Experimental And Theoretical Studies Towards The Development Of A Direct 3-D Diffuse Optical Tomographic Imaging System

Abstract

Diffuse Optical Tomography is a diagnostic imaging modality where optical parameters such as absorption coefficient, scattering coefficient and refractive index distributions are recovered to form the internal tissue metabolic image. Near-infrared (NIR) light has the potential to be used as a noninvasive means of diagnostic imaging within the human breast. Due to the diffusive nature of light in tissue, computational model-based methods are required for functional imaging. The main goal is to recover the spatial variation of optical properties which shed light on the different metabolic states of tissue and tissue like media. This thesis addresses the issue of quantitative recovery of optical properties of tissue-mimicking phantom and pork tissue using diffuse optical tomography (DOT). The main contribution of the present work is the development of robust, efficient and fast optical property reconstruction algorithms for a direct 3-D DOT imaging system. There are both theoretical and experimental contributions towards the development of an imaging system and procedures to minimize accurate data collection time, overall system automation as well as development of computational algorithms. In nurturing the idea of imaging using NIR light into a fully developed direct 3-D imaging system, challenges from the theoretical and computational aspects have to be met. The recovery of the optical property distribution in the interior of the object from the often noisy boundary measurements on light, is an ill-posed ( and nonlinear) problem. This is particularly true, when one is interested in a direct 3-D image reconstruction instead of the often employed stacking of 2-D cross-sections obtained from solving a set of 2-D DOT problems. In order to render the DOT, a useful diagnostic imaging tool and a robust reconstruction procedure giving accurate and reliable parameter recovery in the scenario, where the number of unknowns far outnumbers the number of independent data sets that can be gathered (for example, the direct 3-D recovery mentioned earlier) is essential. Here, the inversion problem is often solved through iterative methods based on nonlinear optimization for the minimization of a data-model misfit function. An interesting development in this direction has been the development of Broyden’ s and adjoint Broyden’ s methods that avoids direct Jacobian computation in each iteration thereby making the full 3-D a reality. Conventional model based iterative image reconstruction (MoBIIR) algorithm uses Newton’ s and it’s variant methods, where it required repeated evaluation of whole Jacobian, which consumes bulk time in reconstruction process. The explicit secant and adjoint information based fast 2-D/3-D image reconstruction algorithms without repeated evaluation of the Jacobian is proposed in diffuse optical tomography, where the computational time has been decreased many folds by updating the Jacobian successively through low rank update. An alternative route to the iterative solution is attempted by introducing an artificial dynamics in the system and treating the steady-state response of the artificially evolving dynamical system as a solution. The objective is to consider a novel family of pseudo-dynamical 2-D and 3-D systems whose numerical integration in time provides an asymptotic solution to the inverse problem at hand. We convert Gauss-Newton’ s equation for updates into a pseudo-dynamical (PD) form by explicitly adding a time derivative term. As the pseudo-time integration schemes do not need such explicit matrix inversion and depending on the pseudo-time step size, provides for a layer of regularization that in turn helps in superior quality of 2-D and 3-D image reconstruction. A cost effective frequency domain Matlab based 2-D/3-D automated imaging system is designed and built. The complete instrumentation (including PC-based control software) has been developed using a single modulated laser source (wavelength 830nm) and a photo-multiplier tube (PMT). The source and detector fiber change their positions dynamically allowing us to gather data at multiple source and detector locations. The fiber positions are adjusted on the phantom surface automatically for scanning variable size phantoms. A heterodyning scheme was used for reading out the measurement using a lock-in-amplifier. The Matlab program carries out sequence of actions such as instrument control, data acquisition, data organization, data calibration and reconstruction of image. The Gauss-Newton’ s, Broyden’ s, adjoint Broyden’ s and pseudo-time integration algorithms are evaluated using the simulation data as well as data from the experimental DOT system. Validation of the system and the reconstruction algorithms were carried out on a real tissue, a pork tissue with an embedded fat inhomogeneity. The results were found to match the known parameters closely.