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Can You Take the Heat? Model of Temperature and Neuronal Membrane Potential Changes in the Brain Tissue due to Deep Brain Stimulation

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Abstract

In the world, millions of people live with neurological conditions such as epilepsy, Parkinson's or major depression disorder (MDD). As a viable treatment for their symptoms, Deep Brain Stimulation (DBS) was created. This medical procedure involves a surgery where a magnetic probe (neurostimulator) is implanted into a specific region of the brain. There, the electrodes in the probe produce electromagnetic pulses to regulate neuronal activity. Albeit this is a verified and reliable procedure, many unknowns arise from DBS; such as the extent of neuronal activity alterations due to the increase of brain temperature due to electromagnetic stimulation. Hence, the objective of this project is to simulate in COMSOL how DBS can influence the brain tissue in terms of temperature variation and neuronal activation. A 2D model of the thalamic and hypothalamic regions of the brain in contact with the DBS probe was created. The model solved the bioheat equation, the Laplace equation for the voltage of the electrodes, the Nernst equation and Hodgkin-Huxley equation for the membrane potential. To attain an accurate model, the process of validation, verification, mesh convergence and sensitivity analysis were also conducted and included in the paper. The results of the model provided insights on how heat transfer takes place from the probe to the thalamus and the hypothalamus as a result of electrical heating. Essentially, the change in temperature in the tissues considering a point 0.01 mm away from the electrode was of 0.0055 ºC in the thalamic region (starting from the initial temperature of 38.5 ºC in the brain, to 38.5055 ºC), whereas in the hypothalamic region it was 0.0048 ºC (where the peak temperature was 38.5048 ºC), after 1 second of heating. The same analysis was performed for a point 0.73 mm away from the electrode and the temperature change was 0.0023 ºC and 0.0020 ºC for the thalamic and hypothalamic regions respectively. When extended to a minute, the thalamus increased in temperature by around 0.042 ºC. The increase in temperature did not exceed 1 ºC, and thus, it can be inferred that the temperature change was optimal. This was validated by a study made by Elwassif et al., where they modeled a brain temperature increase of nearly 0.8 °C after 15 minutes during DBS. Approximating this rate for 1 minute gives a temperature increase of 0.053 ºC, exceeding the 0.042 ºC observed at the point 0.73 mm away from the electrodes. Additionally, considering that same point, the membrane potential sharply increases from -70 mV, which is the resting membrane potential, all the way to +25 mV. The closer point’s membrane potential experienced an increase to +60 mV, which is the maximum action potential. The membrane potential at both points then continues to periodically oscillate between -35 mV and either +25 or +60 mV, respectively. This oscillation is closely mimicking the changes in membrane potential during normal neuronal activity. The temperature and membrane potential trend with varying distance (along a line), in the tissue domain was also observed, exhibiting expected trends of reduction in values with increasing distance from the electrodes with the highest temperature for the thalamic region being 38.5055 ºC and that for the hypothalamic region being 38.5048 ºC after 1 second of stimulation. The membrane potential along an arc in the tissue domain shows a gradual decrease with a maximum value of 60 mV near the electrode and -35 mV at a distance of 10 mm from the electrode. As both temperature and membrane potential values are directly influenced by the voltage from the electrodes, the trend of the 1.8 V pulse sent by the electrode over distance was also assessed. The voltages at 0.01 mm, 0.73 mm, and 6.73 mm from the electrode were found to be 1.8 V, 1.15 V and 0.15 V respectively. Conclusively, the simulation supports the notion that the voltage from the DBS procedure does have an effect on increasing the temperature and the membrane potential of the brain. These results are significant because DBS can induce a high amount of heat accumulation over time in patients who have undergone the procedure, which can also cause serious side effects which may impact brain function. The results of this study welcome further investigation and this can be done by examining modifications in probe features and placement of electrodes to maximize efficiency and reduce overall increase in brain temperature. A study can also be performed to understand the kind of changes induced in the tissue microenvironment due to increase in temperature. Understanding the dynamics of heat transfer can help estimate which regions of the brain can be highly impacted and how this can be mitigated.

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2023-05-17

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Deep Brain Stimulation (DBS); COMSOL; Temperature; Membrane Potential

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Attribution 4.0 International

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