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The recovery of the initial pressure rise distribution tends to be an ill-posed problem in the presence of noise and when limited independent data is available, necessitating regularization. The standard regularization schemes include Tikhonov, l1 -norm, and total-variation. These regularization schemes weigh the singular values equally irrespective of the noise level present in the data. This work introduces a fractional framework to weigh the singular values with respect to a fractional power. This fractional framework was implemented for Tikhonov, l1-norm, and total-variation regularization schemes. The fractional framework outperformed the standard regularization schemes by 54% in terms of observed contrast/signal-to-noise-ratio.

CT and MR perfusion weighted imaging (PWI) enable quantification of perfusion parameters in stroke studies. These parameters are calculated from the residual impulse response function (IRF) based on a physiological model for tissue perfusion. The standard approach for estimating the IRF is deconvolution using oscillatory-limited singular value decomposition (oSVD) 1 or Frequency Domain Deconvolution (FDD). 2 FDD is widely recognized as the fastest approach currently available for deconvolution of CT Perfusion/MR PWI. 2 In this work, three faster methods are proposed. The first is a direct (model based) crude approximation to the final perfusion quantities (Blood flow, Blood volume, Mean Transit Time and Delay) using the Welch-Satterthwaite approximation for gamma fitted concentration time curves (CTC). The second method is a fast accurate deconvolution method, we call Analytical Fourier Filtering (AFF). The third is another fast accurate deconvolution technique using Showalter's method, we call Analytical Showalter's Spectral Filtering (ASSF). Through systematic evaluation on phantom and clinical data, the proposed methods are shown to be computationally more than twice as fast as FDD. The two deconvolution based methods, AFF and ASSF, are also shown to be quantitatively accurate compared to FDD and oSVD.

In this report, we present a Born-ratio type of data normalization for reconstruction of initial acoustic pressure distribution in photoacoustic tomography (PAT). The normalized Born-ratio type of data is obtained as a ratio of photoacoustic pressure obtained with tissue sample in a coupling medium to the one obtained using purely coupling medium. It is shown that this type of data normalization improves the quantitation (intrinsic contrast) of the reconstructed images in comparison to the traditional techniques (unnormalized) that are currently available in PAT. Studies are carried out using various tissue samples. The robustness of the proposed method is studied at various noise levels added to the collected data. The improvement in quantitation can enable accurate estimation of pathophysiological parameter (optical absorption coefficient, μa) of tissue sample under investigation leading to better sensitivity in PAT.

Two techniques to regularize the diffuse optical tomography inverse problem were compared for a variety of simulated test domains. One method repeats the single-step Tikhonov approach until a stopping criteria is reached, regularizing the inverse problem by scaling the maximum of the diagonal of the inversion matrix with a factor held constant throughout the iterative reconstruction. The second method, a modified Levenberg-Marquardt formulation, uses an identical implementation but reduces the factor at each iteration. Four test geometries of increasing complexity were used to test the performance of the two techniques under a variety of conditions including varying amounts of data noise, different initial parameter estimates, and different initial values of the regularization factor. It was found that for most cases tested, holding the scaling factor constant provided images that were more robust to both data noise and initial homogeneous parameter estimates. However, the results for a complex test domain that most resembled realistic tissue geometries were less conclusive.

Cramer-Rao Bounds (CRB) for the expected variance in the parameter space were examined for Diffuse Optical Tomography (DOT), to define the lower bound (CRLB) of an ideal system. The results show that the relative standard deviation in the optical parameter estimate follows an inverse quadratic function with respect to signal to noise ratio (SNR). The CRLB was estimated for three methods of including spatial constraints. The CRLB estimate decreased by a factor of 10 when parameter reduction using spatial constraints (hard-priors) was enforced whereas, inclusion of spatial-priors in the regularization matrix (soft-priors) decreased the CRLB estimate only by a factor of 4. The maximum reduction in variance from the use of spatial-priors, occurred in the background of the imaging domain as opposed to localized target regions. As expected, the variance in the recovered properties increased as the number of parameters to be estimated increased. Additionally, increasing SNR beyond a certain point did not influence the outcome of the optical property estimation when prior information was available.

Recent interest in the use of dual modality imaging in the field of optical Near Infrared (NIR) Tomography has increased, specifically with use of structural information, from for example, MRI. Although MRI images provide high resolution structural information about tissue, they lack the contrast and functional information needed to investigate physiology, whereas NIR data has been established as a high contrast imaging modality, but one which suffers from low resolution. To this effect, the use of dual modality data has been shown to increase the qualitative and quantitative accuracy of clinical information that can be obtained from tissue. Results so far have indicated that providing accurate apriori structural information is available, such dual modality imaging techniques can be used for the detection and characterization of breast cancer in-vivo, as well as the investigation of brain function and physiology in both human and small animal studies. Although there has been much interest and research into the best suitable and robust use of a-priori structural information within the reconstruction of optical properties of tissue, little work has been done into the investigation of how much accuracy is needed from the structural MRI images in order to obtain the most clinically reliable information. In this paper, we will present and demonstrate the two most common application of a-priori information into image reconstruction, namely soft and hard priori. The effect of inaccuracies of the a-priori structural information within the reconstructed NIR images are presented showing that providing that the error of the a-priori information is within 20% in terms of size and location, adequate NIR images can be reconstructed.

Manipulation of Interstitial Fluid Pressure (IFP) has clinical potential when used in conjunction with near infrared spectroscopy for detection and characterization of breast cancer. IFP is a function of blood chemistry, vessel microanatomy, mechanical properties of the tissue, tissue geometry, and external force. IFP has been demonstrated higher in tumors than normal tissue, and it has been suggested that increased IFP can lead to changes in near infrared absorbing and scattering coefficients. While it is known that external forces can increase IFP, the relationship of force to IFP in a viscoelastic, hyperelastic solid such as tissue is complex. Fluid pressure measurements were taken in gelatin phantoms of equivalent elastic modulus to adipose and glandular tissues of the breast using a WaveMap pressure transducer. 3D pressure maps were obtained for the volumes of the phantoms with an externally applied force of 10mmHg, demonstrating the contribution of shear stress, non-linear mechanical properties, and tissue geometry. Linear elastic computational models were formulated for breast tissue with and without an inclusion of tumor-like mechanical properties. Comparison of experimental and computational model data indicates that light external pressure can lead to heterogeneous IFP distribution within tissues and increased IFP gradients around tumor-like inclusions.