Parkinson’s Disease (PD) is a disorder in the central nervous system which includes symptoms such as tremor, rigidity, and Bradykinesia. Deep brain stimulation (DBS) is the most effective method to treat PD motor symptoms especially when the patient is not responsive to other treatments. However, its invasiveness and high risk, involving electrode implantation in the Basal Ganglia (BG), prompt recent research to emphasize non-invasive Transcranial Electrical Stimulation (TES). TES proves to be effective in treating some PD symptoms with inherent safety and no associated risks. This study explores the potential of using TES, to modify the firing pattern of cells in BG that are responsible for motor symptoms in PD. The research employs a mathematical model of the BG to examine the impact of applying TES to the brain. This is conducted using a realistic head model incorporating the Finite Element Method (FEM). According to our findings, the firing pattern associated with Parkinson’s disease shifted towards a healthier firing pattern through the use of tACS. Employing an adaptive algorithm that continually monitored the behavior of BG cells (specifically, Globus Pallidus Pars externa (GPe)), we determined the optimal electrode number and placement to concentrate the current within the intended region. This resulted in a peak induced electric field of 1.9 v/m at the BG area. Our mathematical modeling together with precise finite element simulation of the brain and BG suggests that proposed method effectively mitigates Parkinsonian behavior in the BG cells. Furthermore, this approach ensures an improvement in the condition while adhering to all safety constraints associated with the current injection into the brain.
Apply the Current Constraints Inject the new Current Table 1. Pseudo-algorithm of the proposed method. central line of the two hemispheres to mimic the actual location of the BG41. A cube with the length of 0.07 mm was assumed in the target area as a part of STN to calculate its stimulating current36. This cube represents just a small part of STN area corresponding to the part considered in BG mathematical model36. Due to the small size of the cube the current density and the distributed electric field of the FEM elements in this area are roughly the same. Therefore, the average current density of the STN equals the current density of each FEM node in this area. To avoid lengthy processing time, we used the simple spherical head model for finding the initial weight values and also the best electrode numbers. Therefore, result of both investigations is reported in this section.
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Number of electrodes Three different numbers of electrodes 9, 19, and 32 were examined according to the 1020 standard EEG configuration42. For this study, the electrode numbers were selected to encompass a range from the minimum to the possible average number of electrodes utilized in the literature23,24,34. As it is shown in Fig. 4, after applying the proposed method, the electric field distributed in the target area with 32 electrodes is higher than 19 and 9 electrodes. However, there is not much difference between the electric field distribution of 19 and 32 electrodes (0.238 and 0.243 V/m respectively). While using more electrodes provide more degrees of freedom for the focalization and slightly better results, it increases computational cost and requires more complex hardware. Thus, we adhere to using 19 electrodes for further simulations.
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Initial weight vector In this section we investigated whether the system would converge to the optimal point with different initial weights assigned to the electrodes, using the amplitude of stimulation current as the initial weight vector. Although there is freedom in choosing any initial weight vector within the current constraints, four different initial sets are examined to compare their convergence rates. Suitable initial weight vector leads to faster convergence rate. Considered initial weights include: 1. Equal weights with equal signs (all positive or all negative) 2. Equal weights with arbitrary signs (arbitrary positive or negative numbers) 3. Arbitrary weights with equal signs 4. Arbitrary weights with arbitrary signs
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According to Fig. 5, the best initial point is when equal positive currents are assumed for all electrodes as case (1) converges slightly faster than other methods. Despite the nonlinear feature of the problem, using the proposed adaptive procedure ensures convergence of all initial weight vectors. The study considered the healthy state as
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