Phase transitions in tumor growth IX: gastric cancer metastasis

Abstract

We propose a novel three-compartment heuristic model that recasts gastric cancer metastasis into a framework of non-equilibrium thermodynamics and nonlinear dynamics. The system, encompassing primary, hepatic, and peritoneal tumor populations, exhibits a well-defined route to chaos: as immune surveillance weakens, the dynamics undergo a supercritical Andronov-Hopf bifurcation, giving rise to a limit cycle, followed by a Shilnikov-type saddle-foci bifurcation cascade leading to chaotic attractors. Our central finding is the introduction of a dissipation function, {Psi}, constructed via a sensitivity-weighted, two-factor ansatz that integrates metabolic flux and dynamical influence. This spatially coarse-grained measure captures the systems thermodynamic robustness. The analysis reveals a dynamical phase transition: while tumor aggressiveness peaks in the pre-metastatic limit-cycle regime, {Psi} emerges as the definitive marker of the chaotic, treatment-resistant metastatic state, quantifying a sharp increase in systemic robustness that correlates decisively with advanced clinical stages (TNM III-IV). Consequently, this work provides a predictive framework grounded in the physics of metastasis, demonstrating that {Psi} not only diagnoses but also defines the primary therapeutic target: the underlying thermodynamic robustness of the metastatic system. Thus, effective intervention must shift from merely reducing tumor mass to strategically destabilizing this robust dissipative structure, thereby preventing recurrence. PACS: 05.45.-a; 87.18.-h; 87.19.xj; 05.70.Ln HighlightsO_LIA novel three-compartment heuristic model reveals phase transitions and chaotic dynamics in gastric cancer metastasis. C_LIO_LIThe dissipation function {Psi} emerges as a quantitative thermodynamic metric of systemic robustness in the metastatic regime. C_LIO_LIDecreasing immune surveillance triggers biological phase transitions towards metastatic disease. C_LIO_LIThe framework integrates nonlinear dynamics with TNM staging, identifying the dissipation function {Psi} as a therapeutic target to overcome metastatic recurrence. C_LI Graphical Abstract O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=102 SRC="FIGDIR/small/702339v1_ufig1.gif" ALT="Figure 1"> View larger version (24K): org.highwire.dtl.DTLVardef@1a605c7org.highwire.dtl.DTLVardef@c56e83org.highwire.dtl.DTLVardef@1da7fc8org.highwire.dtl.DTLVardef@1fb30ba_HPS_FORMAT_FIGEXP M_FIG C_FIG