Source-linked AI summary
PPIM: Pennes Physics-Informed Mamba for Heat-Source-Conditioned 3D Bioheat Simulation
Dongyun Lee, Kyungho Yoon, Minwoo Shin
TL;DR
Predicting transient tissue temperatures matters in thermal-therapy settings. This paper compares three neural solvers for a controlled 3D Pennes simulation and proposes PPIM, which achieves the lowest evaluated errors and is effective for approximating the reference final temperature field in this setting.
Problem
Predicting transient temperature distributions in biological tissue is important, particularly in thermal-therapy settings.
Source: §1 · p. 1Method
PPIM extends temporal-subsequence PDE modeling with conditioned heat-source input and Pennes-aware SSM decay initialization for a controlled 3D Pennes simulation.
Source: §1 · p. 2Results
In the representative 600 s run, PPIM had the lowest MAE, relative L1, and relative L2 errors among the evaluated neural solvers and the closest spatial agreement with the FDM reference.
Source: §5 · p. 8Takeaways & Limitations
PPIM is effective for approximating the reference final temperature field in a controlled 3D Pennes bioheat simulation.
Source: §5 · p. 9The study does not model full clinical MWA, including electromagnetic SAR, temperature-dependent SAR redistribution, or large-vessel cooling.
Source: §2 · p. 2
Abstract
from arXiv · showhide
Three-dimensional bioheat simulation aims to predict transient temperature distributions in biological tissue and is commonly modeled using the Pennes bioheat equation, which combines thermal diffusion, perfusion-mediated heat loss, and external heat generation. In this study, we consider a controlled 3D Pennes bioheat simulation under a localized heat-source condition inspired by microwave ablation (MWA). To evaluate neural approximation performance, we compare three neural partial differential equation (PDE) solvers under the same controlled simulation: a spatial Fourier-feature physics-informed neural network (PINN), a generic PINNMamba temporal subsequence model, and Pennes Physics-Informed Mamba (PPIM). PPIM builds on the temporal subsequence model by incorporating conditioned heat-source input and Pennes-aware state-space model (SSM) decay initialization. All three neural models are trained under the same conditions with the same Pennes residual, and an explicit finite-difference method (FDM) solution is used only as the numerical reference. In a representative 600~s run, PPIM achieved the lowest MAE, relative $L_1$ error, and relative $L_2$ error among the evaluated neural solvers. Error maps further showed that the remaining PPIM errors were more concentrated near the heat-source region than across the rest of the domain. These results indicate that PPIM is effective for approximating the FDM reference final temperature field in this controlled simulation. The source code is available at https://github.com/muvYun/PPIM.
1 Introduction
The paper defines a controlled 3D Pennes bioheat simulation with MWA-inspired localized heating and compares neural PDE solvers against an explicit FDM reference. It proposes PPIM, which adds heat-source conditioning and Pennes-aware SSM decay initialization to temporal-subsequence modeling.
1 Introduction
- The controlled problem evaluates neural PDE solvers against an explicit FDM reference under an MWA-inspired localized heat-source condition.MWA is an application-inspired scenario, not a full patient-specific treatment simulation.Source: §1 · p. 2
- Prior work has explored PINNs for Pennes bioheat problems and SSM-based temporal-subsequence modeling, while residual-loss reduction may not ensure solution accuracy.The paper situates PPIM in this sequence-based physics-informed learning context.Source: §1 · p. 2
- PPIM builds on temporal-subsequence modeling with conditioned heat-source input and Pennes-aware SSM decay initialization.These components reflect the localized forcing field and representative diffusion–perfusion time scales.Source: §1 · p. 2
- The study evaluates a spatial Fourier-feature PINN, PINNMamba, and PPIM under the same controlled simulation.The contributions include defining the simulation and comparing the three neural solvers under the same FDM-referenced condition.Source: §1 · p. 2
- PPIM achieves the lowest errors across all evaluated metrics.The evaluation also considers spatial error maps.Source: §1 · p. 2
2 Background
The study frames a controlled 3D Pennes simulation with an MWA-inspired heat source, while distinguishing it from full clinical MWA modeling. It introduces Pennes bioheat terms and SSM temporal sequence modeling used by PINNMamba and PPIM.
2 Background
- This is a controlled MWA-inspired simulation, not a full clinical MWA model; its source is a fixed Gaussian SAR-like surrogate.It excludes full electromagnetic SAR modeling, temperature-dependent SAR redistribution, and large-vessel cooling.Source: §2 · p. 2
2.1 Pennes Bioheat Simulation
- The Pennes formulation predicts temperature elevation using diffusion, perfusion-related heat loss, and localized external forcing, with an explicit FDM solution serving as the numerical reference.The forcing field is shared by the FDM computation and the neural solvers’ Pennes residual.Source: §2.1 · p. 3
2.2 State-Space Sequence Modeling
- SSMs model temporal sequences through recurrent latent-state updates, and Mamba uses input-dependent selection to propagate or suppress temporal information.The study uses this sequence modeling in PINNMamba and PPIM; the overview shows normalized coordinates and qnorm forming tokens for temperature-elevation prediction.Source: §2.2 · p. 3, Figure 1 · p. 4
3 Method
PPIM extends temporal-subsequence SSM modeling with an explicit conditioned heat-source input and Pennes-aware decay initialization. These components incorporate the localized forcing and representative diffusion–perfusion time scales into the model.
3 Method
- PPIM builds on PINNMamba’s temporal-subsequence SSM approach with conditioned heat-source input and Pennes-aware SSM decay initialization.The architecture maps temporal tokens to temperature-elevation predictions.Source: §3 · p. 4
3.1 Conditioned Heat-Source Input
- PPIM concatenates normalized prescribed forcing qnorm with normalized spatio-temporal coordinates to condition each token on heat-source location and relative intensity.The input is derived from the prescribed source, not the FDM solution, and adds no supervised target labels.Source: §3.1 · p. 4
3.2 Pennes-aware SSM Decay Initialization
- PPIM initializes SSM decay rates from representative Pennes diffusion–perfusion time scales, using two families to reflect a range of perfusion attenuation.The initialized parameters remain trainable and serve as a physics-informed prior, not an exact spectral solver for the full temperature-dependent Pennes problem.Source: §3.2 · p. 5
4 Experiments
The experiments compare three neural solvers under a shared controlled 3D Pennes simulation and evaluate their final fields against an FDM reference. PPIM has the lowest reported scalar errors and the closest spatial agreement among the neural solvers.
4.1 Simulation Setup
- The three neural solvers share the controlled 3D Pennes conditions, and the FDM solution is used as the numerical reference.Evaluation uses the final field at t = 600 s with MAE, relative L1, and relative L2 metrics, plus spatial error maps.Source: §4.1 · p. 5
4.2 Heat-Source and Material Settings
- The prescribed source is a localized SAR-like Gaussian surrogate around a 15 mm active segment, rather than an antenna-specific SAR field.A fixed surrogate keeps the forcing field identical for the FDM reference and neural solvers; the stated source-power calibration is a surrogate, not a direct measurement of tissue absorption.Source: §4.2 · pp. 5–6
- The liver thermal parameters are fixed across the FDM reference and all neural solvers.The settings are C = 3.685 J/(cm3 ◦C), k = 0.0055 W/(cm ◦C), and B = 0.05 W/(cm3 ◦C).Source: §4.2 · p. 6
4.3 Training Details
- All neural models use the same discrete Pennes residual and 3000 Adam iterations; PINNMamba and PPIM additionally use length-7 temporal subsequences and subsequence consistency loss.The PINN is non-sequential and does not use sequence consistency loss; source-aware sampling addresses the localized Gaussian source region.Source: §4.3 · p. 6
4.4 Results
- PPIM achieves the lowest MAE, relative L1, and relative L2 errors among the evaluated neural solvers at t = 600 s.The table compares neural solvers against the FDM reference.Source: §4.4 · p. 6, Table 1 · p. 6
- PPIM more closely follows the FDM temperature field and surrounding decay, with the most spatially confined error pattern among the neural solvers.The final heat distributions and signed and absolute error maps show this spatial comparison.Source: §4.4 · p. 7, Figure 2 · p. 7, Figure 3 · p. 8
- PPIM has the lowest and most localized relative-error contribution, while PINN has the largest source-adjacent contribution and PINNMamba reduces it.The maps show pointwise normalized absolute- and squared-error contributions.Source: §4.4 · p. 7, Figure 4 · p. 8
5 Conclusion
The paper proposes PPIM for controlled 3D Pennes bioheat simulation with an MWA-inspired localized heat source. In a representative 600 s run, it has the lowest reported errors and closest spatial agreement with the FDM reference, supporting its use to approximate the reference final temperature field in this setting.
5 Conclusion
- PPIM adds conditioned heat-source input and Pennes-aware SSM decay initialization to PINNMamba-style temporal subsequence modeling.The method is evaluated for a controlled 3D Pennes bioheat simulation under an MWA-inspired localized heat-source condition.Source: §5 · p. 8
- In the representative 600 s run, PPIM achieves the lowest MAE, relative L1, and relative L2 errors among the evaluated neural solvers and the closest spatial agreement with the FDM reference.The evaluation compares PINN, PINNMamba, and PPIM against the FDM numerical reference.Source: §5 · p. 8
- The results indicate PPIM is effective for approximating the reference final temperature field in a controlled 3D Pennes bioheat simulation.Source: §5 · p. 9