Use of Some Standard Mathematical Models in Physiology and Pathology

ABSTRACT

Most of the physical phenomena in the actual world exhibit non-linear character. In recent years, significant advances have occurred in the design, construction, and development of mathematical/analytical models for the solution of these physical problems. If appropriate initial and boundary condition(s) are associated with the models, the whole system generates a mathematical problem. In this way, a mathematical model establishes a relationship between mathematics and the rest of the world (the physical world). Analytical models are developed (or modified) based on mathematical concepts and using mathematical languages and symbolism. The three major advantages of using mathematical tools over others in modelling are • Mathematics can provide well-ordered rules for manipulation -essential in modelling • Mathematics gives unique result for an investigation Mathematics is capable of proving general results from which the results for particular cases may be deduced assigning appropriate values to the parameters (in the admissible range) involved in the investigation. Information about the physical system represented by the model is estimated qualitatively and quantitatively by solving the mathematical problem by applying the best possible mathematical technique. The selection of appropriate mathematical methods for the solution will depend on the purpose for which the model may be applied for investigation. The models are validated by comparing the analytical results of the mathematical problem with the behavior exhibited by the physical problem. If the two do not match, the model is modified by including more parameters or leading to rejection of the model. As the physical models are based on experimental investigation, so they are superior to the mathematical models constructed on the theoretical investigation. But a mathematical model has the advantage of studying the role of key parameters controlling the system within a short period. Mathematical modeling is essential in studying human physiological problems (brain injury, blood flow, population growth, and spread of COVID-19 etc) where experimental investigations cannot be performed to obtain adequate data. So, improved mathematical models are developed (sometimes old models are modified) using suitable symbolism to define the operation of a physical system. As most of the phenomena in the physical world cannot be described by mathematical objects (due to their non-linear character), mathematicians and scientists throughout the globe are continuously developing and modifying mathematical models to solve the practical problems effectively in the domain of physical science, bio-science, social science, medicine, statistics, management, engineering, and technology. They are extensively utilized in making predictions when a particular parameter is varied in a range. The models play a convincing role in health science not only in the prediction of occurrence of critical health irregularities but they may reduce the risk in the treatment of fatal diseases like cardiovascular and neurological dysfunctions, brain injury due to vehicular accidents and soccer games, novel coronavirus infection, absorption of medicine in the human metabolic system leading to morbidity and even death. Our best endeavours is to construct some sophisticated mathematical models for the following types of problems • in the study of Brain Injury Problems • in the study of Blood Flow through an Atherosclerotic (diseased) Arterial Segment • in Decaying of the absorption of a medicine in human rheological system• in estimating the spread of a disease (COVID 19) growing or decaying exponentially • in estimating the population growth in the coming years.We sincerely believe that the book chapter will throw light on the latest developments in the field of mathematical modelling and thus reinforce and solidify the understanding of this ever expanding domain. © 2022 Nova Science Publishers, Inc.