Spreaders and Sponges Define Metastasis in Lung Cancer: A Markov Chain Monte Carlo Mathematical Model

Abstract

The classic view of metastatic cancer progression is that it is a unidirectional process initiated at the primary tumor site, progressing to variably distant metastatic sites in a fairly predictable, though not perfectly understood, fashion. A Markov chain Monte Carlo mathematical approach can determine a pathway diagram that classifies metastatic tumors as ‘spreaders’ or ‘sponges’ and orders the timescales of progression from site to site. In light of recent experimental evidence highlighting the potential significance of self-seeding of primary tumors, we use a Markov chain Monte Carlo (MCMC) approach, based on large autopsy data sets, to quantify the stochastic, systemic, and often multi-directional aspects of cancer progression. We quantify three types of multi-directional mechanisms of progression: (i) self-seeding of the primary tumor; (ii) re-seeding of the primary tumor from a metastatic site (primary re-seeding); and (iii) re-seeding of metastatic tumors (metastasis re-seeding). The model shows that the combined characteristics of the primary and the first metastatic site to which it spreads largely determine the future pathways and timescales of systemic disease. For lung cancer, the main ‘spreaders’ of systemic disease are the adrenal gland and kidney, whereas the main ‘sponges’ are regional lymph nodes, liver, and bone. Lung is a significant self-seeder, although it is a ‘sponge’ site with respect to progression characteristics.

Chemotherapy Counteracts Metastatic Dissemination Induced by Antiangiogenic Treatment in Mice

“…There is the loss of cell-tocell adhesion, increased motility/invasion, intravasation in the bloodstream, extravasation, and homing in a different site. All require permissive angiogenesis, which is also vital for the survival and proliferation of micrometastases (9)(10)(11)(12). The majority of preclinical studies have focused on the effect of antiangiogenic therapy on primary tumor growth, with less attention to metastasis.…”

Capillary collagen as the physical transport barrier in drug delivery to tumor microenvironment

“…Most of these models employ reaction-diffusion-advection equations for mass transports, but some can be hybrid with involving discrete and continuous, 21 or statistical variables. [22][23][24] Drug delivery and distribution models make another group focusing on transport problems, which is well reviewed in Ref.. 25 Most frequently, a sophisticated mathematics seeks to decipher vascularization and fluid mechanics, vascular geometry and extravasation, drug tumor uptake, cellular fate and pharmacodynamics, transport in stroma, advection, or drug vector uptake.…”

Impact of Metabolic Heterogeneity on Tumor Growth, Invasion, and Treatment Outcomes

“…Mathematical models of cancer progression have examined avascular growth [16, 17, 3], angiogenesis [18, 19], vascular growth [20, 21], invasion [22, 23] and metastasis [24, 25]; also see these reviews [26, 17, 27, 25]. Tumor metabolism, specifically glycolytic metabolism and its development has also been extensively studied [28, 2].…”