Talk Title: Development of Efficient Computational Methods for Better Estimation of Optical Properties in Diffuse Optical Tomography

Speaker: Ravi Prasad K. J.

Abstract

Diffuse optical tomography (DOT) is one of the promising imaging modalities that provides functional information of the soft biological tissues in-vivo, such as breast and brain tissues. The near infrared (NIR) light (600-1000 nm) is the interrogating radiation, which is typically delivered and collected using fiber bundles placed on the boundary of the tissue. The internal optical property distribution is estimated via model-based image-reconstruction algorithm using these limited boundary measurements. As NIR light is non-ionizing, the prolonged monitoring of tissue patho-physiology is feasible, making it a strong contender for highly effective molecular imaging of tissue.

Diffuse optical tomographic image reconstruction problem is known to be non-linear, ill-posed, and some times under-determined due to the multiple scattering of NIR light in the tissue. Solving this inverse problem requires regularization to obtain meaningful results, with Tikhonov-type regularization being the most popular one.

The choice of the regularization parameter dictates the reconstructed optical image quality and is typically chosen empirically or based on prior experience. An automated method for optimal selection of regularization parameter that is based on regularized minimal residual method (MRM) is proposed and is compared with the traditional generalized cross-validation method. The results obtained using numerical and gelatin phantom data indicate that the MRM-based method is capable of providing the optimal regularization parameter.

The regularization term, also known as penalty, choice can influence the image characteristics observed in the reconstructed image. As pointed earlier, Tikhonov-type penalty, which is quadratic, is the most popular among them. A new framework that can easily incorporate these penalty terms is developed, mainly to include non-traditional penalty terms and to effectively assess the improvement in the reconstructed image characteristics. These include, L1, Cauchy, Geman-McClure and a systematic comparison with the quadratic regularization is performed as a part of this work. The results obtained using numerical and gelatin phantom data indicate that the non-quadratic penalty terms are capable of improving the reconstructed image characteristics in diffuse optical tomographic imaging.

Effective usage of image guidance by incorporating the refractive index (RI) variation in computational modeling of light propagation in tissue is investigated to assess its impact on optical-property estimation. With the aid of realistic patient breast three-dimensional models, the variation in RI for different regions of tissue under investigation is shown to influence the estimation of optical properties in image-guided diffuse optical tomography (IG-DOT) using numerical simulations. It is also shown that by assuming identical RI for all regions of tissue would lead to erroneous estimation of optical properties. The a priori knowledge of the RI for the segmented regions of tissue in IG-DOT, which is difficult to obtain for the in vivo cases, leads to more accurate estimates of optical properties. Even inclusion of approximated RI values, obtained from the literature, for the regions of tissue resulted in better estimates of optical properties, with values comparable to that of having the correct knowledge of RI for different regions of tissue.

Image guided diffuse optical tomographic image reconstruction procedure involves reduction of the number of optical parameters to be reconstructed equal to the number of distinct regions identified in the structural information provided by the traditional imaging modality. This makes the image reconstruction problem to be well-determined compared to traditional under-determined case. Still, the methods that are deployed in this case are same as the one used for traditional diffuse optical image reconstruction, which involves regularization term as well as computation of the Jacobian. A gradient-free Nelder-Mead simplex method was proposed here to perform the image reconstruction procedure and shown to be providing solutions that are closely matching with ones obtained using established methods. The proposed method also has the distinctive advantage of being more efficient due to being regularization free, involving only repeated forward calculations.