Low-Dimensional Multi-Scale Model And Analysis Of Cerebral Cortogenic Structure

Understanding the relationship between brain structure and function is of great significance for the diagnosis and treatment of some neurodevelopmental diseases and is a widespread concern in clinical and life areas.In recent years,more and more evidence shows that the effect of force has a direct impact on the development of brain structure(such as the formation of ditches),brain trauma,etc.,which has aroused the attention of scholars in various fields such as mathematics,mathematics,physics,life sciences,medicine,and gradually formed a new field of multidisciplinary crossresearch.Because of the ultra-soft properties of brain tissue,the complexity of structural morphology and the multi-scale(from cell level to tissue level)characteristics of its composition,it is difficult to model and analyze its dynamics.How to establish a reasonable model of magic and analyze its behavior of magic brings great challenges to researchers.Elastic thin rod as a mechanical model of slender structure is widely used in civil engineering.For example,it can be used as a mathematical model of bridge,ropeway,ropeway,etc.to study its behavior under the external load.In recent years,it has attracted much attention because of its precise description of the spatial configuration of DNA molecules.The cerebral cortical cortical can be reduced to a one-dimensional elastic morphological rod model under certain symmetry conditions.Because of the heterogeneous structural characteristics of the cerebral cortology,the dynamic equation describing its morphology is a strong nonlinear equation,which brings difficulties to its solution.The first problem studied in this paper is the establishment and analysis of the elastic rod model of cerebral cortique structure.Lie group analysis is a powerful analytical tool,especially for nonlinear equations can be approximated,the second problem studied in this paper is the application of symmetry theory to the analysis of neuroscale dynamics models in the brain.Specific content includes:(1)The one-dimensional elastic rod model of the cerebral cortique and its precise solution are studied.The gray matter layer of the brain is regarded as an elastic thin rod model that is adhesively connected to the white matter layer of the brain,which causes flexion behavior during growth due to differences in the performance of the two substances.The constraint of white mass to gray mass is regarded as the distribution force of elastic fine rod,thus establishing the elastic fine rod equilibrium difference equation which is affected by the substrate,and by introducing the compound curvature,the equilibrium difference equation is represented as the curvature equation form,thus expressing the elastic fine rod equilibrium micro equation affected by the substrate as similar in mathematical form.Based on Kirchhoff's dynamics analogy,a method of comparing schrodinger's equation solution is proposed,and the solution of Schrodinger's equation is transplanted to this curvature equation,thus giving a new kind of analytical solution to the elastic bar equation constrained by the substrate.Based on this solution,the one-dimensional geometric form of the cerebral cortical cortical is drawn,which provides a new way to solve the cerebral cortical model.(2)Noether symmetry and conservation of the multi-scale model of neuron dynamics electromechanical coupling were studied.The well-known Hodgkin-Huxley neuron system model successfully explains the electrophysiological phenomena of neuron cells.However,less attention is paid to the cause-force effect of these electrophysiological phenomena,thus limiting their clinical application.Because of the ultra-soft properties of the cerebral cortical,its mechanical response is complex,so considering the mechanical factors and electro-process coupling,the dynamic equation describing its mechanical behavior is bound to show strong nonlinearity,this part of the symmetry analysis is applied to the model,giving the amount of conservation of its existence.The model of force-electric coupling of the neuron power system of the brain is introduced first--the mechanical and electrical coupling system across scales.Using Hamilton's principle,the Lagrange equation represented by general coordinates of neuron electromechanical coupling system is derived.By calculating the variables of the Hamilton principle of the neuron dynamics model,the noether symmetry judgment of the neuron dynamics model is given,and the form of Noether conservation is derived.The conservation form of neuron dynamics models in different states is discussed.From the specific expression form of conservation,we can get below the resting voltage,that is,the ion channel inactivated state,there will be no brain discharge phenomenon,at this time the brain structure is in the static equilibrium state,but there will be changes in ion concentration and small deformation inside the brain,when the sodium ion channel activation state,due to no external action,at this time closed circuit,there is only microscopic state changes,that is,the transformation between electrical energy and ion dynamic energy,when the neuron system deformation and discharge,Is the transformation relationship between dynamic quantity and electrical quantity.The results can provide a reference for qualitative understanding of the properties of neuron cell dynamics models and numerical calculations.