When a drug is to be developed there is a stage when clinical studies are performed to characterise the drug’s properties and effects in humans. To better understand and quantify the drug effects, mathematical models can be used. For example, it can be to understand how drugs behave inside the body – its concentration over time, how they are absorbed, distributed and eliminated, and what effect they have. These models are often referred to by the abbreviation PK-PD, where PK stands for pharmacokinetics and PD for pharmacodynamics.

To develop the models and calibrate them to measurement data is a complex and computationally difficult problem. The PhD thesis of Jacob Leander presents new computational methods and applications of these, to make calibration to measurement data faster and more efficient when building models. He has also looked into an extension of the models to so-called stochastic models.

– One of the more interesting problems we have investigated has been how to better use the data that the patients collect themselves in their homes. An example is clinical studies in asthma, where patients can measure their lung capacity several times a day for a whole year. This of course provides a lot of data, and we have expanded the modelling framework to incorporate stochastic models. This can help us better understand how the lung functions of the patients vary over time and how the drug affects this.

## Growing area for mathematicians

This may be one of the first examples of model-based analysis of home measurements that has been done, and Jacob hopes that in the future it can be a complement to current analysis methods. Among other things, it could be used to design more informative clinical studies, for example by being able to reduce the number of patients in the study. This is positive from both an ethical and a financial perspective. In the thesis, the methods themselves are also developed. A new method for model calibration has been developed, and this method is now available in one of the most widely used software for modelling of PK-PD. The models as such are general and the methods can therefore be used in many areas where you measure several entities over time, for example in single-cell experiments.

In recent years, drug development has had a strong focus on including mathematical modelling to be able to take decisions during the course of the development, such as which dose to use in a clinical study and for which patients a drug can be expected to have best effects. The development of computers also enables increasingly complex computations and simulations. The future for mathematicians is bright – many modellers are needed in the field!

## Work and studies in parallel

Jacob has always liked mathematics, physics and problem solving. He began studying Engineering Physics in 2007, but when Engineering Mathematics started a year later he changed programme. The main reason was that Engineering mathematics had more focus on mathematics and programming, something he has had great use for in professional life. The first years, Jacob was interested in financial mathematics, but when he was offered to do his degree project for AstraZeneca he changed his mind. Jacob graduated with a master’s degree in 2012 and then studied Advanced Engineeing in Mathematics (AEM), a two-year licentiate programme with close connections to industry.

– I would have liked to continue to a PhD already back then, but the programme was not set up that way, so I started to work as a pharmacometrician at AstraZeneca in 2015 with similar things as I did in my licentiate degree. After a few years, an opportunity came up to start a research project and become a part-time industrial PhD student. It was actually AstraZeneca that took the initiative and my project is very close to what I do otherwise in my daily work.

So since 2017, Jacob has worked part-time and studied for a PhD in the other part-time, affiliated with FCC (Fraunhofer-Chalmers Research Centre for Industrial Mathematics). It has not always been entirely easy to put it together, but he still thinks it has exceeded his expectations. Not least, interesting results have been obtained that will continue to be developed.

– On the plus side, I have been able to decide myself quite a lot which courses to read, there has been a freedom in deciding what is relevant for me, for example I read a course in Uppsala on Monte Carlo methods for dynamic systems. It is exciting to network with PhD students and discover that others are doing similar things. As an industrial PhD student, you unfortunately do not have very strong connections to the department, I think it would be good if you could have more contacts and network better with the academy.*Jacob Leander will defend his PhD thesis “Mixed Effects Modelling of Deterministic and Stochastic Dynamical Systems – Methods and Applications in Drug Development” on June 4 at 10.00 via Zoom. Supervisor is Mats Jirstrand, assistant supervisor Marija Cvijovic.***Text**: Setta Aspström**Picture**: A graphical illustration of a model to describe the concentration and effect of a drug, Jacob Leander**Photo**: private