By Trachette Jackson, Ami Radunskaya
This quantity highlights difficulties from various organic and clinical purposes that may be interpreted as questions on approach habit or keep an eye on. subject matters contain drug resistance in melanoma and malaria, organic fluid dynamics, auto-regulation within the kidney, anti-coagulation remedy, evolutionary diversification and photo-transduction. Mathematical thoughts used to explain and examine those organic and clinical difficulties contain traditional, partial and stochastic differentiation equations, hybrid discrete-continuous ways, in addition to 2 and 3D numerical simulation.
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Additional info for Applications of Dynamical Systems in Biology and Medicine
Lorz, T. Lorenzi, J. Clairambault, A. Escargueil, B. Perthame (2015) Modeling effects of space structure and combination therapies on phenotypic heterogeneity and drug resistance in solid tumors, Bull. Math. Biol. 77(1):1–2 39. O. M. Greene, D. M. Gottesman (2013) The role of cell density and intratumoral heterogeneity in multidrug resistance. Canc. Res. 73(24):7168–7175. 40. J. Greene, O. M. Gottesman, D. Levy (2014) The impact of cell density and mutations in a model of multidrug resistance in solid tumors, Bull.
To further understand the importance of the microenvironmental niche in the case of acquired resistance, we tracked the clonal evolution of the tumor. We found that the microenvironmental niche plays a bigger role in determining the growth and heterogeneity of the tumor when Δdeath is not high. L. Gevertz et al. sufficiently small, the microenvironmental niche influences which cells survive the longest, though all cells will eventually die. Cells originally located near the lowdrug/normoxic niche initially accumulate damage at a much slower rate than their neighbors while still increasing their death threshold.
Within this parameter regime, the tumor is not monotonically decreasing in size, as observed in the no resistance case and in the successful treatment of a tumor with pre-existing resistant cells case (FIG. 3a). There is a transient period of time (approximately five cell cycles in length) during which the cancer cells accumulate drug but do not respond to the drug. Once drug levels have caused enough DNA damage, a transient period of tumor shrinkage occurs. The cancer cells that are eliminated during this period are the ones with adequate access to the drug.
Applications of Dynamical Systems in Biology and Medicine by Trachette Jackson, Ami Radunskaya