Clinical Scenario

We also evaluated our method in simulation in a clinical scenario involving planar needle steering within the human liver for biopsy or drug delivery (as shown in Fig. 4.10). We obtained planar

(a) (b) (c)

(d) (e)

Figure 4.10: Simulation of needle steering in a plane in the human liver for biopsy or drug delivery. (a) Planar imaging slices from scans of a human liver from the U.S. National Library of Medicine’s Visible Human project. The initial state of the needle is specified (in red), the target region is marked in green, and the vessels inside the liver are segmented and marked as obstacles (shown in orange). (b) Ignoring uncertainty can lead to selection of a plan that goes through a very narrow passage between the vessels, thereby considerably decreasing the probability of success, even when using a feedback controller. (c) Consideration of uncertainty under the probability of success criterion efficiently computed using our method selects a high quality plan that has sufficient clearance from the vessels, thereby maximizing probability of successful plan execution. (d) Considerable uncertainty due to actuation and sensing errors, and errors in estimating modeling parameters causes the needle to hit a vessel in the absence of feedback. (e) Our deformation-aware controller guides the needle back to the target region even under considerable uncertainty.

imaging slides from computed tomography (CT) scans of a human liver from the U.S. National Library of Medicine’s Visible Human project database (U.S. National Library of Medicine, 2012). In a clinical procedure, high resolution scans would typically be obtained in the preoperative stage of the procedure. A clinician would specify the initial state of the needle (position and orientation), a desired target region, and specify major blood vessels that must be avoided during the procedure to prevent hemorrhaging during the procedure (Fig. 4.10a).

narrow passage between the vessels (Fig. 4.10b), thereby considerably decreasing the probability of success, even when using a feedback controller. On the other hand, if we choose a high quality plan based on our probability of success criterion, we can compute safe plans that have sufficient clearance from the blood vessels in case of unexpected deviation in the needle pose (Fig. 4.10c), thereby maximizing the probability of successful plan execution.

We simulate actual execution of the procedure with the chosen high quality plan and LQG feedback controller by considering uncertainty due to actuation and sensing errors, and modeling errors due to improper initialization of material parameters. The needle hits the vessel while executing the high quality plan without feedback in the presence of uncertainty (Fig. 4.10d). In contrast, our deformation-aware controller guides the needle back to the target while safely avoiding obstacles under considerable uncertainty (Fig. 4.10e).

4.7

Discussion

We have introduced a new, unified framework for planning and control under uncertainty in highly deformable environments that maximizes the probability of success by accounting for uncertainty in deformation models, noisy sensing, and unpredictable actuation. Unlike prior planners that assume deterministic deformations or treat deformations as a disturbance, our method explicitly considers uncertainty in large, time-dependent deformations. Although the method requires a simulator of the deformable environment, we place no significant restrictions on the simulator used. We have shown that our approach can generate high quality plans for guiding steerable needles through highly deformable tissue under 2D image guidance.

Our approach has a few limitations. First, we operate under the assumption of Gaussian models of uncertainty. This might not be an acceptable approximation in applications where multi-modal beliefs are expected to appear. However, preliminary results from Chapter 3 indicate that the Gaussian approximation is well founded for the problem of needle steering in soft tissue. Second, the feedback controller used in this work does not take bounds on the physical control inputs that can be applied to the system. This is a practical concern for needle steering, since curvature greater than the maximum curvature of the needle cannot be realized. We plan to combine our approach with model predictive control based methods that would use a fast planner (Chapter 2) to correct unexpected perturbations

that cannot be effectively corrected by the LQG controller. Our analytical method for efficiently estimating the probability of success works well for steerable needles but we plan to extend this method to be applicable to non-point robots.

In future work, we plan to investigate improvements to each component in Fig. 4.2. Replacing the standard LQR control framework with integrated approaches for planning and control that compute an approximate solution to the POMDP problem (Platt et al., 2010; van den Berg et al., 2012) may improve controller performance. Similarly, replacing the standard Kalman filter with variants such as the unscented Kalman filter or a particle filter (Simon, 2006) may improve the quality of state estimation during plan execution. Our approach also assumes that a simulator that computes the expected deformations in the environment is available, but such simulators are difficult to construct for general applications. We envision that advances in computational modeling and simulation will further increase the applicability of our method. We also plan to investigate parallelizing the model linearization, which involves multiple, independent simulation runs, to reduce computation times.

CHAPTER 5

Conclusion and Future Work

Steerable medical needles have the potential to improve health care by improving the effective- ness of needle-based clinical procedures such as biopsy, drug delivery, neurosurgery, and radioactive seed implantation for cancer treatment. However, several hurdles need to be overcome before needle steering can be realized in practice. A big part of the challenge stems from the difficulty involved in accurately guiding these needles to clinical targets while safely avoiding sensitive and impenetrable anatomical structures. Creating a needle steering robotic system that assists clinicians and addresses these challenges could enable new needle-based procedures and substantially improve the clinical outcomes of some existing needle-based procedures.

In this dissertation, we have addressed a number of issues related to planning and control of steerable medical needles. We have demonstrated that efficient motion planning and control approaches can facilitate closed-loop guidance of steerable needles to clinical targets within clinically acceptable accuracy while avoiding sensitive and impenetrable anatomical structures. We have proposed two approaches for closed-loop planning and control of steerable needles, overcoming substantial deformations and uncertainty in the process. We have also proposed a data-driven method for creating stochastic models of steerable needle insertion, which could be used to create realistic medical training simulators of steerable needle procedures and to improve the effectiveness of existing planning and control techniques.

Our results, albeit presented in the context of medical needle steering, could be adapted to a number of applications, including manipulation of deformable objects and planning and control of mobile robots.