The forward problem in optical mapping of electrical activity in the heart: application to various imaging methods

Voltage-sensitive dyes have become an important tool in visualizing electrical activity in cardiac tissue. However, there are no established methods for assessing the contribution of intramural electrical excitation to recorded optical signals. Here, we develop algorithms to calculate voltage-dependent optical signals from three-dimensional distributions of transmembrane voltage inside the myocardial wall (the forward problem). Optical diffusion theory is applied for different imaging modes including subsurface imaging or epi-illumination, transillumination and coaxial scanning. We use the solutions of the forward problem to assess these imaging methods with respect to their effectiveness in visualizing two types of 3D cardiac activity: electrical point sources and intramural scroll waves initiated at various depths. Simulations were performed both for fluorescent and absorptive voltage-sensitive dyes. In the case of point sources, we focus on the lateral optical resolution, as a function of the source depth. We find that, among the studied methods, fluorescent coaxial scanning yields the best optical resolution (<2.5 mm). In the case of scroll waves we investigate how well the filament, i.e. the organizing center, can be visualized as function of its depth. Our results show that using absorptive transillumination, filaments can be detected up to 3 mm below the recording surface. The presented results provide a powerful tool for the interpretation of experimental data and are the first step towards the development of inverse procedures.