Application to biomedical signals - Practical Biomedical Signal Analysis Using MATLAB - page 198

group mean maps was based on the three measures of similarity: Kullback-Leibler
(KL) entropy (Sect. 3.4.2), normalized residual magnetic field strength, and devi-
ations in the magnetic field map orientation. The mean values of these parameters
during the depolarization and repolarization were used for the classification with the
help of logistic regression. The features set based on KL entropy demonstrated the
best classification results, namely sensitivity/specificity of 85/80% was reported.
The possibility of identification of inter-atrial conduction pathways by MCG
was reported by [Jurkko et al., 2009]. The experiment involved the patients un-
dergoing catheter ablation of paroxysmal atrial fibrillation. The intra-cardiac elec-
troanatomic mapping was compared with pseudocurrent maps obtained by means of
MCG recorded by 33 triple sensors, namely two planar gradiometers (x-y plane) and
a magnetometer oriented along the z-axis (axis orientation as in Figure 4.27) . Figure
4.45 shows averaged magnetic field density at each z-magnetometer, spatial distribu-
tion of B z component, and pseudocurrent map. The pseudocurrent inversion is used
to characterize the orientation of the magnetic field. The method is based on rotating
the estimated planar gradients of B z component by 90 o :

∂ B z
∂ y

∂ B z
∂ x

b = e x − e y (4.42)

where e x , e y are the perpendicular unit vectors on the sensor array plane. The re-
sulting arrow map provides a zero order approximation (pseudocurrent map) for the
underlying electric current. The conclusions from the above studies were that by in-
specting the pseudocurrent maps the current propagation may be determined and the
damages in conducting pathways may be found. Overall findings imply that the non-
invasive technique of pseudocurrent mapping may assist in the localization of the
breakthroughs in conduction pathways and refining methods for the ablation treat-
ment, if needed.
Biomagnetic methods are well suited to solve the problem of the localization of
bioelectric sources in the body. Although magnetic fields are much less influenced by
the body tissues than electric fields, MCG is to some extent modified by anisotropic
properties of cardiac and torso tissues. The best localization results were obtained
when activity starts in a small well defined area. For solution of inverse problems
in magnetocardiography both the equivalent current dipole approach and effective
magnetic dipole models have been used. It was reported that they may provide local-
ization with accuracy of a few millimeters when realistic and patient tailored torso
models are used [Pesola et al., 1999]. However, the approach is limited to localiz-
ing point-like focal sources such as those appearing, e.g., in focal arrhythmias or
ventricular extrasystole [Fenici and Brisinda, 2006].
In general, multiple current sources are simultaneously activated during the car-
diac cycle; thus the inverse solution based on current density distribution found
several applications in magnetocardiography. For example in [Neonen et al., 2001]
for equivalent current-density estimation in subjects with coronary artery disease, a
patient-specific boundary-element torso model was used. Three different methods of
regularization were confronted with the PET measurements. The results showed that