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Pharmacokinetics and Pharmacodynamics

Introduction



A genuine expression of mathematics in medicine can be seen in pharmacokinetics, PK for short, and pharmacodynamics, PD for short. In general referred to as PK/PD models.  

Pharmacokinetics can be defined as what the body does to the drug, whereas pharmacodynamics as what the drug does to the body. Further, pharmacogenomics can be defined as what the drug does to the genome and vise verse.

Pharmacokinetics concerns the step by step processes that take place from the drug administration to the site of action, while pharmacodynamics studies from the rise of concentration in the site of action to effect. Pharmacodynamics is more complicate, thus advances are relatively recent, mainly due the fact that it requires molecular understanding such as receptor-drug interactions. Thus, we shall present the basic principle on the fields, with a tendency to pharmacokinetics.  

The discovery of drugs was one of the most important steps in science, it gave us a weapon against situations that before certainly would culminate on deaths. According to Katzung et al (2012), the pharmaceutical industry is amongst the most lucrative, and this demonstrates surely the importance of the discovery. Still in accordance with Katzung et al (2012), besides all the development, we still need quantitative and precise approaches to drug development. In harmony with Tozer and Rowland (2006), pharmacokinetic/pharmacodynamic models are important for giving us the opportunity for getting the answers for questions such as How much? How long? How often? Further, empirical studies had contributed a lot for our understanding of drugs, but they had not increased our knowledge about drugs in a general sense, what is common to drugs and what is peculiar. From the viewpoint of new products development, this is an extremely complex case [1].

The most important problematic in the studies of drugs is how to develop them efficiently, in cost and delivery in time [2] (Rosenbaum, 2011).   The difficulties faced by the pharmaceutical industry boils down to the high costs on developing drugs for new diseases, or even some well-known, but still to be understood in a level to nullify it using drugs. The referred problem increases the cost of the final product, making it difficult the access by who really needs them, especially the people with low monthly incomings. 



[1] In Brazil this is well-known on the issues created since the launched of the “genéricos”, cheap drugs, but in theory with the same quality as the conventional ones.
[2] As an example, see the development of the vaccine for the virus that causes the so well-known and feared disease called dengue. See http://agencia.fapesp.br/17988 for more details.   

References

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Collegy of Pharmacy. The University of Rhode Island. IMODR: Basic Pharmacokinetic and Pharmacodynamic Models. Online: http://www.uri.edu/pharmacy/faculty/rosenbaum/basicmodels. Último acesso em: Março, 2014.
Fister, K. R.; Panetta, J. C. Optimal Control Applied to Competing Chemotherapeutic Cell-Kill Strategies. SIAM Journal of Applied Mathematics, 63 (6):1954-71, 2003.
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Ling, S. H.; San, P. P.; Nguyen, H. T. Hypoglycemia Detection for insulin-dependent diabetes mellitus: a evolved fuzzy inference system approach. Lam, H. K; Ling, S. H; Nguyen, H. T (eds). Computational Intelligence and its applications: evolutionary Computation, Fuzzy Logic, Neural Network, and Support Vector Machine Technique. Imperial College Press. 2012.
Katzung, B. G.; Masters, S. B.; Trevor, A. J. Basic and clinical pharmacology. 12th edition. McGraw Hill. 2012.
Källén, A. Computational pharmacokinetics. Chapman and Hall/CRC Biostatistics Series, 2008.
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Pires, J. G.; Duarte, A. S.; Bianchi, R. F.; Santos, Z. A. Da S.; Bianchi, A. G. C. Projeto e desenvolvimento de Produto: proposta e desenvolvimento de dispositivo eletrônico para auxiliar no tratamento da icterícia. Gestão do Produto: engenharia do produto. Simpósio de Engenharia de Produção.  XVI: 1-12, 2009.
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Rosenbaum, S. E Basic pharmacokinetics and pharmacodynamics: an integrated textbook and computer simulations, John Wiley & Sons, 2011.
Siddique, N. Intelligent Control: a hybrid approach based on Fuzzy Logic, Neural Networks, and Genetic Algorithms. Studies in Computational Intelligence 517. Springer: 2014.
Swan, G. W. Applications of optimal control theory in biomedicine, Pure and Applied Mathematics. Marcel Dekker Inc, 1984.
Tozer, T. N.; Rowland, M. Introducion to pharmacokinetics and pharmacodynamics: the quantitative basis of drug theraphy, Lippincott Williams & Wilkins, 2006. 








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