BICOMPLEX AND MULTICOMPLEX ANALYTICAL FLAVOUR OF NON-NEWTONIAN TWO-PHASE BLOOD FLOW IN PULMONARY DISEASES
By
Dheerendra Kumar1 , Mohit Sarkar2 , Sanjib Kumar Datta3* , Surya Kant Chaturvedi4 and Govind Singh5
1Department of Mathematics and Computer Science, R. D. University Jablpur, Madhya Pradesh, India, 482001. 2Department of Mathematics, Fakir Chand College (Diamond Harbour), Diamond Harbour, South 24 Parganas, West Bengal, India, 743331. 3Department of Mathematics, University of Kalyani, Kalyani, Nadia, West Bengal, India, 741235. 4Department of Biological Science, MGCGV Chitrakoot University, Chitrakoot, Satna, Madhya Pradesh, India, 485334. 5Faculty of Engineering & Technology, MGCG University, Chitrakoot, Satna, Madhya Pradesh, India, 485334.
Email: 1dr.dheerendrakmaurya@gmail.com; 2mohitsarkar98@gmail.com; 3∗ sanjibdatta05@gmail.com; 4 suryakantmgcgv@gmail.com; 5 eduinfoexpert@gmail.com (
Received : November 25, 2025; Revised : December 12, 2025; Accepted : June 25, 2026)
DOI: https://doi.org/10.58250/jnanabha.2026.56103
Abstract
In the paper the blood flow of a human suffering from a disease like cancer has been studied through the mathematical model for better treatment in the field of medicine, in which blood fluctuation has been studied through power law model with non-Newtonian tendency and the blood is divided into two phases RBC & plasma. The entire equation used in the present study has been developed and presented in tensorial form in a bio-fluid mechanical setup. For solution, both analytical and numerical techniques have been used. This paper also presents a comprehensive bicomplex and multicomplex analytical extension of the mathematical model for blood fluctuations during pulmonary diseases, extending the classical tensorial power-law formulation. The bicomplex extension introduces dual imaginary components to model mechanical and electrochemical fluctuations simultaneously, while the multicomplex framework captures interactions among multiple blood components such as red blood cells, plasma, white blood cells and platelets. The model integrates these algebraic structures into the governing tensorial equations, develops explicit analytical solutions in cylindrical coordinates and analyzes how bicomplex coupling modifies velocity, pressure and flow-rate behavior in diseased pulmonary vessels. The detailed stepby-step derivations, theoretical proofs and biophysical interpretations demonstrate that the extended framework unifies mechanical hemodynamics with electrophysiological oscillations, offering deeper insights into blood-flow irregularities observed in clinical data.
2020 Mathematical Sciences Classification: 76A05, 92C05, 92C10, 92C35, 92C50, 92B05, 92B20, 37M20, 30G35, 32A30.
Keywords and Phrases: Hemoglobin, Blood fluctuation, Power law model, Cancer, Red blood cells, Plasma, White blood cells, platelets, Bicomplex and multicomplex analytical flavour, Mechanical hemodynamics, Electrophysiological oscillations.