用物理约束的Mamba模型高效模拟微波消融下的组织温升,精度优于现有神经求解器。
PPIM: Pennes Physics-Informed Mamba for Heat-Source-Conditioned 3D Bioheat Simulation

- 基于物理信息的Mamba架构,融合热源条件与佩尼斯方程先验
- 600秒仿真中误差最低,且误差集中于热源附近区域
- 适合需要高精度生物热仿真的医学治疗模拟场景
三维生物热模拟旨在预测生物组织中的瞬态温度分布,通常以佩尼斯生物热方程建模,该方程结合了热扩散、灌注导致的散热以及外部热源。本研究在受控的局部热源条件下(受微波消融启发)开展3D佩尼斯生物热模拟。为评估神经近似性能,比较三种神经偏微分方程求解器:空间傅里叶特征物理信息神经网络(PINN)、通用的时空子序列模型PINNMamba,以及本文提出的佩尼斯物理信息Mamba(PPIM)。PPIM在时序子序列模型基础上引入条件热源输入,并采用佩尼斯感知的状态空间模型(SSM)衰减初始化。所有模型均在相同条件下训练,使用相同的佩尼斯残差项,仅以显式有限差分法(FDM)解作为数值参考。在典型的600秒运行中,PPIM在平均绝对误差(MAE)、相对$L_1$误差和相对$L_2$误差三项指标上均优于其他神经求解器。误差图显示,剩余误差主要集中在热源区域而非整个域。结果表明,PPIM能有效逼近该受控模拟下的FDM参考最终温度场。源代码见https://github.com/muvYun/PPIM。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。