Image data and computational grids for computing brain shift and solving the electrocorticography forward problem.

This article describes the dataset applied in the research reported in NeuroImage article "Patient-specific solution of the electrocorticography forward problem in deforming brain" [1] that is available for download from the Zenodo data repository (https://zenodo.org/record/7687631) [2]. Preoperative structural and diffusion-weighted magnetic resonance (MR) and postoperative computed tomography (CT) images of a 12-year-old female epilepsy patient under evaluation for surgical intervention were obtained retrospectively from Boston Children's Hospital. We used these images to conduct the analysis at The University of Western Australia's Intelligent Systems for Medicine Laboratory using SlicerCBM [3], our open-source software extension for the 3D Slicer medical imaging platform. As part of the analysis, we processed the images to extract the patient-specific brain geometry; created computational grids, including a tetrahedral grid for the meshless solution of the biomechanical model and a regular hexahedral grid for the finite element solution of the electrocorticography forward problem; predicted the postoperative MRI and DTI that correspond to the brain configuration deformed by the placement of subdural electrodes using biomechanics-based image warping; and solved the patient-specific electrocorticography forward problem to compute the electric potential distribution within the patient's head using the original preoperative and predicted postoperative image data. The well-established and open-source file formats used in this dataset, including Nearly Raw Raster Data (NRRD) files for images, STL files for surface geometry, and Visualization Toolkit (VTK) files for computational grids, allow other research groups to easily reuse the data presented herein to solve the electrocorticography forward problem accounting for the brain shift caused by implantation of subdural grid electrodes.

SlicerCBM: automatic framework for biomechanical analysis of the brain.

PURPOSE: Brain shift that occurs during neurosurgery disturbs the brain's anatomy. Prediction of the brain shift is essential for accurate localisation of the surgical target. Biomechanical models have been envisaged as a possible tool for such predictions. In this study, we created a framework to automate the workflow for predicting intra-operative brain deformations. METHODS: We created our framework by uniquely combining our meshless total Lagrangian explicit dynamics (MTLED) algorithm for computing soft tissue deformations, open-source software libraries and built-in functions within 3D Slicer, an open-source software package widely used for medical research. Our framework generates the biomechanical brain model from the pre-operative MRI, computes brain deformation using MTLED and outputs results in the form of predicted warped intra-operative MRI. RESULTS: Our framework is used to solve three different neurosurgical brain shift scenarios: craniotomy, tumour resection and electrode placement. We evaluated our framework using nine patients. The average time to construct a patient-specific brain biomechanical model was 3 min, and that to compute deformations ranged from 13 to 23 min. We performed a qualitative evaluation by comparing our predicted intra-operative MRI with the actual intra-operative MRI. For quantitative evaluation, we computed Hausdorff distances between predicted and actual intra-operative ventricle surfaces. For patients with craniotomy and tumour resection, approximately 95% of the nodes on the ventricle surfaces are within two times the original in-plane resolution of the actual surface determined from the intra-operative MRI. CONCLUSION: Our framework provides a broader application of existing solution methods not only in research but also in clinics. We successfully demonstrated the application of our framework by predicting intra-operative deformations in nine patients undergoing neurosurgical procedures.

Patient-specific solution of the electrocorticography forward problem in deforming brain.

Invasive intracranial electroencephalography (iEEG), or electrocorticography (ECoG), measures electric potential directly on the surface of the brain and can be used to inform treatment planning for epilepsy surgery. Combined with numerical modeling it can further improve accuracy of epilepsy surgery planning. Accurate solution of the iEEG forward problem, which is a crucial prerequisite for solving the iEEG inverse problem in epilepsy seizure onset zone localization, requires accurate representation of the patient's brain geometry and tissue electrical conductivity after implantation of electrodes. However, implantation of subdural grid electrodes causes the brain to deform, which invalidates preoperatively acquired image data. Moreover, postoperative magnetic resonance imaging (MRI) is incompatible with implanted electrodes and computed tomography (CT) has insufficient range of soft tissue contrast, which precludes both MRI and CT from being used to obtain the deformed postoperative geometry. In this paper, we present a biomechanics-based image warping procedure using preoperative MRI for tissue classification and postoperative CT for locating implanted electrodes to perform non-rigid registration of the preoperative image data to the postoperative configuration. We solve the iEEG forward problem on the predicted postoperative geometry using the finite element method (FEM) which accounts for patient-specific inhomogeneity and anisotropy of tissue conductivity. Results for the simulation of a current source in the brain show large differences in electric potential predicted by the models based on the original images and the deformed images corresponding to the brain geometry deformed by placement of invasive electrodes. Computation of the lead field matrix (useful for solution of the iEEG inverse problem) also showed significant differences between the different models. The results suggest that rapid and accurate solution of the forward problem in a deformed brain for a given patient is achievable.

Automatic framework for patient-specific modelling of tumour resection-induced brain shift.

Our motivation is to enable non-biomechanical engineering specialists to use sophisticated biomechanical models in the clinic to predict tumour resection-induced brain shift, and subsequently know the location of the residual tumour and its boundary. To achieve this goal, we developed a framework for automatically generating and solving patient-specific biomechanical models of the brain. This framework automatically determines patient-specific brain geometry from MRI data, generates patient-specific computational grid, assigns material properties, defines boundary conditions, applies external loads to the anatomical structures, and solves differential equations of nonlinear elasticity using Meshless Total Lagrangian Explicit Dynamics (MTLED) algorithm. We demonstrated the effectiveness and appropriateness of our framework on real clinical cases of tumour resection-induced brain shift.

Computer simulation of tumour resection-induced brain deformation by a meshless approach.

Tumour resection requires precise planning and navigation to maximise tumour removal while simultaneously protecting nearby healthy tissues. Neurosurgeons need to know the location of the remaining tumour after partial tumour removal before continuing with the resection. Our approach to the problem uses biomechanical modelling and computer simulation to compute the brain deformations after the tumour is resected. In this study, we use meshless Total Lagrangian explicit dynamics as the solver. The problem geometry is extracted from the patient-specific magnetic resonance imaging (MRI) data and includes the parenchyma, tumour, cerebrospinal fluid and skull. The appropriate non-linear material formulation is used. Loading is performed by imposing intra-operative conditions of gravity and reaction forces between the tumour and surrounding healthy parenchyma tissues. A finite frictionless sliding contact is enforced between the skull (rigid) and parenchyma. The meshless simulation results are compared to intra-operative MRI sections. We also calculate Hausdorff distances between the computed deformed surfaces (ventricles and tumour cavities) and surfaces observed intra-operatively. Over 80% of points on the ventricle surface and 95% of points on the tumour cavity surface were successfully registered (results within the limits of two times the original in-plane resolution of the intra-operative image). Computed results demonstrate the potential for our method in estimating the tissue deformation and tumour boundary during the resection.

Mathematical modeling and computer simulation of needle insertion into soft tissue.

In this study we present a kinematic approach for modeling needle insertion into soft tissues. The kinematic approach allows the presentation of the problem as Dirichlet-type (i.e. driven by enforced motion of boundaries) and therefore weakly sensitive to unknown properties of the tissues and needle-tissue interaction. The parameters used in the kinematic approach are straightforward to determine from images. Our method uses Meshless Total Lagrangian Explicit Dynamics (MTLED) method to compute soft tissue deformations. The proposed scheme was validated against experiments of needle insertion into silicone gel samples. We also present a simulation of needle insertion into the brain demonstrating the method's insensitivity to assumed mechanical properties of tissue.

Image, geometry and finite element mesh datasets for analysis of relationship between abdominal aortic aneurysm symptoms and stress in walls of abdominal aortic aneurysm.

These datasets contain Computed Tomography (CT) images of 19 patients with Abdominal Aortic Aneurysm (AAA) together with 19 patient-specific geometry data and computational grids (finite element meshes) created from these images applied in the research reported in Journal of Surgical Research article "Is There A Relationship Between Stress in Walls of Abdominal Aortic Aneurysm and Symptoms?"[1]. The images were randomly selected from the retrospective database of University Hospitals Leuven (Leuven, Belgium) and provided to The University of Western Australia's Intelligent Systems for Medicine Laboratory. The analysis was conducted using our freely-available open-source software BioPARR (Joldes et al., 2017) created at The University of Western Australia. The analysis steps include image segmentation to obtain the patient-specific AAA geometry, construction of computational grids (finite element meshes), and AAA stress computation. We use well-established and widely used data file formats (Nearly Raw Raster Data or NRRD for the images, Stereolitography or STL format for geometry, and Abaqus finite element code keyword format for the finite element meshes). This facilitates re-use of our datasets in practically unlimited range of studies that rely on medical image analysis and computational biomechanics to investigate and formulate indicators and predictors of AAA symptoms.

Is There a Relationship Between Stress in Walls of Abdominal Aortic Aneurysm and Symptoms?

BACKGROUND: Abdominal aortic aneurysm (AAA) is a permanent and irreversible dilation of the lower region of the aorta. It is typically an asymptomatic condition that if left untreated can expand to the point of rupture. In simple mechanical terms, rupture of an artery occurs when the local wall stress exceeds the local wall strength. It is therefore understandable that numerous studies have attempted to estimate the AAA wall stress and investigate the relationship between the AAA wall stress and AAA symptoms. MATERIALS AND METHODS: We conducted computational biomechanics analysis for 19 patients with AAA (a proportion of these patients were classified as symptomatic) to investigate whether the AAA wall stress fields (both the patterns and magnitude) correlate with the clinical definition of symptomatic and asymptomatic AAAs. For computation of AAA wall stress, we used a very efficient method recently presented by the Intelligent Systems for Medicine Laboratory. The Intelligent Systems for Medicine Laboratory's method uses geometry from computed tomography images and mean arterial pressure as the applied load. The method is embedded in the software platform BioPARR-Biomechanics based Prediction of Aneurysm Rupture Risk, freely available from http://bioparr.mech.uwa.edu.au/. The uniqueness of our stress computation approach is three-fold: i) the results are insensitive to unknown patient-specific mechanical properties of arterial wall tissue; ii) the residual stress is accounted for, according to Y.C. Fung's Uniform Stress Hypothesis; and iii) the analysis is automated and quick, making our approach compatible with clinical workflows. RESULTS: Symptomatic patients could not be identified from the plots (pattern) of AAA wall stress and stress magnitude. Although the largest stress was predicted for a patient who suffered from AAA symptoms, the three patients with the smallest stress were also symptomatic. CONCLUSIONS: The results demonstrate, contrary to the common view, that neither the wall stress magnitude nor the stress distribution appears to be associated with the presence of clinical symptoms.

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.

Suite of meshless algorithms for accurate computation of soft tissue deformation for surgical simulation.

The ability to predict patient-specific soft tissue deformations is key for computer-integrated surgery systems and the core enabling technology for a new era of personalized medicine. Element-Free Galerkin (EFG) methods are better suited for solving soft tissue deformation problems than the finite element method (FEM) due to their capability of handling large deformation while also eliminating the necessity of creating a complex predefined mesh. Nevertheless, meshless methods based on EFG formulation, exhibit three major limitations: (i) meshless shape functions using higher order basis cannot always be computed for arbitrarily distributed nodes (irregular node placement is crucial for facilitating automated discretization of complex geometries); (ii) imposition of the Essential Boundary Conditions (EBC) is not straightforward; and, (iii) numerical (Gauss) integration in space is not exact as meshless shape functions are not polynomial. This paper presents a suite of Meshless Total Lagrangian Explicit Dynamics (MTLED) algorithms incorporating a Modified Moving Least Squares (MMLS) method for interpolating scattered data both for visualization and for numerical computations of soft tissue deformation, a novel way of imposing EBC for explicit time integration, and an adaptive numerical integration procedure within the Meshless Total Lagrangian Explicit Dynamics algorithm. The appropriateness and effectiveness of the proposed methods is demonstrated using comparisons with the established non-linear procedures from commercial finite element software ABAQUS and experiments with very large deformations. To demonstrate the translational benefits of MTLED we also present a realistic brain-shift computation.

A simple method of incorporating the effect of the Uniform Stress Hypothesis in arterial wall stress computations.

PURPOSE: Residual stress has a great influence on the mechanical behaviour of arterial wall. Numerous research groups used the Uniform Stress Hypothesis to allow the inclusion of the effects of residual stress when computing stress distributions in the arterial wall. Nevertheless, the available methods used for this purpose are very computationally expensive, due to their iterative nature. In this paper we present a new method for including the effects of residual stress on the computed stress distribution in the arterial wall. METHODS: The new method, by using the Uniform Stress Hypothesis, enables computing the effect of residual stress by averaging stresses across the thickness of the arterial wall. RESULTS: Being a post-processing method for the computed stress distributions, the proposed method is computationally inexpensive, and thus, better suited for clinical applications than the previously used ones. CONCLUSIONS: The resulting stress distributions and values obtained using the proposed method based on the Uniform Stress Hypothesis are very close to the ones returned by an existing iterative method.

BioPARR: A software system for estimating the rupture potential index for abdominal aortic aneurysms.

An abdominal aortic aneurysm (AAA) is a permanent and irreversible dilation of the lower region of the aorta. It is a symptomless condition that, if left untreated, can expand until rupture. Despite ongoing efforts, an efficient tool for accurate estimation of AAA rupture risk is still not available. Furthermore, a lack of standardisation across current approaches and specific obstacles within computational workflows limit the translation of existing methods to the clinic. This paper presents BioPARR (Biomechanics based Prediction of Aneurysm Rupture Risk), a software system to facilitate the analysis of AAA using a finite element analysis based approach. Except semi-automatic segmentation of the AAA and intraluminal thrombus (ILT) from medical images, the entire analysis is performed automatically. The system is modular and easily expandable, allows the extraction of information from images of different modalities (e.g. CT and MRI) and the simulation of different modelling scenarios (e.g. with/without thrombus). The software uses contemporary methods that eliminate the need for patient-specific material properties, overcoming perhaps the key limitation to all previous patient-specific analysis methods. The software system is robust, free, and will allow researchers to perform comparative evaluation of AAA using a standardised approach. We report preliminary data from 48 cases.

Biomechanical model for computing deformations for whole-body image registration: A meshless approach.

Patient-specific biomechanical models have been advocated as a tool for predicting deformations of soft body organs/tissue for medical image registration (aligning two sets of images) when differences between the images are large. However, complex and irregular geometry of the body organs makes generation of patient-specific biomechanical models very time-consuming. Meshless discretisation has been proposed to solve this challenge. However, applications so far have been limited to 2D models and computing single organ deformations. In this study, 3D comprehensive patient-specific nonlinear biomechanical models implemented using meshless Total Lagrangian explicit dynamics algorithms are applied to predict a 3D deformation field for whole-body image registration. Unlike a conventional approach that requires dividing (segmenting) the image into non-overlapping constituents representing different organs/tissues, the mechanical properties are assigned using the fuzzy c-means algorithm without the image segmentation. Verification indicates that the deformations predicted using the proposed meshless approach are for practical purposes the same as those obtained using the previously validated finite element models. To quantitatively evaluate the accuracy of the predicted deformations, we determined the spatial misalignment between the registered (i.e. source images warped using the predicted deformations) and target images by computing the edge-based Hausdorff distance. The Hausdorff distance-based evaluation determines that our meshless models led to successful registration of the vast majority of the image features. Copyright © 2016 John Wiley & Sons, Ltd.

Controlling seepage in discrete particle simulations of biological systems.

It is now commonplace to represent materials in a simulation using assemblies of discrete particles. Sometimes, one wishes to maintain the integrity of boundaries between particle types, for example, when modelling multiple tissue layers. However, as the particle assembly evolves during a simulation, particles may pass across interfaces. This behaviour is referred to as 'seepage'. The aims of this study were (i) to examine the conditions for seepage through a confining particle membrane and (ii) to define some simple rules that can be employed to control seepage. Based on the force-deformation response of spheres with various sizes and stiffness, we develop analytic expressions for the force required to move a 'probe particle' between confining 'membrane particles'. We analyse the influence that particle's size and stiffness have on the maximum force that can act on the probe particle before the onset of seepage. The theoretical results are applied in the simulation of a biological cell under unconfined compression.

A simple, effective and clinically applicable method to compute abdominal aortic aneurysm wall stress.

Abdominal aortic aneurysm (AAA) is a permanent and irreversible dilation of the lower region of the aorta. It is a symptomless condition that if left untreated can expand to the point of rupture. Mechanically-speaking, rupture of an artery occurs when the local wall stress exceeds the local wall strength. It is therefore desirable to be able to non-invasively estimate the AAA wall stress for a given patient, quickly and reliably. In this paper we present an entirely new approach to computing the wall tension (i.e. the stress resultant equal to the integral of the stresses tangent to the wall over the wall thickness) within an AAA that relies on trivial linear elastic finite element computations, which can be performed instantaneously in the clinical environment on the simplest computing hardware. As an input to our calculations we only use information readily available in the clinic: the shape of the aneurysm in-vivo, as seen on a computed tomography (CT) scan, and blood pressure. We demonstrate that tension fields computed with the proposed approach agree well with those obtained using very sophisticated, state-of-the-art non-linear inverse procedures. Using magnetic resonance (MR) images of the same patient, we can approximately measure the local wall thickness and calculate the local wall stress. What is truly exciting about this simple approach is that one does not need any information on material parameters; this supports the development and use of patient-specific modelling (PSM), where uncertainty in material data is recognised as a key limitation. The methods demonstrated in this paper are applicable to other areas of biomechanics where the loads and loaded geometry of the system are known.

From Finite Element Meshes to Clouds of Points: A Review of Methods for Generation of Computational Biomechanics Models for Patient-Specific Applications.

It has been envisaged that advances in computing and engineering technologies could extend surgeons' ability to plan and carry out surgical interventions more accurately and with less trauma. The progress in this area depends crucially on the ability to create robustly and rapidly patient-specific biomechanical models. We focus on methods for generation of patient-specific computational grids used for solving partial differential equations governing the mechanics of the body organs. We review state-of-the-art in this area and provide suggestions for future research. To provide a complete picture of the field of patient-specific model generation, we also discuss methods for identifying and assigning patient-specific material properties of tissues and boundary conditions.

Numerical investigations of rib fracture failure models in different dynamic loading conditions.

Rib fracture is one of the most common thoracic injuries in vehicle traffic accidents that can result in fatalities associated with seriously injured internal organs. A failure model is critical when modelling rib fracture to predict such injuries. Different rib failure models have been proposed in prediction of thorax injuries. However, the biofidelity of the fracture failure models when varying the loading conditions and the effects of a rib fracture failure model on prediction of thoracic injuries have been studied only to a limited extent. Therefore, this study aimed to investigate the effects of three rib failure models on prediction of thoracic injuries using a previously validated finite element model of the human thorax. The performance and biofidelity of each rib failure model were first evaluated by modelling rib responses to different loading conditions in two experimental configurations: (1) the three-point bending on the specimen taken from rib and (2) the anterior-posterior dynamic loading to an entire bony part of the rib. Furthermore, the simulation of the rib failure behaviour in the frontal impact to an entire thorax was conducted at varying velocities and the effects of the failure models were analysed with respect to the severity of rib cage damages. Simulation results demonstrated that the responses of the thorax model are similar to the general trends of the rib fracture responses reported in the experimental literature. However, they also indicated that the accuracy of the rib fracture prediction using a given failure model varies for different loading conditions.

Discrete Element Framework for Modelling Extracellular Matrix, Deformable Cells and Subcellular Components.

This paper presents a framework for modelling biological tissues based on discrete particles. Cell components (e.g. cell membranes, cell cytoskeleton, cell nucleus) and extracellular matrix (e.g. collagen) are represented using collections of particles. Simple particle to particle interaction laws are used to simulate and control complex physical interaction types (e.g. cell-cell adhesion via cadherins, integrin basement membrane attachment, cytoskeletal mechanical properties). Particles may be given the capacity to change their properties and behaviours in response to changes in the cellular microenvironment (e.g., in response to cell-cell signalling or mechanical loadings). Each particle is in effect an 'agent', meaning that the agent can sense local environmental information and respond according to pre-determined or stochastic events. The behaviour of the proposed framework is exemplified through several biological problems of ongoing interest. These examples illustrate how the modelling framework allows enormous flexibility for representing the mechanical behaviour of different tissues, and we argue this is a more intuitive approach than perhaps offered by traditional continuum methods. Because of this flexibility, we believe the discrete modelling framework provides an avenue for biologists and bioengineers to explore the behaviour of tissue systems in a computational laboratory.

Towards measuring neuroimage misalignment.

To enhance neuro-navigation, high quality pre-operative images must be registered onto intra-operative configuration of the brain. Therefore evaluation of the degree to which structures may remain misaligned after registration is critically important. We consider two Hausdorff Distance (HD)-based evaluation approaches: the edge-based HD (EBHD) metric and the Robust HD (RHD) metric as well as various commonly used intensity-based similarity metrics such as Mutual Information (MI), Normalised Mutual Information (NMI), Entropy Correlation Coefficient (ECC), Kullback-Leibler Distance (KLD) and Correlation Ratio (CR). We conducted the evaluation by applying known deformations to simple sample images and real cases of brain shift. We conclude that the intensity-based similarity metrics such as MI, NMI, ECC, KLD and CR do not correlate well with actual alignment errors, and hence are not useful for assessing misalignment. On the contrary, the EBHD and the RHD metrics correlated well with actual alignment errors; however, they have been found to underestimate the actual misalignment. We also note that it is beneficial to present HD results as a percentile-HD curve rather than a single number such as the 95-percentile HD. Percentile-HD curves present the full range of alignment errors and also facilitate the comparison of results obtained using different approaches. Furthermore, the qualities that should be possessed by an ideal evaluation metric were highlighted. Future studies could focus on developing such an evaluation metric.