A Consideration of the Expanded Partial Differential Equations and the Compartment System as the Background of the ABR System

Abstract

AbstractIt is well known that the characteristics of ABR (Auditory Brainstem Responses) have been used widely on many fields, and especially they have been adapted on the medical and clinical fields. For examples their characters are discussed on the fields of inspection of some consciousness levels etc. But the characters of the ABR detail system, especially with regard to their background theories are not sufficiently discussed. And the ABR characteristics derived directly from the experiment data are not sufficiently analyzed too. Therefore the theories of the ABR system and the detail model derived from the experiments must be made to be developed. Especially in order to analyze the ABR system the fundamental background theory and its expanded consideration must be preformed more widely. In this paper, firstly the fundamental partial differential equations are discussed and the consideration of the relation between their fundamental differential equation formulas and their experimental formulas is described. And secondly the meaning of characters among the partial deferential equations is considered and using the estimated improvement method the expanded partial differential equations is derived and proposed as a kind of more generalized formula of the fundamental characters. Especially the high order partial differential equations are considered and the characteristics of the ABR system are discussed considering the compartment system model. And thirdly an analysis method to use the synthesis technique of compartment system by an inverse procedure of a solution of such ABR differential equation models is described. And finally the conclusion and further works are described.Keywordsthe ABRpartial differential equationscompartment system