Absorbing markov chains to characterize and predict metastasis pathways in childhood cancer

Abstract

Cancer and its metastasis in children have a high degree of lethality and side effects, so its characteristics need to be studied independently of adult cancer. The aim of this work is to model the metastasis pathways of the main childhood cancers worldwide by Absorbing Markov Chains, an important mathematical tool used for different applications in science. Statistical information was collected to detect the main affected organs (primary sites) and those where cancer cells generally spread and metastasize (secondary sites). Taking into account that it is a branching process, a directed graph was developed, and the associated transition matrices for the first and second metastases were constructed. Organs whose cancers generally remain encapsulated and do not spread their cancer cells are considered absorbing states in terms of Markov processes. For the selected organs, the probability of ending up in each of the absorption states according to the primary site was calculated, as well as the number of possible previous metastases until reaching one of these states. Although the lung in childhood cancer is not a characteristic primary site, it is one of the main sites of metastasis. Therefore, this work dedicates a section to including this organ as a site of possible metastasis.