Thermodynamic Modeling And Analysis Of Neural System Based On Canonical Ensemble

With the development of functional magnetic resonance imaging technology,the further research of brain can be achieved by analyzing the signal of BOLD(Blood Oxygenation-Level Dependent).This article tries to analyze the mechanism of neural system in the perspective of dissipative structure by using the theory of canonical ensemble and build canonical ensemble model to analyze the thermodynamic properties of Alzheimer's disease in order to evaluate the neurological function of patients.The content includes the following aspects:First,we construct a thermodynamic model of neural system based on canonical ensemble in the perspective of thermodynamics and statistical physics.The brain region is regarded as the ensemble,and the voxel is the particles of the ensemble.The generalized kinetic energy is used to evaluate the physiological state of particles and calculate the partition function.Based on the partition function,we calculate the free energy,entropy and internal energy and analyze the thermodynamic properties of the brain regions by using these parameters.Through the analysis of experimental result,it is found that the free energy and generalized kinetic energy of the activated brain regions are higher than that of the non-activated brain regions.the entropy of the activated brain regions is lower than that of the non-activated brain regions.The experimental results show that the thermodynamic model of the neural system based on the canonical ensemble can effectively sketch and explain the neural working mechanism of the brain from the perspective of thermodynamics.Then,we propose a hypothesis in the perspective of dissipative system: the nervous system of AD patients will increase its entropy and decrease its free energy due to the loss of physiological tissue order,and the system will change from order to disorder.To prove the hypothesis,we analyze the change in thermodynamic characteristics of AD patients through the thermodynamic model of the neural system based on the canonical ensemble.The time series of thermodynamic parameters such as free energy and entropy can be calculated by combining the model with the window function,and then statistical analysis and pattern classification are performed.According to the experiment results,it can be found that the free energy of AD patients is lower than that of healthy subjects and the entropy of AD patients is higher than that of healthy subjects.This conclusion is consistent with the hypothesis we proposed.Besides,the experimental results also verify the feasibility of the thermodynamic model for the neural system,and show the potential application of thermodynamic parameters in AD assisted diagnosis.Finally,because of the subjective and one-sidedness of the existing methods for assessing neurological function,we propose two methods for assessing neurological function in AD disease based on neuroimaging: the method based on canonical ensemble and the method based on the link strength of brain network.The experimental results show that both models can objectively and effectively distinguish between AD patients and healthy subjects.At the same time,the two scoring results are strongly correlated with the current MMSE score commonly used in clinical diagnosis in hospitals,which proves that the two methods for neurological function assessment are feasible.