On Refining the Input Data set to Mathematical Models Simulating Arterial blood flow in Humans

Abstract

In this paper, we worked on methods to reduce the input data set to the mathematical models developed to simulate blood flow through human arteries. In general, any mathematical model designed to mimic a natural process needs specific information on its model parameters. In our models, the inputs to these parameters are from the human arterial system, i.e., the anatomical data on arteries and physiological data on blood. Besides these, there are few other parameters in the models describing mechanisms, such as the pulsatile nature of the blood flow and the arteries' elastic behavior. These mechanisms described using mathematical relations help assign values to the parameters that satisfy mathematical specifications or requirements. However, with this method of assigning values, there is a possibility that some of the data sets constructed simulate the same state of the system (arterial system) even though the values assigned significantly differ from each other in magnitude. Moreover, identifying such data sets is not an apparent task but requires robust procedures. Thus, in this work, we attempt to shed light on a data size reduction technique to identify all such model parameters' in-significant values and eliminate them from the input data set. We propose the statistical testing procedure to identify a significant difference in the dependent variables' values (whose values are computed using the mathematical models) with the independent variables (the model parameters). This novel approach could efficiently identify the inputs mimicking similar arterial system states and build a refined input data set.