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A new recovery technique based on discretization corrected particle strength exchange (DC PSE) operators is developed in this paper. DC PSE is a collocation method that can be used to compute derivatives directly at nodal points, instead of by projection from Gauss points as is done in many finite element-based recovery techniques. The proposed method is truly meshless and does not require patches of elements to be defined, which makes it generally applicable to point clouds and arbitrary element topologies. Numerical examples show that the proposed method is accurate and robust.

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 they can further improve accuracy of epilepsy surgery planning. Accurate solution of the iEEG or ECoG forward problem, which is a crucial prerequisite for solving the 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.

In this paper, we present a meshless method belonging to the family of element-free Galerkin (EFG) methods. The distinguishing feature of the presented meshless method is that it 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 (FE) method. 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., Comment: 33 pages, 15 figures

In this study we present a kinematic approach to 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) framework 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.