基于最大似然算法的心电逆问题研究

心电逆问题是通过测得的体表电势分布求取心外膜电势分布的过程,具有重要的临床意义和生理意义.本文采用有限元方法对心脏和体腔进行二维建模并求解心电正问题,然后构建状态空间方程,建模得到的体表电势与心外膜电势之间的关系为系统的测量方程,相邻时刻状态之间的关系为系统的状态方程.对于参数的不确定性问题,建立似然函数,引入期望最大化(Expectation Maximization,EM)算法来求解,步骤E(Expectation)采用卡尔曼滤波对参数进行估计,步骤M(Maximization)利用似然函数重新估计约束,步骤E,步骤M循环迭代.最后对整个过程进行仿真,结果显示采用期望最大化(EM)算法时,解的收敛性要好于传统的卡尔曼滤波的解,相对误差也可以得到大幅度的降低.

EM Algorithm for the Inverse Problem of Electrocardiography

The endeavors to solve the inverse problem of electrocardiography embody the approach to calculate the epicardial potentials using the measured body-surface-potential distribution; it is important for pathology and very useful for clinical application. In this paper, we construct the 2D human torso model using the FEM method and solve the forward problem. In the constructed state-space equations, and the relationship between the body surface potentials and epicardial potentials in the FEM torso model is the measurement equation, and the relationship of the adjacent states is the state process equation. To solve the problem of uncertainty of the parameters, we design the likelihood function and introduce the Expectation Maximization (EM) algorithm. Step E (Expectation) estimates the parameters using the Kalman filter; step M (Maximization) re-estimates the parameters using the likelihood functions, step E and step M iterate. Simulations of the whole process show that EM algorithm leads to better convergence of the solutions than does the traditional Kalman filtering, and the relative errors are much smaller than before.