This is a genuinely 2D model, not a flattened 3D scene: it treats the transverse thoracic slice at heart level as a homogeneous resistive sheet — the same abstraction used in electrical impedance tomography (EIT), where current is injected and measured entirely within one cross-sectional plane. A point current source embedded in an infinite 2D conductive sheet obeys the 2D Green's function for Laplace's equation, which falls off as 1/r, not 1/r² as in the 3D case:
V(r) = -(I / 2πσ₂D) · ln(r)
E(r) = -∇V = I / (2πσ₂D · r) · r̂
where σ₂D is the sheet conductivity (siemens, S) — the 3D tissue conductivity σ multiplied by an effective slice thickness t (σ₂D = σ·t). The anode (+I) and cathode (−I) superpose exactly as in the 3D model, but with the r² denominator instead of r³:
E(P) = I/(2πσ₂D) [ (P−r_anode)/|P−r_anode|² − (P−r_cathode)/|P−r_cathode|² ]
Peak current still comes from the stored energy E, transthoracic impedance Z, and effective biphasic pulse duration τ≈8 ms — this part of the physics doesn't change between dimensions:
I_peak ≈ √( 2E / (Z·τ) )
Because the sheet has no depth, anterolateral vs. anteroposterior placement is represented by the two electrodes' positions within this single transverse plane (left–right vs. anterior–posterior), rather than by different heights on the chest — a deliberate simplification the 3D volumetric model doesn't need to make. The 5 V/cm minimum-effective and ~30 V/cm elevated-risk thresholds are the same clinical benchmarks used there.
- Electrode placement — changes both the separation and the angle current takes across the slice, 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 the slice's semi-axes, changing field strength through the 1/r falloff (gentler than the 3D model's 1/r²).
Simplification: a single conductive sheet ignores skin insulation, lung air pockets, bone, and the actual craniocaudal extent of the torso — real EIT reconstructions use many electrodes and finite-element solvers. This model is for building correct intuition about the field's dimensional falloff and the energy/impedance/current relationship, not diagnostic-grade dosimetry.