Forward and inverse problem for cardiac magnetic field and electric potential using two boundary element methods

This paper discusses the forward and inverse problem for cardiac magnetic fields and electric potentials.A torso-heart model established by boundary element method(BEM) is used for studying the distributions of cardiac magnetic fields and electric potentials.Because node-to-node and triangle-to-triangle BEM can lead to discrepant field distributions,their properties and influences are compared.Then based on constructed torso-heart model and supposed current source functional model-current dipole array,the magnetic and electric imaging by optimal constrained linear inverse method are applied at the same time.Through figure and reconstructing parameter comparison,though the magnetic current dipole array imaging possesses better reconstructing effect,however node-to-node BEM and triangleto-triangle BEM make little difference to magnetic and electric imaging.     

基于心磁信号的心脏电流偶极子阵列成像及相关性质的研究

超导量子干涉器（SQUID）能探测到微弱的心脏磁场信号. 通过对所得的心磁信号进行分析，可为许多心脏疾病的诊断提供依据. 利用心磁信号，采用极小范数最小二乘法（MNLS）对心脏的电流偶极子阵列进行重建，从而实现了对心脏内部等效电流源的成像. 在使用MNLS进行电流偶极子阵列反演重建的过程中，反演所需的心磁信号，分别由单电流偶极子和电流多极子作为激发源模拟得到，以及由SQUID实际测量得到. 同时，对不同心磁信号反演得到的电流偶极子的分布规律进行了分析. 此外，还给模拟的人体外心磁信号施加了均匀噪声和随机噪声，研究不同信噪比的均匀噪声和随机噪声对电流偶极子阵列重建的影响.     

Cardiac magnetic source imaging based on current multipole model

It is widely accepted that the heart current source can be reduced into a current multipole. By adopting three linear inverse methods, the cardiac magnetic imaging is achieved in this article based on the current multipole model expanded to the first order terms. This magnetic imaging is realized in a reconstruction plane in the centre of human heart, where the current dipole array is employed to represent realistic cardiac current distribution. The current multipole as testing source generates magnetic fields in the measuring plane, serving as inputs of cardiac magnetic inverse problem. In the heart-torso model constructed by boundary element method, the current multipole magnetic field distribution is compared with that in the homogeneous infinite space, and also with the single current dipole magnetic field distribution. Then the minimum-norm least-squares (MNLS) method, the optimal weighted pseudoinverse method (OWPIM), and the optimal constrained linear inverse method (OCLIM) are selected as the algorithms for inverse computation based on current multipole model innovatively, and the imaging effects of these three inverse methods are compared. Besides, two reconstructing parameters, residual and mean residual, are also discussed, and their trends under MNLS, OWPIM and OCLIM each as a function of SNR are obtained and compared.     

A new magneto-cardiogram study using a vector model with a virtual heart and the boundary element method

A cardiac vector model is presented and verified, and then the forward problem for cardiac magnetic fields and electric potential are discussed based on this model and the realistic human torso volume conductor model, including lungs. A torso-cardiac vector model is used for a 12-lead electrocardiographic (ECG) and magneto-cardiogram (MCG) simulation study by using the boundary element method (BEM). Also, we obtain the MCG wave picture using a compound four-channel HTc ·SQUID system in a magnetically shielded room. By comparing the simulated results and experimental results, we verify the cardiac vector model and then do a preliminary study of the forward problem of MCG and ECG. Therefore, the results show that the vector model is reasonable in cardiac electrophysiology.     

The forward and inverse problem of cardiac magnetic fields based on concentric ellipsoid torso-heart model

<正>This paper constructs a concentric ellipsoid torso-heart model by boundary element method and investigates the impacts of model structures on the cardiac magnetic fields generated by both equivalent primary source—a current dipole and volume currents.Then by using the simulated magnetic fields based on the torso-heart model as input,the cardiac current sources—an array of current dipoles by optimal constrained linear inverse method are constructed.Next, the current dipole array reconstruction considering boundaries are compared with that in an unbounded homogeneous medium.Furthermore,the influence of random noise on reconstruction is also considered and the reconstructing effect is judged by several reconstructing parameters.     

基于心磁信号的心脏电流偶极子阵列成像及相关性质的研究

超导量子干涉器（SQUID）能探测到微弱的心脏磁场信号. 通过对所得的心磁信号进行分析，可为许多心脏疾病的诊断提供依据. 利用心磁信号，采用极小范数最小二乘法（MNLS）对心脏的电流偶极子阵列进行重建，从而实现了对心脏内部等效电流源的成像. 在使用MNLS进行电流偶极子阵列反演重建的过程中，反演所需的心磁信号，分别由单电流偶极子和电流多极子作为激发源模拟得到，以及由SQUID实际测量得到. 同时，对不同心磁信号反演得到的电流偶极子的分布规律进行了分析. 此外，还给模拟的人体外心磁信号施加了均匀噪声和随机噪声，研究不同信噪比的均匀噪声和随机噪声对电流偶极子阵列重建的影响. 关键词： 心磁信号 超导量子干涉器 电流偶极子阵列重建 极小范数最小二乘法     

Inverse computation for cardiac sources using single current dipole and current multipole models

Two cardiac functional models are constructed in this paper.One is a single current model and the other is a current multipole model.Parameters denoting the properties of these two models are calculated by a least-square fit to the measurements using a simulated annealing algorithm.The measured signals are detected at 36 observation nodes by a superconducting quantum interference device (SQUID).By studying the trends of position,orientation and magnitude of the single current dipole model and the current multipole model in the QRS complex during one time span and comparing the reconstructed magnetocardiography (MCG) of these two cardiac models,we find that the current multipole model is a more appropriate model to represent cardiac electrophysiological activity.