Electrocardiogram (ECG) is a non-invasive and painless method for quickly examining the electrical activity of the heart (Einthoven, 1912). The basic concept is for electrodes to be strategically placed on parts of a patient’s body to record the electrical activity of the heart. These electrodes are passive components; that is, they do not produce any form of electrical signal (Lewis, 1912), they only record the signals sensed. Over the years, there has been research into various electrode positions to acquire the best information in the simplest form (Frank, 1956; Mason and Likar, 1966; Dower et al., 1988). Some of the common systems developed include the Mason-Likar lead system (Mason and Likar, 1966), the Frank Vectorcardiogram (VCG) lead system (Frank, 1954), and the EASI lead system (Dower et al., 1988). Amidst these systems, a standard 12-lead system (S12) has been agreed upon (Wilson et al., 1954) (Figure 1). This standard has shaped the nature of electrocardiography ever since and is the commonly used method for diagnosis (AlGhatrif and Lindsay, 2012).

The S12 leads (limb leads - I, II, III, aVR, aVL, aVF and precordial/chest leads – V1, V2, V3, V4, V5, V6) are generated by a mathematical combination of 10 electrodes. Since these electrodes are passive, they record noise artefacts in addition to heart signals. These artefacts can come from the movement of patients during recording, wrong placement of electrodes, electrical interference, or even no-contact between the electrode and the patient’s skin. This has led researchers to consider alternative methods to acquire S12 with fewer electrodes. This can help to recover missing or noisy leads, or even reduce the number of electrodes needed for recording. Moreso, this can help with patients who need to be monitored outside the hospital.

In line with this, devices such as the Holter monitor (Holter, 1961), patch devices, and smart watches have been designed to acquire heart data with minimal contact with the human body. However, they do not provide as much information as S12. This has led researchers to focus on predicting S12 leads with fewer leads. For example, two leads can be used to predict the remaining ten leads (Vemishetty et al., 2019). Over time, many algorithms ranging from linear to non-linear algorithms have been developed for this purpose. These have included the use of linear regression, principal component analysis, independent component analysis, and even neural networks, to create patient-specific or generic models. The patient-specific models aimed at creating algorithms specific to a patient (Schreck et al., 1998), while the generic models aimed at building algorithms that could be used for any patient irrespective of age, race, gender or ailment. None of these algorithms have a perfect reconstruction capability and all have their strengths and drawbacks. It is noteworthy that the inability to perfectly reconstruct ECG is partly due to the complexity, diversity and everchanging nature of the heart (especially with the generic models).

The differences in algorithm capabilities have inspired this work. This paper aims to narratively review the literature on 12-lead ECG reconstruction, highlight various algorithmic approaches and evaluate their predictive strengths. In addition, it investigates the implications of performing reconstruction in particular ways.

The publications chosen for this review were selected from various databases including Institute of Electrical and Electronics Engineers (IEEE), Medline, Scopus, Web of Science, and The Cochrane Library. The time frame chosen for this review was from the year 1980–2023 (spanning 43 years), to capture the traditional methods that were used for ECG reconstruction and the transition into the more recent algorithms that have been adopted. The inclusion criteria for the selected publications were all publications in English language, using either simple mathematical or machine learning methods, and were journal articles or conference papers. The keywords used for the search queries were:

(ECG OR Electrocardiogra* OR EKG) AND (Reconstruct* OR recover* OR regenerat* OR extrapolat* OR retriev* OR reduc* OR predict* OR calculat* OR estimat* OR approximat* OR comput*) AND (12 lead OR twelve lead OR electrode OR reduced electrode).

To reconstruct S12, it is paramount to know the leads that provide the best extrapolatory significance. Using factor analysis, Schreck et al. (1998) aimed to find the smallest set of leads necessary to describe S12. They derived 12 eigenvalues that had a magnitude that correlated to the significance of its eigenvector. Since leads III, aVR, aVL, and aVF could be calculated from leads I and II, they were not used in this analysis. A patient-specific transformation matrix was obtained for this analysis, and the predictive power was tested with varying numbers of leads. They found that using three leads to reconstruct the other leads accounted for most of the information content in S12 (99.12% ± 0.92%). Using more than three leads added very little information to the reconstruction.

Nelwan et al. (2000), in line with Scherer et al. (1989), recommended the use of I, II and V2 (4 electrodes) for reconstruction. A substantial decrease in the correlation between the reconstructed S12 (RS12) and the original S12 was observed when three leads and four leads were used as predictors. The decrease was from an average of 0.994 to 0.983 in the patient-specific models and from 0.963 to 0.926 in the generic models. Nelwan et al. (2004a) proposed that a dependable patient-specific model can be built with I, II and V2, but when a generic model is designed, V5 should be included (5 electrodes). To substantiate the reconstructive power of these four leads, Nelwan et al. (2007) assessed the root mean squared error (RMSE) of the RS12 of four lead systems at the time (Dower et al., 1988; Nelwan et al., 2000). They found that I, II, V2, and V5 had the lowest RMSE. Nelwan et al. (2008a) revisited the significance of various frontal leads in reconstruction and found that, although minute, combination of limb leads other than I and II may improve the results based on the lead being predicted.

However, Wang et al. (2005) argued that only two precordial leads were enough to reconstruct S12. By generating a coefficient matrix using two precordial leads, they reproduced other leads with a minimum coefficient of 0.954. Although there were no specific leads that could reconstruct all leads, it showed that two leads were capable of reliable reconstruction in lead-specific cases. Matyschik et al. (2020) supported this finding when they used only one precordial lead to reconstruct S12 with the help of a more complex patient-specific model. They used a variational autoencoder decoder (VAE) combined with a convolutional neural network (CNN) and either V2, V3, or V4 to reconstruct S12 depending on the patient in question. With the advancement of computing power and the development in machine learning (ML), one precordial lead could be enough to provide a reliable RS12 (Matyschik et al., 2020).

Butchy et al. (2023) decided to determine the lead importance by comparing the correlation between each lead. They found that limb leads were highly correlated with themselves and with V1, V4, V5, and V6. V2 and V3 were more strongly correlated with themselves than with other leads. By comparing the R 2 of the reconstruction of other leads with or without each of the electrodes, it was found that RA, LA, LL, and V 3 had the worst outcomes when excluded as inputs and the best outcomes when included as inputs. This, in their opinion, points to the importance of the limb leads and V3 as the most important leads for reconstruction of S12.

Furthermore, the misplacement of electrodes by physicians due to various reasons requires attention. This causes incorrect signals to be recorded and inadvertently cause incorrect models to be created or poor reconstructions from the available models. Finlay et al. (2009) reported that reconstruction errors become evident when electrodes are placed at least 15 mm from the correct positions. This was when I, II, V2, and V5 were used for reconstruction. In contrast, when EASI electrodes were used for reconstruction, significant errors were not evident until 5 cm from the correct electrode position.

Nonetheless, it is easy to fall into the assumption that there should be a single perfect lead set to reconstruct the remaining S12 leads. It is paramount to consider the complexity of the reconstruction situation (Feild et al., 2008). When choosing the lead set it is important to consider the lead that needs to be reconstructed. Each lead has an optimal lead combination unique to them for the best reconstruction (Yoo et al., 2023). Additionally, choosing a lead set that is in the region that needs to be reconstructed would yield better results than a generic lead set.

In the 39 studies reviewed in this paper, reconstruction algorithms are broadly categorized into linear and non-linear types to draw on the different ways in which these algorithms have been used and their limitations. To assess the performance of these algorithms, the studies employed various metrics such as correlation coefficient, similarity coefficient, mean squared error (MSE), RMSE and r-squared ( R 2 ), though not all were used simultaneously in each study. These metrics provide a basis for evaluating how well the algorithms perform in reconstruction. Correlation defines how well the RS12 changes with respect to the original S12, while RMSE defines the average error over time. These become important when considering the shape of segments of the signal. Additionally, it is important to recognise that the type of model affects the performance of the model. A patient-specific model usually performs better than a generic model. Depending on the application, if a patient-specific model can be designed, it is advisable to do so.

Reconstruction of standard ECG leads has been a major consideration in the field of electrocardiography, aimed at reducing the number of electrodes and recovering missing leads. Feild et al. (2008) outlined a step-by-step procedure of things for this purpose and several key points need to be considered based on related studies seen in this paper. Firstly, the decision of the best input lead set is critical. As seen from all previous works, this affects the model used for transformation. Every model is built with respect to what the inputs and outputs will be. Most models, irrespective of the input leads, demonstrate promising performance based on the nature and size of the data used to build the model. Despite this, the most common input leads that have been used were proposed by Nelwan et al. (2000), in line with Scherer et al. (1989). They recommended the use of I, II and V2 (4 electrodes) for the reconstruction of V1, V3, V4, V5, and V6.

In contrast, Butchy et al. (2023) reported that the best input leads were I, II and V3 (4 electrodes). They found this by comparing the correlation between each lead. They found that limb leads were highly correlated with themselves and with V1, V4, V5, and V6, while V2 and V3 were more strongly correlated with each other than with other leads. Clearly, three leads (including both limb leads, and chest leads) are optimal for the reconstruction. Nevertheless, the model built also plays a large role in determining the accuracy of the reconstruction.

Secondly, a major question that many researchers overlooked is the long-term reliability of their models. The heart is an everchanging organ, it is important to consider how often a new model needs to be designed. Fortunately, a few researchers have commented on this. A model, either generic or patient-specific, can be used for a few days to a few months without notable performance degradation (Scherer et al., 1989; Gussak et al., 2012; Maheshwari et al., 2016). However, more research needs to be conducted to ascertain the timewise reliability of any given model.

The kind of data used to train a model is also important. Though it has been shown that unprocessed ECG can be used as input data with good reconstructions (Obianom et al., 2024), models tend to perform worse in patients with cardiac disorders, than in healthy patients (Vemishetty et al., 2019; Feild et al., 2008; Guldenring et al., 2012; Lee et al., 2016; Gregg et al., 2008). Therefore, the kind of data used during the training of a model is essential to determining the performance of the model. While building a model, a researcher could consider using data from many patients with various heart conditions. This would require a large amount of patient data (thousands) to ensure that the right transforms are made. Conversely, a researcher can consider using data from a particular heart condition group. This would be a population-specific model and would not require as many patients.

More emphasis should also be drawn to the nature of the model. As much as the patient-specific models tend to always have better results, there are cases where the generic or population-specific models might be of great importance (Nelwan et al., 2004b; Nelwan et al., 2004c; Nelwan et al., 2008b). They can be especially useful in cases where quick information needs to be acquired. They can also be used to aid in the prediction of certain heart conditions (Nelwan et al., 2004c; Guldenring et al., 2012). Xue (2007) showed that RS12 predicted from leads I, II, V1 and V5 could be used to train an ML model to classify ischemia patients. Regarding the influence of datasets the model’s nature, any dataset can be employed to develop either a patient-specific or a generic model. For instance, the publicly available PTB database (Goldberger et al., 2000; Bousseljot et al., 1995) have been used to construct both types of models (Table 1, 2). The key takeaway is that patient-specific models typically produce more accurate results because no two human hearts are identical, and a patient’s own heart is the most precise model for itself.

There is the argument of nonlinear models being more effective than linear models in the reconstruction of S12. Many researchers have considered that the complexity of human physiology cannot be summed up in simple linear transforms (Feild et al., 2008). Feild et al. (2008) stresses that the complexity of the models needs to increase to models like Matyschik et al. (2020) and Yoo et al. (2023), beyond the linear transformation models (Dower et al., 1988; Scherer et al., 1989; Scherer and Willems, 1992; Nelwan et al., 2004c). This is attributed to significant limitations of linear models, such as their inability to account for noise artifacts. Counter to that, Xu et al. (2021) claims that linear regression performs better than FFN. Clearly, it is not about the complexity of the equations used in reconstruction, it is about how the equations were used for reconstruction (Mulyadi and Supriyanto, 2019). It is also worth noting that in device development and deployment, neural networks tend to require larger computing power, larger memory size, and have longer building time than classical algorithms. Therefore, choosing a nonlinear algorithm has its down sides particularly in device development.

Smith et al. (2021) also showed that using leads I, II, III, aVR, aVL, aVF, and V2 as inputs, correlations higher than 0.861 could be achieved. Although this might increase the processing power and the complexity of the models being used, this is worth considering. Like the popular I, II, and V2 inputs, these inputs still consist of four electrodes. Butchy et al. (2023) also noted that limb leads are highly correlated with V1, V4, V5, and V6. Therefore, this may provide a greater chance of better accuracy in reconstruction. Additionally, it is worth noting that various leads have stronger correlations with specific leads (Yoo et al., 2023). Therefore, providing all available leads as input may enable the models to give various weight to the necessary leads for reconstructing specific leads rather than relying on a minute lead set for the reconstruction of all leads.

It would also be valuable to analyse the performance of the models reviewed in this paper under a standardised framework. However, it is regrettable that the studies referenced in this paper utilised different databases and inconsistent performance metrics. Additionally, those that employed the same database may have not utilised the complete dataset provided. Nonetheless, the PTB database was predominantly used across various algorithms, input lead combinations, and both patient-specific and population-specific models, and can offer valuable insights (Table 1, 2). The trends discussed throughout this section are evident within these studies; patient-specific models generally yield better results, the nature of the training data affects the model performance, models performed worse with arrhythmic ECG than with rhythmic ECG, and input leads are very key to achieving accurate results.

Finally, the reconstruction of leads is clinically relevant in areas such as cardiac disease prediction systems. Since S12 has considerable redundant information, a model could be built to focus on reconstructing specific information in other leads which can be used as input for prediction models (Nelwan et al., 2004c; Guldenring et al., 2012; Xue, 2007). Furthermore, since the nature of data influences the reconstruction, this factor can be leveraged to reconstruct arrhythmic ECG signals. For instance, Gundlapalle and Acharyya (2022) and Vemishetty et al. (2019) trained models with only myocardial infarction patients and achieved an average correlation of 0.973 (population-specific approach) and 0.889 (patient-specific approach) respectively across all reconstructed leads. This demonstrates that models can reliably reconstruct arrhythmic ECG signals when trained on such data; however, their generalizability remains limited, as a single model has yet to demonstrate efficient reconstruction of both rhythmic and arrhythmic ECG signals (Feild et al., 2008; Guldenring et al., 2012; Lee et al., 2016; Gregg et al., 2008). For clinical applications, there is a need for either a sophisticated ensemble of models tailored to specific ECG rhythm types or a more advanced, unified model capable of reconstructing a broad spectrum of ECG patterns. ECG reconstruction is also highly relevant in the context of telemedicine. Given that most wearable devices have limited number of leads, these models can be used to reconstruct other leads from the recorded leads either on-site or via cloud processing. This enhances the availability of critical ECG information for physicians and prediction models to make accurate diagnosis (Babic et al., 2023; Gussak et al., 2012; Kapfo et al., 2022; Sohn et al., 2020; Panda et al., 2014). Moreover, it has been proven that these reconstruction models remain reliable from a few days to several months. As a result, they can be updated automatically or with scheduled checks to prevent performance degradation.

This paper considered the varying algorithms employed for the reconstruction of ECG from a subset of leads. ECG reconstruction is necessary for a variety of reasons. They are important for out-of-hospital monitoring, where patients are able enough to be discharged but constant monitoring is still needed. They are also important in emergency monitoring, where quick and minor decisions need to be made and can be used for disease prediction to gain quick insight into the plausible conditions of the heart. However, the accuracy of the reconstructions currently varies due to the different perspectives being taken.

This review identified that no single algorithm consistently outperforms others. To develop a reliable reconstruction model, careful consideration must be given to the selection of input leads, model architecture, the characteristics of the training data (particularly the patients’ heart conditions) and the intended purpose of the reconstruction. Following a structured and systematic approach in model development and data processing is essential to achieving high accuracy (Figure 2). These factors collectively contribute to the effectiveness and reliability of the reconstruction process and model.