PPIM: Pennes物理信息Mamba用于热源条件下的三维生物热模拟

中文摘要 AI 辅助

三维生物热模拟旨在预测生物组织中的瞬态温度分布，通常使用Pennes生物热方程进行建模，该方程结合了热扩散、灌注介导的热损失和外部热生成。在本研究中，我们考虑在受微波消融（MWA）启发的局部热源条件下进行受控的三维Pennes生物热模拟。为了评估神经逼近性能，我们在相同的受控模拟下比较了三种神经偏微分方程（PDE）求解器：空间傅里叶特征物理信息神经网络（PINN）、通用PINNMamba时间子序列模型和Pennes物理信息Mamba（PPIM）。PPIM在时间子序列模型的基础上，引入了条件热源输入和Pennes感知的状态空间模型（SSM）衰减初始化。所有三个神经模型在相同条件下使用相同的Pennes残差进行训练，显式有限差分法（FDM）解仅用作数值参考。在代表性的600秒运行中，PPIM在评估的神经求解器中实现了最低的平均绝对误差（MAE）、相对L1误差和相对L2误差。误差图进一步显示，PPIM的剩余误差更集中在热源区域附近，而不是在域的其他部分。这些结果表明，PPIM在该受控模拟中能有效逼近FDM参考最终温度场。源代码可在该https URL获取。

英文摘要

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.

发表机构

• Yonsei University（延世大学）

机构由 AI 辅助整理，请以论文原文为准。