cascades that generate delays in the onset of the constant-rate region, but may involve heat shock protein activity as well. This paper shows that acceptably accurate and much-improved predictions in the simpler Arrhenius models can be obtained by adding a temperature-dependent time delay. Kinetic coefficients and the appropriate time delay are obtained from the constant-rate regions of the measured survival curves. The resulting predictions are seen to provide acceptably accurate results while not overestimating cell death. The method can be relatively easily incorporated into numerical models. Additionally, evidence is presented to support the application of compensation law behavior to the cell death processes—that is, the strong correlation between the kinetic coefficients, ln{A} and Ea, is confirmed.

Topics: Temperature , Delays , Leakage
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(12):121007-121007-9. doi:10.1115/1.4031838.

The mitral valve (MV) is a bileaflet valve positioned between the left atrium and ventricle of the heart. The annulus of the MV has been observed to undergo geometric changes during the cardiac cycle, transforming from a saddle D-shape during systole to a flat (and less eccentric) D-shape during diastole. Prosthetic MV devices, including heart valves and annuloplasty rings, are designed based on these two configurations, with the circular design of some prosthetic heart valves (PHVs) being an approximation of the less eccentric, flat D-shape. Characterizing the effects of these geometrical variations on the filling efficiency of the left ventricle (LV) is required to understand why the flat D-shaped annulus is observed in the native MV during diastole in addition to optimizing the design of prosthetic devices. We hypothesize that the D-shaped annulus reduces energy loss during ventricular filling. An experimental left heart simulator (LHS) consisting of a flexible-walled LV physical model was used to characterize the filling efficiency of the two mitral annular geometries. The strength of the dominant vortical structure formed and the energy dissipation rate (EDR) of the measured fields, during the diastolic period of the cardiac cycle, were used as metrics to quantify the filling efficiency. Our results indicated that the O-shaped annulus generates a stronger (25% relative to the D-shaped annulus) vortical structure than that of the D-shaped annulus. It was also found that the O-shaped annulus resulted in higher EDR values throughout the diastolic period of the cardiac cycle. The results support the hypothesis that a D-shaped mitral annulus reduces dissipative energy losses in ventricular filling during diastole and in turn suggests that a symmetric stent design does not provide lower filling efficiency than an equivalent asymmetric design.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(12):121008-121008-13. doi:10.1115/1.4031794.

With the increased availability of computational resources, the past decade has seen a rise in the use of computational fluid dynamics (CFD) for medical applications. There has been an increase in the application of CFD to attempt to predict the rupture of intracranial aneurysms, however, while many hemodynamic parameters can be obtained from these computations, to date, no consistent methodology for the prediction of the rupture has been identified. One particular challenge to CFD is that many factors contribute to its accuracy; the mesh resolution and spatial/temporal discretization can alone contribute to a variation in accuracy. This failure to identify the importance of these factors and identify a methodology for the prediction of ruptures has limited the acceptance of CFD among physicians for rupture prediction. The International CFD Rupture Challenge 2013 seeks to comment on the sensitivity of these various CFD assumptions to predict the rupture by undertaking a comparison of the rupture and blood-flow predictions from a wide range of independent participants utilizing a range of CFD approaches. Twenty-six groups from 15 countries took part in the challenge. Participants were provided with surface models of two intracranial aneurysms and asked to carry out the corresponding hemodynamics simulations, free to choose their own mesh, solver, and temporal discretization. They were requested to submit velocity and pressure predictions along the centerline and on specified planes. The first phase of the challenge, described in a separate paper, was aimed at predicting which of the two aneurysms had previously ruptured and where the rupture site was located. The second phase, described in this paper, aims to assess the variability of the solutions and the sensitivity to the modeling assumptions. Participants were free to choose boundary conditions in the first phase, whereas they were prescribed in the second phase but all other CFD modeling parameters were not prescribed. In order to compare the computational results of one representative group with experimental results, steady-flow measurements using particle image velocimetry (PIV) were carried out in a silicone model of one of the provided aneurysms. Approximately 80% of the participating groups generated similar results. Both velocity and pressure computations were in good agreement with each other for cycle-averaged and peak-systolic predictions. Most apparent “outliers” (results that stand out of the collective) were observed to have underestimated velocity levels compared to the majority of solutions, but nevertheless identified comparable flow structures. In only two cases, the results deviate by over 35% from the mean solution of all the participants. Results of steady CFD simulations of the representative group and PIV experiments were in good agreement. The study demonstrated that while a range of numerical schemes, mesh resolution, and solvers was used, similar flow predictions were observed in the majority of cases. To further validate the computational results, it is suggested that time-dependent measurements should be conducted in the future. However, it is recognized that this study does not include the biological aspects of the aneurysm, which needs to be considered to be able to more precisely identify the specific rupture risk of an intracranial aneurysm.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(12):121009-121009-7. doi:10.1115/1.4031849.

There is increasing evidence that the regional spatial variations in the biological and mechanical properties of articular cartilage are an important consideration in the pathogenesis of knee osteoarthritis (OA) following kinematic changes at the knee due to joint destabilizing events (such as an anterior cruciate ligament (ACL) injury). Thus, given the sensitivity of chondrocytes to the mechanical environment, understanding the internal mechanical strains in knee articular cartilage under macroscopic loads is an important element in understanding knee OA. The purpose of this study was to test the hypothesis that cartilage from the central and peripheral regions of the tibial plateau has different internal strain distributions under the same applied load. The internal matrix strain distribution for each specimen was measured on osteochondral blocks from the tibial plateau of mature ovine stifle joints. Each specimen was loaded cyclically for 20 min, after which the specimen was cryofixed in its deformed position and freeze fractured. The internal matrix was viewed in a scanning electron microscope (SEM) and internal strains were measured by quantifying the deformation of the collagen fiber network. The peak surface tensile strain, maximum principal strain, and maximum shear strain were compared between the regions. The results demonstrated significantly different internal mechanical strain distributions between the central and peripheral regions of tibial plateau articular cartilage under both the same applied load and same applied nominal strain. These differences in the above strain measures were due to differences in the deformation patterns of the collagen network between the central and peripheral regions. Taken together with previous studies demonstrating differences in the biochemical response of chondrocytes from the central and peripheral regions of the tibial plateau to mechanical load, the differences in collagen network deformation observed in this study help to provide a fundamental basis for understanding the association between altered knee joint kinematics and premature knee OA.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(12):121010-121010-6. doi:10.1115/1.4031891.

Surgical tissue fusion devices ligate blood vessels using thermal energy and coaptation pressure, while the molecular mechanisms underlying tissue fusion remain unclear. This study characterizes the influence of apposition force during fusion on bond strength, tissue temperature, and seal morphology. Porcine splenic arteries were thermally fused at varying apposition forces (10–500 N). Maximum bond strengths were attained at 40 N of apposition force. Bonds formed between 10 and 50 N contained laminated medial layers; those formed above 50 N contained only adventitia. These findings suggest that commercial fusion devices operate at greater than optimal apposition forces, and that constituents of the tunica media may alter the adhesive mechanics of the fusion mechanism.

Commentary by Dr. Valentin Fuster

### Technical Brief

J Biomech Eng. 2015;137(12):124501-124501-7. doi:10.1115/1.4031767.

In this paper, we discuss some of the primary experimental factors that should be considered when interpreting and implementing the published results of skin electroporation studies concerning measurements of mass transport across the stratum corneum (SC) in the Franz cell. It is explained that the pulse magnitude should always be considered in the context of pulse shape and that transport measurements should always be presented in the context of the trans-SC potential difference (instead of the voltage between the electrodes). The condition of the SC prior to the application of the long-duration pulse strongly influences the evolution of the local transport region (LTR). This is quantified in a simple analytical investigation of the conditions that affect the thermodynamic response of the skin.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(12):124502-124502-7. doi:10.1115/1.4031765.

Multiple injury-causing mechanisms, such as wave propagation, skull flexure, cavitation, and head acceleration, have been proposed to explain blast-induced traumatic brain injury (bTBI). An accurate, quantitative description of the individual contribution of each of these mechanisms may be necessary to develop preventive strategies against bTBI. However, to date, despite numerous experimental and computational studies of bTBI, this question remains elusive. In this study, using a two-dimensional (2D) rat head model, we quantified the contribution of head acceleration to the biomechanical response of brain tissues when exposed to blast waves in a shock tube. We compared brain pressure at the coup, middle, and contre-coup regions between a 2D rat head model capable of simulating all mechanisms (i.e., the all-effects model) and an acceleration-only model. From our simulations, we determined that head acceleration contributed 36–45% of the maximum brain pressure at the coup region, had a negligible effect on the pressure at the middle region, and was responsible for the low pressure at the contre-coup region. Our findings also demonstrate that the current practice of measuring rat brain pressures close to the center of the brain would record only two-thirds of the maximum pressure observed at the coup region. Therefore, to accurately capture the effects of acceleration in experiments, we recommend placing a pressure sensor near the coup region, especially when investigating the acceleration mechanism using different experimental setups.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2015;137(12):124503-124503-5. doi:10.1115/1.4031848.

Osteogenesis is the process by which mesenchymal stem cells differentiate to osteoblasts and form bone. The morphology and root mean squared (RMS) traction of four cell types representing different stages of osteogenesis were quantified. Undifferentiated D1, differentiated D1, MC3T3-E1, and MLO-A5 cell types were evaluated using both automated image analysis of cells stained for F-actin and by traction force microscopy (TFM). Undifferentiated mesenchymal stem cell lines were small, spindly, and exerted low traction, while differentiated osteoblasts were large, had multiple processes, and exerted higher traction. Size, shape, and traction all correlated with the differentiation stage. Thus, cell morphology evolved and RMS traction increased with differentiation. The results provide a foundation for further work with these cell lines to study the mechanobiology of bone formation.

Topics: Traction , Shapes , Microscopy
Commentary by Dr. Valentin Fuster