Mathematical Modelling of Cancer Treatment with Immunotherapy and Magnetic Drug Targeting

Abstract

Cancer remains one of the leading causes of death around the globe, whereas cancer therapy continues to be a major challenge for contemporary medicine due to tumor mi- croenvironments which include growth factors (cytokines and hormones), immune cells, extracellular matrix, fibroblasts, signalling molecules (cytokines and chemokines), and other connective tissue cells. As a consequence, many interstitial barriers are lifted, interfering with both convective and diffusive mechanisms of therapeutic drug penetration. Recently, with the advancement of molecular and tumor biology, treatment options such as immunotherapy and magnetic drug targeting (MDT) have significantly changed the paradigm of cancer treatment. Innovative treatment strategies have both been developed to maximize efficacy while minimizing side effects. This research aims to use theoretical analysis and numerical tools to examine the mechanism of tumor-immune dynamics, as well as how to effectively disperse therapeutical drugs to tumor sites during magnetically targeted drug delivery. In this study, we focused on the role of immunotherapy in cancer treatment studied using a fractional-order model for tumor-immune interaction incorporating the treatment of cytokine interleukin-2 (IL-2) aimed at boosting the immune system’s ability to fight cancer. Our results indicate that in some cases, adoptive cellular immunotherapy alone or a combination of the adaptive cellular immunotherapy and cytokine interleukin-2 can achieve satisfactory stable tumor control in such a way that; with little adoptive cellular immunotherapy alone to the system, the situation remains the same as without any treatment. In addition to that, a model magnetic drug targeting to determine the capture conditions on the efficient dispersion of drug-coated nanoparticles in a tumor environment was presented. Thus, drug-coated magnetic nanoparticles are taking longer times to reach the tumor as a result of higher volumes fractions of magnetic particles, the magnetiza-tion of the magnetic field, drug elimination, and source term. Furthermore, increases in tumor-magnet distance, permeability of the microvessels, Peclet number, and radius of the nanoparticles slow the ability of the drug-coated nanoparticles to reach the tumor. As a result of these observations, researchers are able to formulate essential considerations to be used in implementing potential therapeutic intervention aimed at reversing cancer therapy.