Evaluation of mesh morphing and mapping techniques in patient specific modelling of the human pelvis

The Impact of an Open-Book Pelvic Ring Injury on Bone Strain: Validation of a Finite Element Model and Analysis Within the Gait Cycle

The threshold for surgical stabilization for an open-book pelvic fracture is not well defined. The purpose of this research was to validate the biomechanical behavior of a specimen-specific pelvic finite element (FE) model with an open-book fracture with the biomechanical behavior of a cadaveric pelvis in double leg stance configuration under physiologic loading, and to utilize the validated model to compare open book versus intact strain patterns during gait. A cadaveric pelvis was experimentally tested under compressive loading in double leg stance, intact, and with a simulated open-book fracture. An intact FE model of this specimen was reanalyzed with an equivalent simulated open-book fracture. Comparison of the FE generated and experimentally measured strains yielded an R2 value of 0.92 for the open-book fracture configuration. Strain patterns in the intact and fractured models were compared throughout the gait cycle. In double leg stance and heel-strike/heel-off models, tensile strains decreased, especially in the pubic ramus contralateral to the injury, and compressive strains increased in the sacroiliac region of the injured side. In the midstance/midswing gait configuration, higher tensile and compressive FE strains were observed on the midstance side of the fractured versus intact model and decreased along the superior and inferior pubic rami and ischium, with midswing side strains reduced almost to zero in the fractured model. Identified in silico patterns align with clinical understanding of open-book fracture pathology suggesting future potential of FE models to quantify instability and optimize fixation strategies.

Influence of pelvic shape on strain patterns: A computational analysis using finite element mesh morphing techniques

The pelvis functions to transmit upper body loads to the lower limbs and is critical in human locomotion. Semi-automated, finite element (FE) morphing techniques eliminate the need for segmentation and have shown to accelerate the generation of multiple specimen-specific pelvic FE models to enable the study of pelvic mechanical behaviour. The purpose of this research was to produce simulated human pelvic FE models representing android, gynecoid, anthropoid and platypelloid morphologies and to isolate differences in strain patterns due to anatomic shape under physiologic loading. Using five initially generated specimen-specific FE models, each specimen-specific FE model was reconfigured into three different morphologies using FE mesh morphing techniques. Significantly different strains were found comparing the gynecoid (classical female pelvis') to the android ('true male pelvis') models (p = 0.040), with strains twice as high in the superior pubic rami. No significant differences were seen in comparing overall strains between the other pelvic shapes (p = 0.61-0.126). The highest strain regions in all models were found in the supra-acetabular regions, with high strains also found in the regions of the superior pubic rami, the greater sciatic notch and sacral regions about the L5 vertebrae. Quantifying the contributions of shape to strain in the pelvis may increase the understanding of sex and patient-specific differences in fracture risk and motivate the consideration of treatment strategies that account for anatomic pelvic differences.

A Cortical Thickness Mapping Method for the Coxal Bone Using Morphing

As human body finite element models become more integrated with the design of safety countermeasures and regulations, novel models need to be developed that reflect the variation in the population's anthropometry. However, these new models may be missing information which will need to be translated from existing models. During the development of a 5th percentile female occupant model (F05), cortical thickness information of the coxal bone was unavailable due to resolution limits in the computed tomography (CT) scans. In this study, a method for transferring cortical thickness information from a source to a target model with entirely different geometry and architecture is presented. The source and target models were the Global Human Body Models Consortium (GHBMC) 50th percentile male (M50) and F05 coxal bones, respectively. To project the coxal bone cortical thickness from the M50 to the F05, the M50 model was first morphed using a Kriging method with 132 optimized control points to the F05 anthropometry. This technique was found to be accurate with a mean nodal discrepancy of 1.27 mm between the F05 and morphed M50 (mM50) coxal bones. Cortical thickness at each F05 node was determined by taking the average cortical thickness of every mM50 node, non-linearly weighted by its distance to the F05 nodes. The non-linear weighting coefficient, β, had a large effect on the accuracy and smoothness of the projected cortical bone thickness. The optimal projection had β = 4 and was defined when the tradeoff between projection accuracy and smoothness was equal. Finally, a quasi-static pelvis compression was simulated to examine to effect of β. As β, increased from 0 to 4, the failure force decreased by ~100 N, whereas the failure displacement increased by 0.9 mm. Results from quasi-static compression tests of the F05 pelvis were comparable to experimental results. This method could be applied to other anatomical regions where cortical thickness variation is important, such as the femur and ribs and is not limited to GHBMC-family models. Furthermore, this process will aid the development of subject-specific finite element models where accurate cortical bone thickness measurements cannot be obtained.

Patient-specific anisotropic model of human trunk based on MR data

There are many ways to generate geometrical models for numerical simulation, and most of them start with a segmentation step to extract the boundaries of the regions of interest. This paper presents an algorithm to generate a patient-specific three-dimensional geometric model, based on a tetrahedral mesh, without an initial extraction of contours from the volumetric data. Using the information directly available in the data, such as gray levels, we built a metric to drive a mesh adaptation process. The metric is used to specify the size and orientation of the tetrahedral elements everywhere in the mesh. Our method, which produces anisotropic meshes, gives good results with synthetic and real MRI data. The resulting model quality has been evaluated qualitatively and quantitatively by comparing it with an analytical solution and with a segmentation made by an expert. Results show that our method gives, in 90% of the cases, as good or better meshes as a similar isotropic method, based on the accuracy of the volume reconstruction for a given mesh size. Moreover, a comparison of the Hausdorff distances between adapted meshes of both methods and ground-truth volumes shows that our method decreases reconstruction errors faster.

Multiscale geometric modeling of macromolecules II: Lagrangian representation

Geometric modeling of biomolecules plays an essential role in the conceptualization of biolmolecular structure, function, dynamics, and transport. Qualitatively, geometric modeling offers a basis for molecular visualization, which is crucial for the understanding of molecular structure and interactions. Quantitatively, geometric modeling bridges the gap between molecular information, such as that from X-ray, NMR, and cryo-electron microscopy, and theoretical/mathematical models, such as molecular dynamics, the Poisson-Boltzmann equation, and the Nernst-Planck equation. In this work, we present a family of variational multiscale geometric models for macromolecular systems. Our models are able to combine multiresolution geometric modeling with multiscale electrostatic modeling in a unified variational framework. We discuss a suite of techniques for molecular surface generation, molecular surface meshing, molecular volumetric meshing, and the estimation of Hadwiger's functionals. Emphasis is given to the multiresolution representations of biomolecules and the associated multiscale electrostatic analyses as well as multiresolution curvature characterizations. The resulting fine resolution representations of a biomolecular system enable the detailed analysis of solvent-solute interaction, and ion channel dynamics, whereas our coarse resolution representations highlight the compatibility of protein-ligand bindings and possibility of protein-protein interactions.

Geometric modeling of subcellular structures, organelles, and multiprotein complexes

Recently, the structure, function, stability, and dynamics of subcellular structures, organelles, and multiprotein complexes have emerged as a leading interest in structural biology. Geometric modeling not only provides visualizations of shapes for large biomolecular complexes but also fills the gap between structural information and theoretical modeling, and enables the understanding of function, stability, and dynamics. This paper introduces a suite of computational tools for volumetric data processing, information extraction, surface mesh rendering, geometric measurement, and curvature estimation of biomolecular complexes. Particular emphasis is given to the modeling of cryo-electron microscopy data. Lagrangian-triangle meshes are employed for the surface presentation. On the basis of this representation, algorithms are developed for surface area and surface-enclosed volume calculation, and curvature estimation. Methods for volumetric meshing have also been presented. Because the technological development in computer science and mathematics has led to multiple choices at each stage of the geometric modeling, we discuss the rationales in the design and selection of various algorithms. Analytical models are designed to test the computational accuracy and convergence of proposed algorithms. Finally, we select a set of six cryo-electron microscopy data representing typical subcellular complexes to demonstrate the efficacy of the proposed algorithms in handling biomolecular surfaces and explore their capability of geometric characterization of binding targets. This paper offers a comprehensive protocol for the geometric modeling of subcellular structures, organelles, and multiprotein complexes.