The main aim of this study was the formula application of the superficial area of a truncated prolate spheroid (TPS) in Cartesian coordinates in obtaining a cardiac parameter that is not so much discussed in literature, related to the left ventricle (LV) surface area of the human heart, by age and sex. First we obtain a formula for the area of a TPS. Then a simple mathematical model of association of the axes measures of a TPS with the axes of the LV is built. Finally real values of the average dimensions of the humans LV are used to measure surface areas approximations of this heart chamber. As a result, the average superficial area of LV for normal patients is obtained and it is observed that the percentage differences of areas between men and women and their consecutive age groups are constant. A strong linear correlation between the obtained areas and the ventricular volumes normalized by the body areas was observed. The obtained results indicate that the superficial area of the LV, besides enabling a greater knowledge of the geometrical characteristics of the human LV, may be used as one of the normality cardiac verification criteria and be useful for medical and biological applications.

OBJECTIVE In 1996, the Brazilian cardiovascular surgeon, Dr. Randas Batista, introduced a surgical technique called partial left ventriculectomy, where he admitted the possibility of reducing the diameter of the left ventricle through the sectioning of one section of its wall. After the publication of this study, thousands of case reports and procedure analysis have been published, and due to several disappointing results, many doctors and institutions failed to execute it. As the main objective of this study, stands out the search for success cases of ventriculectomy in the last 12 years and if during this period it was achieved some significant development in this procedure that allows obtaining lower mortality rate postoperatively.METHODS Systematic review of indexed scientific literature over the past 12 years and the term "Partial Left Ventriculectomy".RESULTS There has been a considerable number of reported successful cases and highly significant findings in regard to determining the most suitable region for the section, proper selection of the patients indicated to the procedure, including the influence of the coronary artery anatomy in the nomination procedure and the need for preservation of ventricular geometry to ensure better quality of ventricular contractions after the sectioning.CONCLUSION This surgical procedure has been successfully performed, mainly in Japan, improvements in its efficiency were found and the need for a mathematical modeling of the slice to be severed is a prominent factor in many studies.

RESUMONesse trabalho, apresenta-se uma das aplicações da modelagem matemática no sistema cardiovascular, a sua utilização na estimação do volume ventricular esquerdo -um parâmetro fundamental no diagnóstico de doenças cardíacas. Para isso, prepara-se um molde de um ventrículo esquerdo bovino, seu volume real é determinado e, então, comparado com os resultados obtidos por métodos matemáticos médicos e com um novo método proposto, baseado na integral de revolução de uma função polinomial específica. Os resultados preliminares indicam que o método proposto é mais eficiente que os métodos médicos, com diferença de apenas 3,5% do volume real.Palavras-chave: Modelagem Matemática. Novo Método de Cálculo. Volume Ventricular. ABSTRACTIn this work, we presented one of the applications of mathematical modeling to the cardiovascular system, its use in the estimation of the left ventricular volume, which is a basic parameter in the diagnosis of heart disease. To do that, a mold of a bovine left ventricle is prepared, its real volume is determined and then it is compared to the results achieved by medical mathematical methods and with a new proposed method, based on the integral of revolution of a specific polynomial function. Preliminary results indicate that the proposed method is more efficient than medical methods, with a difference of only 3.5% of the actual volume.

O objetivo desse trabalho é obter um modelo matemático para a evolução populacional da cidade de Pirapora/MG, baseando-se apenas nos dados de censos e contagens populacionais do Instituto Brasileiro de Geografia e Estatística (IBGE). Para isso, é utilizada a interpolação por splines cúbicas, pois as técnicas de interpolação linear e polinomial, e também o modelo logístico, não se ajustam bem a essa população. Os dados analisados não são equidistantes, então, utiliza-se como amostra anos separados com passo h de 10 anos. Os valores descartados inicialmente e as estimativas populacionais para esse município, descritos pela Fundação João Pinheiro, serviram para validação do modelo construído, e para a estimativa das diferenças percentuais de previsão, que não ultrapassaram os 2,21%. Ao se considerar que o padrão de evolução populacional de 2000 a 2010 se manterá até 2020, estima-se as populações da cidade de 2011 a 2020, cuja diferença percentual média foi de apenas 0,49%. Conclui-se que o modelo se ajusta muito bem aos dados, e que estimativas populacionais em qualquer ano de 1970 e 2020 são confiáveis. Além disso, o modelo permite a visualização prática de uma aplicação dessa técnica na modelagem populacional, e, portanto, também pode ser utilizada para fins didáticos.Palavras-chave: Splines cúbicas. Interpolação. Modelagem matemática. Evolução populacional. Pirapora.

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The main objective of this article is to determine the existing linear correlation between the real left ventricular volume (RV) from the heart of bovines and the volumes obtained by Teichholz's mathematical model and the volume of the truncated prolate spheroid (TPS) to identify which model has a higher proximity to the RV. For that, ten silicon rubber molds of the left ventricle (LV) were manufactured, and their real volumes were obtained through Archimedes' principle, and their linear dimensions were also obtained. These dimensions were used to feed Teichholz's and the TPS models. It was verified that, for ventricles of lower volume, the models showed relatively close results, and Teichholz's model was the most accurate one. The TPS method shows a grave accuracy mistake for higher volume ventricles. Besides, both methods showed strong linear correlations with the RV, and both with high significance.