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Since 2019, Matheon's application-oriented mathematical research activities are being continued in the framework of the Cluster of Excellence MATH+
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A Realistic Hope to have Children

Mathematicians develop a “virtual hospital” to optimise in-vitro fertilisation.

The birth of some children can be unplanned, and sadly sometimes even unwanted. On the other hand, many couples long dearly for a child but have their wish unfulfilled due to various medical reasons. Statistically, the problem resides about half the time with the man and half the time with the woman. For many years now, however, medical progress has allowed the artificial fertilisation of female egg cells. The egg cells are taken from the woman and fertilisation is performed in-vitro. Before this can be done, the woman’s normal menstrual cycle first has to be gradually “regulated down” by medication over several days in order to be subsequently restarted – again by medication. The aim is to induce as many egg cells as possible to mature so that they can then be harvested. Exactly what medications are used in the procedure, and at what doses, depends on many individual criteria.

Austrian physician Berthold P. Wiesner is regarded as a pioneer in the field of artificial insemination. He performed many of the first tests between 1940 and 1960 in London. However, Wiesner became a controversial figure after it was discovered that he had contributed most of the donor sperms himself. The first “test tube baby” came into the world in 1978. Since then, the number of births after in-vitro fertilisation (IVF) or intracytoplasmic sperm injection (ICSI) has increased drastically. In Germany, about two percent of all children are born through artificial fertilisation by now. The procedure is never truly risk-free; it is difficult and in many cases unsuccessful. The main reasons for this are variability in the female hormonal cycle and the resulting patient-specific differences; especially in cases of fertility disorders. To find solutions, medical practitioners, biologists, computer scientists and mathematicians have teamed up in the EU project PAEON. The mathematical part in this research consortium is being undertaken by Prof. Susanna Röblitz and Dr. Rainald Ehrig of the Zuse Institute Berlin and members of Matheon. Together with the Zuse Institute, the PAEON project involves members from the Lucerne University of Applied Sciences, ETH Zurich and Hannover Medical School. The project is coordinated by scientists of the Università di Roma Sapienza.

An estimated 12–15 percent of couples have their desire for children unfulfilled. On average, these couples spend around 10 percent of their annual income on in-vitro fertilisation. About 40 percent of all female infertility cases can be attributed to hormonal disorders. The success rates of IVF and ICSI have never exceeded 35 percent. “The goal of our mathematical approach is to develop a model-based decision-making aid for the physicians, which firstly contributes towards a better understanding of the highly complex processes in the female cycle and, secondly, provides the opportunity to simulate and optimise the treatment strategy on the computer, thus making it more efficient. Of course, another important aspect is to reduce the costs,” Susanna Röblitz explains.

The female hormonal cycle follows a fixed series of precisely coordinated processes. It begins with the maturation of the follicle containing the egg cells, followed by ovulation, which is the release of the egg cell. Normally only a single egg cell is released from the largest follicle for fertilisation. After ovulation, the so-called corpus luteum starts to develop. If a pregnancy does not occur, then the corpus luteum degenerates and the uterine lining is shed leading to bleeding at the beginning of the next cycle. All of these processes are controlled by hormones. In artificial fertilisation, the task is to stimulate multiple follicles to ovulation so that several fertile egg cells can be harvested from the woman. This stimulation is done by administering hormones externally, meaning by medication.

Unfortunately, the problems already start here: “The treatment standards of clinics vary very much. Even discounting clinical negligence, which surely exists, use of the right medications and their individual dosing is not easy,” says Rainald Ehrig. This is one of the most important starting points for PAEON. Based on medical data, the mathematicians from Berlin have initially modelled an idealised cycle of a healthy woman. “There is still ambiguity regarding the highly variable nature of this cycle in women – for a woman individually as well as across women,” Susanna Röblitz continues. The next step was therefore to model hormone profiles and follicle development accounting for the differences between individuals, the reasons for dysregulation in hormonally caused fertility disorders, and the influence of external factors (e.g. age and smoking). The aim is to integrate treatment options into the model and simulate them on the computer. Rainald Ehrig describes the mathematical task as follows: “We first develop a model that takes into account the cycle, the maturation of the follicle, the changes under medication, and external influencing factors. This model is continuously validated with real patient data in order to finally allow a meaningful prediction that is ultimately introduced into the actual treatment strategy.” For this to be possible, the model must not be restricted to any of the individual components, instead, it must allow a description of the entire complex system.

The starting point is a conceptual model that predicts how the biological system behaves under given external conditions. This conceptual model is then complemented by data from an experimental model. From these two models, the mathematical model is finally developed. “Here we keep in mind Albert Einstein‘s saying, that mathematical models should be made as simple as possible, but not simpler,” Susanna Röblitz says. A major problem, however, is that many model parameters are unmeasurable and therefore unknown. This is compounded by the fact that most biological processes are largely nonlinear and therefore exhibit no easily predictable patterns of behaviour. “Such complex systems can only be studied using new mathematical methods,” the mathematician continues.

Of course the mathematical models include the known effects of various drugs that are administered during an IVF. This is done by modelling the pharmacodynamics of the ingredients of these drugs, for example their concentrations in the blood over time.

The research will ultimately result in a “virtual hospital” based on virtual patients and complemented with real data collected by physicians. Its output will give physicians a data-substantiated suggestion for a targeted and efficient treatment for the individual. When a real patient comes into the clinic with her data profile, her profile can be compared with the existing data. This yields an initial suggestion for the physician as to how the treatment could be performed. From then on, the system accompanies the treatment and can repeatedly propose suggestions over the course of time. Additionally, one can simulate on the computer new combinations of drugs whose actions would otherwise have to be tested on real patients. Yet, the two mathematicians see this still as a long way to go. “For sure our system ought not only to increase the chance of success, but also reduce the risk and the costs. That is a huge mathematical challenge,” Susanna Röblitz asserts.

The project PAEON has been running since 2013. The project has been recently reviewed for the second time and considered as successful. The EU funding, however, is set to expire next year. The two mathematicians expect to have a demonstration of the “virtual hospital” by then. “Unfortunately, EU projects are usually not prolonged. The project group, however, would very much like to continue its research. So far, all partners have been primarily scientifically oriented. Perhaps there will be a commercial partner in future. The EU has great interest in commercialising its projects,” says Susanna Röblitz.

More information: Prof. Susanna Röblitz,
tel.: +49-30-84185156,
email: susanna.roeblitz-aet-zib-punkt-de or

Dr. Rainald Ehrig,
tel.: +49-30-84185282,
email: ehrig-aet-zib-punkt-de

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