Voltage-sensitive fluorescent dyes are commonly used to measure cardiac electrical activity. Recent studies indicate, however, that optical action potentials (OAPs) recorded from the myocardial surface originate from a widely distributed volume beneath the surface and may contain useful information regarding intramural activation. The first step toward obtaining this information is to predict OAPs from known patterns of three-dimensional (3-D) electrical activity. To achieve this goal, we developed a two-stage model in which the output of a 3-D ionic model of electrical excitation serves as the input to an optical model of light scattering and absorption inside heart tissue. The two-stage model permits unique optical signatures to be obtained for given 3-D patterns of electrical activity for direct comparison with experimental data, thus yielding information about intramural electrical activity. To illustrate applications of the model, we simulated surface fluorescence signals produced by 3-D electrical activity during epicardial and endocardial pacing. We discovered that OAP upstroke morphology was highly sensitive to the transmural component of wave front velocity and could be used to predict wave front orientation with respect to the surface. These findings demonstrate the potential of the model for obtaining useful 3-D information about intramural propagation.

Three-dimensional rotors, or scroll waves, provide essential insight into the activity of excitable media. They also are a suspected cause in the formation and maintenance of ventricular fibrillation, whose lethality is well known. It is therefore of considerable interest to find out what configurations can be adopted by such pathologies. A scroll's behavior is embodied in its organizing center or filament, a largely quiescent tube about which the scroll rotates. Predicting filament shape has normally required computer-intensive simulations of the whole scroll in time. We have found a fast and robust principle that yields the prediction for stationary filaments on a purely geometrical basis, blind to the reaction parameters of the medium. The procedure is to calculate the filament shape as a minimal path. We work in singly diffusive media whose diffusivity tensor-and no other feature-varies spatially. Mathematical and numerical evidence is presented for the proposition that a stable filament is a geodesic in a three-dimensional space whose metric is given by the inverse diffusivity tensor of the medium. Away from the boundaries, a stable filament is unaffected by the reaction parameters. The algorithmic aspects of this work are subsidiary to our main purpose of drawing attention to the universal and unexpectedly exact fit of an elementary geodesic principle within reaction-diffusion theories.

Voltage-sensitive dyes are an important tool in visualizing electrical activity in cardiac tissue. Until today, they have mainly been applied in cardiac electrophysiology to subsurface imaging. In the present study, we assess different imaging methods used in optical tomography with respect to their effectiveness in visualizing 3D cardiac activity. To achieve this goal, we simulate optical signals produced by excitation fronts initiated at different depths inside the myocardial wall and compare their properties for various imaging modes. Specifically, we consider scanning and broad-field illumination, including trans- and epi-illumination. We focus on the lateral optical resolution and signal intensity, as a function of the source depth. Optical diffusion theory is applied to derive a computationally efficient approximation of the point-spread function and to predict voltage-sensitive signals. Computations were performed both for fluorescent and absorptive voltage-sensitive dyes. Among all the above-mentioned methods, fluorescent coaxial scanning yields the best resolution (<2.5 mm) and gives the most information about the intramural cardiac activity.