Towards a Physics Engine to Simulate Robotic Laser Surgery: Finite Element Modeling of Thermal Laser-Tissue Interactions

TL;DR

A computational model that simulates the thermal response of laser-irradiated tissue, based on the Finite Element Method, and reveals an average root-mean-square error of less than $1.75 across most experimental conditions.

Abstract

This paper presents a computational model, based on the Finite Element Method (FEM), that simulates the thermal response of laser-irradiated tissue. This model addresses a gap in the current ecosystem of surgical robot simulators, which generally lack support for lasers and other energy-based end effectors. In the proposed model, the thermal dynamics of the tissue are calculated as the solution to a heat conduction problem with appropriate boundary conditions. The FEM formulation allows the model to capture complex phenomena, such as convection, which is crucial for creating realistic simulations. The accuracy of the model was verified via benchtop laser-tissue interaction experiments using agar tissue phantoms and ex-vivo chicken muscle. The results revealed an average root-mean-square error (RMSE) of less than 2 degrees Celsius across most experimental conditions.

Figures (4)

• Figure 2: Graphical representation of an arbitrary two-dimensional (2D) domain $\Omega\subset \mathbb{R}^2$. A point within this domain is represented by $\mathbf{p} = (x,y)$. We define the boundary (a closed line, in this 2D example) as $\partial \Omega$, with local unit normal $\hat{\mathbf{n}}$. The boundary is partitioned into the Dirichlet boundary, $\partial \Omega_u$, and the Neumann boundary, $\partial \Omega_q$. The two boundaries do not intersect but span the entire boundary, i.e., $\partial \Omega_u \cup \partial \Omega_q = \partial \Omega$.
• Figure 3: Domain discretization and bi-unit domain. Without loss of generality, here we assume tissue specimens to be shaped in the form of a cuboid, with a left-handed global frame on the top surface. The tissue geometry is partitioned into an arbitrary number $N_{el}$ of cuboid-shaped elements, each equipped with eight nodes. The coordinates of each node with respect to the global frame are denoted with $\mathbf{p}_e^A$, with the superscript $A$ identifying a specific node ($A = \{1,2,\ldots,8\}$). In the FEM method, candidate solutions for each element are built within a bi-unit domain, where local coordinates are bounded between $-1$ and $1$ along each axis. Eq. \ref{['eq:domain-mapping']} provides a mapping between the physical domain and such bi-unit domain.
• Figure 4: Experiments used a surgical CO$_\text{2}$ laser whose beam is delivered through an articulated (passive) arm. The tissue surface temperature was monitored with an infrared thermal camera at a rate of 20 frames per second (fps), and spatial resolution of 70 $\frac{\text{pixel}}{\text{cm}}$. The distance between the beam's focal point and the tissue surface ($d_f$) was controlled with a robotic arm.
• Figure 5: Simulated temperature results and experimental temperature results on agar tissue phantoms (top) and chicken muscle (bottom). The experimental results are the averages from the 5 trials for each combination of laser distance and tissue type.