The study proposes a method to facilitate the remote follow-up of patients suffering from cardiac pathologies and treated with an implantable device, by synthesizing a 12-lead surface ECG from the intracardiac electrograms (EGM) recorded by the device. Two methods (direct and indirect), based on dynamic Time Delay artificial Neural Networks (TDNN) are proposed and compared with classical linear approaches. The direct method aims to estimate 12 different transfer functions between the EGM and each surface ECG signal. The indirect method is based on a preliminary orthogonalization phase of the available EGM and ECG signals, and the application of the TDNN between these orthogonalized signals, using only three transfer functions. These methods are evaluated on a dataset issued from 15 patients. Correlation coefficients calculated between the synthesized and the real ECG show that the proposed TDNN methods represent an efficient way to synthesize 12-lead ECG, from two or four EGM and perform better than the linear ones. We also evaluate the results as a function of the EGM configuration. Results are also supported by the comparison of extracted features and a qualitative analysis performed by a cardiologist.

The number of patients treated with Implantable Cardiac Devices (ICD) has strongly increased over the past 10 years. According to the American Heart Association [1], an estimated 111 000 defibrillator and 358 000 pacemaker implant procedures were performed for patients in the United States in 2007. These patients require regular in-hospital visits to follow-up the patient’s response to the therapy, to monitor whether the ICD is working optimally and, eventually, to modify the pacing parameters. More recently, wireless remote monitoring of ICD has become a priority for all major ICD constructors, in order to perform this follow-up more frequently, avoiding hospital visits and reducing costs. In both cases, the surface electrocardiogram (ECG) is necessary, since it is the main signal used by the cardiologist for the analysis of the cardiac electrical activity. However, the cardiac electrical activity acquired from the ICD, called electrograms (EGM), are collected by electrodes placed on the endocardium and/or the epicardium and show different morphologies than those of the surface ECG. The synthesis, or reconstruction, of the surface ECG from a set of EGM is thus of first importance in this context.

This challenging problem has been dealt by a number of studies [2–9]. From a methodological point of view, they can be categorized according to the method used to estimate the Transfer Function (TF) between EGM and ECG: i) linear filtering methods based upon Recursive Least Squares (RLS) estimation or by processing the data in blocks [2–4,9], ii) single, fixed-dipole modeling algorithms [8,9], and iii) non linear filtering methods [2,5,6].

Concerning the linear approach, several works have been proposed in the literature. In [2], each surface QRS complex was synthesized using a direct single-input single-output scheme. We showed in this work that the direct ECG synthesis depends strongly on the chosen EGM and that a multivariate approach would be of benefit. In this sense, we proposed in [3,4] an indirect method to estimate the linear TF between three-dimensional (3D) representations of cardiac activity [10], namely the signal EGM_{3 D} , obtained from the orthogonalization of EGM signals and the signal ECG_{3 D} derived through the orthogonalization of ECG signals.

In the same line of the above-mentioned methods, Mendenhall et al presented recently the use of a multivariate linear TF [8,9]. Although the performance of these linear methods is satisfactory, especially for patients with surface ECG containing only one beat morphology, some improvements are still needed. In fact, in a real application, noise, artifacts and the natural evolution of the pathology may influence the relationship, over time, between the EGM and the ECG. Thus stochastic and non linear phenomena crop up, and time series dynamics cannot be robustly described using classical linear filtering.

Two fixed-dipole modeling algorithms were proposed in [8,9]. They require both a QRS detection stage (as in [2]), and the simultaneous measurement of the surface cardiac electrical activity, using the standard 12-lead ECG and the modified-Frank VCG systems. In addition, it is shown in [9] that the synthesis of the surface ECG from EGM by using these two algorithms gave poor results.

Different multivariate non linear approaches have been proposed by our group [5,6]. These methods require simultaneously recorded intracardiac and surface ECG signals of each patient to train a Time Delay artificial Neural Network (TDNN) [11] and are patient specific. This strategy has shown, during our preliminary evaluations, to provide an improved performance compared to RLS, particularly when the patient presents multiple QRS morphologies [5].

This paper can be viewed as a natural extension of our previous works in this field, with significant improvements concerning: i) the optimization of the TDNN structure and parameters, ii) the analysis of the sensitivity of the reconstruction performance to the chosen EGM configuration, and iii) the quantitative and qualitative performance evaluation of the methods through a more comprehensive methodology.

Section II presents in details the two proposed non-linear reconstruction schemes (direct and indirect methods). The database used for the experimentation is described in section III. Section IV is devoted to the results, in terms of optimization of the parameters, selection of the EGM leads and comparison of the synthesis methods. We also discuss the case of real industrial implementation. Finally, section V summarizes the main concerns and conclusions of this study.

As described in the introduction, the ECG synthesis may be performed by a direct or an indirect strategy described in this section. This paragraph also presents the proposed non linear estimation method of the transfer function and the linear approach that will be used for performance comparison.

A. Direct method

Let s(k) = [s(1, k), …, s(M, k)]^T and x(k) = [x(1, k), …, x(N, k)]^T, for k = 1, …, L, denote, respectively, an EGM and an ECG dataset, where M is the number of EGM leads available from the implant, N corresponds to the number of ECG leads and L is the size of the observation vectors. Surface ECG signal synthesis can thus be modeled as follows:

(1)

In other words, the ECG is supposed to be the output of an unspecified non linear function driven by the EGM, corrupted by an additive noise b(k)=[b(1, k), …, b(N, k)]^T.

The estimation of can be performed by a classical two-step procedure, including a training step and a synthesis step as depicted in Figure 1.

1. Training step The objective of this step is to identify the transfer function , specific to each patient, by using a couple of learning datasets s₁(k) (M EGM leads) and x₁(k) (N ECG leads), of length L ₁. N different Multi-In Single-Out (MISO) systems (or transfer functions), , , …, , between the M-rows input vector s ₁(k) and each row of the output vector x ₁(k), namely x ₁(i, k), are identified. Typically, the training step can be performed during the implantation, or whenever s ₁(k) and x ₁(k) can be simultaneously acquired.

2. Synthesis step It is devoted to the follow-up of the patient during a remote monitoring session, or during the regular in-hospital visits. In the latter case, a new EGM dataset s₂(k), of length L ₂, is continuously measured and acquired by the device and used to synthesize a surface ECG x̂ ₂(i, k), by using the estimates , for i = 1, …, N, such that:

(2)

B. Indirect method

The principle of the indirect method is depicted in Figure 2. The main difference relies on the computation of 3D representations of the surface (ECG_{3 D} ) and intracardiac (EGM_{3 D} ) electrical activities of the heart, from the available ECG and EGM signals, through linear transformations W _ECG and W _EGM , respectively. Transfer function will thus be estimated between EGM_{3 D} and ECG_{3 D} , which will be respectively denoted v _{s 1} (k) and v _{x 1} (k). This indirect method implies the application of a specific pre-processing approach for the training and synthesis steps.

1. Three-Dimensional representation of the cardiac electrical activity Contrary to the standard 12-lead ECG, the analysis based on beat loops has been found to i) better compensate the changes in the electrical axis caused by various extracardiac factors [10], such as respiration, body position, electrode positioning, and so forth, ii) give a compact representation of the cardiac electrical activity, minimizing storage needs, and iii) provide a solution to the time synchronization problem which arises in cardiac data.

In [5], we evaluated four different approaches to perform the calculation of the EGM_{3 D} and the ECG_{3 D} : Principal Component Analysis (PCA) [12], Robust Principal Component Analysis (RobPCA) [13], Independent Component Analysis based on Second Order statistics (ICASO) [14] and Independent Component Analysis based on Fourth Order statistics (ICAFO) [15]. We showed that the results can be considered equivalent and that a classical PCA is a satisfactory solution. PCA has thus been retained in this work.

2. Training step v _{s 1} (k) and v _{x 1} (k) can be computed directly from the first datasets of ECG and EGM, s₁(k) and x₁(k), by using the following equations:

(3)

(4)

where W _EGM and W _ECG are (3×M) and (3×N) matrices, v _{s 1} (k) and v _{x 1} (k) are (3×L ₁), in the general case.

Then, the problem can now be modeled as follows:

(5)

where the output v _{x 1} (k) is considered as an unspecified non linear function of the inputs v _{s 1} (k) plus an additive white noise b(k).

Contrary to the direct case, only three different MISO systems, and , between the 3-rows input vector v _{s 1} (k) and each row of the output vector v _{x 1} (k), namely v _{x 1} (i, k), have to be estimated during the training step.

3. Synthesis step It is composed of three phases:

• W _EGM is applied to EGM s₂(k), which provides the (3 × L ₂) EGM_{3 D} matrix v _{s 2} (k).
• The (3 × L ₂) ECG_{3 D} matrix v _{x 2} (k) is computed by using and , learnt during the training step.
• The N-lead ECG x̂₂(k) is obtained by multiplying the pseudo-inverse of the linear transform W _ECG with the estimated ECG_{3 D} v _{x 2} (k).

4. Particular case In the general case where M ≥ 3, PCA is applied to reduce and to orthogonalize the EGM data and we take into account the three largest eigenvalues of the covariance matrix. In the particular case where M = 2, the PCA is not used to reduce the number of components, but just to orthogonalize the EGM data and the two eigenvalues of the covariance matrix are taken into account, so that W _EGM is (2×M) and v _{s 1} (k) and v _{s 2} (k) are (2 × L ₁) and (2 × L ₂) respectively.

D. Linear approach

The performance provided by the two TDNN-based approaches will be compared with a classical linear approach. Indeed, the transfer function between an input y(k) and an output z(k) is commonly supposed to be a linear Wiener filter h, such that:

(6)

where * is the convolution operation and h(k) = [h(0), …, h(L_h ))] is the impulse response of a linear time invariant filter of length L_h . Least square estimation of h leads to the classical relation:

(7)

where R_zz is the autocorrelation matrix of the output, R_zy is the intercorrelation matrix between the output and the input and ĥ is the estimate of h. Several implementations, block or recursive, can be applied to find the optimal estimator of h. In the recursive way, Least Mean Square (LMS), Normalized Least Mean Square (NLMS) or Recursive Least Square (RLS) algorithms have been proposed. Best results were obtained with the RLS approach, moreover known to exhibit fast convergence and the exact implementation of the block form.

In the direct case, the filter represents the transfer function between EGM and ECG signals (as in [9]). During the training step, N MISO filters have to be computed, between the input EGM vector s ₁(k) (y(k) = s ₁(k)) and each row of the output ECG vector x ₁(k) (z(k) = x ₁(i, k) for i = 1, …, N). In the indirect case, the filter represents the transfer function between EGM_{3 D} and ECG_{3 D} signals [4]. During the training step, three MISO filters have to be computed, between the input EGM_{3 D} vector v _{s 1} (k) (y(k) = v _{s 1} (k)) and each row of the output ECG_{3 D} vector v _{x 1} (k) (z(k) = v _{x 1} (i, k) for i = 1, …, 3).

A dataset issued from 15 patients (P1 to P15) is used to evaluate the performance of the above-mentioned ECG reconstruction methods. The ECG and EGM were simultaneously recorded with a GE Cardiolab station during the implant of an ICD with an initial sampling rate equal to 1000 Hz and then subsampled at 128 Hz and low-pass filtered at 45 Hz. Each record of the database is composed of:

• 12 standard surface ECG channels, namely leads I, II, III, aVR, aVL, aVF, V1 to V6;
• Four EGM channels: Bip _A acquired using a bipolar measure between the tip and proximal electrodes of the atrial lead; Bip _V , a bipolar measurement between the tip and proximal electrodes of the ventricular pacing lead; Prox _A between the proximal electrode of the atrial lead and the pacemaker can and Prox _V between the proximal electrode of the ventricular lead and the pacemaker can.

Three EGM configurations will be considered:

• ’Bip’: using the two bipolar channels Bip _A and Bip _V (M = 2);
• ’Prox’: using the two proximal Prox _A and Prox _V (M = 2);
• ’Bip+Prox’: using the four EGM (M = 4).

Each patient file has been segmented into two blocks: the first one, of length L ₁, containing n_t heartbeats of concurrent ECG and EGM signals, is used during the training step, and a different second block, of length L ₂, with n_s beats, is devoted to the synthesis step and performance evaluation. The 15 patient records have been classified into three categories, according to their beat morphologies (Fig. 3):

• Type I: the surface ECG contains only one beat morphology (P1 to P10);
• Type II: the surface ECG contains one prevailing beat morphology, with presence of ventricular ectopic beats (P11 to P13). Ectopic beats are only included in the testing set;
• Type III: at least three different beat morphologies compose the ECG (P14 and P15). Each of them are present both in the training and testing sets.

The behavior of the non linear estimation methods depends on the values of the TDNN parameters, that are optimized on the training dataset in the first part of this section. In a second part, we present the results obtained on the synthesis dataset as a function of the EGM leads and the type of patients. We evaluate the two TDNN-based methods (direct and indirect) and compare the results with an RLS filter (direct and indirect). This leads to four different methods, denoted by:

• D_TDNN: Direct method and estimation of the transfer function by TDNN
• I_TDNN: Indirect method and estimation of the transfer function by TDNN
• D_RLS: Direct method and estimation of the transfer function by a RLS filter
• I_RLS: Indirect method and estimation of the transfer function by a RLS filter.

The last part of this section presents the practical importance of the proposed methodology, in the real configuration of an implantable device. We study the effect of the reconstruction process on parameters extracted from the ECG and in a diagnosis purpose, since the ECG is also used in practice for the control of the device and for arrhythmia detection.

This paper proposes a methodology to synthesize a standard 12-lead ECG from a set of EGM leads, for implanted patients, which is of main practical importance in cardiology. For this purpose, two methods, a direct and an indirect, based on a dynamic TDNN, are proposed and evaluated in this study. Experiments show that four main issues are of concern when performing ECG reconstruction. Firstly, a quantitative comparison, conducted on a database issued from 15 patients, shows that performances of both TDNN-based methods are equivalent and outperform the RLS approach. However, the direct method requires the learning of 12 transfer functions, whereas the indirect method only requires three transfer functions. It is worth to notice that, in practice, it is also possible to compute only eight transfer functions and derive the other four by calculations, since only two of the six extremity leads are independent. Whatever the approach direct or indirect, the transfer functions are patient specific and must be trained either during the implantation or the day just after by collecting as set of synchronous ECG and EGM, eventually by using the telemetric system of the device.

Secondly, interesting results were observed for patients with sinus rhythm or with polymorphic beats if all the beat morphologies are present in the training set (Types I and III). When ectopic complexes are not included in the training set (Type II), both methods show limitations on the reproduction of PVC. However, the synthesized morphologies still remain very different from sinus beats, preserving at least the possibility of identifying a pathological beat.

Thirdly, results have also been presented as a function of the number and the type of EGM leads. As expected, the best reconstructions are obtained using two bipolar and two proximal leads, but we also demonstrated that the two proximal electrodes provide almost the same results.

Finally, we have shown that the industrial configuration, using only two bipolar EGM, leads to quantitative and qualitative efficient performances. These interesting results suggest that the proposed TDNN-based reconstruction module could be embedded into an ICD.

It should be noted that the long term validity of this reconstruction relies on the hypothesis that the ECG morphology is stable over time. This hypothesis can be assumed to hold in healthy subjects and we recently verified this stability in different recording conditions [20,21]. However, this may not be the case in implanted patients, who may present ECG modifications as a consequence of cardiac remodeling, clinical evolution or transient phenomena (new medication, …). These factors represent the main limitations of any ECG reconstruction method from EGM data. One way to minimize the effects of these factors would be to re-estimate the transfer function during the required follow-up visits at the hospital.

This work also opens the way to new telecardiology challenges, such as the optimal management of cardiac rhythm pathologies, the follow-up of implanted patients [22,23], and the continuous control of implantable devices [24]. Indeed, recent studies have demonstrated the interest of a daily data transmission from the implantable device, through a wireless remote monitoring system, to improve the care of cardiac device recipients. It was also claimed in [25] that ambulatory monitoring of the electrocardiogram is an important complement to pacemaker follow-up, particularly about changes in the ST segment of the ECG.