Mathematical and Computational Studies on Progress, Prognosis, Prevention and Panacea of Breast Cancer by Suhrit Dey & Charlie Dey

Author:Suhrit Dey & Charlie Dey
Language: eng
Format: epub
ISBN: 9789811660771
Publisher: Springer Singapore

5.3 Computational Studies

Before using any monoclonal drug, let us study how immunotherapy could be done by using medications that will reduce the rate of growth of cancer all over the computational field representing the human body and at the same time destroy cancer cells. In this regard, we will consider two cases, one with a very poor immune system.

 ,  = fixed for all  = the initial value of

We solved this equation numerically. Regarding the values of on the boundaries, in most cases we have extrapolated these values from the cells near to the boundaries. We have also assumed sometimes that on the boundary There is a reason for that. If cancer cells move individually, they are generally destroyed by our defense mechanism. So very cleverly, they move in a group forming thereby a joint fight against T-cells and B-cells. So within one mesh size possibly they change very little to nothing. However, this may not be happening in every case.

We have considered a case where cancer is growing at the rate of 450%. Medications for immunotherapy are given intravenously, and a fixed dosage is maintained constantly in the blood. The inputs are given in the inputs for Fig. 5.1. the defending cells = 100, which is indeed very poor in comparison with the number of cancer cells in the primary site which is 10000 at each grid point and all over the body at each grid point all over the computational field. Also , the rate at which cancer cells are being eliminated by each element of . This is weak in this setup.

Fig. 5.1Advanced immunotherapy, body’s immune response is weak

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