An Optimal Control Problem for Elastic Registration and Force Estimation in Augmented Surgery

TL;DR

This paper introduces an optimal control framework for elastic registration in augmented surgery, enabling accurate force estimation and physically consistent deformation modeling of soft organs during procedures.

Contribution

It formulates the registration as an optimal control problem to reconstruct actual surface forces, improving physical realism and control over force application in soft tissue modeling.

Findings

Competitive accuracy in phantom experiments

Effective force estimation during simulated surgery

Enhanced physical consistency of deformation fields

Abstract

The nonrigid alignment between a pre-operative biomechanical model and an intra-operative observation is a critical step to track the motion of a soft organ in augmented surgery. While many elastic registration procedures introduce artificial forces into the direct physical model to drive the registration, we propose in this paper a method to reconstruct the surface loading that actually generated the observed deformation. The registration problem is formulated as an optimal control problem where the unknown is the surface force distribution that applies on the organ and the resulting deformation is computed using an hyperelastic model. Advantages of this approach include a greater control over the set of admissible force distributions, in particular the opportunity to choose where forces should apply, thus promoting physically-consistent displacement fields. The optimization problem is solved using a standard adjoint method. We present registration results with experimental phantom data showing that our procedure is competitive in terms of accuracy. In an example of application, we estimate the forces applied by a surgery tool on the organ. Such an estimation is relevant in the context of robotic surgery systems, where robotic arms usually do not allow force measurements, and providing force feedback remains a challenge.