Fast computation of the time domain diffusion forward model for optical tomography in the Born approximation

Diffuse optical tomography is an emerging technique for non-invasively measuring in vivo tissue optical properties. The next generation of DOT time domain imaging systems will allow researchers to create three-dimensional (3D) images of blood volume and oxygenation with unprecedented spatial resolution. We consider common semi-infinite and slab geometries, in the Born approximation to the diffusion equation. Current techniques for computing the 3D time-domain forward problem are computationally intensive: evaluating the required sensitivity matrix involves a numerical convolution in time. We present analytical results for this convolution, for both absorption and diffusion 3-point Green’s functions. This accelerates calculation by up to two orders of magnitude, while improving accuracy.