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In this paper, we present a meshless method belonging to the family of element-free Galerkin (EFG) methods. The presented meshless method allows accurate enforcement of essential boundary conditions. The method uses total Lagrangian formulation with explicit time integration to facilitate code simplicity and robust computations in applications that involve large deformations and non-linear materials. We use a regularized weight function, which closely approximates the Kronecker delta, to generate interpolating shape functions. The imposition of the prescribed displacements on the boundary becomes as straightforward as in the finite element method (FEM). The effectiveness and accuracy of the proposed method is demonstrated using 3D numerical examples that include cylinder indentation by 70% of its initial height, and indentation of the brain.

Computational biomechanics models play a key role in predicting/evaluating pedestrian head kinematics and injury risk in car-to-pedestrian collisions. The human multibody models most commonly used in car-to-pedestrian collision reconstruction, such as pedestrian model by The Netherlands Organisation for Applied Scientific Research TNO, are built using the anthropometry of Western European population as defined in TNO (2013) human multibody model database. In this study, we investigate the effects of the anthropometric differences between the Western European and Chinese populations on the pedestrian head kinematics and injury responses predicted using multibody models. The comparison was conducted through car-to-pedestrian collision simulations using pedestrian multibody models representing anthropometric characteristics of Western European and Chinese populations, three typical vehicle shapes (sedan, SUV and minivan), five initial vehicle impact speeds (30, 35, 40, 45, 50 km/h), and six pedestrian walking postures. The results indicate that the change of pedestrian model anthropometry (from Western European to Chinese) exerts appreciable effects on both the predicted initial boundary conditions of the head-to-windscreen impact (in particular the head-to-windscreen impact angle) and the head injury indices in the impact with the road surface (secondary impact).

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.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.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.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.

We present comprehensive biomechanical analyses of abdominal aortic aneurysms (AAA) for 43 patients. We compare stress magnitudes and stress distributions within arterial walls of abdominal aortic aneurysms (AAA) obtained using two simulation and modelling methods: 1) Fully automated and computationally very efficient linear method embedded in the software platform BioPARR Biomechanics based Prediction of Aneurysm Rupture Risk, freely available from https://bioparr.mech.uwa.edu.au/; 2) More complex and much more computationally demanding Non-LISA Non-Linear Iterative Stress Analysis that uses a non-linear inverse iterative approach and strongly non-linear material model. Both methods predicted localised high stress zones with over 90% of AAA model volume fraction subjected to stress below 20% of the 99th percentile maximum principal stress. However, for the non-linear iterative method, the peak maximum principal stress (and 99th percentile maximum principal stress) was higher and the stress magnitude in the low stress area lower than for the automated linear method embedded in BioPARR. Differences between the stress distributions obtained using the two methods tended to be particularly pronounced in the areas where the AAA curvature was large. Performance of the selected characteristic features of the stress fields (we used 99th percentile maximum principal stress) obtained using BioPARR and Non-LISA in distinguishing between the AAAs that would rupture and remain intact was for practical purposes the same for both methods. This article is protected by copyright. All rights reserved.

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.

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.

We use computational fluid dynamics (CFD) to simulate blood flow in intracranial aneurysms (IAs). Despite ongoing improvements in the accuracy and efficiency of body-fitted CFD solvers, generation of a high quality mesh appears as the bottleneck of the flow simulation and strongly affects the accuracy of the numerical solution. To overcome this drawback, we use an immersed boundary method. The proposed approach solves the incompressible Navier-Stokes equations on a rectangular (box) domain discretized using uniform Cartesian grid using the finite element method. The immersed object is represented by a set of points (Lagrangian points) located on the surface of the object. Grid local refinement is applied using an automated algorithm. We verify and validate the proposed method by comparing our numerical findings with published experimental results and analytical solutions. We demonstrate the applicability of the proposed scheme on patient-specific blood flow simulations in IAs.

In this paper, we develop a meshless collocation scheme for the numerical solution of magnetohydrodynamics (MHD) flow equations. We consider the transient laminar flow of an incompressible, viscous and electrically conducting fluid in a rectangular duct. The flow is driven by the current produced by electrodes placed on the walls of the duct. The method combines a meshless collocation scheme with the newly developed Discretization Corrected Particle Strength Exchange (DC PSE) interpolation method. To highlight the applicability of the method, we discretize the spatial domain by using uniformly (Cartesian) and irregularly distributed nodes. The proposed solution method can handle high Hartmann (Ha) numbers and captures the boundary layers formed in such cases, without the presence of unwanted oscillations, by employing a local mesh refinement procedure close to the boundaries. The use of local refinement reduces the computational cost. We apply an explicit time integration scheme and we compute the critical time step that ensures stability through the Gershgorin theorem. Finally, we present numerical results obtained using different orientation of the applied magnetic field.

Neurosurgery for tumour resection requires precise planning and navigation to maximise tumour removal and at the same time protect healthy tissue. Biomechanical modelling and computer simulation provide a means for brain deformation prediction, facilitating millimetre-accurate neuronavigation. In this contribution, we modelled brain deformation due to tumour resection. We assumed that the brain deformations were caused by stresses on the resected tumour surface released when the tumour is removed. We computed deformations using nonlinear finite element analysis in Abaqus FEA software suite. We used the patient-specific geometry extracted from the pre-operative magnetic resonance image (MRI). We included the parenchyma tissue, cerebral tumour, cerebral ventricles, skull and cerebral falx in our computational biomechanics brain model. We created mixed (consisting of hexahedral and tetrahedral elements) patient-specific finite element mesh, and used realistic material properties together with appropriate contact conditions at boundaries. We compared our predicted intra-operative brain geometry (based on the calculated deformation field) contours with the intra-operative MRI to assess the accuracy of our results. The results indicate that our biomechanical models can complement medical image processing techniques when conducting non-rigid registration.