Improving the reconstruction image contrast of time-domain diffuse optical tomography using high accuracy Jacobian matrix

An algorithm for time-domain diffuse optical tomography using a high accuracy Jacobian matrix has been developed. The Jacobian matrix has been calculated using a new direct method that uses two finite element meshes of different sizes. A low density mesh has been used for the inverse calculations where the tissue optical properties are reconstructed at its nodes' locations. The second mesh has a bigger size and is used to calculate the high accuracy light fluence rates and the Jacobian matrix. The high accuracy light fluence is interpolated to obtain its values at the nodes of the low density mesh and at the detectors' locations. The high accuracy Jacobian matrix at the nodes of the low density mesh are obtained by integrating the Jacobian calculated using the high density mesh. The integration of the Jacobian using the proposed method does not require calculating the Jacobian explicitly at all nodes of the high density mesh which is inefficient in memory requirement and computation speed. The improvement of the Jacobian accuracy while using a low density mesh for the inverse calculations improves the reconstructed image contrast and the computation speed. The optical properties are reconstructed in a region of interest by solving iteratively a self-regularized minimization problem. The minimization problem uses the calculated Jacobian and the light fluence at precisely selected points on the temporal profile of each source-detector pair for the reconstruction. The algorithm has been applied to a three-dimensional model of a neonatal brain and to a three-dimensional model of the mouse for a small animal model. The reconstruction results by the proposed method have been compared with the results using a single mesh for the Jacobian calculations. The effect of using different sizes of the low density mesh for the inverse calculations on the image contrast has been reported.