Robotically Steered Needles: A Survey of Neurosurgical Applications and Technical Innovations

This paper surveys both the clinical applications and main technical innovations related to steered needles, with an emphasis on neurosurgery. Technical innovations generally center on curvilinear robots that can adopt a complex path that circumvents critical structures and eloquent brain tissue. These advances include several needle-steering approaches, which consist of tip-based, lengthwise, base motion-driven, and tissue-centered steering strategies. This paper also describes foundational mathematical models for steering, where potential fields, nonholonomic bicycle-like models, spring models, and stochastic approaches are cited. In addition, practical path planning systems are also addressed, where we cite uncertainty modeling in path planning, intraoperative soft tissue shift estimation through imaging scans acquired during the procedure, and simulation-based prediction. Neurosurgical scenarios tend to emphasize straight needles so far, and span deep-brain stimulation (DBS), stereoelectroencephalography (SEEG), intracerebral drug delivery (IDD), stereotactic brain biopsy (SBB), stereotactic needle aspiration for hematoma, cysts and abscesses, and brachytherapy as well as thermal ablation of brain tumors and seizure-generating regions. We emphasize therapeutic considerations and complications that have been documented in conjunction with these applications

Quantifying the uncertainty in a hyperelastic soft tissue model with stochastic parameters

International audienceWe present a simple open-source semi-intrusive computational method to propagate uncertainties through hyperelastic models of soft tissues. The proposed method is up to two orders of magnitude faster than the standard Monte Carlo method. The material model of interest can be altered by adjusting few lines of (FEniCS) code. The method is able to (1) provide the user with statistical confidence intervals on quantities of practical interest, such as the displacement of a tumour or target site in an organ; (2) quantify the sensitivity of the response of the organ to the associated parameters of the material model. We exercise the approach on the determination of a confidence interval on the motion of a target in the brain. We also show that for the boundary conditions under consideration five parameters of the Ogden-Holzapfel-like model have negligible influence on the displacement of the target zone compared to the three most influential parameters. The benchmark problems and all associated data are made available as supplementary material

Optical Coherence Tomography Image Analysis of Corneal Tissue

Because of the ubiquitous use of contact lenses, there is considerable interest in better understanding the anatomy of the cornea, the part of the eye in contact with an exterior lens. The recent technology developments in high resolution Optical Coherence Tomography (OCT) devices allows for the in-vivo observation of the structure of the human cornea in 3D and at cellular level resolution. Prolonged wear of contact lenses, inflammations, scarring and diseases can change the structure and physiology of the human cornea. OCT is capable of in-vivo, non-contact, 3D imaging of the human cornea. In this research, novel image processing algorithms were developed to process OCT images of the human cornea, in order to determine the corneal optical scattering and transmission. The algorithms were applied to OCT data sets acquired from multiple subjects before, during and after prolonged (3 hours) wear of soft contact lenses and eye patches, in order to investigate the changes in the corneal scattering associated with hypoxia. Results from this study demonstrate the ability of OCT to measure the optical scattering of corneal tissue and to monitor its changes resulting from external stress (hypoxia)

A one point integration rule over star convex polytopes

In this paper, the recently proposed linearly consistent one point integration rule for the meshfree methods is extended to arbitrary polytopes. The salient feature of the proposed technique is that it requires only one integration point within each n-sided polytope as opposed to 3n in Francis et al. (2017) and 13n integration points in the conventional approach for numerically integrating the weak form in two dimensions. The essence of the proposed technique is to approximate the compatible strain by a linear smoothing function and evaluate the smoothed nodal derivatives by the discrete form of the divergence theorem at the geometric center. This is done by Taylor's expansion of the weak form which facilitates the use of the smoothed nodal derivatives acting as the stabilization term. This translates to 50% and 30% reduction in the overall computational time in the two and three dimensions, respectively, whilst preserving the accuracy and the convergence rates. Th

An adapted deflated conjugate gradient solver for robust extended/generalised finite element solutions of large scale, 3D crack propagation problems

An adapted deflation preconditioner is employed to accelerate the solution of linear systems resulting from the discretisation of fracture mechanics problems with well-conditioned extended/generalised finite elements. The deflation space typically used for linear elasticity problems is enriched with additional vectors, accounting for the enrichment functions used, thus effectively removing low frequency components of the error. To further improve performance, deflation is combined, in a multiplicative way, with a block-Jacobi preconditioner, which removes high frequency components of the error as well as near-linear dependencies introduced by enrichment. The resulting scheme is tested on a series of non-planar crack propagation problems and compared to alternative linear solvers in terms of performance

Isogeometric analysis: an overview and computer implementation aspects

Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a single, unified process. The implications to practical engineering design scenarios are profound, since the time taken from design to analysis is greatly reduced, leading to dramatic gains in efficiency. The tight coupling of CAD and analysis within IGA requires knowledge from both fields and it is one of the goals of the present paper to outline much of the commonly used notation. In this manuscript, through a clear and simple Matlab implementation, we present an introduction to IGA applied to the Finite Element (FE) method and related computer implementation aspects. Furthermore, implemen- tation of the extended IGA which incorporates enrichment functions through the partition of unity method (PUM) is also presented, where several examples for both two-dimensional and three-dimensional fracture are illustrated. The open source Matlab code which accompanies the present paper can be applied to one, two and three-dimensional problems for linear elasticity, linear elastic fracture mechanics, structural mechanics (beams/plates/shells including large displacements and rotations) and Poisson problems with or without enrichment. The Bezier extraction concept that allows FE analysis to be performed efficiently on T-spline geometries is also incorporated. The article includes a summary of recent trends and developments within the field of IGA

Fracture mechanism simulation of inhomogeneous anisotropic rocks by extended finite element method

The vast majority of rock masses is anisotropic due to factors such as layering, unequal in-situ stresses, joint sets, and discontinuities. Meanwhile, given the frequently asymmetric distribution of pores, grain sizes or different mineralogical compounds in different locations, they are often classified as inhomogeneous materials. In such materials, stress intensity factors (SIFs) at the crack tip, which control the initiation of failure, strongly depend on mechanical properties of the material near that area. On the other hand, crack propagation trajectories highly depend on the orthotropic properties of the rock mass. In this study, the SIFs are calculated by means of anisotropic crack tip enrichments and an interaction integral are developed for inhomogeneous materials with the help of the extended finite element method (XFEM). We also use the T-stress within the crack tip fields to develop a new criterion to estimate the crack initiation angles and propagation in rock masses. To verify and validate the proposed approach, the results are compared with experimental test results and those reported in the literature. It is found that the ratio of elastic moduli, shear stiffnesses, and material orientation angles have a significant impact on the SIFs. However, the rate of change in material properties is found to have a moderate effect on these factors and a more pronounced effect on the failure force. The results highlight the potential of the proposed formulation in the estimation of SIFs and crack propagation paths in inhomogeneous anisotropic materials