Multiscale modeling in computational biomechanics

Computationally efficient model to predict the deformations of a cellular foot orthotic

BACKGROUND

Foot orthotics (FOs) are frequently prescribed to provide comfortable walking for patients. Finite element (FE) simulation and 3D printing pave the way to analyse, optimize and fabricate functionally graded lattice FOs where the local stiffness can vary to meet the therapeutic needs of each individual patient. Explicit FE modelling of lattice FOs with converged 3D solid elements is computationally prohibitive. This paper presents a more computationally efficient FE model of cellular FOs.

METHOD

The presented FE model features shell elements whose mechanical properties were computed from the numerical homogenization technique. To verify the results, the predictions of the homogenized models were compared to the explicit model's predictions when the FO was under a static pressure distribution of a foot. To validate the results, the predictions were also compared with experimental measurements when the FO was under a vertical displacement at the medial longitudinal arch.

RESULTS

The verification procedure showed that the homogenized model was 46 times faster than the explicit model, while their relative difference was less than 8% to predict the local minimum of out-of-plane displacement. The validation procedure showed that both models predicted the same contact force with a relative difference of less than 1%. The predicted force-displacement curves were also within a 90% confidence interval of the experimental measurements having a relative difference smaller than 10%. In this case, using the homogenized model reduced the computational time from 22 h to 22 min.

CONCLUSION

The presented homogenized model can be therefore employed to speed up the FE simulation to predict the deformations of the cellular FOs.

A multiscale optimization framework for reconstructing binary images using multilevel PCA-based control space reduction

An efficient computational approach for optimal reconstructing parameters of binary-type physical properties for models in biomedical applications is developed and validated. The methodology includes gradient-based multiscale optimization with multilevel control space reduction by using principal component analysis (PCA) coupled with dynamical control space upscaling. The reduced dimensional controls are used interchangeably at fine and coarse scales to accumulate the optimization progress and mitigate side effects at both scales. Flexibility is achieved through the proposed procedure for calibrating certain parameters to enhance the performance of the optimization algorithm. Reduced size of control spaces supplied with adjoint-based gradients obtained at both scales facilitate the application of this algorithm to models of higher complexity and also to a broad range of problems in biomedical sciences. This technique is shown to outperform regular gradient-based methods applied to fine scale only in terms of both qualities of binary images and computing time. Performance of the complete computational framework is tested in applications to 2D inverse problems of cancer detection by the electrical impedance tomography (EIT). The results demonstrate the efficient performance of the new method and its high potential for minimizing possibilities for false positive screening and improving the overall quality of the EIT-based procedures.

A computationally efficient strategy to estimate muscle forces in a finite element musculoskeletal model of the lower limb

Concurrent multiscale simulation strategies are required in computational biomechanics to study the interdependence between body scales. However, detailed finite element models rarely include muscle recruitment due to the computational burden of both the finite element method and the optimization strategies widely used to estimate muscle forces. The aim of this study was twofold: first, to develop a computationally efficient muscle force prediction strategy based on proportional-integral-derivative (PID) controllers to track gait and chair rise experimental joint motion with a finite element musculoskeletal model of the lower limb, including a deformable knee representation with 12 degrees of freedom; and, second, to demonstrate that the inclusion of joint-level deformability affects muscle force estimation by using two different knee models and comparing muscle forces between the two solutions. The PID control strategy tracked experimental hip, knee, and ankle flexion/extension with root mean square errors below 1°, and estimated muscle, contact and ligament forces in good agreement with previous results and electromyography signals. Differences up to 11% and 20% in the vasti and biceps femoris forces, respectively, were observed between the two knee models, which might be attributed to a combination of differing joint contact geometry, ligament behavior, joint kinematics, and muscle moment arms. The tracking strategy developed in this study addressed the inevitable tradeoff between computational cost and model detail in musculoskeletal simulations and can be used with finite element musculoskeletal models to efficiently estimate the interdependence between muscle forces and tissue deformation.

A subject-specific integrative biomechanical framework of the pelvis for gait analysis

Analysis of the human locomotor system using rigid-body musculoskeletal models has increased in the biomechanical community with the objective of studying muscle activations of different movements. Simultaneously, the finite element method has emerged as a complementary approach for analyzing the mechanical behavior of tissues. This study presents an integrative biomechanical framework for gait analysis by linking a musculoskeletal model and a subject-specific finite element model of the pelvis. To investigate its performance, a convergence study was performed and its sensitivity to the use of non-subject-specific material properties was studied. The total hip joint force estimated by the rigid musculoskeletal model and by the finite element model showed good agreement, suggesting that the integrative approach estimates adequately (in shape and magnitude) the hip total contact force. Previous studies found movements of up to 1.4 mm in the anterior-posterior direction, for single leg stance. These results are comparable with the displacement values found in this study: 0-0.5 mm in the sagittal axis. Maximum von Mises stress values of approximately 17 MPa were found in the pelvic bone. Comparing this results with a previous study of our group, the new findings show that the introduction of muscular boundary conditions and the flexion-extension movement of the hip reduce the regions of high stress and distributes more uniformly the stress across the pelvic bone. Thus, it is thought that muscle force has a relevant impact in reducing stresses in pelvic bone during walking of the finite element model proposed in this study. Future work will focus on including other deformable structures, such as the femur and the tibia, and subject-specific material properties.

Understanding the Basics of Computational Models in Orthopaedics: A Nonnumeric Review for Surgeons

Computational models represent more than just finite element analysis, a term that many clinicians may know and globally apply. Over the past 30 years, many published studies have addressed clinically relevant orthopaedic questions with speed and precision by using a wide variety of computational approaches. Given such a wide spectrum of techniques, clinicians often do not have a full understanding of the methods used to create models and therefore do not appreciate the strengths, weaknesses, and potential pitfalls of published results. The short, nonnumeric summaries of the methodologies employed for various computational approaches presented here can help address this issue.

Application of neural networks for the prediction of cartilage stress in a musculoskeletal system

Traditional finite element (FE) analysis is computationally demanding. The computational time becomes prohibitively long when multiple loading and boundary conditions need to be considered such as in musculoskeletal movement simulations involving multiple joints and muscles. Presented in this study is an innovative approach that takes advantage of the computational efficiency of both the dynamic multibody (MB) method and neural network (NN) analysis. A NN model that captures the behavior of musculoskeletal tissue subjected to known loading situations is built, trained, and validated based on both MB and FE simulation data. It is found that nonlinear, dynamic NNs yield better predictions over their linear, static counterparts. The developed NN model is then capable of predicting stress values at regions of interest within the musculoskeletal system in only a fraction of the time required by FE simulation.

An efficient algorithm for mapping imaging data to 3D unstructured grids in computational biomechanics

Geometries for organ scale and multiscale simulations of organ function are now routinely derived from imaging data. However, medical images may also contain spatially heterogeneous information other than geometry that are relevant to such simulations either as initial conditions or in the form of model parameters. In this manuscript, we present an algorithm for the efficient and robust mapping of such data to imaging-based unstructured polyhedral grids in parallel. We then illustrate the application of our mapping algorithm to three different mapping problems: (i) the mapping of MRI diffusion tensor data to an unstructured ventricular grid; (ii) the mapping of serial cyrosection histology data to an unstructured mouse brain grid; and (iii) the mapping of computed tomography-derived volumetric strain data to an unstructured multiscale lung grid. Execution times and parallel performance are reported for each case.

Comparative computational modeling of airflows and vapor dosimetry in the respiratory tracts of rat, monkey, and human

Computational fluid dynamics (CFD) models are useful for predicting site-specific dosimetry of airborne materials in the respiratory tract and elucidating the importance of species differences in anatomy, physiology, and breathing patterns. We improved the imaging and model development methods to the point where CFD models for the rat, monkey, and human now encompass airways from the nose or mouth to the lung. A total of 1272, 2172, and 135 pulmonary airways representing 17±7, 19±9, or 9±2 airway generations were included in the rat, monkey and human models, respectively. A CFD/physiologically based pharmacokinetic model previously developed for acrolein was adapted for these anatomically correct extended airway models. Model parameters were obtained from the literature or measured directly. Airflow and acrolein uptake patterns were determined under steady-state inhalation conditions to provide direct comparisons with prior data and nasal-only simulations. Results confirmed that regional uptake was sensitive to airway geometry, airflow rates, acrolein concentrations, air:tissue partition coefficients, tissue thickness, and the maximum rate of metabolism. Nasal extraction efficiencies were predicted to be greatest in the rat, followed by the monkey, and then the human. For both nasal and oral breathing modes in humans, higher uptake rates were predicted for lower tracheobronchial tissues than either the rat or monkey. These extended airway models provide a unique foundation for comparing material transport and site-specific tissue uptake across a significantly greater range of conducting airways in the rat, monkey, and human than prior CFD models.

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 model's 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.

A data-driven surrogate model to connect scales between multi-domain biomechanics simulations

A data driven surrogate was developed to bridge the gap between finite element and multibody modeling and to expand the information available from a rigid multibody cartilage simulation. An indentation experiment performed on canine stifle cartilage was modeled in both paradigms with acceptable accuracy and the data were used to create the surrogate. Neural networks were found to adequately approximate the von Mises stress calculated by the finite element model based on force values provided from the multibody model with a correlation coefficient over 0.96.