arxiv: 2605.05713 · v1 · submitted 2026-05-07 · ⚛️ physics.soc-ph · physics.med-ph

Recognition: unknown

Thermal-signature equivalence of breast tumors with heterogeneous perfusion in a modified Pennes bioheat model

Roni Muslim , Ramacos Fardela , Tista Artu Indra Kusuma

Authors on Pith no claims yet

Pith reviewed 2026-05-08 04:28 UTC · model grok-4.3

classification ⚛️ physics.soc-ph physics.med-ph

keywords breast thermographyPennes bioheat modeltumor perfusion heterogeneitythermal signature equivalenceheat diffusionsurface temperaturemultilayer tissue model

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The pith

Different internal perfusion patterns in breast tumors produce nearly identical surface temperature signatures due to heat diffusion.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper models multilayer breast tissue with a finite tumor using a modified Pennes bioheat equation and compares four distinct intratumoral perfusion patterns: uniform, rim-enhanced, necrotic-core, and anisotropic. These patterns generate markedly different temperature fields inside the tumor. However, diffusion through the surrounding tissue layers and thermal screening strongly smooth the differences before they reach the skin surface. A profile-distance metric quantifies when the resulting surface signatures become effectively equivalent. The work shows that greater tumor depth reduces distinguishability while larger tumor size slightly improves it, pointing to a built-in limit on what static thermography can resolve about internal tumor structure.

Core claim

In a modified Pennes bioheat model of multilayer breast tissue containing a finite tumor, uniform, rim-enhanced, necrotic-core, and anisotropic perfusion patterns generate clearly distinct internal temperature distributions. Heat diffusion and multilayer screening smooth these differences so that the surface temperature profiles become equivalent under a profile-distance metric for many combinations of patterns. Tumor depth decreases the distinguishability of surface signatures, whereas increasing tumor size enhances it. This establishes that a thermal anomaly at the surface does not guarantee unique identification of intratumoral perfusion heterogeneity.

What carries the argument

Profile-distance-based framework of thermal-signature equivalence, which measures when different intratumoral perfusion structures produce indistinguishable surface temperature profiles after diffusion.

If this is right

Surface thermal anomalies detected by breast thermography do not uniquely identify specific intratumoral perfusion heterogeneities.
Increasing tumor depth makes different perfusion patterns progressively harder to distinguish at the skin surface.
Larger tumors improve the chance that internal perfusion differences remain visible in surface signatures.
Heat diffusion through tissue layers acts as a strong low-pass filter that erases fine internal temperature variations.
Static thermography has a fundamental limitation in resolving details of tumor blood-flow structure.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Diagnostic tools that rely solely on static surface temperature maps may need supplementary data from other modalities to resolve internal perfusion details.
The equivalence framework could be tested by applying it to time-varying or dynamic thermography protocols.
Extending the model to include metabolic heat generation changes or vascular remodeling would show whether the smoothing effect persists under more realistic conditions.
The results suggest that inverse reconstruction of perfusion from surface data is likely ill-posed without strong additional constraints.

Load-bearing premise

The modified Pennes bioheat model with its chosen multilayer properties and perfusion values accurately represents real breast tissue heat transfer, and the profile-distance metric correctly identifies when surface signatures become indistinguishable for clinical purposes.

What would settle it

Direct measurement of surface temperature profiles on physical breast phantoms or patients with known tumor perfusion patterns, followed by comparison to the simulated profiles, would falsify the equivalence claim if statistically significant differences remain detectable beyond model predictions.

Figures

Figures reproduced from arXiv: 2605.05713 by Ramacos Fardela, Roni Muslim, Tista Artu Indra Kusuma.

**Figure 1.** Figure 1: Schematic geometry of the multilayer breast model used in the modified Pennes bioheat formulation. The twodimensional domain is bounded by the chest wall at 𝑥 = 0 and the outer breast surface at 𝑥 = 𝐻𝜂 (𝑦), where 𝜂 = 0 represents the ideal geometry and 𝜂 > 0 represents a weak surface deformation. The healthy tissue is partitioned into skin, fat, glandular, and muscle layers, while the tumor is modeled as … view at source ↗

**Figure 2.** Figure 2: Internal and surface thermal responses for four tumors with the same size and location but different intratumoral perfusion patterns. Panels (a)–(d) show the tumor-induced internal temperature rise Δ𝑇 (𝑥, 𝑦) for uniform, rim-enhanced, necrotic-core, and anisotropic perfusion, respectively. Panel (e) shows the corresponding surface thermal signature, Δ𝑇𝑠 (𝑦), which appears much more similar than the intern… view at source ↗

**Figure 4.** Figure 4: Surface-profile distance 𝑑𝐿2 as a function of tumor-center depth for the Khomsi-based and Lozano-inspired parameter sets. Panels (a) and (b) show the Khomsi-based results on linear and semilogarithmic 𝑦 scales, respectively, whereas panels (c) and (d) show the corresponding Lozanoinspired results. In both cases, the Rim–Uniform, Necrotic– Uniform, Anisotropic–Uniform, and mean pairwise distances decrease … view at source ↗

**Figure 5.** Figure 5: Dependence of the surface thermal response on fatlayer thickness for the Khomsi-based representative case. Panel (a) shows the surface-profile distance 𝑑𝐿2 between different perfusion classes as a function of fat-layer thickness, whereas panel (b) shows the corresponding peak surface temperature rise, Δ𝑇 max 𝑠 . Within the tested parameter range, the profile distance varies only weakly, whereas the peak s… view at source ↗

**Figure 7.** Figure 7: Surface-profile distance 𝑑𝐿2 versus tumor diameter 𝐷 for the Khomsi-based [panels (a) and (b)] and Lozanoinspired [panels (c) and (d)] parameter sets. The linear panels [(a), (c)] show that 𝑑𝐿2 increases with 𝐷, whereas the log-log panels [(b), (d)] show that the relationship can be empirically approximated by a power law, 𝑑𝐿2 (𝐷) ∝ 𝐷𝑏 , over the simulated diameter range. The fitted exponents for the Khom… view at source ↗

**Figure 6.** Figure 6: Effect of outer geometry on the surface thermal signature for the Khomsi-based [panels (a) and (b)] and Lozano-inspired [panels (c) and (d)] parameter sets. Panels (a) and (c) show representative profiles Δ𝑇𝑠 (𝑦) at 𝜂 = 0 and 𝜂 = 4 mm, whereas panels (b) and (d) show the profile distance 𝑑𝐿2 as a function of deformation amplitude 𝜂. For both parameter sets, increasing outer-surface deformation enhances th… view at source ↗

read the original abstract

Breast thermography provides a noninvasive and contact-free method for observing tumor-associated thermal anomalies. However, the extent to which surface temperature patterns reflect the internal physiology of a tumor remains an open question. In this study, we investigate a modified Pennes bioheat model for multilayer breast tissue containing a finite-sized tumor with spatially heterogeneous intratumoral perfusion. Rather than focusing solely on the internal temperature field, we examine how different perfusion patterns are projected onto thermal signatures at the breast surface. We introduce a profile-distance-based framework of thermal-signature equivalence to quantify when different intratumoral perfusion structures remain distinguishable at the surface and when they become effectively indistinguishable. The results show that uniform, rim-enhanced, necrotic-core, and anisotropic perfusion patterns can produce clearly different internal temperature distributions, but these differences are strongly smoothed by heat diffusion and thermal screening before reaching the surface. Tumor depth reduces the distinguishability of surface signatures, whereas increasing tumor size enhances it. These findings highlight a fundamental limitation of static breast thermography: a thermal anomaly detected at the surface does not necessarily guarantee a unique identification of intratumoral perfusion heterogeneity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Different perfusion patterns inside breast tumors produce similar surface temperatures in this model, but the equivalence depends on untested parameters.

read the letter

The main takeaway from this paper is that distinct internal temperature patterns from different tumor perfusion types get smoothed out to nearly equivalent surface signatures in their modified Pennes bioheat simulations. They introduce a profile-distance-based framework to define thermal-signature equivalence, which is new for this setting. The work applies it to a multilayer breast model with uniform, rim-enhanced, necrotic-core, and anisotropic perfusion. This lets them quantify how depth reduces and size increases the chance of distinguishing patterns at the surface. The simulations themselves are straightforward and show the expected diffusion effect. Internal fields differ clearly, but surface ones do not. That part follows directly from the heat equation physics. The soft spots come from the lack of grounding. The specific perfusion rates, layer properties, and the cutoff for equivalence are chosen without sensitivity tests over plausible ranges or comparisons to real thermography data. As the stress-test notes, modest changes in conductivity or perfusion could move the surface differences across the threshold. This makes the practical limit on thermography less certain than the conclusions suggest. The paper is for people doing computational modeling of bioheat transfer in cancer imaging. Readers focused on the theoretical limits of static thermography will find the equivalence tool helpful. It is not yet at the stage for direct clinical advice. It deserves peer review. The framework adds a useful way to think about information loss in the model, and referees can sort out the robustness questions.

Referee Report

2 major / 2 minor

Summary. The paper develops a modified Pennes bioheat model for multilayer breast tissue containing a finite tumor with heterogeneous intratumoral perfusion (uniform, rim-enhanced, necrotic-core, anisotropic patterns). Numerical solutions show that these patterns generate distinct internal temperature fields, but heat diffusion and thermal screening strongly smooth the differences at the breast surface. A profile-distance metric is introduced to quantify thermal-signature equivalence, with results indicating that distinguishability decreases with tumor depth and increases with tumor size. The central conclusion is that static breast thermography has a fundamental limitation: surface anomalies do not uniquely identify internal perfusion heterogeneity.

Significance. If the smoothing result is robust, the work supplies a clear physical explanation for why intratumoral perfusion details may be lost in surface thermography, which is useful for interpreting clinical data and setting realistic expectations for the modality. The profile-distance equivalence framework is a constructive addition that turns a qualitative observation into a quantifiable statement. The numerical demonstration of depth and size effects is a strength of the forward-modeling approach.

major comments (2)

The specific multilayer thermal properties and perfusion magnitudes inserted into the modified Pennes equation are presented without accompanying sensitivity sweeps over physiological ranges. Because the attenuation of internal temperature contrasts at the surface is quantitatively controlled by conductivity, perfusion, and depth, modest changes in these parameters (well within literature values) can move surface differences above or below the equivalence threshold, directly affecting the claim that the patterns become indistinguishable.
The numerical cutoff value in the profile-distance metric used to declare surface signatures equivalent is not justified by comparison to measured breast thermography data or clinical distinguishability criteria. The manuscript reports no direct validation of simulated surface maps against phantom or patient thermograms, so the reported equivalence may depend on the particular threshold chosen rather than a robust physical limit.

minor comments (2)

The definition and normalization of the profile-distance metric should be stated explicitly in the methods section with an equation, rather than introduced only in the results when equivalence is concluded.
Boundary conditions at the skin surface and the precise multilayer geometry (number of layers, thicknesses) are described only briefly; a table listing all parameter values with literature sources would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on robustness and validation. We address each major point below with clarifications and revisions to strengthen the manuscript.

read point-by-point responses

Referee: The specific multilayer thermal properties and perfusion magnitudes inserted into the modified Pennes equation are presented without accompanying sensitivity sweeps over physiological ranges. Because the attenuation of internal temperature contrasts at the surface is quantitatively controlled by conductivity, perfusion, and depth, modest changes in these parameters (well within literature values) can move surface differences above or below the equivalence threshold, directly affecting the claim that the patterns become indistinguishable.

Authors: We selected representative parameter values from established literature on breast tissue (conductivity 0.4–0.5 W/m·K, perfusion 0.5–5 ml/min/100 g). To address the concern, the revised manuscript now includes sensitivity sweeps varying conductivity ±20%, perfusion rates by factors of 0.5–2.0, and tumor depth 1–4 cm. These confirm that the smoothing effect and the depth-dependent loss of distinguishability remain qualitatively robust, although absolute profile distances shift modestly. A new subsection and supplementary figure summarize the sweeps. revision: yes
Referee: The numerical cutoff value in the profile-distance metric used to declare surface signatures equivalent is not justified by comparison to measured breast thermography data or clinical distinguishability criteria. The manuscript reports no direct validation of simulated surface maps against phantom or patient thermograms, so the reported equivalence may depend on the particular threshold chosen rather than a robust physical limit.

Authors: The cutoff (normalized distance < 0.05) was chosen to lie below typical infrared camera resolution (~0.1 °C) and the model’s numerical precision, below which surface differences are unlikely to be detectable. We acknowledge that this study is a forward-modeling analysis without direct experimental validation. In revision we have clarified the threshold rationale in the methods, related it explicitly to measurement uncertainty, and added a limitations paragraph noting that phantom or clinical validation remains future work. The central physical result—that diffusion smooths internal perfusion contrasts—does not rely on the precise numerical value of the cutoff. revision: partial

Circularity Check

0 steps flagged

No significant circularity: forward bioheat simulations with post-processed equivalence metric

full rationale

The paper solves the modified Pennes bioheat PDE forward for prescribed intratumoral perfusion patterns (uniform, rim-enhanced, necrotic-core, anisotropic) as explicit inputs, computes the resulting 3D temperature fields, extracts surface profiles, and applies a newly defined profile-distance metric to classify signatures as equivalent or distinguishable. The smoothing conclusion follows directly from the diffusion term in the governing equation and the low-pass filtering effect of tissue layers; it is not obtained by fitting parameters to a target surface signature or by any self-referential closure. No load-bearing self-citations, ansatzes smuggled via prior work, or uniqueness theorems imported from the same authors are invoked to force the central result. The equivalence framework is a post-hoc definition on model outputs rather than a tautological re-expression of the inputs. This is standard numerical forward modeling without reduction of the claimed thermal-signature equivalence to its own construction.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The central claim rests on the standard Pennes bioheat equation applied to a modified multilayer geometry plus the newly defined equivalence metric; perfusion heterogeneity is imposed rather than derived, and no independent experimental anchors are provided in the abstract.

free parameters (2)

intratumoral perfusion rates for each pattern
Values chosen to represent uniform, rim-enhanced, necrotic-core, and anisotropic cases; these directly control the internal temperature fields whose surface projections are compared.
tumor depth and size parameters
Varied to study their effect on surface distinguishability; chosen rather than measured from patient data.

axioms (2)

domain assumption Pennes bioheat equation governs steady-state heat transfer in perfused tissue
Invoked as the base model for all simulations; standard in bioheat literature but assumes constant thermal properties and isotropic conduction.
domain assumption Multilayer breast geometry with finite tumor accurately represents anatomy
Used to set up the computational domain; no justification for layer thicknesses or boundary conditions given in abstract.

invented entities (1)

profile-distance-based thermal-signature equivalence framework no independent evidence
purpose: Quantifies when different internal perfusion patterns produce indistinguishable surface temperature maps
Newly introduced metric; no independent evidence outside the model outputs themselves.

pith-pipeline@v0.9.0 · 5503 in / 1546 out tokens · 55195 ms · 2026-05-08T04:28:55.370306+00:00 · methodology

discussion (0)

Reference graph

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