Home Calculus • Download PDF by Trachette Jackson, Ami Radunskaya: Applications of Dynamical Systems in Biology and Medicine

Download PDF by Trachette Jackson, Ami Radunskaya: Applications of Dynamical Systems in Biology and Medicine

By Trachette Jackson, Ami Radunskaya

This quantity highlights difficulties from a number organic and scientific purposes that may be interpreted as questions about approach habit or keep an eye on. issues comprise drug resistance in melanoma and malaria, organic fluid dynamics, auto-regulation within the kidney, anti-coagulation treatment, evolutionary diversification and photo-transduction. Mathematical suggestions used to explain and examine those organic and scientific difficulties contain traditional, partial and stochastic differentiation equations, hybrid discrete-continuous techniques, in addition to 2 and 3D numerical simulation.

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This work showed that administration of the chemotherapy with the goal of stabilization of tumor size instead of eradication would yield better results than use of maximum tolerated doses, thus preventing or at least delaying tumor relapse. The authors demonstrated that fast growing sensitive cells can serve as a shield keeping the resistant cells trapped inside the tumor. Lorz et al used a continuous model of anti-cancer therapy resistance under the assumption that resistance is induced by adaptation to drug environmental pressures [37].

26) with a fixed spring constant, k, and fixed rest lengths sj since the spherical elastic vesicle is held together by N points connected by Hookean springs. The rest lengths of the springs, sij for point Xi connected to all other points Xj , j = 1, . . , N, are set to be the initial distances between points in a spherical configuration. For example, given a Hookean spring between two points located at X and Y with rest length s, the general form for the force at either end of the Hookean spring is: fspring = ± k X−Y ||X − Y|| −1 .

This allowed the authors to explore how cells evolve (and may be selected for) under stress imposed by cytotoxic drugs [39]. The same group has also investigated how trait selection may give rise to different types of resistance and what implications this may have for tumor heterogeneity (at the level of mutations) [40]. A recent work of Powathil et al, that uses the Cellular Potts framework has been employed to investigate how the cell-cycle dynamics and oxygen concentration changes influence the development of resistance [41].

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