Modelo teórico e experimental da reciclagem do Carbono-13 em tecidos de mamíferos e aves

A diferença entre fontes alimentares da ordem de 14, originárias de plantas com ciclos fotossintéticos Carbono-3 (C3) e Carbono-4 (C4) e seus subprodutos, abre novas perspectivas para o estudo do metabolismo do carbono em aves e animais de pequeno porte. Os autores propõem um modelo teórico e experimental capaz de exprimir os resultados de enriquecimento relativo, delta per mil (delta) da razão 13C/12C versus tempo em diferentes tecidos. Utilizou-se a equação y(t) = (y0 -- q/k) e-kt + q/k onde, y(t) é a concentração isotópica no tempo desejado, y0 a concentração isotópica inicial existente no tecido, k é uma constante de troca isotópica com unidade 1/tempo, t é unidade de tempo e q é a taxa de entrada de metabólitos que contém carbono, com valores de delta/tempo. Para fígado de galinhas que tiveram a ração de ciclo fotossintético C4 substituída por dieta C3 obteve-se a equação delta13C = -24,74 + 12,37 e-0.237(nT), com meia-vida (T) de 2,9 dias. O patamar de equilíbrio de substituição do carbono foi alcançado em --24,48, de modo que praticamente 98,4% do conteúdo isotópico do C4 no fígado foi substituído por C3 após 5,6 meias-vidas. O modelo foi adequado para determinar o tempo de reciclagem total ou parcial da concentração de carbono nos tecidos em estudo.Food source differences of about 14 from plants with carbon-3 (C3) and carbon-4 (C4) photosynthetic cycles and their derived products make carbon metabolism studies possible in birds and small mammals. The authors suggest a theorical and experimental model for determining the relative enrichment results, delta per thousand (delta) of the 13C/12C ratio as a function of time for different tissues. The following equation was used: y(t) = (y0 -- q/k) e-kt + q/k where, y(t) is the isotopic concentration at time t, y0 is the initial isotopic concentration in the tissue, k is the turnover constant expressed in 1/time, and q is the input of metabolites which contain carbon expressed in delta/time. The equation below was obtained from the analysis of hen livers, the carbon-4 photosynthetic cycle ration of which was switched to a carbon-3 diet: delta13C = -24.74 + 12.37 e-0.237(nT) with 2.9 day half-life. The carbon switching steady-state was reached at --24.48 so that nearly 98.4% of the C4 isotopic content in the liver was replaced by C3 after 5.6 half-lives. The proposed model is suitable to determine the partial or entire turnover of carbon concentration in some selected tissues

TRAPEZOIDAL PRODUCT INTEGRATION METHOD TO RESOLVE GENERAL IZED ABEL LINEAR INTEGRAL EQUATIONS OF FIRST KIND

Não disponívelThis dissertation is concerned with the Trapezoidal Product Integration Method to resolve Generalized Abel Linear Integral Equations of first -kind. Special attention is given to theorem of the convergence of the trapezoidal method. Mathematical results and a discussion about the existence and uniqueness of the solutions of the Generalized Abel Linear Integral. Equations are presented in chapter one. Theorems related with the convergence of the trapezoidal method are shown in chapters two and three. In chapter four it is analized the implicit backward difference product integration methods, proved its convergence,and also it is applied a sufficient condition to the root condition of the trapezoidal method. Numerical result is shown in chapter five

TRAPEZOIDAL PRODUCT INTEGRATION METHOD TO RESOLVE GENERAL IZED ABEL LINEAR INTEGRAL EQUATIONS OF FIRST KIND

Não disponívelThis dissertation is concerned with the Trapezoidal Product Integration Method to resolve Generalized Abel Linear Integral Equations of first -kind. Special attention is given to theorem of the convergence of the trapezoidal method. Mathematical results and a discussion about the existence and uniqueness of the solutions of the Generalized Abel Linear Integral. Equations are presented in chapter one. Theorems related with the convergence of the trapezoidal method are shown in chapters two and three. In chapter four it is analized the implicit backward difference product integration methods, proved its convergence,and also it is applied a sufficient condition to the root condition of the trapezoidal method. Numerical result is shown in chapter five

Modelo teórico e experimental da reciclagem do Carbono-13 em tecidos de mamíferos e aves

A diferença entre fontes alimentares da ordem de 14 , originárias de plantas com ciclos fotossintéticos Carbono-3 (C3) e Carbono-4 (C4) e seus subprodutos, abre novas perspectivas para o estudo do metabolismo do carbono em aves e animais de pequeno porte. Os autores propõem um modelo teórico e experimental capaz de exprimir os resultados de enriquecimento relativo, delta per mil (delta ) da razão 13C/12C versus tempo em diferentes tecidos. Utilizou-se a equação y(t) = (y0 -- q/k) e-kt + q/k onde, y(t) é a concentração isotópica no tempo desejado, y0 a concentração isotópica inicial existente no tecido, k é uma constante de troca isotópica com unidade 1/tempo, t é unidade de tempo e q é a taxa de entrada de metabólitos que contém carbono, com valores de delta /tempo. Para fígado de galinhas que tiveram a ração de ciclo fotossintético C4 substituída por dieta C3 obteve-se a equação delta13C = -24,74 + 12,37 e-0.237(nT), com meia-vida (T) de 2,9 dias. O patamar de equilíbrio de substituição do carbono foi alcançado em --24,48 , de modo que praticamente 98,4% do conteúdo isotópico do C4 no fígado foi substituído por C3 após 5,6 meias-vidas. O modelo foi adequado para determinar o tempo de reciclagem total ou parcial da concentração de carbono nos tecidos em estudo.Food source differences of about 14 from plants with carbon-3 (C3) and carbon-4 (C4) photosynthetic cycles and their derived products make carbon metabolism studies possible in birds and small mammals. The authors suggest a theorical and experimental model for determining the relative enrichment results, delta per thousand (delta ) of the 13C/12C ratio as a function of time for different tissues. The following equation was used: y(t) = (y0 -- q/k) e-kt + q/k where, y(t) is the isotopic concentration at time t, y0 is the initial isotopic concentration in the tissue, k is the turnover constant expressed in 1/time, and q is the input of metabolites which contain carbon expressed in delta /time. The equation below was obtained from the analysis of hen livers, the carbon-4 photosynthetic cycle ration of which was switched to a carbon-3 diet: delta13C = -24.74 + 12.37 e-0.237(nT) with 2.9 day half-life. The carbon switching steady-state was reached at --24.48 so that nearly 98.4% of the C4 isotopic content in the liver was replaced by C3 after 5.6 half-lives. The proposed model is suitable to determine the partial or entire turnover of carbon concentration in some selected tissues

A mathematical model of chemotherapy response to tumour growth

A simple mathematical model, developed to simulate the chemotherapy response to tumour growth with stabilized vascularization, is presented as a system of three differential equations associated with the normal cells, cancer cells and chemotherapy agent. Cancer cells and normal cells compete by available resources. The response to chemotherapy killing action on both normal and cancer cells obey MichaelisMenten saturation function on the chemotherapy agent. Our aim is to investigate the efficiency of the chemotherapy in order to eliminate the cancer cells. For that, we analyse the local stability of the equilibria and the global stability of the cure equilibrium for which there is no cancer cells. We show that there is a region of parameter space that the chemotherapy may eliminate the tumour for any initial conditions. Based on numerical simulations, we present the bifurcation diagram in terms of the infusion rate and the killing action on cancer cells, that exhibit, for which infusion conditions, the system evolves to the cure state

The effect of lenvatinib and pembrolizumab on thyroid cancer refractory to iodine 131I simulated by mathematical modeling

International audienceImmunotherapy and targeted therapy are alternative treatments to differentiated thyroid cancer (DTC), which is usually treated with surgery and radioactive iodine. However, in advanced thyroid carcinomas, molecular alterations can cause a progressive loss of iodine sensitivity, thereby making cancer resistant to radioactive iodine-refractory (RAIR). In the treatment of cancer, tyrosine kinase inhibitors are administered to prevent the growth of cancer cells. One such inhibitor, lenvatinib, forms a targeted therapy for RAIR-DTC, while the immunotherapeutic pembrolizumab, a humanized antibody, prevents the binding of programmed cell death ligand 1 (PD-L1) to the PD-1 receptor. As one of the first studies on treatments for thyroid cancer with mathematical model involving immunotherapy and targeted therapy, we developed an ordinary differential system and tested variables such as concentration of lenvatinib and pembrolizumab, total cancer cells, and number of immune cells (i.e., T cells and natural killer cells). Analyzing local and global stability and the simulated action of drugs in patients with RAIR-DTC, revealed the combined effect of the targeted therapy with pembrolizumab. The scenarios obtained favor the combined therapy as the best treatment option, given its unrivaled ability to boost the immune system’s rate of eliminating tumor cells

Mathematical models applied to thyroid cancer

Thyroid cancer is the most prevalent endocrine neoplasia in the world. The use of mathematical models on the development of tumors has yielded numerous results in this field and modeling with differential equations is present in many papers on cancer. In order to know the use of mathematical models with differential equations or similar in the study of thyroid cancer, studies since 2006 to date was reviewed. Systems with ordinary or partial differential equations were the means most frequently adopted by the authors. The models deal with tumor growth, effective half-life of radioiodine applied after thyroidectomy, the treatment with iodine-131, thyroid volume before thyroidectomy, and others. The variables usually employed in the models includes tumor volume, thyroid volume, amount of iodine, thyroglobulin and thyroxine hormone, radioiodine activity, and physical characteristics such as pressure, density, and displacement of the thyroid molecules. In conclusion, the mathematical models used so far with differential equations approach several aspects of thyroid cancer, including participation in methods of execution or follow-up of treatments. With the development of new models, an increase in the current understanding of the detection, evolution, and treatment of diseases is a step that should be considered