The inverse problem of electrocardiography: From a clinical point of view

Abstract

Background

The 12-lead electrocardiogram (ECG) records body-surface potentials that represent cardiac electrical activity filtered through the torso. Recovering the original cardiac sources from these surface signals—the inverse problem of electrocardiography—is mathematically ill-posed: multiple distinct source configurations produce identical tracings. This constraint is seldom discussed in clinical practice, yet it underlies many recognized ECG diagnostic limitations.

Methods

This narrative review provides a clinician-oriented summary of the forward and inverse formulations, and then organizes ECG interpretive pitfalls into five mechanistic categories: volume-conductor filtering, source-model ambiguity, cardiac motion during repolarization, patient-specific anatomy and lead-placement variability, and signal noise and filtering. Each category is linked to quantitative clinical data and to practical reporting recommendations.

Results

Volume-conductor attenuation limits VA localization accuracy to 38.9% at the AHA-segment level. Source ambiguity allows 59% of combined anterior–inferior ST elevation to originate from RCA rather than LAD occlusion, and permits unrelated diseases (pulmonary embolism, arrhythmogenic cardiomyopathy) to produce identical repolarization patterns. Cardiac motion during repolarization introduces time-variant geometric distortion independent of pathology. The Mason–Likar lead system erases established inferior infarctions and shifts QRS axes by up to 60°. Fragmented QRS detects scar (sensitivity 68%, specificity 80%) but fails territorial localization (sensitivity 1.7%). Electrocardiographic imaging reduces localization error but cannot recover spatial detail lost to the torso filter.

Conclusions

The inverse problem imposes identifiability limits on every 12-lead ECG. Territorial labels should be treated as probabilistic and corroborated with imaging or hemodynamics when localization carries therapeutic consequences.

Graphical Abstract