) recorded when the tissue is at rest. Fluxes captured during an AP are denoted by F. The signal due only to the AP itself is . We shall rather use the usual renormalization:
(1)
Fig. 1.
The optical imaging setup: (1) CCD camera, (2) emission filter, (3) LED illumination, (4) tissue sample, (5) ECG electrode, (6) bipolar stimulating electrode.
3 Model
3.1 Forward Problem
In order to write the mathematical model of these observations, we assume the following: the cameras record photon fluxes through the surfaces, the light interacts with the tissue material in the diffusive regime [2], and a Robin boundary condition can be used to model the interaction between the tissue and its environment. Hence the illumination light is described by its photon density that solves the diffusion equation
where represents the slab of tissue, is the illuminated surface, and n is the unit normal to , outward of . The fluorescent light is assumed to be proportional to the TMP and the illumination light (multiplicative factor
(2)
(3)