Application Of Homotopy To The Ageing Process Of Human Bone

Vidhya K.R, Parvathy C.R


This article presents the ageing process of human bone which can play a major role in the structure of the human body from the concept of homotopy in algebraic topology. The structure of the human bone, which is precisely connected is consider here to be topologically equivalent to a cylinder. The elegant but complex skeletal shape of the human bone is described by the Cartesian functions of α = S1 X I and H, H' : α -> α. The bone shape of the human body at an early stage. That is the bone shape of the newborn is called α = S1 X I homotopy. The process of continuous ageing bone is considered to be family of homotopy based on its functions. The study discusses algebraic topology of homotopies through the homotopy of stable functions of the human bone from infancy to old age.


Homomorphism, Homotopy, Homology, Chain complex, Topological Space.

Full Text:



Allen Hatcher, Algebraic Topology, Cambridge University press – 2002.

Andrew H. Wallace, Algebraic Topology: Homology and Cohomology, University of Pennsylvania – 1970.

J. Dugundji, Topology, Allen and Bacon, Inc. – 1966.

James R. Munkres, A first course in Topology, Prencite – Hall. Inc. New Jersey – 1967.

W. S. Massey, A Basic course in Algebraic Topology, Springer-verlag, New York.

Lewis Brew, William Obeng-Denteh, David Delali Zigli. Application of Homotopy to the Ageing Process of Human Body within the framework of Algebraic Topology. Journal of Mathematics Research – Vol. 11, No. 4; August 2019.

Laurence Boxer, Ismet Karaca, Ahmet Oztel. (2011) Topological Invariants in Digital Images, Journal of Mathematical Sciences: Advances and Application. 11(2), 109-140.

J. L. Giavitto and O. Michel. (2003) Modeling the Topological Organization of Cellular Processes, Bio systems. 70(2), 149-163.

Anas A. M. Arafa, S. Z. Rida, Hegagi Mohamed Ali. Homotopy Analysis Method for solving Biological population Model. Vol. 56, No. 5, November 15, 2011.

F. Guerrero, F. J. Santonja, R. J. Villanueva. Solving a model for the evolution of smoking habit in Spain with homotopy analysis method. 14(2013) 549-558.



  • There are currently no refbacks.

Copyright (c) 2023 Vidhya K.R, Parvathy C.R

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.