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Research Papers

J Biomech Eng. 2017;139(9):091001-091001-14. doi:10.1115/1.4037100.

Knowledge of the muscle, ligament, and joint forces is important when planning orthopedic surgeries. Since these quantities cannot be measured in vivo under normal circumstances, the best alternative is to estimate them using musculoskeletal models. These models typically assume idealized joints, which are sufficient for general investigations but insufficient if the joint in focus is far from an idealized joint. The purpose of this study was to provide the mathematical details of a novel musculoskeletal modeling approach, called force-dependent kinematics (FDK), capable of simultaneously computing muscle, ligament, and joint forces as well as internal joint displacements governed by contact surfaces and ligament structures. The method was implemented into the anybody modeling system and used to develop a subject-specific mandible model, which was compared to a point-on-plane (POP) model and validated against joint kinematics measured with a custom-built brace during unloaded emulated chewing, open and close, and protrusion movements. Generally, both joint models estimated the joint kinematics well with the POP model performing slightly better (root-mean-square-deviation (RMSD) of less than 0.75 mm for the POP model and 1.7 mm for the FDK model). However, substantial differences were observed when comparing the estimated joint forces (RMSD up to 24.7 N), demonstrating the dependency on the joint model. Although the presented mandible model still contains room for improvements, this study shows the capabilities of the FDK methodology for creating joint models that take the geometry and joint elasticity into account.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2017;139(9):091002-091002-9. doi:10.1115/1.4037071.

Computational modeling is critical to medical device development and has grown in its utility for predicting device performance. Additionally, there is an increasing trend to use absorbable polymers for the manufacturing of medical devices. However, computational modeling of absorbable devices is hampered by a lack of appropriate constitutive models that capture their viscoelasticity and postyield behavior. The objective of this study was to develop a constitutive model that incorporated viscoplasticity for a common medical absorbable polymer. Microtensile bars of poly(L-lactide) (PLLA) were studied experimentally to evaluate their monotonic, cyclic, unloading, and relaxation behavior as well as rate dependencies under physiological conditions. The data were then fit to a viscoplastic flow evolution network (FEN) constitutive model. PLLA exhibited rate-dependent stress–strain behavior with significant postyield softening and stress relaxation. The FEN model was able to capture these relevant mechanical behaviors well with high accuracy. In addition, the suitability of the FEN model for predicting the stress–strain behavior of PLLA medical devices was investigated using finite element (FE) simulations of nonstandard geometries. The nonstandard geometries chosen were representative of generic PLLA cardiovascular stent subunits. These finite element simulations demonstrated that modeling PLLA using the FEN constitutive relationship accurately reproduced the specimen’s force–displacement curve, and therefore, is a suitable relationship to use when simulating stress distribution in PLLA medical devices. This study demonstrates the utility of an advanced constitutive model that incorporates viscoplasticity for simulating PLLA mechanical behavior.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2017;139(9):091003-091003-8. doi:10.1115/1.4037101.

Computational models of diarthrodial joints serve to inform the biomechanical function of these structures, and as such, must be supplied appropriate inputs for performance that is representative of actual joint function. Inputs for these models are sourced from both imaging modalities as well as literature. The latter is often the source of mechanical properties for soft tissues, like ligament stiffnesses; however, such data are not always available for all the soft tissues nor is it known for patient-specific work. In the current research, a method to improve the ligament stiffness definition for a computational foot/ankle model was sought with the greater goal of improving the predictive ability of the computational model. Specifically, the stiffness values were optimized using artificial neural networks (ANNs); both feedforward and radial basis function networks (RBFNs) were considered. Optimal networks of each type were determined and subsequently used to predict stiffnesses for the foot/ankle model. Ultimately, the predicted stiffnesses were considered reasonable and resulted in enhanced performance of the computational model, suggesting that artificial neural networks can be used to optimize stiffness inputs.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2017;139(9):091004-091004-8. doi:10.1115/1.4037150.

Acoustic droplet vaporization has the potential to shorten treatment time of high-intensity focused ultrasound (HIFU) while minimizing the possible effects of microbubbles along the propagation path. Distribution of the bubbles formed from the droplets during the treatment is the major factor shaping the therapeutic region. A numerical model was proposed to simulate the bubble area evolution during this treatment. Using a linear acoustic equation to describe the ultrasound field, a threshold range was defined that determines the amount of bubbles vaporized in the treated area. Acoustic parameters, such as sound speed, acoustic attenuation coefficient, and density, were treated as a function of the bubble size distribution and the gas void fraction, which were related to the vaporized bubbles in the medium. An effective pressure factor was proposed to account for the influence of the existing bubbles on the vaporization of the nearby droplets. The factor was obtained by fitting one experimental result and was then used to calculate bubble clouds in other experimental cases. Comparing the simulation results to these other experiments validated the model. The dynamic change of the pressure and the bubble distribution after exposure to over 20 pulses of HIFU are obtained. It is found that the bubble area grows from a grainlike shape to a “tadpole,” with comparable dimensions and shape to those observed in experiments. The process was highly dynamic with the shape of the bubble area changing with successive HIFU pulses and the focal pressure. The model was further used to predict the shape of the bubble region triggered by HIFU when a bubble wall pre-exists. The results showed that the bubble wall helps prevent droplet vaporization on the distal side of the wall and forms a particularly shaped region with bubbles. This simulation model has predictive potential that could be beneficial in applications, such as cancer treatment, by parametrically studying conditions associated with these treatments and designing treatment protocols.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2017;139(9):091005-091005-9. doi:10.1115/1.4037202.

Because of the heterogeneous nature of articular cartilage tissue, penetration of potential therapeutic molecules for osteoarthritis (OA) through the articular surface (AS) is complex, with many factors that affect transport of these solutes within the tissue. Therefore, the goal of this study is to investigate how the size of antibody (Ab) variants, as well as application of cyclic mechanical loading, affects solute transport within healthy cartilage tissue. Penetration of fluorescently tagged solutes was quantified using confocal microscopy. For all the solutes tested, fluorescence curves were obtained through the articular surface. On average, diffusivities for the solutes of sizes 200 kDa, 150 kDa, 50 kDa, and 25 kDa were 3.3, 3.4, 5.1, and 6.0 μm2/s from 0 to 100 μm from the articular surface. Diffusivities went up to a maximum of 16.5, 18.5, 20.5, and 23.4 μm2/s for the 200 kDa, 150 kDa, 50 kDa, and 25 kDa molecules, respectively, from 225 to 325 μm from the surface. Overall, the effect of loading was very significant, with maximal transport enhancement for each solute ranging from 2.2 to 3.4-fold near 275 μm. Ultimately, solutes of this size do not diffuse uniformly nor are convected uniformly, through the depth of the cartilage tissue. This research potentially holds great clinical significance to discover ways of further optimizing transport into cartilage and leads to effective antibody-based treatments for OA.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2017;139(9):091006-091006-11. doi:10.1115/1.4037102.

In this study, statistical models are developed for modeling uncertain heterogeneous permeability and porosity in tumors, and the resulting uncertainties in pressure and velocity fields during an intratumoral injection are quantified using a nonintrusive spectral uncertainty quantification (UQ) method. Specifically, the uncertain permeability is modeled as a log-Gaussian random field, represented using a truncated Karhunen–Lòeve (KL) expansion, and the uncertain porosity is modeled as a log-normal random variable. The efficacy of the developed statistical models is validated by simulating the concentration fields with permeability and porosity of different uncertainty levels. The irregularity in the concentration field bears reasonable visual agreement with that in MicroCT images from experiments. The pressure and velocity fields are represented using polynomial chaos (PC) expansions to enable efficient computation of their statistical properties. The coefficients in the PC expansion are computed using a nonintrusive spectral projection method with the Smolyak sparse quadrature. The developed UQ approach is then used to quantify the uncertainties in the random pressure and velocity fields. A global sensitivity analysis is also performed to assess the contribution of individual KL modes of the log-permeability field to the total variance of the pressure field. It is demonstrated that the developed UQ approach can effectively quantify the flow uncertainties induced by uncertain material properties of the tumor.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2017;139(9):091007-091007-12. doi:10.1115/1.4037223.

Bone ingrowth and remodeling are two different evolutionary processes which might occur simultaneously. Both these processes are influenced by local mechanical stimulus. However, a combined study on bone ingrowth and remodeling has rarely been performed. This study is aimed at understanding the relationship between bone ingrowth and adaptation and their combined influence on fixation of the acetabular component. Based on three-dimensional (3D) macroscale finite element (FE) model of implanted pelvis and microscale FE model of implant–bone interface, a multiscale framework has been developed. The numerical prediction of peri-acetabular bone adaptation was based on a strain-energy density-based formulation. Bone ingrowth in the microscale models was simulated using the mechanoregulatory algorithm. An increase in bone strains near the acetabular rim was observed in the implanted pelvis model, whereas the central part of the acetabulum was observed to be stress shielded. Consequently, progressive bone apposition near the acetabular rim and resorption near the central region were observed. Bone remodeling caused a gradual increase in the implant–bone relative displacements. Evolutionary bone ingrowth was observed around the entire acetabular component. Poor bone ingrowth of 3–5% was predicted around the centro-inferio and inferio-posterio-superio-peripheral regions owing to higher implant–bone relative displacements, whereas the anterio-inferior and centro-superior regions exhibited improved bone ingrowth of 35–55% due to moderate implant–bone relative displacement. For an uncemented acetabular CoCrMo component, bone ingrowth had hardly any effect on bone remodeling; however, bone remodeling had considerable influence on bone ingrowth.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2017;139(9):091008-091008-10. doi:10.1115/1.4037289.

A new asymptotically correct contact model has been developed for conical tip based atomic force microscopy (AFM) nanoindentation. This new model provides both elastic and nonspecific adhesion properties of cells and soft gels by taking sample thickness at the point of indentation and its depth of indentation into consideration. The bottom substrate effect (BSE) is the most common source of error in the study of “AFM force maps” of the cellular sample. The present model incorporates an asymptotically correct correction term as a function of depth of indentation to eliminate the substrate effect in the analysis. Later, the model is extended to analyze the unloading portion of the indentation curve to extract the stiffness and adhesive properties simultaneously. A comparative study of the estimated material properties using other established contact models shows that the provided corrections effectively curb the errors coming from infinite thickness assumption. Nonspecific adhesive nature of a cell is represented in terms of adhesion parameter (γa) based on the “work of adhesion,” this is an alternative to the peak value of tip–sample attractive (negative) force commonly used as representative adhesion measurement. The simple analytical expression of the model can help in estimating more realistic and accurate biomechanical properties of cells from atomic force microscopy based indentation technique.

Commentary by Dr. Valentin Fuster

Technical Brief

J Biomech Eng. 2017;139(9):094501-094501-7. doi:10.1115/1.4037220.

A procedure for modeling wheelchair-users undergoing vibrations was developed. Experimental data acquired with a wheelchair simulator were used to develop a model of a seated wheelchair user. Maximum likelihood estimation procedure was used to determine the model complexity required to characterize wheelchair-user's response. It was determined that a two segment rotational link model is adequate for characterization of vibratory response. The parameters of the proposed model were identified using the experimental data and verified using additional experimental results. The proposed approach can be used to develop subject-specific design criteria for wheelchair seating and suspension.

Commentary by Dr. Valentin Fuster

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