Ron Alterovitz

Planning for Steerable Bevel-tip Needle Insertion Through 2D Soft Tissue with Obstacles

We explore motion planning for a new class of highly flexible bevel-tip medical needles that can be steered to previously unreachable targets in soft tissue. Planning for these procedures is difficult because the needles bend during insertion and cause the surrounding soft tissues to displace and deform. In this paper, we develop a planning algorithm for insertion of highly flexible bevel-tip needles into soft tissues with obstacles in a 2D imaging plane. Given an initial needle insertion plan specifying location, orientation, bevel rotation, and insertion distance, the planner combines soft tissue modeling and numerical optimization to generate a needle insertion plan that compensates for simulated tissue de formations, locally avoids polygonal obstacles, and minimizes needle insertion distance. The simulator computes soft tissue deformations using a finite element model that incorporates the effects of needle tip and frictional forces using a 2D mesh. We formulate the planning problem as a constrained nonlinear optimization problem that is locally minimized using a penalty method that converts the formulation to a sequence of unconstrained optimization problems. We apply the planner to bevel-right and bevel-left needles and generate plans for targets that are unreachable by rigid needles.

The Stochastic Motion Roadmap: A Sampling Framework for Planning with Markov Motion Uncertainty.

We present a new motion planning framework that explicitly considers uncertainty in robot motion to maximize the probability of avoiding collisions and successfully reaching a goal. In many motion planning applications ranging from maneuvering vehicles over unfamiliar terrain to steering flexible medical needles through human tissue, the response of a robot to commanded actions cannot be precisely predicted. We propose to build a roadmap by sampling collision-free states in the configuration space and then locally sampling motions at each state to estimate state transition probabilities for each possible action. Given a query specifying initial and goal configurations, we use the roadmap to formulate a Markov Decision Process (MDP), which we solve using Infinite Horizon Dynamic Programming in polynomial time to compute stochastically optimal plans. The Stochastic Motion Roadmap (SMRM) thus combines a sampling-based roadmap representation of the configuration space, as in PRMs, with the well-established theory of MDPs. Generating both states and transition probabilities by sampling is far more flexible than previous Markov motion planning approaches based on problem-specific or grid-based discretizations. In this paper, we formulate SMRM and demonstrate it by generating non-holonomic plans for steerable needles, a new class of medical needles that follow curved paths through soft tissue and can be modeled as a variant of a Dubins car. Using randomized simulations, we show that SMRM is computationally faster than a previously reported MDP method and confirm that SMRM generates motion plans with a significantly higher probability of success compared to shortest-path plans.

Interactive simulation of surgical needle insertion and steering

We present algorithms for simulating and visualizing the insertion and steering of needles through deformable tissues for surgical training and planning. Needle insertion is an essential component of many clinical procedures such as biopsies, injections, neurosurgery, and brachytherapy cancer treatment. The success of these procedures depends on accurate guidance of the needle tip to a clinical target while avoiding vital tissues. Needle insertion deforms body tissues, making accurate placement difficult. Our interactive needle insertion simulator models the coupling between a steerable needle and deformable tissue. We introduce (1) a novel algorithm for local remeshing that quickly enforces the conformity of a tetrahedral mesh to a curvilinear needle path, enabling accurate computation of contact forces, (2) an efficient method for coupling a 3D finite element simulation with a 1D inextensible rod with stick-slip friction, and (3) optimizations that reduce the computation time for physically based simulations. We can realistically and interactively simulate needle insertion into a prostate mesh of 13,375 tetrahedra and 2,763 vertices at a 25 Hz frame rate on an 8-core 3.0 GHz Intel Xeon PC. The simulation models prostate brachytherapy with needles of varying stiffness, steering needles around obstacles, and supports motion planning for robotic needle insertion. We evaluate the accuracy of the simulation by comparing against real-world experiments in which flexible, steerable needles were inserted into gel tissue phantoms.

Motion planning under uncertainty using iterative local optimization in belief space

We present a new approach to motion planning under sensing and motion uncertainty by computing a locally optimal solution to a continuous partially observable Markov decision process (POMDP). Our approach represents beliefs (the distributions of the robot’s state estimate) by Gaussian distributions and is applicable to robot systems with non-linear dynamics and observation models. The method follows the general POMDP solution framework in which we approximate the belief dynamics using an extended Kalman filter and represent the value function by a quadratic function that is valid in the vicinity of a nominal trajectory through belief space. Using a belief space variant of iterative LQG (iLQG), our approach iterates with second-order convergence towards a linear control policy over the belief space that is locally optimal with respect to a user-defined cost function. Unlike previous work, our approach does not assume maximum-likelihood observations, does not assume fixed estimator or control gains, takes into account obstacles in the environment, and does not require discretization of the state and action spaces. The running time of the algorithm is polynomial (O[n6]) in the dimension n of the state space. We demonstrate the potential of our approach in simulation for holonomic and non-holonomic robots maneuvering through environments with obstacles with noisy and partial sensing and with non-linear dynamics and observation models.

Motion Planning Under Uncertainty for Image-guided Medical Needle Steering

We develop a new motion planning algorithm for a variant of a Dubins car with binary left/right steering and apply it to steerable needles, a new class of flexible bevel-tip medical needle that physicians can steer through soft tissue to reach clinical targets inaccessible to traditional stiff needles. Our method explicitly considers uncertainty in needle motion due to patient differences and the difficulty in predicting needle/tissue interaction. The planner computes optimal steering actions to maximize the probability that the needle will reach the desired target. Given a medical image with segmented obstacles and target, our method formulates the planning problem as a Markov decision process based on an efficient discretization of the state space, models motion uncertainty using probability distributions and computes optimal steering actions using dynamic programming. This approach only requires parameters that can be directly extracted from images, allows fast computation of the optimal needle entry point and enables intra-operative optimal steering of the needle using the pre-computed dynamic programming look-up table. We apply the method to generate motion plans for steerable needles to reach targets inaccessible to stiff needles, and we illustrate the importance of considering uncertainty during motion plan optimization.

Steering flexible needles under Markov motion uncertainty

When inserted into soft tissues, flexible needles with bevel tips have been shown experimentally to follow a path of constant curvature in the direction of the bevel. By controlling 2 degrees of freedom at the needle base (bevel direction and insertion distance), these needles can be steered around obstacles to reach targets inaccessible to rigid needles. Motion planning for needle steering is a type of nonholonomic planning for a Dubins car with no reversal. We develop a motion planning algorithm based on dynamic programming where the path of the needle is uncertain due to uncertainty in tissue properties, needle mechanics, and interaction forces. The algorithm computes a discrete control sequence of insertions and direction changes so the needle reaches a target in an imaging plane while minimizing expected cost due to insertion distance, direction changes, and obstacle collisions. We efficiently sample the state space of needle tip positions and orientations and define bounds on the errors due to discretization. We formulate the motion planning problem as a Markov decision process (MDP) and use infinite horizon dynamic programming to compute an optimal control sequence. We first apply the method to the deterministic motion case where the needle precisely follows a path of constant curvature and then to the uncertain motion case where state transitions are defined by a probability distribution. Our implementation generates motion plans for bevel-tip needles that reach targets inaccessible to rigid needles and demonstrates that accounting for uncertainty can lead to significantly different motion plans.

Needle insertion and radioactive seed implantation in human tissues: simulation and sensitivity analysis

To facilitate training and planning for medical procedures such as prostate brachytherapy, we are developing an interactive simulation of needle insertion and radioactive seed implantation in soft tissues. We describe a new 2D dynamic FEM model based on a reduced set of scalar parameters such as needle friction, sharpness, and velocity, where the mesh is updated to maintain element boundaries along the needle shaft and the effects of needle tip and frictional forces are simulated. The computational complexity of our model grows linearly with the number of elements in the mesh and achieves 24 frames per second for 1250 triangular elements on a 750 MHz PC. We use the simulator to characterize the sensitivity of seed placement error to physician-controlled and biological parameters. Results indicate that seed placement error is highly sensitive to physician-controlled parameters such as needle position, sharpness, and friction, and less sensitive to patient-specific parameters such as tissue stiffness and compressibility.

Robot-Assisted Needle Steering

Needle insertion is a critical aspect of many medical treatments, diagnostic methods, and scientific studies, and is considered to be one of the simplest and most minimally invasive medical procedures. Robot-assisted needle steering has the potential to improve the effectiveness of existing medical procedures and enable new ones by allowing increased accuracy through more dexterous control of the needle-tip path and acquisition of targets not accessible by straight-line trajectories. In this article, we describe a robot-assisted needle-steering system that uses three integrated controllers: a motion planner concerned with guiding the needle around obstacles to a target in a desired plane, a planar controller that maintains the needle in the desired plane, and a torsion compensator that controls the needle-tip orientation about the axis of the needle shaft.

Registration of MR prostate images with biomechanical modeling and nonlinear parameter estimation

Magnetic resonance imaging (MRI) and magnetic resonance spectroscopic imaging (MRSI) have been shown to be very useful for identifying prostate cancers. For high sensitivity, the MRI/MRSI examination is often acquired with an endorectal probe that may cause a substantial deformation of the prostate and surrounding soft tissues. Such a probe is removed prior to radiation therapy treatment. To register diagnostic probe-in magnetic resonance (MR) images to therapeutic probe-out MR images for treatment planning, a new deformable image registration method is developed based on biomechanical modeling of soft tissues and estimation of uncertain tissue parameters using nonlinear optimization. Given two-dimensional (2-D) segmented probe-in and probe-out images, a finite element method (FEM) is used to estimate the deformation of the prostate and surrounding tissues due to displacements and forces resulting from the endorectal probe. Since FEM requires tissue stiffness properties and external force values as input, the method estimates uncertain parameters using nonlinear local optimization. The registration method is evaluated using images from five balloon and five rigid endorectal probe patient cases. It requires on average 37 s of computation time on a 1.6 GHz Pentium-M PC. Comparing the prostate outline in deformed probe-out images to corresponding probe-in images, the method obtains a mean Dice Similarity Coefficient (DSC) of 97.5% for the balloon probe cases and 98.1% for the rigid probe cases. The method improves significantly over previous methods (P < 0.05) with greater improvement for balloon probe cases with larger tissue deformations.

Simulating needle insertion and radioactive seed implantation for prostate brachytherapy.

We are developing a simulation of needle insertion and radioactive seed implantation to facilitate surgeon training and planning for brachytherapy for treating prostate cancer. Inserting a needle into soft tissues causes the tissues to displace and deform: ignoring these effects during seed implantation leads to imprecise seed placements. Surgeons should learn to compensate for these effects so seeds are implanted close to their pre-planned locations. We describe a new 2-D dynamic FEM model based on a 7-phase insertion sequence where the mesh is updated to maintain element boundaries along the needle shaft. The locations of seed implants are predicted as the tissue deforms. The simulation, which achieves 24 frames per second using a 1250 triangular element mesh on a 750Mhz Pentium III PC, is available for surgeon testing by contacting ron@ieor.berkeley.edu.