The mesh-matching algorithm: an automatic 3D mesh generator for finite element structures

Subject-Specific Head Model Generation by Mesh Morphing: A Personalization Framework and Its Applications

Finite element (FE) head models have become powerful tools in many fields within neuroscience, especially for studying the biomechanics of traumatic brain injury (TBI). Subject-specific head models accounting for geometric variations among subjects are needed for more reliable predictions. However, the generation of such models suitable for studying TBIs remains a significant challenge and has been a bottleneck hindering personalized simulations. This study presents a personalization framework for generating subject-specific models across the lifespan and for pathological brains with significant anatomical changes by morphing a baseline model. The framework consists of hierarchical multiple feature and multimodality imaging registrations, mesh morphing, and mesh grouping, which is shown to be efficient with a heterogeneous dataset including a newborn, 1-year-old (1Y), 2Y, adult, 92Y, and a hydrocephalus brain. The generated models of the six subjects show competitive personalization accuracy, demonstrating the capacity of the framework for generating subject-specific models with significant anatomical differences. The family of the generated head models allows studying age-dependent and groupwise brain injury mechanisms. The framework for efficient generation of subject-specific FE head models helps to facilitate personalized simulations in many fields of neuroscience.

An anatomically detailed and personalizable head injury model: Significance of brain and white matter tract morphological variability on strain

Finite element head (FE) models are important numerical tools to study head injuries and develop protection systems. The generation of anatomically accurate and subject-specific head models with conforming hexahedral meshes remains a significant challenge. The focus of this study is to present two developmental works: first, an anatomically detailed FE head model with conforming hexahedral meshes that has smooth interfaces between the brain and the cerebrospinal fluid, embedded with white matter (WM) fiber tracts; second, a morphing approach for subject-specific head model generation via a new hierarchical image registration pipeline integrating Demons and Dramms deformable registration algorithms. The performance of the head model is evaluated by comparing model predictions with experimental data of brain-skull relative motion, brain strain, and intracranial pressure. To demonstrate the applicability of the head model and the pipeline, six subject-specific head models of largely varying intracranial volume and shape are generated, incorporated with subject-specific WM fiber tracts. DICE similarity coefficients for cranial, brain mask, local brain regions, and lateral ventricles are calculated to evaluate personalization accuracy, demonstrating the efficiency of the pipeline in generating detailed subject-specific head models achieving satisfactory element quality without further mesh repairing. The six head models are then subjected to the same concussive loading to study the sensitivity of brain strain to inter-subject variability of the brain and WM fiber morphology. The simulation results show significant differences in maximum principal strain and axonal strain in local brain regions (one-way ANOVA test, p < 0.001), as well as their locations also vary among the subjects, demonstrating the need to further investigate the significance of subject-specific models. The techniques developed in this study may contribute to better evaluation of individual brain injury and the development of individualized head protection systems in the future. This study also contains general aspects the research community may find useful: on the use of experimental brain strain close to or at injury level for head model validation; the hierarchical image registration pipeline can be used to morph other head models, such as smoothed-voxel models.

Personalized biomechanical tongue models based on diffusion-weighted MRI and validated using optical tracking of range of motion

For advanced tongue cancer, the choice between surgery and organ-sparing treatment is often dependent on the expected loss of tongue functionality after treatment. Biomechanical models might assist in this choice by simulating the post-treatment function loss. However, this function loss varies between patients and should, therefore, be predicted for each patient individually. In the present study, the goal was to better predict the postoperative range of motion (ROM) of the tongue by personalizing biomechanical models using diffusion-weighted MRI and constrained spherical deconvolution reconstructions of tongue muscle architecture. Diffusion-weighted MRI scans of ten healthy volunteers were obtained to reconstruct their tongue musculature, which were subsequently registered to a previously described population average or atlas. Using the displacement fields obtained from the registration, the segmented muscle fiber tracks from the atlas were morphed back to create personalized muscle fiber tracks. Finite element models were created from the fiber tracks of the atlas and those of the individual tongues. Via inverse simulation of a protruding, downward, left and right movement, the ROM of the tongue was predicted. This prediction was compared to the ROM measured with a 3D camera. It was demonstrated that biomechanical models with personalized muscles bundles are better in approaching the measured ROM than a generic model. However, to achieve this result a correction factor was needed to compensate for the small magnitude of motion of the model. Future versions of these models may have the potential to improve the estimation of function loss after treatment for advanced tongue cancer.

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.

An anatomically detailed and personalizable head injury model: Significance of brain and white matter tract morphological variability on strain

Finite element head (FE) models are important numerical tools to study head injuries and develop protection systems. The generation of anatomically accurate and subject-specific head models with conforming hexahedral meshes remains a significant challenge. The focus of this study is to present two developmental works: first, an anatomically detailed FE head model with conforming hexahedral meshes that has smooth interfaces between the brain and the cerebrospinal fluid, embedded with white matter (WM) fiber tracts; second, a morphing approach for subject-specific head model generation via a new hierarchical image registration pipeline integrating Demons and Dramms deformable registration algorithms. The performance of the head model is evaluated by comparing model predictions with experimental data of brain-skull relative motion, brain strain, and intracranial pressure. To demonstrate the applicability of the head model and the pipeline, six subject-specific head models of largely varying intracranial volume and shape are generated, incorporated with subject-specific WM fiber tracts. DICE similarity coefficients for cranial, brain mask, local brain regions, and lateral ventricles are calculated to evaluate personalization accuracy, demonstrating the efficiency of the pipeline in generating detailed subject-specific head models achieving satisfactory element quality without further mesh repairing. The six head models are then subjected to the same concussive loading to study the sensitivity of brain strain to inter-subject variability of the brain and WM fiber morphology. The simulation results show significant differences in maximum principal strain and axonal strain in local brain regions (one-way ANOVA test, p < 0.001), as well as their locations also vary among the subjects, demonstrating the need to further investigate the significance of subject-specific models. The techniques developed in this study may contribute to better evaluation of individual brain injury and the development of individualized head protection systems in the future. This study also contains general aspects the research community may find useful: on the use of experimental brain strain close to or at injury level for head model validation; the hierarchical image registration pipeline can be used to morph other head models, such as smoothed-voxel models.

Biomechanical modeling and computer simulation of the brain during neurosurgery

Computational biomechanics of the brain for neurosurgery is an emerging area of research recently gaining in importance and practical applications. This review paper presents the contributions of the Intelligent Systems for Medicine Laboratory and its collaborators to this field, discussing the modeling approaches adopted and the methods developed for obtaining the numerical solutions. We adopt a physics-based modeling approach and describe the brain deformation in mechanical terms (such as displacements, strains, and stresses), which can be computed using a biomechanical model, by solving a continuum mechanics problem. We present our modeling approaches related to geometry creation, boundary conditions, loading, and material properties. From the point of view of solution methods, we advocate the use of fully nonlinear modeling approaches, capable of capturing very large deformations and nonlinear material behavior. We discuss finite element and meshless domain discretization, the use of the total Lagrangian formulation of continuum mechanics, and explicit time integration for solving both time-accurate and steady-state problems. We present the methods developed for handling contacts and for warping 3D medical images using the results of our simulations. We present two examples to showcase these methods: brain shift estimation for image registration and brain deformation computation for neuronavigation in epilepsy treatment.

Development and validation of a semi-automatic landmark extraction method for mesh morphing

Currently, landmark-based mesh morphing technology is widely used to rapidly obtain meshes with specific geometry, which is suitable to develop parametric human finite element (FE) models. However it takes too much time for landmark extraction to obtain high geometric accuracy. The purpose of this study is to develop and validate a semi-automatic landmark extraction method to reduce the time of manual selection of landmarks without sacrificing the accuracy of identifying landmarks in the process of mesh morphing. A few contour edge landmarks were extracted manually. Mathematical landmarks and pseudo-landmarks were extracted automatically by user-defined algorithm. The radial basis function (RBF) was used to morph the baseline FE model into the target geometry based on these landmarks. The cervical vertebra (C5), rib (R7) and femur were selected as the target geometries to verify the effectiveness of the method. The maximum mean geometric error of the three types of target geometries was less than 1 mm. The mesh quality of the morphed FE model was similar to that of the baseline FE model. Compared to the traditional manual method, 2/3 to 3/4 of the time for landmark extraction was saved by the semi-automatic method.

Morphing the feature-based multi-blocks of normative/healthy vertebral geometries to scoliosis vertebral geometries: development of personalized finite element models

Personalized Finite Element (FE) models and hexahedral elements are preferred for biomechanical investigations. Feature-based multi-block methods are used to develop anatomically accurate personalized FE models with hexahedral mesh. It is tedious to manually construct multi-blocks for large number of geometries on an individual basis to develop personalized FE models. Mesh-morphing method mitigates the aforementioned tediousness in meshing personalized geometries every time, but leads to element warping and loss of geometrical data. Such issues increase in magnitude when normative spine FE model is morphed to scoliosis-affected spinal geometry. The only way to bypass the issue of hex-mesh distortion or loss of geometry as a result of morphing is to rely on manually constructing the multi-blocks for scoliosis-affected spine geometry of each individual, which is time intensive. A method to semi-automate the construction of multi-blocks on the geometry of scoliosis vertebrae from the existing multi-blocks of normative vertebrae is demonstrated in this paper. High-quality hexahedral elements were generated on the scoliosis vertebrae from the morphed multi-blocks of normative vertebrae. Time taken was 3 months to construct the multi-blocks for normative spine and less than a day for scoliosis. Efforts taken to construct multi-blocks on personalized scoliosis spinal geometries are significantly reduced by morphing existing multi-blocks.

A Centerline-Based Model Morphing Algorithm for Patient-Specific Finite Element Modeling of the Left Ventricle

GOAL

Hexahedral automatic model generation is a recurrent problem in computer vision and computational biomechanics. It may even become a challenging problem when one wants to develop a patient-specific finite element (FE) model of the left ventricle (LV), particularly when only low resolution images are available. In the present study, a fast and efficient algorithm is presented and tested to address such a situation.

METHODS

A template FE hexahedral model was created for an LV geometry using a general electric ultrasound (US) system. A system of centerline was considered for this LV mesh. Then, the nodes located over the endocardial and epicardial surfaces are, respectively, projected from this centerline onto the actual endocardial and epicardial surfaces reconstructed from a patient's US data. Finally, the position of the internal nodes is derived by finding the deformations with minimal elastic energy. This approach was applied to eight patients suffering from congestive heart disease. An FE analysis was performed to derive the stress induced in the LV tissue by diastolic blood pressure on each of them.

RESULTS

Our model morphing algorithm was applied successfully and the obtained meshes showed only marginal mismatches when compared to the corresponding US geometries. The diastolic FE analyses were successfully performed in seven patients to derive the distribution of principal stresses.

CONCLUSION

The original model morphing algorithm is fast and robust with low computational cost.

SIGNIFICANCE

This low-cost model morphing algorithm may be highly beneficial for future patient-specific reduced-order modeling of the LV with potential application to other crucial organs.

Atlas-Based Automatic Generation of Subject-Specific Finite Element Tongue Meshes

Generation of subject-specific 3D finite element (FE) models requires the processing of numerous medical images in order to precisely extract geometrical information about subject-specific anatomy. This processing remains extremely challenging. To overcome this difficulty, we present an automatic atlas-based method that generates subject-specific FE meshes via a 3D registration guided by Magnetic Resonance images. The method extracts a 3D transformation by registering the atlas' volume image to the subject's one, and establishes a one-to-one correspondence between the two volumes. The 3D transformation field deforms the atlas' mesh to generate the subject-specific FE mesh. To preserve the quality of the subject-specific mesh, a diffeomorphic non-rigid registration based on B-spline free-form deformations is used, which guarantees a non-folding and one-to-one transformation. Two evaluations of the method are provided. First, a publicly available CT-database is used to assess the capability to accurately capture the complexity of each subject-specific Lung's geometry. Second, FE tongue meshes are generated for two healthy volunteers and two patients suffering from tongue cancer using MR images. It is shown that the method generates an appropriate representation of the subject-specific geometry while preserving the quality of the FE meshes for subsequent FE analysis. To demonstrate the importance of our method in a clinical context, a subject-specific mesh is used to simulate tongue's biomechanical response to the activation of an important tongue muscle, before and after cancer surgery.

A statistical human rib cage geometry model accounting for variations by age, sex, stature and body mass index

In this study, we developed a statistical rib cage geometry model accounting for variations by age, sex, stature and body mass index (BMI). Thorax CT scans were obtained from 89 subjects approximately evenly distributed among 8 age groups and both sexes. Threshold-based CT image segmentation was performed to extract the rib geometries, and a total of 464 landmarks on the left side of each subject׳s ribcage were collected to describe the size and shape of the rib cage as well as the cross-sectional geometry of each rib. Principal component analysis and multivariate regression analysis were conducted to predict rib cage geometry as a function of age, sex, stature, and BMI, all of which showed strong effects on rib cage geometry. Except for BMI, all parameters also showed significant effects on rib cross-sectional area using a linear mixed model. This statistical rib cage geometry model can serve as a geometric basis for developing a parametric human thorax finite element model for quantifying effects from different human attributes on thoracic injury risks.

Accounting for patient variability in finite element analysis of the intact and implanted hip and knee: a review

It is becoming increasingly difficult to differentiate the performance of new joint replacement designs using available preclinical test methods. Finite element analysis is commonly used and the majority of published studies are performed on representative anatomy, assuming optimal implant placement, subjected to idealised loading conditions. There are significant differences between patients and accounting for this variability will lead to better assessment of the risk of failure. This review paper provides a comprehensive overview of the techniques available to account for patient variability. There is a brief overview of patient-specific model generation techniques, followed by a review of multisubject patient-specific studies performed on the intact and implanted femur and tibia. In particular, the challenges and limitations of manually generating models for such studies are discussed. To efficiently account for patient variability, the application of statistical shape and intensity models (SSIM) are being developed. Such models have the potential to synthetically generate thousands of representative models generated from a much smaller training set. Combined with the automation of the prosthesis implantation process, SSIM provides a potentially powerful tool for assessing the next generation of implant designs. The potential application of SSIM are discussed along with their limitations.

Quality metrics for high order meshes: analysis of the mechanical simulation of the heart beat

The quality of a computational mesh is an important characteristic for stable and accurate simulations. Quality depends on the regularity of the initial mesh, and in mechanical simulations it evolves in time, with deformations causing changes in volume and distortion of mesh elements. Mesh quality metrics are therefore relevant for both mesh personalization and the monitoring of the simulation process. This work evaluates the significance, in meshes with high order interpolation, of four quality metrics described in the literature, applying them to analyse the stability of the simulation of the heart beat. It also investigates how image registration and mesh warping parameters affect the quality and stability of meshes. Jacobian-based metrics outperformed or matched the results of coarse geometrical metrics of aspect ratio or orthogonality, although they are more expensive computationally. The stability of simulations of a complete heart cycle was best predicted with a specificity of 61%, sensitivity of 85%, and only nominal differences were found changing the intra-element and per-element combination of quality values. A compromise between fitting accuracy and mesh stability and quality was found. Generic geometrical quality metrics have a limited success predicting stability, and an analysis of the simulation problem may be required for an optimal definition of quality.

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

Robust generation of pelvic finite element models is necessary to understand the variation in mechanical behaviour resulting from differences in gender, aging, disease and injury. The objective of this study was to apply and evaluate mesh morphing and mapping techniques to facilitate the creation and structural analysis of specimen-specific finite element (FE) models of the pelvis. A specimen-specific pelvic FE model (source mesh) was generated following a traditional user-intensive meshing scheme. The source mesh was morphed onto a computed tomography scan generated target surface of a second pelvis using a landmarked-based approach, in which exterior source nodes were shifted to target surface vertices, while constrained along a normal. A second copy of the morphed model was further refined through mesh mapping, in which surface nodes of the initial morphed model were selected in patches and remapped onto the surfaces of the target model. Computed tomography intensity based material properties were assigned to each model. The source, target, morphed and mapped models were analyzed under axial compression using linear static FE analysis and their strain distributions evaluated. Morphing and mapping techniques were effectively applied to generate good quality geometrically complex specimen-specific pelvic FE models. Mapping significantly improved strain concurrence with the target pelvis FE model.

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

Robust generation of pelvic finite element models is necessary to understand variation in mechanical behaviour resulting from differences in gender, aging, disease and injury. The objective of this study was to apply and evaluate mesh morphing and mapping techniques to facilitate the creation and structural analysis of specimen-specific finite element (FE) models of the pelvis. A specimen-specific pelvic FE model (source mesh) was generated following a traditional user-intensive meshing scheme. The source mesh was morphed onto a computed tomography scan generated target surface of a second pelvis using a landmarked-based approach, in which exterior source nodes were shifted to target surface vertices, while constrained along a normal. A second copy of the morphed model was further refined through mesh mapping, in which surface nodes of the initial morphed model were selected in patches and remapped onto the surfaces of the target model. Computed tomography intensity-based material properties were assigned to each model. The source, target, morphed and mapped models were analyzed under axial compression using linear static FE analysis, and their strain distributions were evaluated. Morphing and mapping techniques were effectively applied to generate good quality and geometrically complex specimen-specific pelvic FE models. Mapping significantly improved strain concurrence with the target pelvis FE model.

Headform and N95 filtering facepiece respirator interaction: contact pressure simulation and validation

This article presents a computational and experimental study of contact pressure between six N95 filtering facepiece respirators (FFRs) and five newly developed digital headforms (small, medium, large, long/narrow, and short/wide). Contact interaction is simulated using the finite element method and validated by experiments using a pressure mapping system. The headform model has multiple layers: a skin layer, muscle layer, fatty tissue layer, and bone layer. Each headform is divided into five parts (two parts for the cheeks, one part for the upper forehead, one part for the chin, and one part for the back side of the head). Each respirator model comprises multiple layers and two straps. The simulation process has two stages for each respirator/headform combination. The first stage is to wrap the straps around the back of the headform and pull the respirator away from the face. The second stage is to release the respirator so that the respirator moves toward the face. Strap forces and contact interactions are generated between the respirators and the headforms. Meanwhile, a real-time surface pressure mapping system is used to record the pressures at six key locations to validate the computational results. There is a strong correlation between computational and experimental results (R(2) = 0.88). By comparing the pressure values from simulations and experiments, we have validated the simulation models.

Automated subject-specific, hexahedral mesh generation via image registration

Generating subject-specific, all-hexahedral meshes for finite element analysis continues to be of significant interest in biomechanical research communities. To date, most automated methods "morph" an existing atlas mesh to match with a subject anatomy, which usually result in degradation in mesh quality because of mesh distortion. We present an automated meshing technique that produces satisfactory mesh quality and accuracy without mesh repair. An atlas mesh is first developed using a script. A subject-specific mesh is generated with the same script after transforming the geometry into the atlas space following rigid image registration, and is transformed back into the subject space. By meshing the brain in 11 subjects, we demonstrate that the technique's performance is satisfactory in terms of both mesh quality (99.5% of elements had a scaled Jacobian >0.6 while <0.01% were between 0 and 0.2) and accuracy (average distance between mesh boundary and geometrical surface was 0.07 mm while <1% greater than 0.5mm). The combined computational cost for image registration and meshing was <4 min. Our results suggest that the technique is effective for generating subject-specific, all-hexahedral meshes and that it may be useful for meshing a variety of anatomical structures across different biomechanical research fields.

Real-Time Nonlinear Finite Element Computations on GPU - Application to Neurosurgical Simulation

Application of biomechanical modeling techniques in the area of medical image analysis and surgical simulation implies two conflicting requirements: accurate results and high solution speeds. Accurate results can be obtained only by using appropriate models and solution algorithms. In our previous papers we have presented algorithms and solution methods for performing accurate nonlinear finite element analysis of brain shift (which includes mixed mesh, different non-linear material models, finite deformations and brain-skull contacts) in less than a minute on a personal computer for models having up to 50.000 degrees of freedom. In this paper we present an implementation of our algorithms on a Graphics Processing Unit (GPU) using the new NVIDIA Compute Unified Device Architecture (CUDA) which leads to more than 20 times increase in the computation speed. This makes possible the use of meshes with more elements, which better represent the geometry, are easier to generate, and provide more accurate results.

Evaluation of the generality and accuracy of a new mesh morphing procedure for the human femur

Various papers described mesh morphing techniques for computational biomechanics, but none of them provided a quantitative assessment of generality, robustness, automation, and accuracy in predicting strains. This study aims to quantitatively evaluate the performance of a novel mesh-morphing algorithm. A mesh-morphing algorithm based on radial-basis functions and on manual selection of corresponding landmarks on template and target was developed. The periosteal geometries of 100 femurs were derived from a computed tomography scan database and used to test the algorithm generality in producing finite element (FE) morphed meshes. A published benchmark, consisting of eight femurs for which in vitro strain measurements and standard FE model strain prediction accuracy were available, was used to assess the accuracy of morphed FE models in predicting strains. Relevant parameters were identified to test the algorithm robustness to operative conditions. Time and effort needed were evaluated to define the algorithm degree of automation. Morphing was successful for 95% of the specimens, with mesh quality indicators comparable to those of standard FE meshes. Accuracy of the morphed meshes in predicting strains was good (R(2)>0.9, RMSE%<10%) and not statistically different from the standard meshes (p-value=0.1083). The algorithm was robust to inter- and intra-operator variability, target geometry refinement (p-value>0.05) and partially to the number of landmark used. Producing a morphed mesh starting from the triangularized geometry of the specimen requires on average 10 min. The proposed method is general, robust, automated, and accurate enough to be used in bone FE modelling from diagnostic data, and prospectively in applications such as statistical shape modelling.

Development of subject-specific and statistical shape models of the knee using an efficient segmentation and mesh-morphing approach

Subject-specific finite element models developed from imaging data provide functional representation of anatomical structures and have been used to evaluate healthy and pathologic knee mechanics. The creation of subject-specific models is a time-consuming process when considering manual segmentation and hexahedral (hex) meshing of the articular surfaces to ensure accurate contact assessment. Previous studies have emphasized automated mesh mapping to bone geometry from computed tomography (CT) scans, but have not considered cartilage and soft tissue structures. Statistical shape modeling has been proposed as an alternative approach to develop a population of subject models, but still requires manual segmentation and registration of a training set. Accordingly, the aim of the current study was to develop an efficient, integrated mesh-morphing-based segmentation approach to create hex meshes of subject-specific geometries from scan data, to apply the approach to natural femoral, tibial, and patellar cartilage from magnetic resonance (MR) images, and to demonstrate the creation of a statistical shape model of the knee characterizing the modes of variation using principal component analysis. The platform was demonstrated on MR scans from 10 knees and enabled hex mesh generation of the knee articular structures in approximately 1.5h per subject. In a subset of geometries, average root mean square geometric differences were 0.54 mm for all structures and in quasi-static analyses over a range of flexion angles, differences in predicted peak contact pressures were less than 5.3% between the semi-automated and manually generated models. The integrated segmentation, mesh-morphing approach was employed in the efficient development of subject-specific models and a statistical shape model, where populations of subject-specific models have application to implant design evaluation or surgical planning.

A fast and robust patient specific Finite Element mesh registration technique: application to 60 clinical cases

Finite Element mesh generation remains an important issue for patient specific biomechanical modeling. While some techniques make automatic mesh generation possible, in most cases, manual mesh generation is preferred for better control over the sub-domain representation, element type, layout and refinement that it provides. Yet, this option is time consuming and not suited for intraoperative situations where model generation and computation time is critical. To overcome this problem we propose a fast and automatic mesh generation technique based on the elastic registration of a generic mesh to the specific target organ in conjunction with element regularity and quality correction. This Mesh-Match-and-Repair (MMRep) approach combines control over the mesh structure along with fast and robust meshing capabilities, even in situations where only partial organ geometry is available. The technique was successfully tested on a database of 5 pre-operatively acquired complete femora CT scans, 5 femoral heads partially digitized at intraoperative stage, and 50 CT volumes of patients' heads. In the latter case, both skin and bone surfaces were taken into account by the mesh registration process in order to model the face muscles and fat layers. The MMRep algorithm succeeded in all 60 cases, yielding for each patient a hex-dominant, Atlas based, Finite Element mesh with submillimetric surface representation accuracy, directly exploitable within a commercial FE software.

Morphing methods to parameterize specimen-specific finite element model geometries

Shape plays an important role in determining the biomechanical response of a structure. Specimen-specific finite element (FE) models have been developed to capture the details of the shape of biological structures and predict their biomechanics. Shape, however, can vary considerably across individuals or change due to aging or disease, and analysis of the sensitivity of specimen-specific models to these variations has proven challenging. An alternative to specimen-specific representation has been to develop generic models with simplified geometries whose shape is relatively easy to parameterize, and can therefore be readily used in sensitivity studies. Despite many successful applications, generic models are limited in that they cannot make predictions for individual specimens. We propose that it is possible to harness the detail available in specimen-specific models while leveraging the power of the parameterization techniques common in generic models. In this work we show that this can be accomplished by using morphing techniques to parameterize the geometry of specimen-specific FE models such that the model shape can be varied in a controlled and systematic way suitable for sensitivity analysis. We demonstrate three morphing techniques by using them on a model of the load-bearing tissues of the posterior pole of the eye. We show that using relatively straightforward procedures these morphing techniques can be combined, which allows the study of factor interactions. Finally, we illustrate that the techniques can be used in other systems by applying them to morph a femur. Morphing techniques provide an exciting new possibility for the analysis of the biomechanical role of shape, independently or in interaction with loading and material properties.

Mesh morphing and response surface analysis: quantifying sensitivity of vertebral mechanical behavior

Vertebrae provide essential biomechanical stability to the skeleton. In this work novel morphing techniques were used to parameterize three aspects of the geometry of a specimen-specific finite element (FE) model of a rat caudal vertebra (process size, neck size, and end-plate offset). Material properties and loading were also parameterized using standard techniques. These parameterizations were then integrated within an RSM framework and used to produce a family of FE models. The mechanical behavior of each model was characterized by predictions of stress and strain. A metamodel was fit to each of the responses to yield the relative influences of the factors and their interactions. The direction of loading, offset, and neck size had the largest influences on the levels of vertebral stress and strain. Material type was influential on the strains, but not the stress. Process size was substantially less influential. A strong interaction was identified between dorsal-ventral offset and dorsal-ventral off-axis loading. The demonstrated approach has several advantages for spinal biomechanical analysis by enabling the examination of the sensitivity of a specimen to multiple variations in shape, and of the interactions between shape, material properties, and loading.

Computational reconstruction of cell and tissue surfaces for modeling and data analysis

We present a method for the computational reconstruction of the 3-D morphology of biological objects, such as cells, cell conjugates or 3-D arrangements of tissue structures, using data from high-resolution microscopy modalities. The method is based on the iterative optimization of Voronoi representations of the spatial structures. The reconstructions of biological surfaces automatically adapt to morphological features of varying complexity with flexible degrees of resolution. We show how 3-D confocal images of single cells can be used to generate numerical representations of cellular membranes that may serve as the basis for realistic, spatially resolved computational models of membrane processes or intracellular signaling. Another example shows how the protocol can be used to reconstruct tissue boundaries from segmented two-photon image data that facilitate the quantitative analysis of lymphocyte migration behavior in relation to microanatomical structures. Processing time is of the order of minutes depending on data features and reconstruction parameters.

Parametric and subject-specific finite element modelling of the lower cervical spine. Influence of geometrical parameters on the motion patterns

Morphometrical and postural features of the cervical spine are supposed to significantly influence its biomechanical behaviour. However, the effects of these geometrical parameters are quite difficult to evaluate. An original numerical method is proposed in order to automatically generate parametric and subject-specific meshes of the lower cervical spine. Sixteen finite element models have been built from cadaver specimens using low dose biplanar X-rays. All the generated meshes fulfilled the quality criteria. A preliminary evaluation was performed on the C5-C6 functional units using a database of previous experimental tests. The principal and coupled motions were simulated. The responses of the numerical models were within the experimental standard deviation corridors in most cases. Rotation-moment relationships were then compared to assess the influence of geometry on the mechanical response. Geometry was found to play a significant role in the motion patterns.

Suite of finite element algorithms for accurate computation of soft tissue deformation for surgical simulation

Real time computation of soft tissue deformation is important for the use of augmented reality devices and for providing haptic feedback during operation or surgeon training. This requires algorithms that are fast, accurate and can handle material nonlinearities and large deformations. A set of such algorithms is presented in this paper, starting with the finite element formulation and the integration scheme used and addressing common problems such as hourglass control and locking. The computation examples presented prove that by using these algorithms, real time computations become possible without sacrificing the accuracy of the results. For a brain model having more than 7,000 degrees of freedom, we computed the reaction forces due to indentation with frequency of around 1,000 Hz using a standard dual core PC. Similarly, we conducted simulation of brain shift using a model with more than 50,000 degrees of freedom in less than one minute. The speed benefits of our models result from combining the Total Lagrangian formulation with explicit time integration and low order finite elements.

Development and validation of subject-specific finite element models for blunt trauma study

This study developed and validated finite element (FE) models of swine and human thoraxes and abdomens that had subject-specific anatomies and could accurately and efficiently predict body responses to blunt impacts. Anatomies of the rib cage, torso walls, thoracic, and abdominal organs were reconstructed from X-ray computed tomography (CT) images and extracted into geometries to build FE meshes. The rib cage was modeled as an inhomogeneous beam structure with geometry and bone material parameters determined directly from CT images. Meshes of soft components were generated by mapping structured mesh templates representative of organ topologies onto the geometries. The swine models were developed from and validated by 30 animal tests in which blunt insults were applied to swine subjects and CT images, chest wall motions, lung pressures, and pathological data were acquired. A comparison of the FE calculations of animal responses and experimental measurements showed a good agreement. The errors in calculated response time traces were within 10% for most tests. Calculated peak responses showed strong correlations with the experimental values. The stress concentration inside the ribs, lungs, and livers produced by FE simulations also compared favorably to the injury locations. A human FE model was developed from CT images from the Visible Human project and was scaled to simulate historical frontal and side post mortem human subject (PMHS) impact tests. The calculated chest deformation also showed a good agreement with the measurements. The models developed in this study can be of great value for studying blunt thoracic and abdominal trauma and for designing injury prevention techniques, equipments, and devices.

Comparison of computed tomography based parametric and patient-specific finite element models of the healthy and metastatic spine using a mesh-morphing algorithm

STUDY DESIGN

A comparative analysis of parametric and patient-specific finite element (FE) modeling of spinal motion segments.

OBJECTIVES

To develop patient-specific FE models of spinal motion segments using mesh-morphing methods applied to a parametric FE model. To compare strain and displacement patterns in parametric and morphed models for both healthy and metastatically involved vertebrae.

SUMMARY OF BACKGROUND DATA

Parametric FE models may be limited in their ability to fully represent patient-specific geometries and material property distributions. Generation of multiple patient-specific FE models has been limited because of computational expense. Morphing methods have been successfully used to generate multiple specimen-specific FE models of caudal rat vertebrae.

METHODS

FE models of a healthy and a metastatic T6-T8 spinal motion segment were analyzed with and without patient-specific material properties. Parametric and morphed models were compared using a landmark-based morphing algorithm.

RESULTS

Morphing of the parametric FE model and including patient-specific material properties both had a strong impact on magnitudes and patterns of vertebral strain and displacement.

CONCLUSION

Small but important geometric differences can be represented through morphing of parametric FE models. The mesh-morphing algorithm developed provides a rapid method for generating patient-specific FE models of spinal motion segments.

Mesh-morphing algorithms for specimen-specific finite element modeling

Despite recent advances in software for meshing specimen-specific geometries, considerable effort is still often required to produce and analyze specimen-specific models suitable for biomechanical analysis through finite element modeling. We hypothesize that it is possible to obtain accurate models by adapting a pre-existing geometry to represent a target specimen using morphing techniques. Here we present two algorithms for morphing, automated wrapping (AW) and manual landmarks (ML), and demonstrate their use to prepare specimen-specific models of caudal rat vertebrae. We evaluate the algorithms by measuring the distance between target and morphed geometries and by comparing response to axial loading simulated with finite element (FE) methods. First a traditional reconstruction process based on microCT was used to obtain two natural specimen-specific FE models. Next, the two morphing algorithms were used to compute mappings from the surface of one model, the source, to the other, the target, and to use this mapping to morph the source mesh to produce a target mesh. The microCT images were then used to assign element-specific material properties. In AW the mappings were obtained by wrapping the source and target surfaces with an auxiliary triangulated surface. In ML, landmarks were manually placed on corresponding locations on the surfaces of both source and target. Both morphing algorithms were successful in reproducing the shape of the target vertebra with a median distance between natural and morphed models of 18.8 and 32.2 microm, respectively, for AW and ML. Whereas AW-morphing produced a surface more closely resembling that of the target, ML guaranteed correspondence of the landmark locations between source and target. Morphing preserved the quality of the mesh producing models suitable for FE simulation. Moreover, there were only minor differences between natural and morphed models in predictions of deformation, strain and stress. We therefore conclude that it is possible to use mesh-morphing techniques to produce accurate specimen-specific FE models of caudal rat vertebrae. Mesh morphing techniques provide advantages over conventional specimen-specific finite element modeling by reducing the effort required to generate multiple target specimen models, facilitating intermodel comparisons through correspondence of nodes and maintenance of connectivity, and lends itself to parametric evaluation of "artificial" geometries with a focus on optimizing reconstruction.

A three-dimensional articulatory model of the velum and nasopharyngeal wall based on MRI and CT data

An original three-dimensional (3D) linear articulatory model of the velum and nasopharyngeal wall has been developed from magnetic resonance imaging (MRI) and computed tomography images of a French subject sustaining a set of 46 articulations, covering his articulatory repertoire. The velum and nasopharyngeal wall are represented by generic surface triangular meshes fitted to the 3D contours extracted from MRI for each articulation. Two degrees of freedom were uncovered by principal component analysis: first, VL accounts for 83% of the velum variance, corresponding to an oblique vertical movement seemingly related to the levator veli palatini muscle; second, VS explains another 6% of the velum variance, controlling a mostly horizontal movement possibly related to the sphincter action of the superior pharyngeal constrictor. The nasopharyngeal wall is also controlled by VL for 47% of its variance. Electromagnetic articulographic data recorded on the velum fitted these parameters exactly, and may serve to recover dynamic velum 3D shapes. The main oral and nasopharyngeal area functions controlled by the articulatory model, complemented by the area functions derived from the complex geometry of each nasal passage extracted from coronal MRIs, were fed to an acoustic model and gave promising results about the influence of velum movements on the spectral characteristics of nasals.

Geometric modeling of living tissue for subject-specific finite element analysis

We introduce shape morphing approach to generate subject-specific finite element (FE) models. Different from the conventional approaches, our method generate individual (FE) model by applying spatial transformation to a reference model. It does not, therefore, require time-consuming works such as segmentation and mesh generation. The proposed method was applied to FE model generation of fingertips. The spatial trans-formation was computed using volume registration technique. The registration and the FE model morphing were carried out for two subjects. The morphing results showed good agreement in shape both for phalanxes and soft tissue.

Anisotropic finite element modeling for patient-specific mandible

This paper presents an ad hoc modular software tool to quasi-automatically generate patient-specific three-dimensional (3D) finite element (FE) model of the human mandible. The main task is taking into account the complex geometry of the individual mandible, as well as the inherent highly anisotropic material law. At first, by computed tomography data (CT), the individual geometry of the complete range of mandible was well reproduced, also the separation between cortical and cancellous bone. Then, taking advantage of the inherent shape nature as 'curve' long bone, the algorithm employed a pair of B-spline curves running along the entire upper and lower mandible borders as auxiliary baselines, whose directions are also compatible with that of the trajectory of maximum material stiffness throughout the cortical bone of the mandible. And under the guidance of this pair of auxiliary baselines, a sequence of B-spline surfaces were interpolated adaptively as curve cross-sections to cut the original geometry. Following, based on the produced curve contours and the corresponding curve cross-section surfaces, quite well structured FE volume meshes were constructed, as well as the inherent trajectory vector fields of the anisotropic material (orthotropic for cortical bone and transversely isotropic for cancellous bone). Finally, a sensitivity analysis comprising various 3D FE simulations was carried out to reveal the relevance of elastic anisotropy for the load carrying behavior of the mandible.

Simulations of the consequences of tongue surgery on tongue mobility: implications for speech production in post-surgery conditions

BACKGROUND

We studied the ability of a three-dimensional (3D) biomechanical model of the oral cavity to predict the consequences of tongue surgery on tongue movements, according to the size and location of the tissue loss and the nature of the flap used by the surgeon.

METHOD

The core of our model consists of a 3D biomechanical model representing the tongue as a finite element structure with hexahedral elements and hyperelastic properties, in which muscles are represented by specific subsets of elements. This model is inserted in the oral cavity including jaw, palate and pharyngeal walls. Hemiglossectomy and large resection of the mouth floor are simulated by removing the elements corresponding to the tissue losses. Three kinds of reconstruction are modelled, assuming flaps with low, medium or high stiffness.

RESULTS

The consequences of these different surgical treatments during the activation of some of the main tongue muscles are shown. Differences in global 3D tongue shape and in velocity patterns are evaluated and interpreted in terms of their potential impact on speech articulation. These simulations have been shown to be efficient in accounting for some of the clinically observed consequences of tongue surgery.

CONCLUSION

Further improvements still need to be done before being able to generate patient-specific models easily and to decrease the computation time significantly. However, this approach should represent a significant improvement in planning tongue surgery systems and should be a very useful means of improving the understanding of muscle behaviour after partial resection.

Automated finite-element analysis for deformable registration of prostate images

Two major factors preventing the routine clinical use of finite-element analysis for image registration are: 1) the substantial labor required to construct a finite-element model for an individual patient's anatomy and 2) the difficulty of determining an appropriate set of finite-element boundary conditions. This paper addresses these issues by presenting algorithms that automatically generate a high quality hexahedral finite-element mesh and automatically calculate boundary conditions for an imaged patient. Medial shape models called m-reps are used to facilitate these tasks and reduce the effort required to apply finite-element analysis to image registration. Encouraging results are presented for the registration of CT image pairs which exhibit deformation caused by pressure from an endorectal imaging probe and deformation due to swelling.

Improving the finite element forward model of the human head by warping using elastic deformation

As the use of realistic geometry in the forward model of electrical impedance tomography (EIT) of brain function appears to improve image reconstruction, the generation of patient-specific finite element meshes has been the subject of much recent work. This paper presents a more rapid method of generating more geometrically accurate finite element meshes of the human head by warping existing meshes such that the surface boundary beneath the electrodes closely matches that of the subject with minimal degradation to the quality of the mesh. Pre-existing meshes of spheres and adult head models incorporating key internal anatomical features are warped, using elastic deformation, to match a phantom latex tank incorporating a real skull. The algorithm is described and tests are carried out to optimize the key parameters to ensure minimal degradation of mesh quality and distortion of internal features. Results show that the algorithm operating with the optimum parameters produces meshes of sound quality and could represent an important step in the timely and productive creation of forward models in clinical applications.

Heterogeneous meshing and biomechanical modeling of human spine

We aim to develop a patient-specific biomechanical model of human spine for the purpose of surgical training and planning. In this paper, we describe the development of a finite-element model of the spine from the VHD Male Data. The finite-element spine model comprises volumetric elements suitable for deformation and other finite-element analysis using ABAQUS. The mesh generation solution accepts segmented radiological slices as input, and outputs three-dimensional (3D) volumetric finite element meshes that are ABAQUS compliant. The proposed mesh generation method first uses a grid plane to divide the contours of the anatomical boundaries and its inclusions into discrete meshes. A grid frame is then built to connect the grid planes between any two adjacent planes using a novel scheme. The meshes produced consist of brick elements in the interior of the contours and with tetrahedral and wedge elements at the boundaries. The nodal points are classified according to their materials and hence, elements can be assigned different properties. The resultant spine model comprises a detailed model of the 7 cervical vertebrae, 12 thoracic vertebrae, 5 lumbar vertebrae, and S1. Each of the vertebrae and intervertebral disc has between 1200 and 6000 elements, and approximately 1200 elements, respectively. The accuracy of the resultant VHD finite element spine model was good based on visual comparison of volume-rendered images of the original CT data, and has been used in a computational analysis involving needle insertion and static deformation. We also compared the mesh generated using our method against two automatically generated models; one consists of purely tetrahedral elements and the other hexahedral elements.

Reliable simulations of the human proximal femur by high-order finite element analysis validated by experimental observations

BACKGROUND

The mechanical response of patient-specific bone to various load conditions is of major clinical importance in orthopedics. Herein we enhance the methods presented in Yosibash et al. [2007. A CT-based high-order finite element analysis of the human proximal femur compared to in-vitro experiments. ASME Journal of Biomechanical Engineering 129(3), 297-309.] for the reliable simulations of the human proximal femur by high-order finite elements (FEs) and validate the simulations by experimental observations.

METHOD OF APPROACH

A fresh-frozen human femur was scanned by quantitative computed tomography (QCT) and thereafter loaded (in vitro experiments) by a quasi-static force of up to 1250 N. QCT scans were manipulated to generate a high-order FE bone model with distinct cortical and trabecular regions having inhomogeneous isotropic elastic properties with Young's modulus represented by continuous spatial functions. Sensitivity analyses were performed to quantify parameters that mostly influence the mechanical response. FE results were compared to displacements and strains measured in the experiments.

RESULTS

Young moduli correlated to QCT Hounsfield Units by relations in Keyak and Falkinstein [2003. Comparison of in situ and in vitro CT scan-based finite element model predictions of proximal femoral fracture load. Medical Engineering and Physics 25, 781-787.] were found to provide predictions that match the experimental results closely. Excellent agreement was found for both the displacements and strains. The presented study demonstrates that reliable and validated high-order patient-specific FE simulations of human femurs based on QCT data are achievable for clinical computer-aided decision making.

A CT-Based High-Order Finite Element Analysis of the Human Proximal Femur Compared to In-vitro Experiments

The prediction of patient-specific proximal femur mechanical response to various load conditions is of major clinical importance in orthopaedics. This paper presents a novel, empirically validated high-order finite element method (FEM) for simulating the bone response to loads. A model of the bone geometry was constructed from a quantitative computerized tomography (QCT) scan using smooth surfaces for both the cortical and trabecular regions. Inhomogeneous isotropic elastic properties were assigned to the finite element model using distinct continuous spatial fields for each region. The Young’s modulus was represented as a continuous function computed by a least mean squares method. p-FEMs were used to bound the simulation numerical error and to quantify the modeling assumptions. We validated the FE results with in-vitro experiments on a fresh-frozen femur loaded by a quasi-static force of up to 1500N at four different angles. We measured the vertical displacement and strains at various locations and investigated the sensitivity of the simulation. Good agreement was found for the displacements, and a fair agreement found in the measured strain in some of the locations. The presented study is a first step toward a reliable p-FEM simulation of human femurs based on QCT data for clinical computer aided decision making.