Homeorhesis-based modelling and fast numerical analysis for oncogenic hyperplasia under radiotherapy

Abstract

A few previous works of the authors derived and discussed the space-time mathematical description, the PhasTraM model, for oncogenic hyperplasia regarded as a genotoxically activated homeorhetic dysfunction. The model is based on the fluid-tosolid-and-back transitions and nonlinear reaction-diffusion equation relevant to a series of the key biomedical facts and distinguishing features of living systems. The first computer-simulation results have also been reported. The present work generalizes the PhasTraM model for the effect of radiation therapies (RTs), both external and internal. The resulting model also includes the autocrine mechanism promoting oncogenic hyperplasia and the suppression of this process by certain drugs. The autocrine signalling is implemented by the transforming-growth-factor-α (TGF-α) molecules released by the cells and bound to the epidermal-growth-factor receptors (EGFRs) at the cell surface. The suppression can be carried out by a drug deactivating the mentioned molecules. The work also presents and discusses examples of the computer-simulation results for four different settings of the applied RT. A few directions for future research as well as prospective applications of the model and developed software are also discussed.

Nutrient Requirements of Zebu and Crossbred Cattle - BR-CORTE

“…Although there are mathematical models attempting to explain homeorhesis (Mamontov, 2007;Psiuk-Maksymowicz and Mamontov, 2008), their application to nutrient breakdown in pregnant cows is still far from what could be proposed to estimate nutritional requirements. It is known that there is wide interaction between maternal tissues and the gravid uterus that implies modification in the efficiency of use of the nutrients on the part of the maternal tissues.…”

Exigências Nutricionais de Zebuínos Puros e Cruzados - BR-CORTE

“…Embora existam modelos matemáticos para tentar explicar a homeorrese (Mamontov, 2007;Psiuk-Maksymowicz e Mamontov, 2008), a aplicação dos mesmos ao particionamento de nutrientes em fêmeas bovinas gestantes ainda está distante do que se pode propor para estimativa das exigências nutricionais. Sabe-se que há ampla interação entre tecidos maternos e o útero gravídico, que implicam em modificações na eficiência de uso dos nutrientes por parte dos tecidos maternos.…”

Modelling homeorhesis by ordinary differential equations

“…The above scheme in the case of one-dimensional state of the system and one counter-creode is implemented in the PhasTraM nonlinear reaction-diffusion mathematical model for hyperplastic oncogeny based on (4.9)-(4.11) and described in [16]- [18]. Here the counter-creode represents the hyperplastic-tumor state.…”

“…It may result from one or another approximation which does not apply function in (4.8). Simplification (4.9)-(4.11) of model (4.1)-(4.7) is used in the PhasTraM nonlinear reaction-diffusion model for onco-geny and the corresponding computer simulation in works [16], [17], [6, the text on (A.12) and (A.13)], and [18]. Some other aspects of the proposed model (4.1)-(4.7) are discussed in the next section.…”

“…The model can be specified in different ways depending on specific system and specific purposes of this analysis. An example of the specification is the homeorhesis-aware model for hyperplastic oncogeny in works [16]- [18]. Here each of the employed characteristics and parameters is of a distinct biological, biophysical, or biomedical meaning (e.g., see [17, Tables 1 and 2], [18, Tables 1 and 2]).…”