In the quasi-static limit (defibrillation pulses are slow enough that capacitive/inductive effects are negligible), the thorax behaves as a purely resistive volume conductor. A single electrode delivering current I into a homogeneous medium of conductivity σ acts as a point current source; its potential and field fall off exactly like a point charge's:
V(r) = I / (4πσr)
E(r) = -∇V = I / (4πσ r²) · r̂
The anode (+I) and cathode (−I, a current sink) are modeled together and their fields superposed — the same monopole-pair construction used in bioelectric dosimetry to estimate transmyocardial gradients:
E(P) = I/(4πσ) [ (P−r_anode)/|P−r_anode|³ − (P−r_cathode)/|P−r_cathode|³ ]
The peak current delivered depends on the stored energy E, the patient's transthoracic impedance Z, and the pulse duration τ (≈8 ms for a typical biphasic truncated-exponential waveform):
I_peak ≈ √( 2E / (Z·τ) )
Clinical defibrillation research (e.g. Zhou et al., transmyocardial gradient studies) puts the minimum field needed at the myocardium for reliable cardioversion around 5 V/cm, with fields above roughly 30 V/cm adding avoidable myocardial and skin-burn risk without improving success.
- Electrode placement — anterolateral (sternum–apex) vs. anteroposterior (front–back) changes the geometric path the current takes through the chest, and therefore the field reaching the heart.
- Energy / impedance — set the peak current via the formula above; a higher impedance needs more energy to drive the same current.
- Chest size — scales electrode separation, which changes field strength through the inverse-square falloff.
Simplification: this model treats the torso as a single homogeneous conductor in free space (point-source superposition), ignoring the insulating skin boundary, lung air pockets, and bone — real dosimetry uses finite-element torso models. It is intended to build correct intuition about field geometry and the energy/impedance/current relationship, not to be diagnostic-grade.