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

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.

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.

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.

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.