How Mathematics Can Help in the Fight Against Cancer

Saskia Haupt1, Michael Jendrusch2, Aysel Ahadova2, Magnus von Knebel Doeberitz2, Vincent Heuveline1, Matthias Kloor2

1Engineering Mathematics and Computing Lab (EMCL), Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Heidelberg, Germany. 2Department of Applied Tumor Biology, University Hospital Heidelberg and Cooperation Unit Applied Tumor Biology, German Cancer Research Center (DKFZ), Heidelberg, Germany



Mathematical oncology incorporates different aspects. First, the increasing amount of molecular data, particularly whole genome and exome data, provides new possibilities that allow studying the evolution and biology of tumours at an unprecedented accuracy and variability. However, managing this huge amount of data requires dedicated mathematical techniques. Furthermore, mathematical models can be used to evaluate hypotheses about tumour evolution, which in turn can be used to analyse and optimise different approaches for tumour prevention including chemoprevention and vaccination.



We suggest mathematical models for addressing some of the most relevant unanswered questions in Lynch syndrome (LS) management, which all contribute to a comprehensive understanding of LS tumour evolution following the three main pathways [Ahadova et al., IJC, 2018].



For this, we begin with the genetic level by modelling the role and proportion of MMR deficiency-initiated tumours in LS, which correspond to one way of LS pathogenesis.

We continue with the molecular level by identifying and analysing molecular differences between subtypes of LS cancers, e.g. prevalent and incident cancers undergoing regular colonoscopy screening potentially guiding colonoscopy strategies in the future.

We conclude with the consequences of the considered scenarios on a population level incorporating differences in cumulative LS cancer risks between the four MMR genes.



While the understanding of LS cancer development has dramatically increased during the last years, key questions with immediate implications for clinical management and prevention strategies remain still unanswered. Mathematical oncology helps answering these questions by using mathematical modeling approaches.

Abstract references

Ahadova, Aysel, et al. “Three molecular pathways model colorectal carcinogenesis in Lynch syndrome.” International journal of cancer 143.1 (2018): 139-150.