Cross-Approach Evaluations of ECG Lead Selection and BSM Lead Reconstruction: Thorax Model Approach and Actual ECG Data Approach

Noriyuki Takano^ab, Juha Nousiainen^a, Jari Hyttinen^a

^aRagnar Granit Institute, Tampere University of Technology, Tampere, Finland
^bInstitute of Signal Processing, Tampere University of Technology, Tampere, Finland

Correspondence: Noriyuki Takano, Ragnar Granit Institute, Tampere University of Technology, P.O. Box 692, FIN-33101 Tampere, Finland. E-mail: noriyuki.takano@tut.fi, phone +358 3115 2524, fax +358 3 3115 2162

1.  Introduction

ECG lead selection studies are often aimed at specifying leads or electrode sites sufficient to obtain information contents equivalent in a sense of clinical importance or information theory to those available from a comprehensive body surface potential mapping (BSM) system which uses numerous electrodes. These studies may be classified into two approaches, one using actual ECG data and the other using volume conductor thorax models. The present study has taken such a cross-approach style that lead selections and coefficients to estimate (reconstruct) the entire BSM are computed from models and actual datasets and they are tested for applications to both. The results will suggest how well actual entire BSM or simulated ones will be estimated in the cross-approach applications.

2.  Method

The sequential lead selection method introduced by Lux and colleagues [Lux et. al. 1978] selects N = 1, , M leads, calculating the reconstruction coefficient matrix H for each N with respect to the least squared error reconstruction of A such that , where A consists of M rows for ECG voltage data of M leads, say full-set leads,  of N rows in A associated with the selected leads, and the reconstruction error is .

In the model approach, the sequential lead selection method can be applied to a transfer matrix C which is set in a model to transform a vector u of ECG sources (e.g. distributed current dipoles) to v of ECG voltages at M leads such as v=Cu.  transforms u into  of selected leads, and the transfer matrix of the full-set leads is reconstructed as  with the error . H also transforms  into of the full-set leads because .

In the experiments, lead selections and H were calculated from A or C in a process called training, and then in tests they were applied to other matrices. The reconstruction error ratio was defined as  or , where  expresses the Frobenius norm.

3.  Material

Two inhomogeneous volume conductor thorax models derived from magnetic resonance imaging (MRI) data of one individual were used. They were rectangular grid models for the finite difference method (FDM) of electric field computing, being made identical to each other except for the heart regions, one containing a heart model of end-systolic cardiac phase formed by 12032 nodes and the other of end-diastolic phase by 13120 nodes (node distances 3mm).

Actual ECG data samples, referred to as the full dataset, of 236 normal, 300 myocardial infarction, and 305 left ventricular hypertrophy subjects were used for the training whose results were used for the transfer matrix reconstruction tests. For the dataset reconstruction test, the full dataset was divided into a training dataset of 177 subjects (59 from each diagnostic category) and a test dataset (177 from each). Data sample of each subject comprised ensemble averages of ECG voltages at 52 time points set in a time-normalized P-to-T complex waveform [Kornreich et. al. 1989].

A 120-lead BSM lead system [Montague et. al. 1981] was taken as the full-set leads. The 120 leads are all unipolar leads including 3 limb leads and 117 torso surface leads.

4.  Results

During the training minimum number of leads N to obtain error ratio target were determined as seen in the first (left) section of Table 1, and these lead selections and the incorporated coefficient matrices H caused  as test results which are displayed in the second section. n in the third section is the minimum number of leads to satisfy the target in a test using lead selections and H calculated by the training indicated on the row.

Table 1.   ECG lead selectinon training and reconstruction test results.

On the rows of datasets, * indicates that the training used the training dataset, otherwise the full dataset. The dataset reconstructed in the tests was always the test dataset.

When training results from one model were applied to the other model, the test results,  and n, were almost the same as observed in the training, or maximally about two folds. However, when they were applied to the test dataset, the increases were modest only in case of target = 0.1, otherwise  became more than about four times as large as in the training and n more than twice.

When data-based training results for target = 0.1 and 0.01 were applied to the models,  were about four to five times as large as in the training, and n twice or four times. The increases were mild when the target was 0.001 because N determined by the training was large.

5.  Conclusions

The reconstruction test results of model-based lead selections and reconstruction coefficients were not considerably affected by the cardiac phases represented by the models. However, in the actual ECG dataset reconstruction tests, these model-based selections and coefficients worked as they were aimed at only when the desired reconstruction accuracy was relatively low. Thus a thorax model of single individual is expected to provide the basic properties of ECG leads, but for highly accurate analysis the modeling approach may have to be modified, e.g. using multiple individual models and assuming physiologically reasonable ECG source activities.

 Similarly even a large ECG dataset did not explain the lead sensitivities (transfer matrix C) obtained from a model. The large ECG dataset represents an “average” volume conductor plus the correlation of the source terms. The results reported here indicated that if data-based selections and reconstruction coefficients are used in model simulations, the lead selection should be one determined for an especially low reconstruction error ratio; that means, ECG leads and electrode sites in the model should not significantly be reduced.

Acknowledgements

The MRI data were provided by Professor Robert Patterson, University of Minnesota. The ECG measurement data were provided by Professor Fred Kornreich, Vrije Universiteit Brussel.

References

Kornreich F, Montague TJ, Rautaharju PM, Kavadis M, Horacek MB, Taccardi B, Multigroup diagnosis of body surface potential maps, Journal of Electrocardiology, 22 Supplement: 169-178, 1989.

Lux RA, Smith CR, Wyatt F, G, Abildskov. Limited lead selection for estimation of boby surface maps in electrocardiology, IEEE Transactions of Biomedical Engineering, 25: 270-275, May 1978.

Montague TJ, Smith ER, Cameron DA, Rautaharju PM, Klassen GA, Flemington CS, Horaceck BM. Isointegral analysis of body surface maps: Surface distribution and temporal variability in normal subjects, Circulation, 63: 1166-1172, May 1981.