用于动态状态和参数估计的可微心脏电生理模拟
Differentiable Cardiac Electrophysiology Simulations for Dynamical State and Parameter Estimation
AI总结：
研究心脏电生理模拟，提出可微模拟方法，通过定义损失函数并经基于梯度的优化最小化，结合有限差分法和平滑粒子流体动力学方法，能学习参数恢复动态，可应用于多种数据，有助于心律异常诊断及心脏个性化模型发展。
AI中文摘要：
心脏收缩由动作电位波触发，其在心肌中传播并在不同心律下呈现多样时空动态，在心脏电生理模拟中用偏微分方程建模。然而，将此类模型与测量数据拟合以开发数字孪生或患者特定计算机模型具有挑战性。本文引入可微心脏电生理模拟，通过将模拟动态与观测数据比较定义损失函数，经基于梯度的优化最小化。通过可微偏微分方程求解器反向传播损失梯度能学习参数并恢复完整动态，即使数据稀疏、有噪声或不完整。该模拟框架用有限差分法和平滑粒子流体动力学方法实现，可应用于多种数据。利用此方法，在3D双心室模拟几何结构中定位早期激活位点，并将现象学模型拟合到心脏单层细胞培养中电压螺旋波的成像数据。使用实验数据时，采用基于视频联合嵌入预测架构的感知损失以拟合噪声成像数据，并用生成扩散模型估计初始条件和约束解。可微心脏电生理模拟可改善患者心律异常诊断，促进心脏个性化模型或数字孪生的发展。
英文摘要：
The heart's contractions are triggered by action potential waves, which propagate through the cardiac muscle and exhibit diverse spatio-temporal dynamics during different heart rhythms. The dynamics are modeled with partial differential equations (PDEs) in cardiac electrophysiology simulations. However, fitting such models to measurement data to develop digital twins or patient-specific computer models is challenging. Here, we introduce differentiable cardiac electrophysiology simulations that can be fitted automatically to spatio-temporal measurement data of action potential waves in cardiac tissue. By comparing the simulated dynamics with the observation data, we define a loss function that is minimized via gradient-based optimization. Backpropagating the loss gradient through the differentiable PDE solver enables us to learn the parameters and recover the full dynamics, even with sparse, noisy, or partial observations. Implemented using both the finite-difference and smoothed particle hydrodynamics methods, our simulation framework can be applied to pixel-, voxel-, or point-based data, such as 2D or 3D slabs, or arbitrary shapes, such as the heart's ventricles. Using this methodology, we locate early activation sites inside a 3D bi-ventricular simulation geometry and fit a phenomenological model to imaging data of a voltage spiral wave in a cardiac monolayer cell culture. With experimental data, we employed a perceptual loss based on the Video Joint-Embedding Predictive Architecture, which enables fitting to noisy imaging data, and a generative diffusion model to estimate initial conditions and constrain solutions. Differentiable cardiac electrophysiology simulations could improve the diagnosis of rhythm abnormalities in patients and facilitate the development of personalized models or digital twins of the heart.
