Regulation of Tumor Dormancy and Role of Microenvironment: A Mathematical Model

Abstract

Herein, a mathematical model of a molecular control system for the regulation of secondary tumors is formulated and analyzed to explore how secondary tumors can be controlled by a primary tumor with/without a surgery and the microenvironment. This control system is composed of fibroblast growth factor-2 (FGF2), urokinase-type plasminogen activator (uPA), plasmin, transforming growth factor-beta (TGFβ), latent TGFβ (LTGFβ), and tumor density. The control of secondary tumors by primary tumors was first modeled by Boushaba, Nilsen-Hamiton and Levine in [46]. The model is based on the idea that the vascularization of a secondary tumor can be suppressed by inhibitors from a larger primary tumor. The emergence of tumors at secondary sites 5-7 cm from a primary site was observed after surgical removal of the primary tumor in silico. The model supports the notion that the fate of secondary tumors after surgery depends on the distance from the primary tumor and the surrounding microenvironment. As such, the primary tumor did not influence the growth of remote secondary tumors, but it could effectively suppress the growth of the secondary tumors if they were too close to the primary tumor, even after it was removed. Thus, the model predicts the emergence of secondary tumors after the excision of the primary tumor when the distance between these tumors is in the "distance window." It also predicts that the growth behaviors of the secondary tumors depend on the local microenvironment. Based on these findings, we propose several treatment options for better clinical outcomes.

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.…”

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.…”

“…In 2000, Iwata and colleagues used imaging data from one patient with metastatic hepatocellular carcinoma to introduce a more formalistic and biologically-based approach that relied on the description of the temporal dynamics of a population of metastatic colonies, with equations written at the organ or organism scale (10). In parallel, several studies have sought to include additional variables when modeling tumor growth, such as angiogenesis (11), stem cell behavior (12), tumor-immune interactions (13) and microenvironment influences (14), among numerous others. To date, the majority of mathematical studies in cancer modeling have focused on primary tumor and relatively few have investigated the metastatic development (15–22).…”

Mathematical Modeling of the Metastatic Process

“…Boushaba and colleagues [40,41] considered an anti-angiogenic factor secreted by the primary which would keep spatially separated, yet local, metastases in a dormant state and reported a critical distance window in which this effect was active. This result is difficult to interpret in hematogenous metastasis as the idea of a diffusion 'distance' for any factor secreted by the primary is not trivially understood because of the fluid dynamics involved in blood flow as compared to diffusion through tissue.…”