TITLE:
A Study on Multipeutics
AUTHORS:
Jens Christian Larsen
KEYWORDS:
Cancer, Mass Action Kinetic System, Quadrapeutics, Immune Therapy
JOURNAL NAME:
Applied Mathematics,
Vol.8 No.5,
May
27,
2017
ABSTRACT: Multipeutics is the simultaneous application of m ≥ 4 cancer treatments. m = 4 is quadrapeutics, which was invented by researchers at Rice University, Northeastern University, MD Anderson Cancer Centre and China Medical University, see [1]. Multipeutics is our idea. From section 6 Summary, it follows that multipeutics can be more potent than quadrapeutics by comparing these two mathematical models. The first two treatments in quadrapeutics are systemically administered nano gold particles G and lysosomal chemo therapeutic drug D. They form mixed clusters M primarily in cancer cells and can be excited by a laser pulse, the third treatment, to form plasmonic nanobubbles N. These nanobubbles can kill the cancer cells by mechanical impact. If they do not the chemo therapeutic drug can be released into the cytoplasm, which might be lethal to the cancer cell. The fourth treatment is x rays X and the cancer cells have been sensitized to x rays by the treatment. We present an ODE (ordinary differential equations) model of quadrapeutics and of multipeutics, which is quadrapeutics and n ≥ 1 immune or chemo therapies. In the present paper we have found a polynomial p of degree at most 2(n + 3), such that a singular point (C, D, G, M, N, I1, …, In) will have p(M) = 0 Here I1, …, In are immune or chemo therapies. So this gives us candidates for singular points. Quadrapeutics is treated extensively. We find in theorem 3 a polynomium s of degree at most six in M such that a positive singular point (C, D, G, M, N) of the quadrapeutics system will have s(M) = 0. The main theorem of the present paper is the multipeutics theorem, saying that the more treatments we apply the lower the cancer burden, even if we take the doses of each treatment smaller. From the proof of this theorem, we can say, that quadrapeutics can outperform chemo radiation if the nanobubble kill rate k21 is sufficiently big. See also Figure 1 and Figure 2 and the text explaining them.