On the growth and dissemination laws in a mathematical model of metastatic growth

摘要

Metastasis represents one of the main clinical challenge in cancer treatmentsince it is associated with the majority of deaths. Recent technologicaladvances allow quantification of the dynamics of the process by means ofnoninvasive techniques such as longitudinal tracking of bioluminescent cells.The metastatic process was simplified here into two essential components --dissemination and colonization -- which were mathematically formalized in termsof simple quantitative laws. The resulting mathematical model was confronted toin vivo experimental data of spontaneous metastasis after primary tumorresection. We discuss how much information can be inferred from confrontationof theories to the data with emphasis on identifiability issues. It is shownthat two mutually exclusive assumptions for the secondary growth law (namelysame or different from the primary tumor growth law) could fit equally well thedata. Similarly, the fractal dimension coefficient in the dissemination lawcould not be uniquely determined from data on total metastatic burden only.Together, these results delimitate the range of information that can berecovered from fitting data of metastatic growth to already simplifiedmathematical models.