Capillary network, cancer and kleiber law

G Dattoli, S Licciardi, C Guiot, TS Deisboeck - arXiv preprint arXiv …, 2014 - arxiv.org
G Dattoli, S Licciardi, C Guiot, TS Deisboeck
arXiv preprint arXiv:1403.4443, 2014arxiv.org
We develop a heuristic model embedding Kleiber and Murray laws to describe mass growth,
metastasis and vascularization in cancer. We analyze the relevant dynamics using different
evolution equations (Verhulst, Gompertz and others). Their extension to reaction diffusion
equation of the Fisher type is then used to describe the relevant metastatic spreading in
space. Regarding this last point, we suggest that cancer diffusion may be regulated by Levy
flights mechanisms and discuss the possibility that the associated reaction diffusion …
We develop a heuristic model embedding Kleiber and Murray laws to describe mass growth, metastasis and vascularization in cancer. We analyze the relevant dynamics using different evolution equations (Verhulst, Gompertz and others). Their extension to reaction diffusion equation of the Fisher type is then used to describe the relevant metastatic spreading in space. Regarding this last point, we suggest that cancer diffusion may be regulated by Levy flights mechanisms and discuss the possibility that the associated reaction diffusion equations are of the fractional type, with the fractional coefficient being determined by the fractal nature of the capillary evolution.
arxiv.org
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