Monte Carlo simulation-based approach to model the size distribution of metastatic tumors

Kinetics of cancer metastasis

The formation of metastases during cancer is now considered to be induced by migrating metastatic stem cells (MetSCs) in preexisting niches or niches induced by MetSCs or tumor-derived exosomes (TDEs). I propose and compare two simplest generic models describing these two scenarios. The number of tumors is predicted (i) to increase exponentially in the case of preexisting niches and (ii) to diverge during a finite time interval in the case of induced niches. The latter prediction is novel and of interest because rapid collapse in the end of a finite time interval is a well-known feature of the cancer metastasis. Two advanced models describing the two scenarios of cancer metastasis have been scrutinized as well. These models clarify the likely role of various specific factors in the metastasis. In particular, the equations derived in the framework of the advanced model with preexisting niches have been solved analytically allowing (i) to clarify the factors determining the duration of the period from the initiation of the primary tumor to the phase when the metastases start to dominate, (ii) to estimate the number of metastases in the end of this period, and (iii) to explains why the use of chemotherapy typically results in the improvement of the patient state only for a relatively short period. The equations derived in the framework of the advanced model with induced niches have no analytical solution, and their analysis merits additional attention.

Modeling breast cancer survival and metastasis rates from moderate-sized clinical data

Predicting time-dependent survival probability of a breast cancer patient using information such as primary tumor size, grade, node spread status, and patient age at the time of surgery can be of immense help in managing life expectations and strategizing postoperative treatment. However, for moderate-sized clinical datasets the application of standard Kaplan-Meier theory to determine survival probability as a function of multiple cofactors can become challenging when continuous variables like tumor diameter and survival time are segmented into a large number of narrow intervals, a problem commonly termed the curse of dimensionality. We circumvent this problem by modeling the patient-to-patient distribution of primary tumor diameter with a realistic, right-skewed function, and then matching the diameter-marginalized survival with the mean Kaplan-Meier survival for the data. We apply this procedure on a recent clinical data from 1875 breast cancer patients and develop parameters that can be readily used to estimate post-surgery survival for an arbitrary time length. Finally, we show that the observed fraction of node-positive patients can be quantitatively explained within a simple tumor growth and metastasis framework. Employing two different tumor growth models from the literature (i.e., Gompertz and logistic growth models), we utilize the observed fraction-node-positive data to determine metastasis rates from the surface of a primary tumor and its patient-to-patient distribution.