Fractional pennes' bioheat equation: theoretical and numerical studies

In this work we provide a new mathematical model for the Pennes’ bioheat equation, assuming a fractional time derivative of single order. Alternative versions of the bioheat equation are studied and discussed, to take into account the temperature-dependent variability in the tissue perfusion, and both finite and infinite speed of heat propagation. The proposed bioheat model is solved numerically using an implicit finite difference scheme that we prove to be convergent and stable. The numerical method proposed can be applied to general reaction diffusion equations, with a variable diffusion coefficient. The results obtained with the single order fractional model, are compared with the original models that use classical derivatives.

Fractional bioheat equation

In this work we develop a new mathematical model for the Pennes’ bioheat equation assuming a fractional time derivative of single order. A numerical method for the solu- tion of such equations is proposed, and, the suitability of the new model for modelling real physical problems is studied and discussed

Comparison of different numerical methods for the solution of the time-fractional reaction-diffusion equation with variable diffusion coefficient

In this work we perform a comparison of two different numerical schemes for the solution of the time-fractional diffusion equation with variable diffusion coefficient and a nonlinear source term. The two methods are the implicit numerical scheme presented in [M.L. Morgado, M. Rebelo, Numerical approximation of distributed order reaction- diffusion equations, Journal of Computational and Applied Mathematics 275 (2015) 216-227] that is adapted to our type of equation, and a colocation method where Chebyshev polynomials are used to reduce the fractional differential equation to a system of ordinary differential equations

Historical analysis of the Brazilian cervical cancer screening program from 2006 to 2013: a time for reflection

BACKGROUND: The Cervical Cancer Database of the Brazilian National Health Service (SISCOLO) contains information regarding all cervical cytological tests and, if properly explored, can be used as a tool for monitoring and managing the cervical cancer screening program. The aim of this study was to perform a historical analysis of the cervical cancer screening program in Brazil from 2006 to 2013. MATERIAL AND METHODS: The data necessary to calculate quality indicators were obtained from the SISCOLO, a Brazilian health system tool. Joinpoint analysis was used to calculate the annual percentage change. RESULTS: We observed important trends showing decreased rates of low-grade squamous intraepithelial lesions (LSIL) and high-grade squamous intraepithelial lesions (HSIL) and an increased rate of rejected exams from 2009 to 2013. The index of positivity was maintained at levels below those indicated by international standards; very low frequencies of unsatisfactory cases were observed over the study period, which partially contradicts the low rate of positive cases. The number of positive cytological diagnoses was below that expected, considering that developed countries with low frequencies of cervical cancer detect more lesions annually. CONCLUSIONS: The evolution of indicators from 2006 to 2013 suggests that actions must be taken to improve the effectiveness of cervical cancer control in Brazil.