Localizaton - protocol• Learning data base: all simulated maps obtained for single

preexcitation sites.

• Selection of optimal subsets with 8, 10, 12, …, 32 leads for the 64 and 128 lead MFM, and 117 lead BSPM (Fig. 6)

• Random generation of subsets with 8, 10, …, 32 leads

• Localization of single preexcitation sites with the single dipole model using optimally and randomly obtained subsets

• Comparing the localization results with those obtained by the complete 64 and 128 lead MFM, and 117 lead BSPM (Fig. 7)

SimulationWe use the human ventricular model [3] (Fig. 6) to simulate activation sequences. From these sequences we calculate BSPMs and MFMs (Fig. 7) with the oblique dipole model of cardiac sources in combination with the boundary element torso model [4].

AlgorithmStatistical estimation technique [1]:

(1)

• xe estimated electric or magnetic data at unmeasured sites • xm electric or magnetic data at measured sites • Kmm is a covariance matrix of the measured potential/field • Kum is a cross covariance matrix between the measured and unmeasured data.

An optimal subset of recording sites was found by sequential algorithm [1]: The recording site which had the highest correlated power with all other sites was found at each step. This estimator minimizes the root mean square error (RMS).

Evaluation criteria:

We used various criteria, like RMS error and maximum (MAX) error, relative difference (RD), correlation coefficient (CC) and amplitude-weighted correlation coefficient (WCC):

For different time intervals, like P-wave, QRS, S-ST, ST-T and PQRST, we calculated the mean values and standard deviations of the RMS, MAX, RD and CC values. In addition, we calculated amplitude weighted correlation coefficient WCC and isointegral maps on those time intervals.

AIMS•To find optimal subsets of recording sites from which the total body surface potential map (BSPM) and magnetic field map (MFM) data sets can be estimated to a specified degree of accuracy.

•To evaluate the influence of limited lead selection on source localization.

Influence of limited lead selection on source localization in magnetocardiography and electrocardiography

Vojko Jazbinšek, Rok Hren, and Zvonko Trontelj, Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Ljubljana, Slovenia

Fig. 2: Example of optimally selected recording sites when using measured data of three volunteers as a training set: a) 238 anterior/posterior MFM and b) 148-lead BSPM. Encircled numbers show the order of selected sites.

Measured data • BSPMs and MFMs obtained from 4 healthy volunteers [2].

• MFMs over a large area with diameter of 37 cm near the front and the back thorax with a dense 119 Bz channels (Fig. 1).

• 148 lead BSPMs were concurrently recorded.

• estimated noise: 200 fT and 10 µV for the MFMs and BSPMs.

We used various combinations of these data sets as learning (xm) and test (ym) sets. Results are shown in Figs. 2-5.

Fig. 1 Schematic layout of a) 119 anterior MFM and b) 148-lead

BSPM.

Discussion

Results – measured data

Acknowledgment We thank PTB, Institut Berlin for giving us opportunity to perform measurements with their multichannel system and dr. Olaf Kosch and Uwe Steinhoff for their assistance.

References[1] Lux RL, Smith CR, Wyatt RF, Abildskov JA. Limited lead selection for estimation of body surface potential maps in electrocardiography. IEEE Trans. Biomed. Eng. 1978, 25: 270-276. [2] Jazbinsek V, Kosch O, Meindl P, Steinhoff U, Trontelj Z, Trahms L. Multichannel vector MFM and BSPM of chest and back. In: Nenonen J, Ilmoniemi RJ, Katila T, Eds., 12th Int. Conf. on Biomagnetism, Espoo, Helsinki Univ. of Technology, 2001.[3] Hren R, Stroink G, Horáček BM. Spatial resolution of body surface potential maps and magnetic field maps: A simulation study applied to the identification of ventricular preexcitation sites. Med. Biol. Eng. Comp. 1998, 36:145-57.[4] Hren R, Stroink G, Horáček BM. Accuracy of single-dipole inverse solution when localising ventricular pre-excitation sites: simulation study. Med. Biol. Eng. Comp. 1998, 36:323-9.

[5] Horáček, B.M. Digital model for studies in magnetocardiography, IEEE Trans. Magn.

1973, MAG-9:440--444.[6] Burghoff M, Nenonen J, Trahms L, Katila T. Conversion of magnetocardiographic recordings between two different multichannel SQUID devices, IEEE Trans. Biomed. Eng. 2000, 47: 869-875.

a)

b)

Fig. 3: Mean RMS, MAX, RD, CC and WCC vs. number of selected sites for a) MFMs and b) BSPMs when using all four combinations of

learning (xm) and test (ym) data sets in cases where measurements on the three of the four volunteers are used as xm and measurements

on the remaining volunteer are used as ym. After each selected site, maps ye are estimated from ym (1). For each ye, values of RMS, MAX,

RD and CC are calculated. These results are then averaged over all maps for different time intervals, Pwave(◊), QRS(∆), S-ST( �), Twave(○)

and PQRST(×). The WCCs and the integral maps are also calculated for those intervals.

Mean RMS, MAX, RD and CC for the integral maps are displayed for c) MFMs and d) BSPMs.

Fig. 4: MFMs and BSPMs at some characteristic time points estimated after 20 selected sites from Fig. 2.

Fig. 8: Average difference (±SD) between localizaton results obtained by the complete lead systems versus optimally and randomly selected subset of leads.

Fig. 7: Schematic layout of a) 117-lead BSPM on Horacek [5] torso model,

b) 64 anterior MFM and c) 128 anterior and posterior MFM grid.

Fig. 6: Basal view of the human ventricular model shown with 10 preexcitation sites along the atrio-ventricular ring. Right ventricle is to the left, left ventricle is to the right, and pulmonary artery is to the bottom. This model was developed at Dalhousie University [3] and includes:

Results - localization

Results – optimal grid

The main finding of our study is that markedly smaller number of leads, in comparison to that currently employed in systems for MFM recordings, may be sufficient to extract pertinent information.

We obtain the average WCC of 0.98±0.01 for estimated MFMs from 20 sites in the whole PQRST interval. This is evidently better then results in [6] (0.94±0.02 and 0.93±0.03), where the conversion between two MFM measuring system was evaluated by two methods, multipole expansion and minimum norm estimates.

Localization results displayed in Fig. 8 show evident superiority of the optimal selection for all measuring modalities (117 lead BSPM, 64 and 128 lead MFM). After 20 optimally selected leads, we obtain dipole locations which are on average only within few millimeters

away from the locations calculated from complete lead systems. It seems that 20 optimally selected leads may be sufficient for localization of single preexcitation sites with the single-dipole model.

Our results corroborate the finding in [1] that the "optimal" lead selection is non-unique, i.e., that slightly shifted position of the first lead could generate quite different lead sets, which perform equally well. The database of our study consisted of healthy volunteers. The natural extension of this study could include patients, for instance those with old myocardial infarction. The methodology developed in this study could also be used in selecting the optimal lead configuration for specific type of cardiac abnormalities, e.g., the limited array of magnetocardiographic leads for monitoring ST-segment changes caused by acute coronary ischemia.

a) b)

c)

d)

Fig. 5: MFM and BSPM integral maps for some time intervals estimated after 12 selected sites from Fig. 2.

•anatomically accurate geometry, with resolution of 0.5 mm•realistic intramural fiber structure with rotating anisotropy•propagation algorithm based on physiological principle of excitatory current flow