I need a good model of ordinary differantial equation (ode) for evaluate a tumor cell under different stimulation. after simulation , I want to do experiment and evaluate effectiveness of my model.
Dear Emad,
There are two good papers on this subject called 'Mathematical Modelling of Tumour Growth Treatment' by Heiko Enderling and A. J. Chaplain (2014), and 'A mathematical model of tumour growth and its response to single irradiation' by Yoichi Watenabe, Erik L. Dahlman, Kevin Z. Leder and Susanta K. Hui (2016).
You can either model this problem via cancer cell growth in terms of c, as in the first paper, or by using the volumetric, V, increase of the tumour as in the second.
A simple model would be to commence by solving either of the two following ODEs:
dV/dt = bV .............................................................................................(1)
representing the tumour's exponential cancer growth in terms of volume, V, to obtain:
V = A Exp(bt)..........................................................................................(2)
or you could adopt the Logistic Equation:
dV/dt = aV(K - V)/K............................................................................... (3)
to obtain:
V(t) = AK/(A + Exp(-at))..........................................................................(4)
where a, b, A, and K are constants to be determined. You should be aware that, certainly in equations (3) and (4), K represents the carrying capacity, presumably of the region around the tumour. I think that in equations (3) and (4), Enderling and Chaplain (2014) denote the volume, V, by c, the latter representing the net growth of cancerous cells.
Hope that this helps.
Kind regards
Stephen Mason
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