Grand Roman Joldes

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.

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.

Real-Time Prediction of Brain Shift Using Nonlinear Finite Element Algorithms

Patient-specific biomechanical models implemented using specialized nonlinear (i.e., taking into account material and geometric nonlinearities) finite element procedures were applied to predict the deformation field within the brain for five cases of craniotomy-induced brain shift. The procedures utilize the Total Lagrangian formulation with explicit time stepping. The loading was defined by prescribing deformations on the brain surface under the craniotomy. Application of the computed deformation fields to register the preoperative images with the intraoperative ones indicated that the models very accurately predict the intraoperative positions and deformations of the brain anatomical structures for limited information about the brain surface deformations. For each case, it took less than 40 s to compute the deformation field using a standard personal computer, and less than 4 s using a Graphics Processing Unit (GPU). The results suggest that nonlinear biomechanical models can be regarded as one possible method of complementing medical image processing techniques when conducting non-rigid registration within the real-time constraints of neurosurgery.

Meshless algorithm for soft tissue cutting in surgical simulation

Computation of soft tissue mechanical responses for surgery simulation and image-guided surgery has been dominated by the finite element (FE) method that utilises a mesh of interconnected elements as a computational grid. Shortcomings of such mesh-based discretisation in modelling of surgical cutting include high computational cost and the need for re-meshing in the vicinity of cutting-induced discontinuity. The meshless total Lagrangian adaptive dynamic relaxation (MTLADR) algorithm we present here does not exhibit such shortcomings, as it relies on spatial discretisation in a form of a cloud of nodes. The cutting-induced discontinuity is modelled solely through changes in nodal domains of influence, which is done through efficient implementation of the visibility criterion using the level set method. Accuracy of our MTLADR algorithm with visibility criterion is confirmed against the established nonlinear solution procedures available in the commercial FE code Abaqus.

Biomechanical Model as a Registration Tool for Image-Guided Neurosurgery: Evaluation Against BSpline Registration

In this paper we evaluate the accuracy of warping of neuro-images using brain deformation predicted by means of a patient-specific biomechanical model against registration using a BSpline-based free form deformation algorithm. Unlike the BSpline algorithm, biomechanics-based registration does not require an intra-operative MR image which is very expensive and cumbersome to acquire. Only sparse intra-operative data on the brain surface is sufficient to compute deformation for the whole brain. In this contribution the deformation fields obtained from both methods are qualitatively compared and overlaps of Canny edges extracted from the images are examined. We define an edge based Hausdorff distance metric to quantitatively evaluate the accuracy of registration for these two algorithms. The qualitative and quantitative evaluations indicate that our biomechanics-based registration algorithm, despite using much less input data, has at least as high registration accuracy as that of the BSpline algorithm.

Beyond finite elements: A comprehensive, patient-specific neurosurgical simulation utilizing a meshless method

To be useful in clinical (surgical) simulations, a method must use fully nonlinear (both geometric and material) formulations to deal with large (finite) deformations of tissues. The method must produce meaningful results in a short time on consumer hardware and not require significant manual work while discretizing the problem domain. In this paper, we showcase the Meshless Total Lagrangian Explicit Dynamics Method (MTLED) which meets these requirements, and use it for computing brain deformations during surgery. The problem geometry is based on patient-specific MRI data and includes the parenchyma, tumor, ventricles and skull. Nodes are distributed automatically through the domain rendering the normally difficult problem of creating a patient-specific computational grid a trivial exercise. Integration is performed over a simple, regular background grid which does not need to conform to the geometry boundaries. Appropriate nonlinear material formulation is used. Loading is performed by displacing the parenchyma surface nodes near the craniotomy and a finite frictionless sliding contact is enforced between the skull (rigid) and parenchyma. The meshless simulation results are compared to both intraoperative MRIs and Finite Element Analysis results for multiple 2D sections. We also calculate Hausdorff distances between the computed deformed surfaces of the ventricles and those observed intraoperatively. The difference between previously validated Finite Element results and the meshless results presented here is less than 0.2mm. The results are within the limits of neurosurgical and imaging equipment accuracy (~1 mm) and demonstrate the methods ability to fulfill all of the important requirements for surgical simulation.

Biomechanical Modeling of the Brain for Computer-Assisted Neurosurgery

During neurosurgery, the brain significantly deforms. Despite the enormous complexity of the brain (see Chap. 2) many aspects of its response can be reasonably described in purely mechanical terms, such as displacements, strains and stresses. They can therefore be analyzed using established methods of continuum mechanics. In this chapter, we discuss approaches to biomechanical modeling of the brain from the perspective of two distinct applications: neurosurgical simulation and neuroimage registration in image-guided surgery. These two challenging applications are described below.1

Patient-specific computational biomechanics of the brain without segmentation and meshing

Motivated by patient-specific computational modelling in the context of image-guided brain surgery, we propose a new fuzzy mesh-free modelling framework. The method works directly on an unstructured cloud of points that do not form elements so that mesh generation is not required. Mechanical properties are assigned directly to each integration point based on fuzzy tissue classification membership functions without the need for image segmentation. Geometric integration is performed over an underlying uniform background grid. The verification example shows that, while requiring no hard segmentation and meshing, the proposed model gives, for all practical purposes, equivalent results to a finite element model.

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.

More accurate neuronavigation data provided by biomechanical modeling instead of rigid registration.

It is possible to improve neuronavigation during image-guided surgery by warping the high-quality preoperative brain images so that they correspond with the current intraoperative configuration of the brain. In this work, the accuracy of registration results obtained using comprehensive biomechanical models is compared to the accuracy of rigid registration, the technology currently available to patients. This comparison allows us to investigate whether biomechanical modeling provides good quality image data for neuronavigation for a larger proportion of patients than rigid registration. Preoperative images for 33 cases of neurosurgery were warped onto their respective intraoperative configurations using both biomechanics-based method and rigid registration. We used a Hausdorff distance-based evaluation process that measures the difference between images to quantify the performance of both methods of registration. A statistical test for difference in proportions was conducted to evaluate the null hypothesis that the proportion of patients for whom improved neuronavigation can be achieved, is the same for rigid and biomechanics-based registration. The null hypothesis was confidently rejected (p-value<10−4). Even the modified hypothesis that less than 25% of patients would benefit from the use of biomechanics-based registration was rejected at a significance level of 5% (p-value = 0.02). The biomechanics-based method proved particularly effective for cases experiencing large craniotomy-induced brain deformations. The outcome of this analysis suggests that our nonlinear biomechanics-based methods are beneficial to a large proportion of patients and can be considered for use in the operating theatre as one possible method of improving neuronavigation and surgical outcomes.It is possible to improve neuronavigation during image-guided surgery by warping the high-quality preoperative brain images so that they correspond with the current intraoperative configuration of the brain. In this paper, the accuracy of registration results obtained using comprehensive biomechanical models is compared with the accuracy of rigid registration, the technology currently available to patients. This comparison allows investigation into whether biomechanical modeling provides good-quality image data for neuronavigation for a larger proportion of patients than rigid registration. Preoperative images for 33 neurosurgery cases were warped onto their respective intraoperative configurations using both the biomechanics-based method and rigid registration. The Hausdorff distance-based evaluation process, which measures the difference between images, was used to quantify the performance of both registration methods. A statistical test for difference in proportions was conducted to evaluate the null hypothesis that the proportion of patients for whom improved neuronavigation can be achieved is the same for rigid and biomechanics-based registration. The null hypothesis was confidently rejected (p < 10(-4)). Even the modified hypothesis that fewer than 25% of patients would benefit from the use of biomechanics-based registration was rejected at a significance level of 5% (p = 0.02). The biomechanics-based method proved particularly effective in cases demonstrating large craniotomy-induced brain deformations. The outcome of this analysis suggests that nonlinear biomechanics-based methods are beneficial to a large proportion of patients and can be considered for use in the operating theater as a possible means of improving neuronavigation and surgical outcomes.