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Sampling-Based Model Predictive Control for Volumetric Ablation in Robotic Laser Surgery

Vincent Y. Wang, Ravi Prakash, Siobhan R. Oca, Ethan J. LoCicero, Patrick J. Codd, Leila J. Bridgeman

TL;DR

A sampling-based model predictive control scheme to plan ablation sequences for arbitrary tissue volumes using a steady-state point ablation model to simulate a single laser-tissue interaction and a random search technique explores the reachable state space while preserving sensitive tissue regions.

Abstract

Laser-based surgical ablation relies heavily on surgeon involvement, restricting precision to the limits of human error. The interaction between laser and tissue is governed by various laser parameters that control the laser irradiance on the tissue, including the laser power, distance, spot size, orientation, and exposure time. This complex interaction lends itself to robotic automation, allowing the surgeon to focus on high-level tasks, such as choosing the region and method of ablation, while the lower-level ablation plan can be handled autonomously. This paper describes a sampling-based model predictive control (MPC) scheme to plan ablation sequences for arbitrary tissue volumes. Using a steady-state point ablation model to simulate a single laser-tissue interaction, a random search technique explores the reachable state space while preserving sensitive tissue regions. The sampled MPC strategy provides an ablation sequence that accounts for parameter uncertainty without violating constraints, such as avoiding critical nerve bundles or blood vessels.

Sampling-Based Model Predictive Control for Volumetric Ablation in Robotic Laser Surgery

TL;DR

A sampling-based model predictive control scheme to plan ablation sequences for arbitrary tissue volumes using a steady-state point ablation model to simulate a single laser-tissue interaction and a random search technique explores the reachable state space while preserving sensitive tissue regions.

Abstract

Laser-based surgical ablation relies heavily on surgeon involvement, restricting precision to the limits of human error. The interaction between laser and tissue is governed by various laser parameters that control the laser irradiance on the tissue, including the laser power, distance, spot size, orientation, and exposure time. This complex interaction lends itself to robotic automation, allowing the surgeon to focus on high-level tasks, such as choosing the region and method of ablation, while the lower-level ablation plan can be handled autonomously. This paper describes a sampling-based model predictive control (MPC) scheme to plan ablation sequences for arbitrary tissue volumes. Using a steady-state point ablation model to simulate a single laser-tissue interaction, a random search technique explores the reachable state space while preserving sensitive tissue regions. The sampled MPC strategy provides an ablation sequence that accounts for parameter uncertainty without violating constraints, such as avoiding critical nerve bundles or blood vessels.
Paper Structure (15 sections, 15 equations, 6 figures, 3 tables, 1 algorithm)

This paper contains 15 sections, 15 equations, 6 figures, 3 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. METHODS
  3. Single-Point Ablation Model
  4. Nonlinear Optimization Algorithm
  5. Graph Search Algorithm
  6. Nodal Sampling
  7. Laser Position Sampling
  8. Laser Power Sampling
  9. Feedback Control Loop
  10. NUMERICAL EXPERIMENTS
  11. Planning Algorithm Comparison
  12. Feedback Control for Uncertainty Compensation
  13. 3D Simulations on Brain Tumor Volume Data
  14. DISCUSSION
  15. Proof of Linear Superposition in Nonangular Case

Figures (6)

  • Figure 1: The effect of a single-point ablation according to the model \ref{['eq:singleablation']}. A given point, $\vec{p}$, is displaced along the direction of the laser axis by a distance, $\Delta p$, as a Gaussian function of the normal distance to the axis, $d$. The laser position is marked as $x_L$.
  • Figure 2: Linear superposition of individual ablations with zero angular components. The net ablation (red) is a combination of two single ablations (blue). Using the notation defined in \ref{['eq:superposition']}, the ablation in this figure illustrates that the distance between point $2$ and point $A$ is $\Delta p_{T2}=\Delta p_{12}+\Delta p_{32}$.
  • Figure 3: Two laser profiles are shown: profile 1 in black with laser settings $\left[x_L=0, \theta_L=0, E_L=5\right]$ and profile 2 in blue with laser settings $\left[x_L=-0.25, \theta_L=0.3491, E_L=5\right]$. The net ablation that results from applying cuts in the order of profile 1-2 (red) differs from the net ablation that results from applying cuts in the order of profile 2-1 (green).
  • Figure 4: A visual representation of \ref{['alg1']}. A random node is selected (blue), after which a random input is applied (red), leading to a new node (green) appended to the graph.
  • Figure 5: Results of numerical simulations. \ref{['fig:results_a']}, \ref{['fig:results_b']}, \ref{['fig:results_c']} show a comparison between the nonlinear optimization algorithm and the graph search algorithm with nominal system values for a square well, sawtooth, and two-cut boundary respectively. Note that since the system is nominal and has no error, only a feedforward method is presented. \ref{['fig:results_d']} displays a repeat of the two-cut experiment, but includes a 5% error between the nominal system values provided to the controller and the real parameters simulated by the plant. FB denotes "feedback".
  • ...and 1 more figures