Compartment modelling and eigenvalue expansion to study the drug concentration in capillary and tissue regions surrounding the malignant tumour

Abstract

The drug transport mechanism in the biological tissue can be modelled for its effective and efficient performance. Mathematics is playing a key role in almost all biomedical research problems including drug kinetics. A mathematical model based on reaction–diffusion equation has been formulated to understand the drug transport and its diffusion in a cancerous tissue. The eigenvalue expansion has been used to obtain the solution of the ordinary differential equations concerning the rate of change of drug concentration in different compartments including capillary and tissue regions surrounding the malignant tumour cells. The graphs were plotted to illustrate the variation of drug concentration with respect to time using MATLAB software. It has been observed from the graphs that the drug concentration decreases in the first compartment and gradually increases in the second compartment to some value and then decreases again in association with the concentration of the drug. Moreover, the behaviour of the tumour cells with changing drug concentration is simulated with respect to time and the results were compared and verified with the empirical data of (Unni and Seshaiyer in Comput Math Methods Med 2019:4079298, 2019).