The Growth Laws of Brain Metastases

Tumor growth is the result of the interplay of complex biological processes in huge numbers of individual cells living in changing environments. Effective simple mathematical laws have been shown to describe tumor growth in vitro, or simple animal models with bounded-growth dynamics accurately. However, results for the growth of human cancers in patients are scarce. Our study mined a large dataset of 1133 brain metastases (BMs) with longitudinal imaging follow-up to find growth laws for untreated BMs and recurrent treated BMs. Untreated BMs showed high growth exponents, most likely related to the underlying evolutionary dynamics, with experimental tumors in mice resembling accurately the disease. Recurrent BMs growth exponents were smaller, most probably due to a reduction in tumor heterogeneity after treatment, which may limit the tumor evolutionary capabilities. In silico simulations using a stochastic discrete mesoscopic model with basic evolutionary dynamics led to results in line with the observed data. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This research has been supported by the James S. Mc. Donnell Foundation (USA) 21st Century Science Initiative in Mathematical and Complex Systems Approaches for Brain Cancer (Collaborative award 220020450, doi:10.37717/220020560), Junta de Comunidades de Castilla-La Mancha (grant SBPLY/21/180501/000145) and by the Spanish Ministerio de Ciencia e Innovación (grant PID2019-110895RB-100 funded by MCIN/AEI/ 10.13039/501100011033). ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: Ethics committee of Fundación Instituto Valenciano de Oncología gave ethical approval for this work. I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable. Yes All data produced in the present study are available upon reasonable request to the authors.