Métodos Computacionais em Biomedicina

Calculus I and Calculus II.

The teaching of the curricular unit consists of theoretical (T) and practical-laboratory (PL) classes.
The T aim to study models and teach numerical analysis techniques, as students need tools to solve each of the problems, computationally applied to the field of Biomedicine. These classes encourage understanding and integration of knowledge.
PL classes are computational practices using MatLab, which allow the implementation and practical application of the studied methods, and promote group work and discussion.
The evaluation will consist of two works, with a 4 mark each, and a final exam of 12 marks – minimum of 5.5 marks (to be carried out in normal and/or recourse periods). The final grade will be the sum of the work with the exam grade, if the student has minimum grades. The student is approved in the subject if he has a final grade of at least 10 points. The exam of the special season is a written exam and quoted at 20 points.

– Acquire knowledge of mathematical modeling applied to biological systems and biomedicine.
– Provide the student with numerical tools that enable the obtaining of one or more approximate solutions to problems whose resolution cannot be carried out analytically.
– Apply this knowledge in solving, by computational means, problems in the field of biomedicine.
– Recognize the importance of computational methods in solving complex problems in areas associated with biological and medical processes.
– Strengthen programming skills and understanding of the specifics of algorithms studied for the resolution of specific problems in the field of biomedical engineering
– Develop critical thinking and analysis of results.

1.    Mathematical models studied using Numerical Analysis techniques:
1.1.    Mathematical models of population growth
1.2.    Mathematical ecosystem models
1.3.    -Epidemiological models
1.4.    Mathematical Model for Immunotherapy
1.5.    Drug release models
1.6.    Nerve impulse propagation model
1.7.    Cardiovascular Model
2.    Numerical analysis bases:
2.1.    Polynomial interpolation.
2.2.    Numerical differentiation.
2.3.    Numerical integration: Trapeze and Simpson rules.
2.4.    Roots of nonlinear equations: bisection and Newton-Raphson methods.
2.5.    Linear systems of equations: numerical resolution – iterative methods.
2.6.    Numerical resolution of nonlinear systems: Newton’s method.
2.7.    Numerical resolution of ordinary differential equations and systems of differential equations: Euler, Runge-Kutta and predictor-corrector methods.
2.8.    Numerical resolution of partial derivative equations: finite difference method.

NAO

• S. Dunn. (2005). Numerical methods in Biomedical Engineering. Academic Press.
• Pascoal Martins da Silva. (2024). Apontamentos de apoio às aulas teóricas acetatos – Métodos Computacionais em Biomedicina. DFM, ISEC.
• A. Friedman, C.Y. Kao. (2014). Mathematical Modeling of Biological Processes, Lecture note on mathematical modeling in the life sciences. Springer.
• Atkinson, K. E., An Introduction to Numerical Analysis. John Wiley.
• Chapra, S. C. e Canale, R.P. Numerical Methods for Engineers. McGraw-Hill.
• Conte, S. D. e De Boor, C. Elementary Numerical Analysis. McGraw-Hill.
• Faires, J. D. e Burden, R. Numerical Methods (2nd Ed.). Brooks / Cole Publishing Company.
• J.D. Murray. (2001). Mathematical Biology I: An Introduction. (Third Edition). IAM- Springer.
• J.D. Murray. (2000). Mathematical Biology II: Spatial models and biomedical applications. (Third Edition). IAM- Springer.
• Valença, M. R. Métodos Numéricos. Instituto Nacional de Investigação Científica.
• Batel Anjo, A. J., Fernandes, R. e Carvalho, A. S.. Curso de MatLab. Principia
• J. A. Rodrigues. (2003). Métodos Numéricos, Introdução, Aplicação e Programação. (1ªedição). Edições Sílado.
• R. Rodrigues, P.M. Silva, P.M. Rosa, Matemática e Animações. em http://www2.isec.pt/~ppr/.
• P. DeVries, J. Hasbun. (2010). A First Course in Computational Physics. Jones & Bartlett Publishers.
• C. Moler. (2008). Numerical Computing with MATLAB. SIAM.
• G. Smith. (1985). Numerical Solution of Partial Differential Equations: Finite Difference Methods. Clarendon Press.
• J. Faires, R. Burden. (2005). Numerical Analysis. Brooks/Cole.