This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. Conventional tomographic approaches for optical imaging are best suited for data sets that contain measurements from a large number of source-detector pairs but few wavelengths (i.e., spatially 'rich,'but spectrally 'sparse'). Due to technical complexities, quantitative broadband spectroscopic technologies are difficult to implement in traditional imaging configurations. As a result, these conventional tomography approaches are not easily implemented with broadband spectroscopy techniques that use only a limited number of source-detector pairs. Our effort in 'sparse tomography,'pr 'parametric reconstruction,'is geared towards data sets that are spectrally 'rich'but spatially 'sparse.' There is evidence that a relatively simple tomographic approach may be a good compromise between the demand for handheld-acquired broadband spectra and the need for depth-sectioned imaging in cancer applications. Based on our analysis of breast clinical data with a forward finite element modeling procedure, we believe the spatial extent of a breast lesion's optical properties is much larger than the structural confines of the tumor as measured by conventional radiological methods (Figure XXX). The top-left panel represents the traditional view of a tumor: a perturbation in optical properties neatly segmented between background (subscript 'bkg') and heterogeneity (subscript 'het'). In a typical Diffuse Optical Spectroscopy measurement, the source (S) and detector (D) are scanned in tandem across a tissue. The results of an actual Diffuse Optical spectroscopy measurement are provided (circles) in comparison with a forward model simulation using a radiative transport model of the SDA provided by the Finite Element Method (squares). We discovered that there was no physical set of simulated optical properties that could replicate the clinical measurement. On the right side of Figure XXX, we present a different view of the tumor: a gradient in optical properties. By varying the properties of the optical property distribution, the clinical and simulated data share a much closer agreement (bottom-right). In a pilot study of 10 patients, we further found that the best agreement between the modeling results and the clinical data is achieved when the spatial extent of the optical property distribution is much larger than radiological size estimates. This is especially true for malignant lesions. The larger spatial extent of the lesion relaxes the number of source-detector pairs necessary to visualize the target. Moreover, by constraining the spatial distribution of optical properties to those given by a Gaussian (or other) distribution also reduces the number of reconstructed variables. Simple reconstructions using such an approach, which we refer to as """"""""sparse tomography,"""""""" also eliminates the need for regularization parameters. Our proposed sparse tomography procedure can be used with any imaging data, although it may work best with systems that have limited imaging capabilities. We will first use our DOS/I instrument to take scans of breast lesions. The data will be processed within the VTS to recover the optical properties that provide a least squares fits to semi-infinite homogenous diffusion models. Next we invoke a Finite Element Model diffusion-based model of a breast lesion with a Gaussian spatial distribution of a perturbation in optical absorption and scattering properties relative to the background optical properties. Simulated data will then be generated with this model using finite element methods. Next the simulated data will be processed with the same least-squares fit to the same semi-infinite homogenous diffusion model. Finally, we will compare our clinical observation with our simulated result, in a chi-squared sense. This process will be iterated until the chi-squared is minimized. We realize that this procedure is in effect """"""""blurring"""""""" the location of the target. However we do not believe that this description of a tumor is unphysical because it is well known that the margins of tumors can be quite extensive compared to the radiologically-determined size.
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