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What has mathematics got to do with drugs?

Prof. Johannes Schropp and Gilbert Koch from the University of Constance are developing mathematical models for the pharmaceutical company Nycomed. These models examine the relationship between the concentration and the effect of administered drugs.

The impact of mathematics on all areas of life and work is greater than that of any other discipline. Mathematics is a science with many facets and numerous applications. The German Federal Ministry of Education and Research and others who are organising the “Year of Mathematics 2008” event are very keen to convey this message to the wider public. The Faculty of Mathematics at the University of Constance is an excellent example that shows that mathematics has far more to offer than simply the resolution of mathematical problems on a purely academic basis. A small team of researchers from the University of Constance have been working with the Constance-based company Nycomed for quite some time.

Interdisciplinary cooperation

Prof. Dr. Johannes Schropp, mathematician at the University of Constance, develops mathematical models that provide information on the efficacy of drugs. (Photo: Peter Schmidt)
Prof. Johannes Schropp and his colleague Gilbert Koch are developing mathematical models for Nycomed that enable the analysis of the relationship between the concentration and effect of administered drugs. With this applicable mathematical approach to biological and medical issues, the scientists are making an important contribution to drug development. In this interdisciplinary field, cooperation between mathematicians and experts of other disciplines is indispensable.

The project, which began in summer 2006, also involves the biologist Dr. Antje Walz and the chemist Dr. Thomas Wagner from Nycomed’s Department of Pharmacometrics. A major prerequisite for the close cooperation between scientists from different disciplines is a willingness to learn from each other and an open-minded approach to unknown methods and ways of thinking, all of which generate successful synergies. “In order to find a common basis, all scientists need to look beyond their special research area and be honest when they haven’t understood something from a colleague’s field of expertise.”

Investigation of the dose-effect relationship

Drug development involves the investigation of what happens in the body with a specific drug. This is referred to as pharmacokinetics (PK) and describes the temporal course of administered drugs. The PK process consists of several phases: absorption, distribution (blood), metabolism (liver) and elimination (kidneys). Pharmacodynamics (PD) defines the biological and physiological response to the administered drug. For example, it can destroy proliferating cells in cancer. The major question is: when, how much and how often must a certain drug be administered in order to reach a maximum efficacy with minimum adverse effects? In order to better predict drug action, it is necessary to establish a mathematical and theoretical link between pharmacokinetic and pharmacodynamic processes.

With differential equations to marketable drug

This special type of mathematical modelling, known as PK/PD modelling, requires close cooperation between biologists, medical doctors and mathematicians. Modelling mainly focuses on differential equations. “Such equations are especially well suited for describing the temporal course of natural processes,” said Koch. However, the actual validity of such complex models can only be tested by mathematicians in theoretical investigations. What are the advantages of mathematical modelling? Both biochemical and physiological processes, transformed into mathematical formula, and hypotheses can be tested very effectively and will provide information about drug action. This abstraction enables a greater understanding of the complex processes in animal models. If the modelling succeeds in sensibly reducing the complexity of the query, then the model can be called predictive, which means that it delivers correct predictions of different experiments. Therefore, animal models will enable well-founded statements to be made on the potential outcome of subsequent patient studies.

With the predictive model, it is possible to simulate all possible dosage strategies in a very short time. Thus, pharmaceutical companies, which are usually under huge time pressure, have earlier access to data that would otherwise have to be obtained in time-consuming experimental series. Therefore, drugs can be launched more rapidly and in a more targeted way, making the whole process more efficient and cheaper. In ethical terms, the acquisition of theoretical data enables the pharmaceutical industry to reduce the number of animal experiments.

Computer simulations to investigate adverse effects

Scientists from pharmaceutical companies also focus on the possibility of reducing the adverse effects of new drugs. The drug can be tested in computer simulations for its tolerability and efficacy early in the drug development process. This makes treatment considerably safer. Factors such as weight, age and sex of patients can be taken into account in the calculation of the appropriate dose. “It is devastating for pharmaceutical companies to have to withdraw drugs from the market because of unforeseen adverse effects; this often puts them out of business,” said Antje Walz. The simulation of drug effects also enables pharmaceutical companies to identify drug candidates with the best chance of clinical success and eliminate flawed candidates. In order to simulate the efficacy of a drug, the free parameters of the PK/PD model need to be adjusted to the data sets acquired. This optimisation process, which is numerically highly complex, can now be done with standard computers within a reasonable period of time. The parameters obtained will then be used to characterise the properties of the drug under investigation and to simulate different dosage regimens.

Mathematical modelling can be used in many areas

From the outset of their cooperation, the scientists have been focusing on the further development of a tumour growth model that has played an important role in the validation and selection of drugs which were then in the development phase. This model provides information on the process of tumour growth and the death of cancer cells when the tumour is treated with drugs. Following Nycomed’s decision to sell its oncology programmes, the group of researchers is now focused on the simulation of therapies in other indications, for example inflammation. However, the mathematical simulation is not limited to biochemical processes. “It can be used in many scientific applications,” said Schropp calling for increased funding in this field. The Faculty of Mathematics at Constance University has already taken this into account by including mathematical modelling in the “Modelling” module which is mandatory for all mathematics bachelor degree students. In addition, the cooperation between the Faculty of Mathematics and Nycomed also attracts more investments in the form of third-party funding as well as giving rise to interesting doctorate options.

The collaboration with the mathematicians also has its benefits for Nycomed. According to Antje Walz, the University of Constance is an important cooperation partner for Nycomed in the Lake Constance area: “The simulations allow us to identify and assess the risks and opportunities of drugs a lot earlier than before.” Johannes Schropp is convinced that promoting mathematics is a worthwhile endeavour since it can make very important contributions to other fields of science as well as solving many problems. “It is wonderful to work in a field that can cure illnesses.”

Source: uni'kon 32/08 (mst - 1 November 2008)

Website address: https://www.gesundheitsindustrie-bw.de/en/article/news/what-has-mathematics-got-to-do-with-drugs