Infinite-Dimensional Adaptive Boundary Observer for Inner-Domain Temperature Estimation of 3D Electrosurgical Processes using Surface Thermography Sensing

Abstract

We present a novel 3D adaptive observer framework for use in the determination of subsurface organic tissue temperatures in electrosurgery. The observer structure leverages pointwise 2D surface temperature readings obtained from a real-time infrared thermographer for both parameter estimation and temperature field observation. We introduce a novel approach to decoupled parameter adaptation and estimation, wherein the parameter estimation can run in realtime, while the observer loop runs on a slower time scale. To achieve this, we introduce a novel parameter estimation method known as attention-based noise-robust averaging, in which surface thermography time series are used to directly estimate the tissue's diffusivity. Our observer contains a realtime parameter adaptation component based on this diffusivity adaptation law, as well as a Luenberger-type corrector based on the sensed surface temperature. In this work, we also present a novel model structure adapted to the setting of robotic surgery, wherein we model the electrosurgical heat distribution as a compactly supported magnitude-and velocity-controlled heat source involving a new nonlinear input mapping. We demonstrate satisfactory performance of the adaptive observer in simulation, using real-life experimental ex vivo porcine tissue data.

Minimally Invasive Live Tissue High-Fidelity Thermophysical Modeling Using Real-Time Thermography

“…Our method relies solely on surface thermographer readings, and thus serves to obtain a model of the apparent thermodynamics of the tissue, as observed on a 2D surface. Extensions to a 3D domain based on 2D observations have been discussed in related work [8], where an observer for 3D tissue temperature has been developed; such an extension is, however, beyond the scope of the current work.…”

“…To enable direct estimation of parameters, we leverage a set of noise-robust gradient operators introduced by P. Holoborodko [12], [13]; these combine the capabilities of finite difference operators with those of a low-pass filter, allowing for noise-robust gradient computation [8]. In essence, our method reduces the parameter estimation problem from an optimization problem over the solution of (5) to that of balancing differential equations, as will be shown next.…”

“…It suffices to wait for the final heat wave to propagate outside of the field of view of the thermographer, after which the free response of the tissue can be observed. The latter has been the object of study in [8], in which a novel method known as attention-based noise-robust averaging (ANRA) has been developed to solve for the tissue's thermal diffusivity a given the free response.…”

“…multiple times to obtain an optimal parameter estimate, precluding the use of such an algorithm for real-time adaptation and safety region mapping during clinical procedures on live tissue. More importantly, multivariate optimization often fails to yield accurate parameter combinations owing to the existence of local minima encountered by optimization algorithms [8]. These local minima often necessitate the use of prior knowledge about the parameters to constrain the search space [6], [7], thereby inadvertently forcing preconceived biases on the obtained parameter estimates.…”

“…In contrast to the above methods, in [8] we presented a method that relies fully on non-invasive remote infrared thermography, in which a thermal camera is used to capture the surface temperature of the tissue. Our approach does not rely on explicitly solving the governing PDEs, but instead employs noise-robust gradient operators to directly obtain the PDE's governing parameters by balancing the underlying model differential equations based on the thermographic data.…”