Seeing the Invisible: How Mathematical Models Uncover Tumor Dormancy, Reconstruct the Natural History of Cancer, and Assess the Effects of Treatment

Abstract

The hypothesis of early metastasis was debated for several decades. Dormant cancer cells and surgery-induced acceleration of metastatic growth were first observed in clinical studies and animal experiments conducted more than a century ago; later, these findings were confirmed in numerous modern studies.In this primarily methodological work, we discuss critically important, yet largely unobservable, aspects of the natural history of cancer, such as (1) early metastatic dissemination; (2) dormancy of secondary tumors; (3) treatment-related interruption of metastatic dormancy, induction of angiogenesis, and acceleration of the growth of vascular metastases; and (4) the existence of cancer stem cells. The hypothesis of early metastasis was debated for several decades. Dormant cancer cells and surgery-induced acceleration of metastatic growth were first observed in clinical studies and animal experiments conducted more than a century ago; later, these findings were confirmed in numerous modern studies.We focus on the unique role played by very general mathematical models of the individual natural history of cancer that are entirely mechanistic yet, somewhat paradoxically, essentially free of assumptions about specific nature of the underlying biological processes. These models make it possible to reconstruct in considerable detail the individual natural history of cancer and retrospectively assess the effects of treatment. Thus, the models can be used as a tool for generation and validation of biomedical hypotheses related to carcinogenesis, primary tumor growth, its metastatic dissemination, growth of metastases, and the effects of various treatment modalities. We discuss in detail one such general model and review the conclusions relevant to the aforementioned aspects of cancer progression that were drawn from fitting a parametric version of the model to data on the volumes of bone metastases in one breast cancer patient and 12 prostate cancer patients.

Abscopal Benefits of Localized Radiotherapy Depend on Activated T-cell Trafficking and Distribution between Metastatic Lesions

“…This augments an understanding of the modulation of distant tumors from the primary, a phenomena recognized more than 100 years ago and termed "concomitant immunity" (41). Third, surgical removal of the primary tumor may trigger progression of existing metastatic sites, which has been seen in the clinic (27)(28)(29)(30) as well as in animal experiments (42,43) and mathematical models (44,45). With 93% of breast cancer (early stage I and II), 98% of colon cancer (stage I, II, and III), and 71% of nonsmall cell lung cancer (early stage I and II) patients undergoing surgery as a part of their treatment (46), systemic perturbation by the presumed local treatment needs to be explored further.…”

A “universal” model of metastatic cancer, its parametric forms and their identification: what can be learned from site-specific volumes of metastases

“…Another fundamental difficulty is that cancer progression is impelled through a number of sporadically occurring critical microevents (such as appearance of the first malignant clonogenic cell, inception of the primary tumor, shedding of viable metastases off the primary tumor, and their inception at various secondary sites) whose timing cannot be determined on mechanistic grounds. In this paper we employed a very different approach to cancer modeling that was first conceptualized by Hanin (2012). This approach is phenomenological in nature and is focused on the timing and rates of the most important and clinically relevant processes such as primary tumor origination, inception and growth, shedding of metastases, their selection, dormancy, inception and growth at various secondary sites.…”

Modeling Spontaneous Metastasis following Surgery: An In Vivo-In Silico Approach

“…However, this would add at least one degree of freedom (thus deteriorating the reliability of the estimation) and invalidate the convolution formula used for computation of the metastatic burden in a model with non-autonomous g ( t , v ) (instead of g ( v )), and therefore was not considered here. Importantly, theoretical integration of higher order phenomena for the biological dynamics of metastatic development has been considered elsewhere (14,16,18,54) and recent findings in the organism-scale dynamics of metastases (such as the self-seeding phenomenon (5,6) or the influence of the (pre-) metastatic niche (55)) could be embedded within the general formalism developed in our model. This could lead to complex models, however, and given the amount of information contained in our present data, reliable identification of such dynamics was not realistic.…”