The 2D images reconstructed using single wavelength data are shown in , together with the original target distributions. The results show that good separation between the absorption and reduced scatter is achieved; however, the reconstructed values show an over estimation of the absorption by 10% and the reduced scatter by 5%. The ability to separate both the optical absorption and reduced scatter is important and is known to be non-unique when intensity only boundary data are applied [63
]. Specifically, it has been shown that the use of absorption and reduced scatter-based imaging can provide useful pathophysiological information regarding the breast tissue being imaged [25
]; therefore, accurate quantitative separation of these two parameters is crucial for adequate clinical application. It should also be noted that given a set of boundary data that comprises of both intensity and phase of the measurement, it is imperative to incorporate the normalization of the Jacobian by the initial estimate of the optical properties, Equation (14)
For the case of using spectral data and reconstruction, , the best reconstructed image occurs for deoxy-hemoglobin while cross talk is evident in the reconstructed images of water and scatter power. The concentration of the recovered value for oxy- and deoxy-hemoglobin is within 0.002 mM of the target, and the reconstructed concentration of the water content is accurate to within 17%. It has been previously shown that there exists a set of optimum wavelengths that should in theory yield the best data for the separation of chromophores and scattering properties [10
]; however, the choice of wavelengths in this example has been limited to those available within a clinical imaging system developed at Dartmouth [64
]. The superior reconstruction of deoxy-hemoglobin is in part due to the large simulated contrast, but these levels are typical of values observed clinically [25
]. This method of spectral imaging has been extensively tested in phantom studies and shown to produce superior results compared with those generated from the combination of multiple single wavelength image reconstructions [9
The 3D images reconstructed from the breast geometry represent a realistic clinical case, in which different layers of adipose and glandular tissue have been considered together with a tumor region, . In the first instance where a single 785 nm wavelength has been considered, the region of interest (the tumor) has been successfully recovered, , but with lower reconstructed values of both absorption and reduced scatter. It is evident from these images, that although the information about the adipose and glandular layer is relatively poor, the recovered location of the tumor is correct even if its optical properties are not quantitatively accurate. The largest image artifacts appear at the external tissue boundaries, specifically at the locations of optical fiber contact.
The quantitative accuracy of the 3D images, as compared with 2D results has been considered previously [4
]. The challenges of quantitative 3D imaging are many folds and include partial volume effects, the increase in the number of unknowns as well as the 3D of photon pathways and associated sensitivity function. Several techniques have been proposed to improve the quantitative accuracy of 3D imaging such as, the use of spatial priors [22
In the spectral reconstruction case, the tumor region has been successfully located in all cases with excellent recovery of the target values, , except for deoxy-hemoglobin, which was recovered with less than 50% of the expected level. Again, although detailed information about the adipose and glandular layers are less evident, the reconstructed concentration of oxy-hemoglobin of the tumor is accurate to within 0.001 mM and the water concentration is accurate to within 15%. The recovered values for scatter amplitude and scatter power are each accurate to within 10%.
It has been previously demonstrated that small errors within the absorption and scatter images at each specific wavelength, which are then combined to create chromophore and scatter distributions, lead to large errors in recovered chromophore values [47
]. Therefore, although single wavelength images may provide a good qualitative indication, the application of spectral imaging provides the quantitative accuracy required for clinical applications.
It is also worth noting that the modeled tumor does not lie exactly within the imaging plane, which is the plane where the optical fibers were applied. This situation is realistic, because it is likely that breast tissue undergoes internal deformation due to its varying mechanical properties of soft tissue, upon the application of external pressures via the optical fibers.