Estimulação cerebral profunda: análise térmica via métodos bayesianos

Abstract

The Deep Brain Stimulation (DBS) technique, a neurosurgical procedure commonly employed in the treatment of motor symptoms, is characterized by the use of stimulation leads that receive electrical pulses. Depending on the electrical potential applied, these pulses can cause an increase in temperature in regions adjacent to the electrical application. In this context, enhancing the accuracy of thermal analysis, considering uncertainties in the physical-mathematical parameters, and performing the estimation of unknown parameters are crucial measures to prevent thermal damage or excessive heating resulting from the use of the leads. This work concentrates on the application of Bayesian approaches through computational simulation to analyze the temperature field in a brain with a DBS lead. The classical equation of bioheat transfer in tissues was employed to model heat transfer in the tissue, considering that the heating due to electrical pulses from the lead is represented by a source term symbolizing the electric field generated by the applied potential. The solution to the associated direct problem in this physical-mathematical problem was obtained using numerical approaches such as finite element and finite difference methods. The analysis of the temperature field and parameter estimation were carried out through inverse problems, employing Bayesian inference with the application of particle filters and the Markov Chain Monte Carlo method. In the computational simulations performed, the effects produced by simulated temperature measurements obtained through a sensor located within the brain lead were considered. The results obtained, considering these simulated measurements with varying noise levels, demonstrated accurate estimations of parameters and state variables. The presented methodology also takes into account uncertainties associated with thermophysical parameters and models, proving promising for reducing the risk of injuries related to the DBS technique.