Numerical modelling and image reconstruction in diffuse optical tomography

Abstract

The development of diffuse optical tomography as a functional imaging modality has relied largely on the use of model-based image reconstruction. The recovery of optical parameters from boundary measurements of light propagation within tissue is inherently a difficult one, because the problem is nonlinear, ill-posed and ill-conditioned. Additionally, although the measured near-infrared signals of light transmission through tissue provide high imaging contrast, the reconstructed images suffer from poor spatial resolution due to the diffuse propagation of light in biological tissue. The application of model-based image reconstruction is reviewed in this paper, together with a numerical modelling approach to light propagation in tissue as well as generalized image reconstruction using boundary data. A comprehensive review and details of the basis for using spatial and structural prior information are also discussed, whereby the use of spectral and dual-modality systems can improve contrast and spatial resolution.

Figure 1

Example of a mesh used for the reconstruction of images from measured clinical data. Information about data collection geometry was used for mesh generation. (a) Conical-shaped mesh used for the calculation of the Jacobian. (b) Conical-shaped mesh used for the reconstruction basis.

Figure 2

Reconstructed images of (a) absorption and (b) reduced scattering at each wavelength from measured volunteer data: (i) 761 nm, (ii) 785 nm, (iii) 808 nm, (iv) 826 nm. (c) Calculated maps of blood content: (i) Hb, (ii) HbO₂, (iii) Hb_T, (iv) S _tO₂. Each slice represents a plane through the mesh, from the bottom near the nipple to the top near the chest. The images are coronal views of the cross section through the breast at the 10th iteration at the wavelengths indicated.

Figure 3

Comparison of images obtained by applying the spectrally constrained direct chromophore reconstruction and the conventional technique of separate wavelength optical properties recovery on measurements from a gelatin phantom with a 25 mm inclusion. The gelatin phantom contained whole blood and TiO₂ for scattering and the inclusion was filled with 4% pig blood and 0.75% Intralipid in buffered saline. (a) The expected images are shown for (i) [Hb_T] (μM), (ii) oxygen saturation S _tO₂(%), (iii) water H₂O(%), (iv) scattering amplitude a and (v) scattering power b, along with (b) conventional technique images and (c) spectral method images.

Figure 4

Breast tissue property images for a healthy female volunteer estimated using four different reconstruction methods. (a) The T1 axial and oblique coronal MRI of this patient defined the spatial constraints, which relate to (b) the internal distribution of adipose and glandular tissues (two-dimensional FEM mesh defines imaging geometry and spatial prior). In (c)(i), only the outer boundary of the imaging domain and the location of the optical fibre measurement sites are specified (no priors). (ii) A spatially constrained algorithm was used (spatial priors). (iii) Spectral constraints were applied and chromophore concentrations and scattering parameters were reconstructed directly (spectral priors). (iv) Both spatial and spectral constraints were combined (spectral and spatial priors).