# Solving the Inverse Problem of Electrocardiography for Cardiac Digital Twins: A Survey

arXiv: https://arxiv.org/abs/2406.11445 · HTML: https://mlsanity.com/paper/2406.11445/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 305 references that are in the map.
- First posted on arXiv 17 Jun 2024.

## Builds on (most cited first, 28 of 28)

- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Evaluation of Algorithms for Multi-Modality Whole Heart Segmentation: An Open-Access Grand Challenge](https://mlsanity.com/paper/1902.07880/) (2019)
- [Multimodal Intelligence: Representation Learning, Information Fusion, and Applications](https://mlsanity.com/paper/1911.03977/) (2019)
- [Solving Inverse Problems With Deep Neural Networks -- Robustness Included?](https://mlsanity.com/paper/2011.04268/) (2020)
- [Cardiac Segmentation on Late Gadolinium Enhancement MRI: A Benchmark Study from Multi-Sequence Cardiac MR Segmentation Challenge](https://mlsanity.com/paper/2006.12434/) (2020)
- [Solution of Physics-based Bayesian Inverse Problems with Deep Generative Priors](https://mlsanity.com/paper/2107.02926/) (2021)
- [MyoPS: A Benchmark of Myocardial Pathology Segmentation Combining Three-Sequence Cardiac Magnetic Resonance Images](https://mlsanity.com/paper/2201.03186/) (2022)
- [Multi-Modality Cardiac Image Computing: A Survey](https://mlsanity.com/paper/2208.12881/) (2022)
- [Towards Enabling Cardiac Digital Twins of Myocardial Infarction Using Deep Computational Models for Inverse Inference](https://mlsanity.com/paper/2307.04421/) (2023)
- [Physics-constrained Deep Learning for Robust Inverse ECG Modeling](https://mlsanity.com/paper/2107.12780/) (2021)
- [Deep Computational Model for the Inference of Ventricular Activation Properties](https://mlsanity.com/paper/2208.04028/) (2022)
- [Inference of ventricular activation properties from non-invasive electrocardiography](https://mlsanity.com/paper/2010.15214/) (2020)
- [GEASI: Geodesic-based Earliest Activation Sites Identification in cardiac models](https://mlsanity.com/paper/2102.09962/) (2021)
- [Generative Modeling and Inverse Imaging of Cardiac Transmembrane Potential](https://mlsanity.com/paper/1905.04803/) (2019)
- [Bayesian Optimization on Large Graphs via a Graph Convolutional Generative Model: Application in Cardiac Model Personalization](https://mlsanity.com/paper/1907.01406/) (2019)
- [Graph convolutional regression of cardiac depolarization from sparse endocardial maps](https://mlsanity.com/paper/2009.14068/) (2020)
- [Learning cardiac activation maps from 12-lead ECG with multi-fidelity Bayesian optimization on manifolds](https://mlsanity.com/paper/2203.06222/) (2022)
- [MedalCare-XL: 16,900 healthy and pathological 12 lead ECGs obtained through electrophysiological simulations](https://mlsanity.com/paper/2211.15997/) (2022)
- [Few-shot Generation of Personalized Neural Surrogates for Cardiac Simulation via Bayesian Meta-Learning](https://mlsanity.com/paper/2210.02967/) (2022)
- [Digital twinning of cardiac electrophysiology models from the surface ECG: a geodesic backpropagation approach](https://mlsanity.com/paper/2308.08410/) (2023)
- [PIEMAP: Personalized Inverse Eikonal Model from cardiac Electro-Anatomical Maps](https://mlsanity.com/paper/2008.10724/) (2020)
- [Space-time shape uncertainties in the forward and inverse problem of electrocardiography](https://mlsanity.com/paper/2010.16104/) (2020)
- [Reducing Line-of-block Artifacts in Cardiac Activation Maps Estimated Using ECG Imaging: A Comparison of Source Models and Estimation Methods](https://mlsanity.com/paper/2108.06602/) (2021)
- [A machine learning approach to reconstruction of heart surface potentials from body surface potentials](https://mlsanity.com/paper/1802.02240/) (2018)
- [Fast Posterior Estimation of Cardiac Electrophysiological Model Parameters via Bayesian Active Learning](https://mlsanity.com/paper/2110.06851/) (2021)
- [Influence of Myocardial Infarction on QRS Properties: A Simulation Study](https://mlsanity.com/paper/2304.01796/) (2023)
- [A Self-Taught Artificial Agent for Multi-Physics Computational Model Personalization](https://mlsanity.com/paper/1605.00303/) (2016)
- [Non-invasive Localization of the Ventricular Excitation Origin Without Patient-specific Geometries Using Deep Learning](https://mlsanity.com/paper/2209.08095/) (2022)

## Built on by (most cited first, 14 of 14)

- [End-to-End 4D Heart Mesh Recovery Across Full-Stack and Sparse Cardiac MRI](https://mlsanity.com/paper/2509.12090/) (2025)
- [Personalized Topology-Informed Localization of Standard 12-Lead ECG Electrode Placement from Incomplete Cardiac MRIs for Efficient Cardiac Digital Twins](https://mlsanity.com/paper/2408.13945/) (2024)
- [PrIntMesh: Precise Intersection Surfaces for 3D Organ Mesh Reconstruction](https://mlsanity.com/paper/2511.16186/) (2025)
- [Learning geometry-dependent lead-field operators for forward ECG modeling](https://mlsanity.com/paper/2602.22367/) (2026)
- [VecHeart: Holistic Four-Chamber Cardiac Anatomy Modeling via Hybrid VecSets](https://mlsanity.com/paper/2604.19403/) (2026)
- [Personalized 4D Whole-Heart Mesh Reconstruction from Cine MRI via Multi-Scale Temporal Modeling and Differentiable Contour Rendering](https://mlsanity.com/paper/2607.01952/) (2026)
- [Comprehensive Signal Quality Evaluation of a Wearable Textile ECG Garment: A Sex-Balanced Study](https://mlsanity.com/paper/2508.21554/) (2025)
- [Towards Deep Learning Surrogate for the Forward Problem in Electrocardiology: A Scalable Alternative to Physics-Based Models](https://mlsanity.com/paper/2512.13765/) (2025)
- [Geometry-Free Conditional Diffusion Modeling for Solving the Inverse Electrocardiography Problem](https://mlsanity.com/paper/2601.18615/) (2026)
- [Chain of Flow: ECG-Conditioned 4D Cardiac Cine Generation from Patient-Specific Anatomical Anchor](https://mlsanity.com/paper/2602.22919/) (2026)
- [Physiology and Anatomy Aware Inverse Inference of Myocardial Infarction for Cardiac Digital Twin](https://mlsanity.com/paper/2605.22044/) (2026)
- [HAPI-EP: Towards Hybrid, Adaptive, and Predictive Digital Twins of Cardiac Electrophysiology](https://mlsanity.com/paper/2606.15637/) (2026)
- [Cardiovascular Digital Twins from Physics Based to Data Driven Approaches](https://mlsanity.com/paper/2608.02135/) (2026)
- [Anatomy-Aligned Surface Field Learning for Myocardial Reconstruction from Sparse Short-Axis Cine MRI](https://mlsanity.com/paper/2609.29825/) (2026)

## Abstract (arXiv)

Cardiac digital twins (CDTs) are personalized virtual representations used to understand complex cardiac mechanisms. A critical component of CDT development is solving the ECG inverse problem, which enables the reconstruction of cardiac sources and the estimation of patient-specific electrophysiology (EP) parameters from surface ECG data. Despite challenges from complex cardiac anatomy, noisy ECG data, and the ill-posed nature of the inverse problem, recent advances in computational methods have greatly improved the accuracy and efficiency of ECG inverse inference, strengthening the fidelity of CDTs. This paper aims to provide a comprehensive review of the methods of solving ECG inverse problem, the validation strategies, the clinical applications, and future perspectives. For the methodologies, we broadly classify state-of-the-art approaches into two categories: deterministic and probabilistic methods, including both conventional and deep learning-based techniques. Integrating physics laws with deep learning models holds promise, but challenges such as capturing dynamic electrophysiology accurately, accessing accurate domain knowledge, and quantifying prediction uncertainty persist. Integrating models into clinical workflows while ensuring interpretability and usability for healthcare professionals is essential. Overcoming these challenges will drive further research in CDTs.