Orbital and maxillofacial computer aided surgery: patient-specific finite element models to predict surgical outcomes

This paper addresses an important issue raised for the clinical relevance of Computer-Assisted Surgical applications, namely the methodology used to automatically build patient-specific finite element (FE) models of anatomical structures. From this perspective, a method is proposed, based on a technique called the mesh-matching method, followed by a process that corrects mesh irregularities. The mesh-matching algorithm generates patient-specific volume meshes from an existing generic model. The mesh regularization process is based on the Jacobian matrix transform related to the FE reference element and the current element.This method for generating patient-specific FE models is first applied to computer-assisted maxillofacial surgery, and more precisely, to the FE elastic modelling of patient facial soft tissues. For each patient, the planned bone osteotomies (mandible, maxilla, chin) are used as boundary conditions to deform the FE face model, in order to predict the aesthetic outcome of the surgery. Seven FE patient-specific models were successfully generated by our method. For one patient, the prediction of the FE model is qualitatively compared with the patient's post-operative appearance, measured from a computer tomography scan. Then, our methodology is applied to computer-assisted orbital surgery. It is, therefore, evaluated for the generation of 11 patient-specific FE poroelastic models of the orbital soft tissues. These models are used to predict the consequences of the surgical decompression of the orbit. More precisely, an average law is extrapolated from the simulations carried out for each patient model. This law links the size of the osteotomy (i.e. the surgical gesture) and the backward displacement of the eyeball (the consequence of the surgical gesture).     

Growing multiblock structures: a semi-automated approach to block placement for multiblock hexahedral meshing

Finite element (FE) analysis is a cornerstone of orthopaedic biomechanics research. Three-dimensional medical imaging provides sufficient resolution for the subject-specific FE models to be generated from these data-sets. FE model development requires discretisation of a three-dimensional domain, which can be the most time-consuming component of a FE study. Hexahedral meshing tools based on the multiblock method currently rely on the manual placement of building blocks for mesh generation. We hypothesise that angular analysis of the geometric centreline for a three-dimensional surface could be used to automatically generate building block structures for the multiblock hexahedral mesh generation. Our algorithm uses a set of user-defined points and parameters to automatically generate a multiblock structure based on a surface's geometric centreline. This significantly reduces the time required for model development. We have applied this algorithm to 47 bones of varying geometries and successfully generated a FE mesh in all cases. This work represents significant advancement in automatically generating multiblock structures for a wide range of geometries.     

Growing multiblock structures: a semi-automated approach to block placement for multiblock hexahedral meshing

Finite element (FE) analysis is a cornerstone of orthopaedic biomechanics research. Three-dimensional medical imaging provides sufficient resolution for the subject-specific FE models to be generated from these data-sets. FE model development requires discretisation of a three-dimensional domain, which can be the most time-consuming component of a FE study. Hexahedral meshing tools based on the multiblock method currently rely on the manual placement of building blocks for mesh generation. We hypothesise that angular analysis of the geometric centreline for a three-dimensional surface could be used to automatically generate building block structures for the multiblock hexahedral mesh generation. Our algorithm uses a set of user-defined points and parameters to automatically generate a multiblock structure based on a surface's geometric centreline. This significantly reduces the time required for model development. We have applied this algorithm to 47 bones of varying geometries and successfully generated a FE mesh in all cases. This work represents significant advancement in automatically generating multiblock structures for a wide range of geometries.     

3-D finite element modelling of facial soft tissue and preliminary application in orthodontics

Prediction of soft tissue aesthetics is important for achieving an optimal outcome in orthodontic treatment planning. Previously, applicable procedures were mainly restricted to 2-D profile prediction. In this study, a generic 3-D finite element (FE) model of the craniofacial soft and hard tissue was constructed, and individualisation of the generic model based on cone beam CT data and mathematical transformation was investigated. The result indicated that patient-specific 3-D facial FE model including different layers of soft tissue could be obtained through mathematical model transformation. Average deviation between the transformed model and the real reconstructed one was 0.47?±?0.77?mm and 0.75?±?0.84?mm in soft and hard tissue, respectively. With boundary condition defined according to treatment plan, such FE model could be used to predict the result of orthodontic treatment on facial soft tissue.     

3-D finite element modelling of facial soft tissue and preliminary application in orthodontics

Prediction of soft tissue aesthetics is important for achieving an optimal outcome in orthodontic treatment planning. Previously, applicable procedures were mainly restricted to 2-D profile prediction. In this study, a generic 3-D finite element (FE) model of the craniofacial soft and hard tissue was constructed, and individualisation of the generic model based on cone beam CT data and mathematical transformation was investigated. The result indicated that patient-specific 3-D facial FE model including different layers of soft tissue could be obtained through mathematical model transformation. Average deviation between the transformed model and the real reconstructed one was 0.47 ± 0.77 mm and 0.75 ± 0.84 mm in soft and hard tissue, respectively. With boundary condition defined according to treatment plan, such FE model could be used to predict the result of orthodontic treatment on facial soft tissue.     

Strategies towards rapid generation of forefoot model incorporating realistic geometry of metatarsals encapsulated into lumped soft tissues for personalized finite element analysis

Use of finite element (FE) foot model as a clinical diagnostics tool is likely to improve the specificity of foot injury predictions in the diabetic population. Here we proposed a novel workflow for rapid construction of foot FE model incorporating realistic geometry of metatarsals encapsulated into lumped forefoot’s soft tissues. Custom algorithms were implemented to perform unsupervised segmentation and mesh generation to directly convert CT data into a usable FE model. The automatically generated model provided higher efficiency and comparable numerical accuracy when compared to the model constructed using a traditional solid-based mesh process. The entire procedure uses MATLAB as the main platform, and makes the present approach attractive for creating personalized foot models to be used in clinical studies.     

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.     

Development and validation of a subject-specific finite element model of a human clavicle

This study aimed to develop and validate a finite element (FE) model of a human clavicle which can predict the structural response and bone fractures under both axial compression and anterior–posterior three-point bending loads. Quasi-static non-injurious axial compression and three-point bending tests were first conducted on a male clavicle followed by a dynamic three-point bending test to fracture. Then, two types of FE models of the clavicle were developed using bone material properties which were set to vary with the computed tomography image density of the bone. A volumetric solid FE model comprised solely of hexahedral elements was first developed. A solid-shell FE model was then created which modelled the trabecular bone as hexahedral elements and the cortical bone as quadrilateral shell elements. Finally, simulations were carried out using these models to evaluate the influence of variations in cortical thickness, mesh density, bone material properties and modelling approach on the biomechanical responses of the clavicle, compared with experimental data. The FE results indicate that the inclusion of density-based bone material properties can provide a more accurate reproduction of the force–displacement response and bone fracture timing than a model with uniform bone material properties. Inclusion of a variable cortical thickness distribution also slightly improves the ability of the model to predict the experimental response. The methods developed in this study will be useful for creating subject-specific FE models to better understand the biomechanics and injury mechanism of the clavicle.     

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.

     

Automated hexahedral meshing of anatomic structures using deformable registration

This work introduces a novel method of automating the process of patient-specific finite element (FE) model development using a mapped mesh technique. The objective is to map a predefined mesh (template) of high quality directly onto a new bony surface (target) definition, thereby yielding a similar mesh with minimal user interaction. To bring the template mesh into correspondence with the target surface, a deformable registration technique based on the FE method has been adopted. The procedure has been made hierarchical allowing several levels of mesh refinement to be used, thus reducing the time required to achieve a solution. Our initial efforts have focused on the phalanx bones of the human hand. Mesh quality metrics, such as element volume and distortion were evaluated. Furthermore, the distance between the target surface and the final mapped mesh were measured. The results have satisfactorily proven the applicability of the proposed method.     

The use of sparse CT datasets for auto-generating accurate FE models of the femur and pelvis

The finite element (FE) method when coupled with computed tomography (CT) is a powerful tool in orthopaedic biomechanics. However, substantial data is required for patient-specific modelling. Here we present a new method for generating a FE model with a minimum amount of patient data. Our method uses high order cubic Hermite basis functions for mesh generation and least-square fits the mesh to the dataset. We have tested our method on seven patient data sets obtained from CT assisted osteodensitometry of the proximal femur. Using only 12 CT slices we generated smooth and accurate meshes of the proximal femur with a geometric root mean square (RMS) error of less than 1 mm and peak errors less than 8 mm. To model the complex geometry of the pelvis we developed a hybrid method which supplements sparse patient data with data from the visible human data set. We tested this method on three patient data sets, generating FE meshes of the pelvis using only 10 CT slices with an overall RMS error less than 3 mm. Although we have peak errors about 12 mm in these meshes, they occur relatively far from the region of interest (the acetabulum) and will have minimal effects on the performance of the model. Considering that linear meshes usually require about 70-100 pelvic CT slices (in axial mode) to generate FE models, our method has brought a significant data reduction to the automatic mesh generation step. The method, that is fully automated except for a semi-automatic bone/tissue boundary extraction part, will bring the benefits of FE methods to the clinical environment with much reduced radiation risks and data requirement.     

From high-resolution CT data to finite element models: development of an integrated modular framework

This work introduces a novel method of automating the process of patient-specific finite element (FE) model development using a mapped mesh technique. The objective is to map a predefined mesh (template) of high quality directly onto a new bony surface (target) definition, thereby yielding a similar mesh with minimal user interaction. To bring the template mesh into correspondence with the target surface, a deformable registration technique based on the FE method has been adopted. The procedure has been made hierarchical allowing several levels of mesh refinement to be used, thus reducing the time required to achieve a solution. Our initial efforts have focused on the phalanx bones of the human hand. Mesh quality metrics, such as element volume and distortion were evaluated. Furthermore, the distance between the target surface and the final mapped mesh were measured. The results have satisfactorily proven the applicability of the proposed method.     

Subject specific finite element mesh generation of the pelvis from biplanar x-ray images: application to 120 clinical cases

Several Finite Element (FE) models of the pelvis have been developed to comprehensively assess the onset of pathologies and for clinical and industrial applications. However, because of the difficulties associated with the creation of subject-specific FE mesh from CT scan and MR images, most of the existing models rely on the data of one given individual. Moreover, although several fast and robust methods have been developed for automatically generating tetrahedral meshes of arbitrary geometries, hexahedral meshes are still preferred today because of their distinct advantages but their generation remains an open challenge. Recently, approaches have been proposed for fast 3D reconstruction of bones based on X-ray imaging. In this study, we adapted such an approach for the fast and automatic generation of all-hexahedral subject-specific FE models of the pelvis based on the elastic registration of a generic mesh to the subject-specific target in conjunction with element regularity and quality correction. The technique was successfully tested on a database of 120 3D reconstructions of pelvises from biplanar X-ray images. For each patient, a full hexahedral subject-specific FE mesh was generated with an accurate surface representation.     

Gaussian curvature analysis allows for automatic block placement in multi-block hexahedral meshing

Musculoskeletal finite element analysis (FEA) has been essential to research in orthopaedic biomechanics. The generation of a volumetric mesh is often the most challenging step in a FEA. Hexahedral meshing tools that are based on a multi-block approach rely on the manual placement of building blocks for their mesh generation scheme. We hypothesise that Gaussian curvature analysis could be used to automatically develop a building block structure for multi-block hexahedral mesh generation. The Automated Building Block Algorithm incorporates principles from differential geometry, combinatorics, statistical analysis and computer science to automatically generate a building block structure to represent a given surface without prior information. We have applied this algorithm to 29 bones of varying geometries and successfully generated a usable mesh in all cases. This work represents a significant advancement in automating the definition of building blocks.     

Gaussian curvature analysis allows for automatic block placement in multi-block hexahedral meshing

Musculoskeletal finite element analysis (FEA) has been essential to research in orthopaedic biomechanics. The generation of a volumetric mesh is often the most challenging step in a FEA. Hexahedral meshing tools that are based on a multi-block approach rely on the manual placement of building blocks for their mesh generation scheme. We hypothesise that Gaussian curvature analysis could be used to automatically develop a building block structure for multi-block hexahedral mesh generation. The Automated Building Block Algorithm incorporates principles from differential geometry, combinatorics, statistical analysis and computer science to automatically generate a building block structure to represent a given surface without prior information. We have applied this algorithm to 29 bones of varying geometries and successfully generated a usable mesh in all cases. This work represents a significant advancement in automating the definition of building blocks.     

Finite element model development of a child pelvis with optimization-based material identification

A finite element (FE) model of a 10-years-old child pelvis was developed and validated against experimental data from lateral impacts of pediatric pelves. The pelvic bone geometry was reconstructed from a set of computed tomography images, and a hexahedral mesh was generated using a new octree-based hexahedral meshing technique. Lateral impacts to the greater trochanter and iliac wing of the seated pelvis were simulated. Sensitivity analysis was conducted to identify material parameters that substantially affected the model response. An optimization-based material identification method was developed to obtain the most favorable material property set by minimizing differences in biomechanical responses between experimental and simulation results. This study represents a pilot effort in the development and validation of age-dependent musculoskeletal FE models for children, which may ultimately serve to evaluate injury mechanisms and means of protection for the pediatric population.     

Comparison of hexahedral and tetrahedral elements in finite element analysis of the foot and footwear

Finite element analysis has been widely used in the field of foot and footwear biomechanics to determine plantar pressures as well as stresses and strains within soft tissue and footwear materials. When dealing with anatomical structures such as the foot, hexahedral mesh generation accounts for most of the model development time due to geometric complexities imposed by branching and embedded structures. Tetrahedral meshing, which can be more easily automated, has been the approach of choice to date in foot and footwear biomechanics. Here we use the nonlinear finite element program Abaqus (Simulia, Providence, RI) to examine the advantages and disadvantages of tetrahedral and hexahedral elements under compression and shear loading, material incompressibility, and frictional contact conditions, which are commonly seen in foot and footwear biomechanics. This study demonstrated that for a range of simulation conditions, hybrid hexahedral elements (Abaqus C3D8H) consistently performed well while hybrid linear tetrahedral elements (Abaqus C3D4H) performed poorly. On the other hand, enhanced quadratic tetrahedral elements with improved stress visualization (Abaqus C3D10I) performed as well as the hybrid hexahedral elements in terms of contact pressure and contact shear stress predictions. Although the enhanced quadratic tetrahedral element simulations were computationally expensive compared to hexahedral element simulations in both barefoot and footwear conditions, the enhanced quadratic tetrahedral element formulation seems to be very promising for foot and footwear applications as a result of decreased labor and expedited model development, all related to facilitated mesh generation.     

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

Several authors have employed finite element analysis for stress and strain analysis in orthopaedic biomechanics. Unfortunately, the definition of three-dimensional models is time consuming (mainly because of the manual 3D meshing process) and consequently the number of analyses to be performed is limited. The authors have investigated a new patient-specific method allowing automatically 3D mesh generation for structures as complex as bone for example. This method, called the mesh-matching (M-M) algorithm, generated automatically customized 3D meshes of anatomical structures from an already existing model. The M-M algorithm has been used to generate FE models of 10 proximal human femora from an initial one which had been experimentally validated. The automatically generated meshes seemed to demonstrate satisfying results.     

Mesh considerations for finite element blast modelling in biomechanics

Finite element (FE) modelling is a popular tool for studying human body response to blast exposure. However, blast modelling is a complex problem owing to more numerous fluid–structure interactions (FSIs) and the high–frequency loading that accompanies blast exposures. This study investigates FE mesh design for blast modelling using a sphere in a closed-ended shock tube meshed with varying element sizes using both tetrahedral and hexahedral elements. FSI was consistent for sphere-to-fluid element ratios between 0.25 and 4, and acceleration response was similar for both element types (R² = 0.997). Tetrahedral elements were found to become increasingly volatile following shock loading, causing higher pressures and stresses than predicted with the hexahedral elements. Deviatoric stress response was dependent on the sphere mesh size (p < 0.001), while the pressure response was dependent on the shock tube mesh size (p < 0.001). The results of this study highlight the necessity for mesh sensitivity analysis in blast models.