A perceptron-based learning method for solving the inverse problem of the brain model via poroelastodynamics

Computer simulations and in silico models are currently the best tools for understanding complex biological processes. However, the complexity of biological tissues, with multiple cellular mechanisms in response to changing physical and chemical external stimuli, makes the corresponding mathematical models highly nonlinear with numerous parameters. These parameters are crucial to the models but are often fitted for specific conditions, making the conclusions drawn difficult to generalize. Moreover, some of these parameters will be hard to obtain through either clinical measurements or experiments. Hence, in this study, we introduced a perceptron-based method to determine unknown parameters of water transfer coefficients in the cerebral multi-compartmental poroelasticity model. Based on the nature and conditions of the available data, we designed a straightforward and functional model to solve a steady-state inverse problem. Moreover, we added an analytical solution to restrict the learning tendency of the model. It is to be noted that we only evaluated the unknown parameters without fitting the solution of PDEs. We believe that this study presents a functional perceptron-based approach for investigating and demonstrating unknown parameters using the cerebral multi-compartmental poroelasticity model. Besides, the algorithm was fully presented since we believed that our scheme has the ability to utilise in various field for those who need to estimate unknown parameters in PDEs. Furthermore, we tested the efficiency and effectiveness of the proposed method and demonstrated how the framework can help estimate the parameters rapidly. Finally, we discussed the unmet needs and forecasted future tasks of this framework.