Real-time Error Control for Surgical Simulation

Objective: To present the first real-time a posteriori error-driven adaptive finite element approach for real-time simulation and to demonstrate the method on a needle insertion problem. Methods: We use corotational elasticity and a frictional needle/tissue interaction model. The problem is solved using finite elements within SOFA. The refinement strategy relies upon a hexahedron-based finite element method, combined with a posteriori error estimation driven local $h$-refinement, for simulating soft tissue deformation. Results: We control the local and global error level in the mechanical fields (e.g. displacement or stresses) during the simulation. We show the convergence of the algorithm on academic examples, and demonstrate its practical usability on a percutaneous procedure involving needle insertion in a liver. For the latter case, we compare the force displacement curves obtained from the proposed adaptive algorithm with that obtained from a uniform refinement approach. Conclusions: Error control guarantees that a tolerable error level is not exceeded during the simulations. Local mesh refinement accelerates simulations. Significance: Our work provides a first step to discriminate between discretization error and modeling error by providing a robust quantification of discretization error during simulations.Comment: 12 pages, 16 figures, change of the title, submitted to IEEE TBM

Cutting in deformable objects

Virtual reality simulations of surgical procedures allow such procedures to be practiced on computers instead of patients and test-animals. The core of such a system is a soft tissue simulation, that has to react very quickly but be realistic at the same time. This thesis discusses how deformable models can be simulated for this context, using an existing mathematical technique, the Finite Element Method. This method represents the object with a mesh, the material is subdivided in geometric primitives, such as triangles. Both the number of primitives and their shape influence the speed of a simulation. Hence, when the mesh changes, e.g. when simulating a procedure, this has to be done with care. This thesis shows how the interaction of meshing and simulation can be handled in software

Realistic tool-tissue interaction models for surgical simulation and planning

Surgical simulators present a safe and potentially effective method for surgical training, and can also be used in pre- and intra-operative surgical planning. Realistic modeling of medical interventions involving tool-tissue interactions has been considered to be a key requirement in the development of high-fidelity simulators and planners. The soft-tissue constitutive laws, organ geometry and boundary conditions imposed by the connective tissues surrounding the organ, and the shape of the surgical tool interacting with the organ are some of the factors that govern the accuracy of medical intervention planning.\ud \ud This thesis is divided into three parts. First, we compare the accuracy of linear and nonlinear constitutive laws for tissue. An important consequence of nonlinear models is the Poynting effect, in which shearing of tissue results in normal force; this effect is not seen in a linear elastic model. The magnitude of the normal force for myocardial tissue is shown to be larger than the human contact force discrimination threshold. Further, in order to investigate and quantify the role of the Poynting effect on material discrimination, we perform a multidimensional scaling study. Second, we consider the effects of organ geometry and boundary constraints in needle path planning. Using medical images and tissue mechanical properties, we develop a model of the prostate and surrounding organs. We show that, for needle procedures such as biopsy or brachytherapy, organ geometry and boundary constraints have more impact on target motion than tissue material parameters. Finally, we investigate the effects surgical tool shape on the accuracy of medical intervention planning. We consider the specific case of robotic needle steering, in which asymmetry of a bevel-tip needle results in the needle naturally bending when it is inserted into soft tissue. We present an analytical and finite element (FE) model for the loads developed at the bevel tip during needle-tissue interaction. The analytical model explains trends observed in the experiments. We incorporated physical parameters (rupture toughness and nonlinear material elasticity) into the FE model that included both contact and cohesive zone models to simulate tissue cleavage. The model shows that the tip forces are sensitive to the rupture toughness. In order to model the mechanics of deflection of the needle, we use an energy-based formulation that incorporates tissue-specific parameters such as rupture toughness, nonlinear material elasticity, and interaction stiffness, and needle geometric and material properties. Simulation results follow similar trends (deflection and radius of curvature) to those observed in macroscopic experimental studies of a robot-driven needle interacting with gels

SMART IMAGE-GUIDED NEEDLE INSERTION FOR TISSUE BIOPSY

M.S

Dynamic analysis of a needle insertion for soft materials: Arbitrary Lagrangian-Eulerian-based three-dimensional finite element analysis

Background: Our goal was to develop a three-dimensional finite element model that enables dynamic analysis of needle insertion for soft materials. To demonstrate large deformation and fracture, we used the arbitrary Lagrangian-Eulerian (ALE) method for fluid analysis. We performed ALE-based finite element analysis for 3% agar gel and three types of copper needle with bevel tips. Methods: To evaluate simulation results, we compared the needle deflection and insertion force with corresponding experimental results acquired with a uniaxial manipulator. We studied the shear stress distribution of agar gel on various time scales. Results: For 30°, 45°, and 60°, differences in deflections of each needle between both sets of results were 2.424, 2.981, and 3.737. mm, respectively. For the insertion force, there was no significant difference for mismatching area error (p<0.05) between simulation and experimental results. Conclusions: Our results have the potential to be a stepping stone to develop pre-operative surgical planning to estimate an optimal needle insertion path for MR image-guided microwave coagulation therapy and for analyzing large deformation and fracture in biological tissues. © 2014 Elsevier Ltd.Yamaguchi S., Tsutsui K., Satake K., et al. Dynamic analysis of a needle insertion for soft materials: Arbitrary Lagrangian-Eulerian-based three-dimensional finite element analysis. Computers in Biology and Medicine 53, 42 (2014); https://doi.org/10.1016/j.compbiomed.2014.07.012

Modeling and simulation of an active robotic device for flexible needle insertion

Master'sMASTER OF ENGINEERIN

Development of an online progressive mathematical model of needle deflection for application to robotic-assisted percutaneous interventions

A highly flexible multipart needle is under development in the Mechatronics in Medicine Laboratory at Imperial College, with the aim to achieve multi-curvature trajectories inside biological soft tissue, such as to avoid obstacles during surgery. Currently, there is no dedicated software or analytical methodology for the analysis of the needle’s behaviour during the insertion process, which is instead described empirically on the basis of experimental trials on synthetic tissue phantoms. This analysis is crucial for needle and insertion trajectory design purposes. It is proposed that a real-time, progressive, mathematical model of the needle deflection during insertion be developed. This model can serve three purposes, namely, offline needle and trajectory design in a forward solution of the model, when the loads acting on needle from the substrate are known; online, real-time identification of the loads that act on the needle in a reverse solution, when the deflections at discrete points along the needle length are known; and the development of a sensitivity matrix, which enables the calculation of the corrective loads that are required to drive the needle back on track, if any deviations occur away from a predefined trajectory. Previously developed mathematical models of needle deflection inside soft tissue are limited to small deflection and linear strain. In some cases, identical tip path and body shape after full insertion of the needle are assumed. Also, the axial load acting on the needle is either ignored or is calculated from empirical formulae, while its inclusion would render the model nonlinear even for small deflection cases. These nonlinearities are a result of the effects of the axial and transverse forces at the tip being co-dependent, restricting the calculation of the independent effects of each on the needle’s deflection. As such, a model with small deflection assumptions incorporating tip axial forces can be called “quasi-nonlinear” and a methodology is proposed here to tackle the identification of such axial force in the linear range. During large deflection of the needle, discrepancies between the shape of the needle after the insertion and its tip path, computed during the insertion, also significantly increase, causing errors in a model based on the assumption that they are the same. Some of the models developed to date have also been dependent on existing or experimentally derived material models of soft tissue developed offline, which is inefficient for surgical applications, where the biological soft tissue can change radically and experimentation on the patient is limited. Conversely, a model is proposed in this thesis which, when solved inversely, provides an estimate for the contact stiffness of the substrate in a real-time manner. The study and the proposed model and techniques involved are limited to two dimensional projections of the needle movements, but can be easily extended to the 3-dimensional case. Results which demonstrate the accuracy and validity of the models developed are provided on the basis of simulations and via experimental trials of a multi-part 2D steering needle in gelatine.Open Acces

Closed-Loop Planning and Control of Steerable Medical Needles

Steerable needles have the potential to increase the effectiveness of needle-based clinical procedures such as biopsy, drug delivery, and radioactive seed implantation for cancer treatment. These needles can trace curved paths when inserted into tissue, thereby increasing maneuverability and targeting accuracy while reaching previously inaccessible targets that are behind sensitive or impenetrable anatomical regions. Guiding these flexible needles along an intended path requires continuously inserting and twisting the needle at its base, which is not intuitive for a human operator. In addition, the needle often deviates from its intended trajectory due to factors such as tissue deformation, needle-tissue interaction, noisy actuation and sensing, modeling errors, and involuntary patient motions. These challenges can be addressed with the assistance of robotic systems that automatically compensate for these perturbations by performing motion planning and feedback control of the needle in a closed-loop fashion under sensory feedback. We present two approaches for efficient closed-loop guidance of steerable needles to targets within clinically acceptable accuracy while safely avoiding sensitive or impenetrable anatomical structures. The first approach uses a fast motion planning algorithm that unifies planning and control by continuously replanning, enabling correction for perturbations as they occur. We evaluate our method using a needle steering system in phantom and ex vivo animal tissues. The second approach integrates motion planning and feedback control of steerable needles in highly deformable environments. We demonstrate that this approach significantly improves the probability of success compared to prior approaches that either consider uncertainty or deformations but not both simultaneously. We also propose a data-driven method to estimate parameters of stochastic models of steerable needle motion. These models can be used to create realistic medical simulators for clinicians wanting to train for steerable needle procedures and to improve the effectiveness of existing planning and control methods. This dissertation advances the state of the art in planning and control of steerable needles and is an important step towards realizing needle steering in clinical practice. The methods developed in this dissertation also generalize to important applications beyond medical needle steering, such as manipulating deformable objects and control of mobile robots.Doctor of Philosoph