Thesis (M.S.)--University of Missouri-Columbia, 2004. / Typescript. Includes bibliographical references (leaves 100-104). Also available on the Internet.

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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.

<p>Small animal imaging is a valuable tool in preclinical biomedical research which relies on the use of animal models to understand human disease. Newly emerging optical imaging techniques such as bioluminescence tomography offer an inexpensive and sensitive alternative to more established imaging technologies. These techniques are capable of non-invasively imaging a variety of cellular and molecular processes <em>in vivo</em>. As an emerging technology, current bioluminescence imaging methods suffer from several limitations, preventing them from reaching their full potential.</p> <p>In this work, we describe the design and characterization of an integrated imaging system capable of multispectral bioluminescence tomography (BLT), diffuse optical tomography (DOT), and X-ray computed tomography (CT). The system addresses many of the inherent problems encountered in planar bioluminescence imaging techniques, allowing for the recovery of more accurate and quantitative bioluminescence data. The integrated X-ray CT scanner provides anatomical information which aids in the visualization and localization of the recovered bioluminescence distributions and also helps to constrain the inverse reconstruction in the diffuse optical tomography system. It was found that the inclusion of spatial priors from X-ray CT improved the reconstructed image quality dramatically. Four image reconstruction algorithms were evaluated for their ability to recover the effective attenuation coefficients of a series of test phantoms. Two of the algorithms (a modified Levenberg-Marquardt method, and a single-step Tikhonov method) did not use any <em>a priori</em> spatial information. Two other algorithms (hard priors and soft priors) used <em>a priori </em>structural information from X-ray CT to constrain the reconstruction process. The two methods incorporating spatial prior information resulted in recovered optical property distributions with RMS errors ranging from 8 % to 15 % in a series of test phantoms versus errors of 11 % to 26 % for non-spatial methods. The soft priors method was shown to be more resilient to imperfect <em>a priori</em> information.</p> <p>The multispectral BLT component was used to recover accurate bioluminescence distributions in test phantoms using <em>a priori</em> background optical properties recovered from the DOT system. Multispectral measurements were shown to provide an accurate method for estimating the position of a bioluminescence source due to the wavelength dependent attenuation of tissue. Experimental measurements are presented which explore the importance of accurate estimates of background optical properties in BLT. The hard spatial prior method was found to provide the best overall recovery of total source strength, position, and fidelity at all source depths up to 12.5 mm. The total source strength was recovered to within 8 %, while the source position was recovered to within 0.16 mm in all cases. Errors in recovered power and position showed no dependence on depth up to the maximum of 12.5 mm.</p> / Doctor of Philosophy (PhD)

Fluorescence tomography (FT) is an emerging non-invasive in vivo molecular imaging modality that aims at quantification and three-dimensional (3D) localization of fluorescent tagged inclusions, such as cancer lesions and drug molecules, buried deep in human and animal subjects. Depth-resolved 3D reconstruction of fluorescent inclusions distributed over the volume of optically turbid biological tissue using the diffuse fluorescent photons detected on the skin poses a highly ill-conditioned problem, as depth information must be extracted from boundary data. Due to this ill-posed nature of FT reconstructions, noise and errors in the data can severely impair the accuracy of the 3D reconstructions. Consequently, improvements in the signal-to-noise ratio (SNR) of the data significantly enhance the quality of the FT reconstructions. Furthermore, enhancing the SNR of the FT data can greatly contribute to the speed of FT scans. The pivotal factor in the SNR of the FT data is the power of the radiation illuminating the subject and exciting the administered fluorescent agents. In existing single-point illumination FT systems, the illumination power level is limited by the skin maximum radiation exposure levels. In this research, a multiplexed architecture governed by the Hadamard transform was conceptualized, developed, and experimentally implemented for orders-of-magnitude enhancement of the SNR and the robustness of FT reconstructions. The multiplexed FT system allows for Hadamard-coded multi-point illumination of the subject while maintaining the maximal information content of the FT data. The significant improvements offered by the multiplexed FT system were validated by numerical and experimental studies carried out using a custom-built multiplexed FT system developed exclusively in this work. The studies indicate that Hadamard multiplexing offers significantly enhanced robustness in reconstructing deep fluorescent inclusions from low-SNR FT data.

Herein we present the development of a fluorescence-enhanced, frequency-domain radiative transport reconstruction system designed for small animal optical tomography. The system includes a time-dependent data acquisition instrument, a radiative transport based forward model for prediction of time-dependent propagation of photons in small, non-diffuse volumes, and an algorithm which utilizes the forward model to reconstruct fluorescent yields from air/tissue boundary measurements. The major components of the instrumentation include a charge coupled device camera, an image intensifier, signal generators, and an optical switch. Time-dependent data were obtained in the frequency-domain using homodyne techniques on phantoms with 0.2% to 3% intralipid solutions. Through collaboration with Transpire, Inc., a fluorescence-enhanced, frequency-domain, radiative transport equation (RTE) solver was developed. This solver incorporates the discrete ordinates, source iteration with diffusion synthetic acceleration, and linear discontinuous finite element differencing schemes, to predict accurately the fluence of excitation and emission photons in diffuse and transport limited systems. Additional techniques such as the first scattered distributed source method and integral transport theory are used to model the numerical apertures of fiber optic sources and detectors. The accuracy of the RTE solver was validated against diffusion and Monte Carlo predictions and experimental data. The comparisons were favorable in both the diffusion and transport limits, with average errors of the RTE predictions, as compared to experimental data, typically being less than 8% in amplitude and 7% in phase. These average errors are similar to those of the Monte Carlo and diffusion predictions. Synthetic data from a virtual mouse were used to demonstrate the feasibility of using the RTE solver for reconstructing fluorescent heterogeneities in small, non-diffuse volumes. The current version of the RTE solver limits the reconstruction to one iteration and the reconstruction of marginally diffuse, frequency-domain experimental data using RTE was not successful. Multiple iterations using a diffusion solver successfully reconstructed the fluorescent heterogeneities, indicating that, when available, multiple iterations of the RTE based solver should also reconstruct the heterogeneities.

Herein we present the development of a fluorescence-enhanced, frequency-domain radiative transport reconstruction system designed for small animal optical tomography. The system includes a time-dependent data acquisition instrument, a radiative transport based forward model for prediction of time-dependent propagation of photons in small, non-diffuse volumes, and an algorithm which utilizes the forward model to reconstruct fluorescent yields from air/tissue boundary measurements. The major components of the instrumentation include a charge coupled device camera, an image intensifier, signal generators, and an optical switch. Time-dependent data were obtained in the frequency-domain using homodyne techniques on phantoms with 0.2% to 3% intralipid solutions. Through collaboration with Transpire, Inc., a fluorescence-enhanced, frequency-domain, radiative transport equation (RTE) solver was developed. This solver incorporates the discrete ordinates, source iteration with diffusion synthetic acceleration, and linear discontinuous finite element differencing schemes, to predict accurately the fluence of excitation and emission photons in diffuse and transport limited systems. Additional techniques such as the first scattered distributed source method and integral transport theory are used to model the numerical apertures of fiber optic sources and detectors. The accuracy of the RTE solver was validated against diffusion and Monte Carlo predictions and experimental data. The comparisons were favorable in both the diffusion and transport limits, with average errors of the RTE predictions, as compared to experimental data, typically being less than 8% in amplitude and 7% in phase. These average errors are similar to those of the Monte Carlo and diffusion predictions. Synthetic data from a virtual mouse were used to demonstrate the feasibility of using the RTE solver for reconstructing fluorescent heterogeneities in small, non-diffuse volumes. The current version of the RTE solver limits the reconstruction to one iteration and the reconstruction of marginally diffuse, frequency-domain experimental data using RTE was not successful. Multiple iterations using a diffusion solver successfully reconstructed the fluorescent heterogeneities, indicating that, when available, multiple iterations of the RTE based solver should also reconstruct the heterogeneities.

Optical imaging of soft biological tissue is highly desirable since it is nonionizing and provides sensitive contrast information which enables the detection of physiological functions and abnormalities, including potentially early cancer detection. However, due to the diffusive nature of light in soft biological tissue, it is difficult to achieve simultaneously good spatial resolution and good imaging depth with pure optical imaging modalities. This work focuses on the ultrasound-modulated optical tomography (UOT): a hybrid technique which combines the advantages of ultrasonic resolution and optical contrast. In this technique, focused ultrasound and optical radiation of high temporal coherence are simultaneously applied to soft biological tissue. The intensity of the sideband, or ultrasound ‗tagged‘ photons depends on the optical absorption in the region of interest where the ultrasound is focused. Demodulation of the optical speckle pattern yields the intensity of tagged photons for each location of the ultrasonic focal spot. Thus UOT yields an image with spatial resolution of the focused ultrasound — typically submillimeter — whose contrast is related to local optical absorption and the diffusive properties of light in the organ. Thus it extends all the advantages of optical imaging deep into highly scattering tissue. However lack of efficient tagged light detection techniques has so far prevented ultrasound-modulated optical tomography from achieving maturity. The signal-to-noise ratio (SNR) and imaging speed are two of the most important figures of merit and need further improvement for UOT to become widely applicable. In the first part of this work, nonlinear optics detection methods have been implemented to demodulate the ―tagged‖ photons. The most common of these is photorefractive (PR) two wave mixing (TWM) interferometry, which is a time-domain filtering technique. When used for UOT, it is found that this approach extracts not only optical properties but also mechanical properties for the area of interest. To improve on TWM, PR four wave mixing (FWM) experiments were performed to read out only the modulated light and at the same time strongly suppressing the ‗untagged‘ light. Spectral-hole burning (SHB) in a rare-earth-ion-doped crystal has been developed for UOT more recently. Experiments in Tm3 :Y3Al5O12 (Tm:YAG) show the outstanding features of SHB: large angle acceptance (etendue), light speckle processing in parallel (insensitive to the diffusive light nature) and real-time signal collection (immune to light speckle decorrelation). With the help of advanced laser stabilization techniques, two orders of magnitude improvement of SNR have been achieved in a persistent SHB material (Pr^3 :Y2SiO5) compared to Tm:YAG. Also slow light with PSHB further reduces noise in Pr:YSO UOT that is caused by polarization leakage by performing time-domain filtering.

In this dissertation, two recent problems from tomographic imaging are studied, and results from numerical simulations with synthetic data are presented. The first part deals with ultrasound modulated optical tomography, a method for imaging interior optical properties of partially translucent media that combines optical contrast with ultrasound resolution. The primary application is the optical imaging of soft tissue, for which scattering and absorption rates contain important functional and structural information about the physiological state of tissue cells. We developed a mathematical model based on the diffusion approximation for photon propagation in highly scattering media. Simple reconstruction schemes for recovering optical absorption rates from boundary measurements with focused ultrasound are presented. We show numerical reconstructions from synthetic data generated for mathematical absorption phantoms. The results indicate that high resolution imaging with quantitatively correct values of absorption is possible. Synthetic focusing techniques are suggested that allow reconstruction from measurements with certain types of non-focused ultrasound signals. A preliminary stability analysis for a linearized model is given that provides an initial explanation for the observed stability of reconstruction. In the second part, backprojection schemes are proposed for the detection of small amounts of highly enriched nuclear material inside 3D volumes. These schemes rely on the geometrically singular structure that small radioactive sources represent, compared to natural background radiation. The details of the detection problem are explained, and two types of measurements, collimated and Compton-type measurements, are discussed. Computationally, we implemented backprojection by counting the number of particle trajectories intersecting each voxel of a regular rectangular grid covering the domain of detection. For collimated measurements, we derived confidence estimates indicating when voxel trajectory counts are deviating significantly from what is expected from background radiation. Monte Carlo simulations of random background radiation confirm the estimated confidence values. Numerical results for backprojection applied to synthetic measurements are shown that indicate that small sources can be detected for signal-to-noise ratios as low as 0.1%.

Fluorescence-enhanced optical imaging using near-infrared (NIR) light developed for in-vivo molecular targeting and reporting of cancer provides promising opportunities for diagnostic imaging. However, prior to the administration of unproven contrast agents, the benefits of fluorescence-enhanced optical imaging must be assessed in feasibility phantom studies. A novel intensified charge-coupled device (ICCD) imaging system has been developed to perform 3-D fluorescence tomographic imaging in the frequency-domain using near-infrared contrast agents. This study is unique since it (i) employs a large tissue-mimicking phantom (~1087 cc), which is shaped and sized to resemble a female breast and part of the extended chest wall region, and (ii) enables rapid data acquisition in the frequency-domain by using a gain-modulated ICCD camera. Diagnostic 3-D fluorescence-enhanced optical tomography is demonstrated using 0.5-1 cc single and multiple targets contrasted from their surrounding by ??M concentrations of Indocyanine green (ICG) in the breast-shaped phantom (10 cm diameter), under varying conditions of target-to-background absorption contrast ratios (1:0 and 100:1) and target depths (up to 3 cm deep). Boundary surface fluorescence measurements of referenced amplitude and phase shift were used along with the coupled diffusion equation of light propagation in order to perform 3-D image reconstructions using the approximate extended Kalman filter (AEKF) algorithm, and hence differentiate the target from the background based on fluorescent optical contrast. Detection of single and multiple targets is demonstrated under various conditions of target depths (up to 2 cm deep), absorption optical contrast ratio (1:0 and 100:1), target volumes (0.5-1 cc), and multiple targets (up to three 0.5 cc targets). The feasibility of 3-D image reconstructions from simultaneous multiple point excitation sources are presented. Preliminary lifetime imaging studies with 1:2 and 2:1 optical contrast in fluorescence lifetime of the contrast agents is also demonstrated. The specificity of the optical imager is further assessed from homogeneous phantom studies containing no fluorescently contrasted targets. While nuclear imaging currently provides clinical diagnostic opportunities using radioactive tracers, molecular targeting of tumors using non-ionizing NIR contrast agents tomographically imaged using the frequency-domain ICCD imaging system could possibly become a new method of diagnostic imaging.