Jason P. Halloran

Considerations for reporting finite element analysis studies in biomechanics.

Simulation-based medicine and the development of complex computer models of biological structures is becoming ubiquitous for advancing biomedical engineering and clinical research. Finite element analysis (FEA) has been widely used in the last few decades to understand and predict biomechanical phenomena. Modeling and simulation approaches in biomechanics are highly interdisciplinary, involving novice and skilled developers in all areas of biomedical engineering and biology. While recent advances in model development and simulation platforms offer a wide range of tools to investigators, the decision making process during modeling and simulation has become more opaque. Hence, reliability of such models used for medical decision making and for driving multiscale analysis comes into question. Establishing guidelines for model development and dissemination is a daunting task, particularly with the complex and convoluted models used in FEA. Nonetheless, if better reporting can be established, researchers will have a better understanding of a models value and the potential for reusability through sharing will be bolstered. Thus, the goal of this document is to identify resources and considerate reporting parameters for FEA studies in biomechanics. These entail various levels of reporting parameters for model identification, model structure, simulation structure, verification, validation, and availability. While we recognize that it may not be possible to provide and detail all of the reporting considerations presented, it is possible to establish a level of confidence with selective use of these parameters. More detailed reporting, however, can establish an explicit outline of the decision-making process in simulation-based analysis for enhanced reproducibility, reusability, and sharing.

Multiscale Mechanics of Articular Cartilage: Potentials and Challenges of Coupling Musculoskeletal, Joint, and Microscale Computational Models

Articular cartilage experiences significant mechanical loads during daily activities. Healthy cartilage provides the capacity for load bearing and regulates the mechanobiological processes for tissue development, maintenance, and repair. Experimental studies at multiple scales have provided a fundamental understanding of macroscopic mechanical function, evaluation of the micromechanical environment of chondrocytes, and the foundations for mechanobiological response. In addition, computational models of cartilage have offered a concise description of experimental data at many spatial levels under healthy and diseased conditions, and have served to generate hypotheses for the mechanical and biological function. Further, modeling and simulation provides a platform for predictive risk assessment, management of dysfunction, as well as a means to relate multiple spatial scales. Simulation-based investigation of cartilage comes with many challenges including both the computational burden and often insufficient availability of data for model development and validation. This review outlines recent modeling and simulation approaches to understand cartilage function from a mechanical systems perspective, and illustrates pathways to associate mechanics with biological function. Computational representations at single scales are provided from the body down to the microstructure, along with attempts to explore multiscale mechanisms of load sharing that dictate the mechanical environment of the cartilage and chondrocytes.

Concurrent musculoskeletal dynamics and finite element analysis predicts altered gait patterns to reduce foot tissue loading

Current computational methods for simulating locomotion have primarily used muscle-driven multibody dynamics, in which neuromuscular control is optimized. Such simulations generally represent joints and soft tissue as simple kinematic or elastic elements for computational efficiency. These assumptions limit application in studies such as ligament injury or osteoarthritis, where local tissue loading must be predicted. Conversely, tissue can be simulated using the finite element method with assumed or measured boundary conditions, but this does not represent the effects of whole body dynamics and neuromuscular control. Coupling the two domains would overcome these limitations and allow prediction of movement strategies guided by tissue stresses. Here we demonstrate this concept in a gait simulation where a musculoskeletal model is coupled to a finite element representation of the foot. Predictive simulations incorporated peak plantar tissue deformation into the objective of the movement optimization, as well as terms to track normative gait data and minimize fatigue. Two optimizations were performed, first without the strain minimization term and second with the term. Convergence to realistic gait patterns was achieved with the second optimization realizing a 44% reduction in peak tissue strain energy density. The study demonstrated that it is possible to alter computationally predicted neuromuscular control to minimize tissue strain while including desired kinematic and muscular behavior. Future work should include experimental validation before application of the methodology to patient care.

Adaptive Surrogate Modeling for Efficient Coupling of Musculoskeletal Control and Tissue Deformation Models

Finite element (FE) modeling and multibody dynamics have traditionally been applied separately to the domains of tissue mechanics and musculoskeletal movements, respectively. Simultaneous simulation of both domains is needed when interactions between tissue and movement are of interest, but this has remained largely impractical due to the high computational cost. Here we present a method for the concurrent simulation of tissue and movement, in which state of the art methods are used in each domain, and communication occurs via a surrogate modeling system based on locally weighted regression. The surrogate model only performs FE simulations when regression from previous results is not within a user-specified tolerance. For proof of concept and to illustrate feasibility, the methods were demonstrated on an optimization of jumping movement using a planar musculoskeletal model coupled to a FE model of the foot. To test the relative accuracy of the surrogate model outputs against those of the FE model, a single forward dynamics simulation was performed with FE calls at every integration step and compared with a corresponding simulation with the surrogate model included. Neural excitations obtained from the jump height optimization were used for this purpose and root mean square (RMS) difference between surrogate and FE model outputs (ankle force and moment, peak contact pressure and peak von Mises stress) were calculated. Optimization of the jump height required 1800 iterations of the movement simulation, each requiring thousands of time steps. The surrogate modeling system only used the FE model in 5% of time steps, i.e., a 95% reduction in computation time. Errors introduced by the surrogate model were less than 1 mm in jump height and RMS errors of less than 2 N in ground reaction force, 0.25 Nm in ankle moment, and 10 kPa in peak tissue stress. Adaptive surrogate modeling based on local regression allows efficient concurrent simulations of tissue mechanics and musculoskeletal movement.

An Elaborate Data Set Characterizing the Mechanical Response of the Foot

Mechanical properties of the foot are responsible for its normal function and play a role in various clinical problems. Specifically, we are interested in quantification of foot mechanical properties to assist the development of computational models for movement analysis and detailed simulations of tissue deformation. Current available data are specific to a foot region and the loading scenarios are limited to a single direction. A data set that incorporates regional response, to quantify individual function of foot components, as well as the overall response, to illustrate their combined operation, does not exist. Furthermore, the combined three-dimensional loading scenarios while measuring the complete three-dimensional deformation response are lacking. When combined with an anatomical image data set, development of anatomically realistic and mechanically validated models becomes possible. Therefore, the goal of this study was to record and disseminate the mechanical response of a foot specimen, supported by imaging data. Robotic testing was conducted at the rear foot, forefoot, metatarsal heads, and the foot as a whole. Complex foot deformations were induced by single mode loading, e.g., compression, and combined loading, e.g., compression and shear. Small and large indenters were used for heel and metatarsal head loading, an elevated platform was utilized to isolate the rear foot and forefoot, and a full platform compressed the whole foot. Three-dimensional tool movements and reaction loads were recorded simultaneously. Computed tomography scans of the same specimen were collected for anatomical reconstruction a priori. The three-dimensional mechanical response of the specimen was nonlinear and viscoelastic. A low stiffness region was observed starting with contact between the tool and foot regions, increasing with loading. Loading and unloading responses portrayed hysteresis. Loading range ensured capturing the toe and linear regions of the load deformation curves for the dominant loading direction, with the rates approximating those of walking. A large data set was successfully obtained to characterize the overall and the regional mechanical responses of an intact foot specimen under single and combined loads. Medical imaging complemented the mechanical testing data to establish the potential relationship between the anatomical architecture and mechanical responses and to further develop foot models that are mechanically realistic and anatomically consistent. This combined data set has been documented and disseminated in the public domain to promote future development in foot biomechanics.

A general framework for application of prestrain to computational models of biological materials

It is often important to include prestress in computational models of biological tissues. The prestress can represent residual stresses (stresses that exist after the tissue is excised from the body) or in situ stresses (stresses that exist in vivo, in the absence of loading). A prestressed reference configuration may also be needed when modeling the reference geometry of biological tissues in vivo. This research developed a general framework for representing prestress in finite element models of biological materials. It is assumed that the material is elastic, allowing the prestress to be represented via a prestrain. For prestrain fields that are not compatible with the reference geometry, the computational framework provides an iterative algorithm for updating the prestrain until equilibrium is satisfied. The iterative framework allows for enforcement of two different constraints: elimination of distortion in order to address the incompatibility issue, and enforcing a specified in situ fiber strain field while allowing for distortion. The framework was implemented as a plugin in FEBio (www.febio.org), making it easy to maintain the software and to extend the framework if needed. Several examples illustrate the application and effectiveness of the approach, including the application of in situ strains to ligaments in the Open Knee model (simtk.org/home/openknee). A novel method for recovering the stress-free configuration from the prestrain deformation gradient is also presented. This general purpose theoretical and computational framework for applying prestrain will allow analysts to overcome the challenges in modeling this important aspect of biological tissue mechanics.

Evaluation of a post-processing approach for multiscale analysis of biphasic mechanics of chondrocytes.

Understanding the mechanical behaviour of chondrocytes as a result of cartilage tissue mechanics has significant implications for both evaluation of mechanobiological function and to elaborate on damage mechanisms. A common procedure for prediction of chondrocyte mechanics (and of cell mechanics in general) relies on a computational post-processing approach where tissue-level deformations drive cell-level models. Potential loss of information in this numerical coupling approach may cause erroneous cellular-scale results, particularly during multiphysics analysis of cartilage. The goal of this study was to evaluate the capacity of first- and second-order data passing to predict chondrocyte mechanics by analysing cartilage deformations obtained for varying complexity of loading scenarios. A tissue-scale model with a sub-region incorporating representation of chondron size and distribution served as control. The post-processing approach first required solution of a homogeneous tissue-level model, results of which were used to drive a separate cell-level model (same characteristics as the sub-region of control model). The first-order data passing appeared to be adequate for simplified loading of the cartilage and for a subset of cell deformation metrics, for example, change in aspect ratio. The second-order data passing scheme was more accurate, particularly when asymmetric permeability of the tissue boundaries was considered. Yet, the method exhibited limitations for predictions of instantaneous metrics related to the fluid phase, for example, mass exchange rate. Nonetheless, employing higher order data exchange schemes may be necessary to understand the biphasic mechanics of cells under lifelike tissue loading states for the whole time history of the simulation.

Evaluation of a post-processing approach for multiscale analysis of biphasic mechanics of chondrocytes, DOI: 10.1080/10255842.2013.809711

Evaluation of a post-processing approach for multiscale analysis of biphasic mechanics of chondrocytes, DOI: 10.1080/10255842.2013.809711 Scott C. Sibole, Steve Maas, Jason P. Halloran, Jeffrey A. Weiss and Ahmet Erdemir* Computational Biomodeling (CoBi) Core, Lerner Research Institute, Cleveland Clinic, Cleveland, OH, USA; Department of Biomedical Engineering, Lerner Research Institute, Cleveland Clinic, Cleveland, OH, USA; Department of Bioengineering, University of Utah, Salt Lake City, UT, USA; Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT, USA; Department of Orthopaedics, University of Utah, Salt Lake City, UT, USA

The potential for intercellular mechanical interaction: Simulations of single chondrocyte versus anatomically based distribution

Computational studies of chondrocyte mechanics, and cell mechanics in general, have typically been performed using single cell models embedded in an extracellular matrix construct. The assumption of a single cell microstructural model may not capture intercellular interactions or accurately reflect the macroscale mechanics of cartilage when higher cell concentrations are considered, as may be the case in many instances. Hence, the goal of this study was to compare cell-level response of single and eleven cell biphasic finite element models, where the latter provided an anatomically based cellular distribution representative of the actual number of cells for a commonly used