A Homotopical Framework for Modeling Continuous Deformations in Human Body Shape and Ageing

Abstract

This study applies homotopy theory to model the continuous deformations in human body shape and ageing process. We extend the existing work by adding genetic factors and examining the deformation of the body and ageing process, where it is shown that for every growth process and ageing is attained, there exist a growth and ageing threshold for the deformation of the body. The homotopy concept is used to describe the corresponding connected surface of the structure of the body and ageing process. The ageing increases at time variable t. The performance of the continuous deformation functions ,  and  on the map depend on the adjusted interval [0,1], [1,2], [2,3], [3,4], ..., [r,n] to produce the sequence of age up to deformation point at natural death which is the limiting point of the deformed body or point of discontinuity.