Quantifying thermal-signature equivalence in infrared breast thermography using a modified Pennes bioheat model

Abstract

Infrared breast thermography measures skin-surface temperature, but heat diffusion and thermal screening can obscure intratumoral physiology. We introduce a tolerance-aware, full-profile framework to determine when distinct intratumoral perfusion patterns become observationally equivalent at the breast surface. We solve a steady-state modified Pennes model for a two-dimensional multilayer breast containing a finite tumor with uniform, rim-enhanced, necrotic-core, or anisotropic perfusion. A conservative finite-difference scheme with a BiCGSTAB solver and an incomplete-LU (IncompleteLUT) preconditioner is verified by mesh refinement and an analytical benchmark. For a representative configuration, equivalent-pair fractions are $2/6$, $5/6$, and $6/6$ at tolerances of $0.020$, $0.050$, and $0.100{}^{\circ }\mathrm{C}$, respectively. Noise tests show that classification depends on how profile-level uncertainty is modeled. Matching tumor-averaged perfusion reduces rim-enhanced--uniform and necrotic-core--uniform profile distances by $97.7\%$ and $99.0\%$, respectively, whereas anisotropic perfusion remains more distinguishable. Greater tumor depth increases thermal-signature equivalence, while larger diameter enhances distinguishability. Among four parameter groups, heat generation has the strongest positive influence on mean profile separation. For fixed representative geometry and perfusion-pattern shapes, a 300-point Latin-hypercube analysis with independent uniform $\pm 20\%$ perturbations of these parameter groups finds that about $79\%$ of sampled configurations retain at least one equivalent pair at ${\epsilon }_T=0.020{}^{\circ }\mathrm{C}$. Our results show that a detectable static surface anomaly does not uniquely determine its internal perfusion structure.

arXiv comment32 pages, 12 figures