Figure 8

Schematics illustrating the relation between a volume change of some blood filled lumen (such as e.g. a ventricle) and the sum of dipoles that represent the first order alteration of the E-field due to the volume change, as explained in the first subsection of the Appendix. a: The initial volume of blood (at τ=0) is bounded by a closed surface ${\mathcal{A}}_0$ (indicated by the dashed line) that has non-zero values of s ₀. At each surface element δ A _i of the surface ${\mathcal{A}}_0$, there is a charge q _i that is proportional to (E ₀ · δ A _i ). The charges on the boundary surface ${\mathcal{A}}_0$ are indicated by the ⊕and ⊖signs. (Evidently, in an applied AC current field, the boundary charges change signs continuously, along with the direction of the arrow of the applied E ₀, with the same frequency f of the AC current. In this schematic however, only the moments in time are depicted in which the arrows point in one specific direction). b: Situation at some time τ>0during the same cardiac cycle. The volume of blood has become smaller, and is now bounded by the non-zero values of s(τ). c: Subtraction of the volumes from (a) and (b), in which the volume difference V(τ)−V(0)is indicated by the grey shade. If the voltage distributions on the thoracic skin in situation (a) and (b) are denoted by Φ(x,0)and Φ(x,τ), respectively, then the voltage change Φ(x,τ)−Φ(x,0)corresponds to s(x,τ)−s ₀(x), and hence also corresponds to the dipoles in (b) minus the dipoles in (a). d: The grey-shaded volume difference V(τ)−V(0)equals the sum of a set of small rectangular beams : $V\left(\tau \right)-V\left(0\right)=\sum _i{\mathbf{h}}_i·\left(\delta {\mathbf{A}}_i\right)$, which is quite similar to the sum of the dipoles formed by the charges at the end-points of the rectangular beams, corresponding to the dipole interpretation of the charges in (c).