An artificial neural network based on radial basis methodology using delay effects in the Parkinson's disease model

Area of Science:

• Computational neuroscience
• Mathematical modeling of diseases
• Artificial intelligence in medicine

Background:

• Parkinson's disease is a complex neurodegenerative disorder.
• Mathematical models are crucial for understanding disease dynamics.
• Accurate numerical solutions are needed for delay differential equations in biological systems.

Purpose of the Study:

• To develop and implement a computing neural network framework for solving the delay Parkinson's disease model.
• To numerically simulate the interactions between five key components of the disease: neurons, microglia, and T-cells.
• To validate the accuracy and efficiency of the proposed computational approach.

Main Methods:

• A two-layered neural network architecture utilizing radial basis functions.
• Dataset generation via the implicit Runge-Kutta method.
• Model training using Bayesian regularization with distinct training, testing, and validation sets.

Main Results:

• Achieved high accuracy with absolute error values ranging from 10^-07 to 10^-09.
• Demonstrated optimal training performance with error values between 10^-11 and 10^-13.
• Validated the proposed scheme through error histograms, regression analysis, and state transition plots.

Conclusions:

• The proposed two-layered neural network framework provides an accurate and reliable method for solving the delay Parkinson's disease model.
• This computational approach offers a robust tool for simulating and analyzing neurodegenerative disease progression.
• The findings highlight the potential of AI-driven methods in advancing our understanding of complex biological systems and diseases.