Identification of the Blood Perfusion Rate for Laser-Induced Thermotherapy in the Liver

TL;DR

This work tackles identifying the liver blood perfusion rate $\xi$ during laser-induced interstitial thermotherapy from MR thermometry data. It formulates a PDE-constrained optimization using the Pennes bio-heat equation with a $P1$-radiation model and Arrhenius tissue damage, where $\xi$ acts as the control. An adjoint-based gradient is derived to efficiently compute $\hat{J}'(\xi)$, enabling a projected quasi-Newton solver (L-BFGS) to recover $\xi$ under nonnegativity constraints. Numerical experiments on synthetic noiseless and noisy data show that perfusion near the applicator can be identified, with L-BFGS outperforming gradient descent and multiple measurements significantly improving accuracy. The approach supports online monitoring and personalized treatment prediction, with planned validation on real MR thermometry data.

Abstract

Using PDE-constrained optimization we introduce a parameter identification approach which can identify the blood perfusion rate from MR thermometry data obtained during the treatment with laser-induced thermotherapy (LITT). The blood perfusion rate, i.e., the cooling effect induced by blood vessels, can be identified during the first stage of the treatment. This information can then be used by a simulation to monitor and predict the ongoing treatment. The approach is tested with synthetic measurements with and without artificial noise as input data.

Figures (11)

• Figure 1: Schematic of the setup and the boundary decomposition.
• Figure 2: Problem setting.
• Figure 3: Identified perfusion rates.
• Figure 4: Convergence history of the optimization methods.
• Figure 5: Evolution of the error in temperature over time for one measurement.

Theorems & Definitions (1)

• Proposition 3.1