Optical diffusion imaging using a direct inversion method

Diffuse optical tomography in the presence of a chest wall

Diffuse optical tomography (DOT) has been employed to derive spatial maps of physiologically important chromophores in the human breast, but the fidelity of these images is often compromised by boundary effects such as those due to the chest wall. We explore the image quality in fast, data-intensive analytic and algebraic linear DOT reconstructions of phantoms with subcentimeter target features and large absorptive regions mimicking the chest wall. Experiments demonstrate that the chest wall phantom can introduce severe image artifacts. We then show how these artifacts can be mitigated by exclusion of data affected by the chest wall. We also introduce and demonstrate a linear algebraic reconstruction method well suited for very large data sets in the presence of a chest wall.

Optical imaging modalities for biomedical applications

Optical photographic imaging is a well known imaging method that has been successfully translated into biomedical applications such as microscopy and endoscopy. Although several advanced medical imaging modalities are used today to acquire anatomical, physiological, metabolic, and functional information from the human body, optical imaging modalities including optical coherence tomography, confocal microscopy, multiphoton microscopy, multispectral endoscopy, and diffuse reflectance imaging have recently emerged with significant potential for non-invasive, portable, and cost-effective imaging for biomedical applications spanning tissue, cellular, and molecular levels. This paper reviews methods for modeling the propagation of light photons in a biological medium, as well as optical imaging from organ to cellular levels using visible and near-infrared wavelengths for biomedical and clinical applications.

Multiple projection optical diffusion tomography with plane wave illumination

We describe a new data collection scheme for optical diffusion tomography in which plane wave illumination is combined with multiple projections in the slab imaging geometry. Multiple projection measurements are performed by rotating the slab around the sample. The advantage of the proposed method is that the measured data are more compatible with the dynamic range of most commonly used detectors. At the same time, multiple projections improve image quality by mutually interchanging the depth and transverse directions, and the scanned (detection) and integrated (illumination) surfaces. Inversion methods are derived for image reconstructions with extremely large data sets. Numerical simulations are performed for fixed and rotated slabs.

Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging

Three-dimensional diffuse optical tomography (DOT) of breast requires large data sets for even modest resolution (1 cm). We present a hybrid DOT system that combines a limited number of frequency domain (FD) measurements with a large set of continuous wave (cw) measurements. The FD measurements are used to quantitatively determine tissue averaged absorption and scattering coefficients. The larger cw data sets (10(5) measurements) collected with a lens coupled CCD, permit 3D DOT reconstructions of a 1-liter tissue volume. To address the computational complexity of large data sets and 3D volumes we employ finite difference based reconstructions computed in parallel. Tissue phantom measurements evaluate imaging performance. The tests include the following: point spread function measures of resolution, characterization of the size and contrast of single objects, field of view measurements and spectral characterization of constituent concentrations. We also report in vivo measurements. Average tissue optical properties of a healthy breast are used to deduce oxy- and deoxy-hemoglobin concentrations. Differential imaging with a tumor simulating target adhered to the surface of a healthy breast evaluates the influence of physiologic fluctuations on image noise. This tomography system provides robust, quantitative, full 3D image reconstructions with the advantages of high data throughput, single detector-tissue coupling path, and large (1L) imaging domains. In addition, we find that point spread function measurements provide a useful and comprehensive representation of system performance.

Inverse scattering with diffusing waves

We consider the problem of imaging the optical properties of a highly scattering medium probed by diffuse light. An analytic solution to this problem is derived from the singular value decomposition of the forward-scattering operator, which leads to explicit inversion formulas for the inverse scattering problem with diffusing waves. Computer simulations are used to illustrate these results in model systems.

Kirchhoff approximation for diffusive waves

Quantitative measurements of diffuse media, in spectroscopic or imaging mode, rely on the generation of appropriate forward solutions, independently of the inversion scheme employed. For complex boundaries, the use of numerical methods is generally preferred due to implementation simplicity, but usually results in great computational needs, especially in three dimensions. Analytical expressions are available, but are limited to simple geometries such as a diffusive slab, a sphere or a cylinder. An analytical approximation, the Kirchhoff approximation, also called the tangent-plane method is presented for the case of diffuse light. Using this approximation, analytical solutions of the diffusion equation for arbitrary boundaries and volumes can be derived. Also, computation time is minimized since no matrix inversion is involved. The accuracy of this approximation is evaluated on comparison with results from a rigorous numerical technique calculated for an arbitrary geometry. Performance of the approximation as a function of the optical properties and the size of the medium is examined and it is demonstrated that the computation time of the direct scattering model is reduced at least by two orders of magnitude.

Inverse scattering for the diffusion equation with general boundary conditions

We consider the inverse scattering problem for the diffusion equation. A solution to this problem in the form of an explicit inversion formula is derived. Computer simulations are used illustrate our approach in model systems.

Inverse problem in optical diffusion tomography. I. Fourier-Laplace inversion formulas

We consider the inverse problem of reconstructing the absorption and diffusion coefficients of an inhomogeneous highly scattering medium probed by diffuse light. Inversion formulas based on the Fourier-Laplace transform are used to establish the existence and uniqueness of solutions to this problem in planar, cylindrical, and spherical geometries.

Developments toward diagnostic breast cancer imaging using near-infrared optical measurements and fluorescent contrast agents

The use of near-infrared (NIR) light to interrogate deep tissues has enormous potential for molecular-based imaging when coupled with NIR excitable dyes. More than a decade has now passed since the initial proposals for NIR optical tomography for breast cancer screening using time-dependent measurements of light propagation in the breast. Much accomplishment in the development of optical mammography has been demonstrated, most recently in the application of time-domain, frequency-domain, and continuous-wave measurements that depend on endogenous contrast owing to angiogenesis and increased hemoglobin absorbance for contrast. Although exciting and promising, the necessity of angiogenesis-mediated absorption contrast for diagnostic optical mammography minimizes the potential for using NIR techniques to assess sentinel lymph node staging, metastatic spread, and multifocality of breast disease, among other applications. In this review, we summarize the progress made in the development of optical mammography, and focus on the emerging work underway in the use of diagnostic contrast agents for the molecular-based, diagnostic imaging of breast.

Optical tomography in the presence of void regions

There is a growing interest in the use of near-infrared spectroscopy for the noninvasive determination of the oxygenation level within biological tissue. Stemming from this application, there has been further research in the use of this technique for obtaining tomographic images of the neonatal head, with the view of determining the levels of oxygenated and deoxygenated blood within the brain. Owing to computational complexity, methods used for numerical modeling of photon transfer within tissue have usually been limited to the diffusion approximation of the Boltzmann transport equation. The diffusion approximation, however, is not valid in regions of low scatter, such as the cerebrospinal fluid. Methods have been proposed for dealing with nonscattering regions within diffusing materials through the use of a radiosity-diffusion model. Currently, this new model assumes prior knowledge of the void region location; therefore it is instructive to examine the errors introduced in applying a simple diffusion-based reconstruction scheme in cases in which there exists a nonscattering region. We present reconstructed images of objects that contain a nonscattering region within a diffusive material. Here the forward data is calculated with the radiosity-diffusion model, and the inverse problem is solved with either the radiosity-diffusion model or the diffusion-only model. The reconstructed images show that even in the presence of only a thin nonscattering layer, a diffusion-only reconstruction will fail. When a radiosity-diffusion model is used for image reconstruction, together with a priori information about the position of the nonscattering region, the quality of the reconstructed image is considerably improved. The accuracy of the reconstructed images depends largely on the position of the anomaly with respect to the nonscattering region as well as the thickness of the nonscattering region.

Boundary conditions for light propagation in diffusive media with nonscattering regions

The diffusion approximation proves to be valid for light propagation in highly scattering media, but it breaks down in the presence of nonscattering regions. We present a compact expression of the boundary conditions for diffusive media with nonscattering regions, taking into account small-index mismatch. Results from an integral method based on the extinction theorem boundary condition are contrasted with both Monte Carlo and finite-element-method simulations, and a study of its limit of validity is presented. These procedures are illustrated by considering the case of the cerebro-spinal fluid in the brain, for which we demonstrate that for practical situations in light diffusion, these boundary conditions yield accurate results.

Near-field diffraction tomography with diffuse photon density waves

An angular spectrum algorithm is presented for fast, near-field diffraction tomographic imaging with diffuse photon density waves in highly scattering media. A general relation in K space is derived that connects the spatial variations of the optical properties of heterogeneities to the spatial spectra of the measured scattered diffuse photon density waves. The theory is verified experimentally for situations when boundary effects can be neglected. We further describe how to reconstruct absorption and scattering properties simultaneously, and how to incorporate boundary conditions into this angular spectrum algorithm for a turbid medium of finite size (e.g., the slab medium). Limitations and potential improvements of the near-field diffraction tomography are also discussed.

Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement

We present quantitative optical images of human breast in vivo. The images were obtained by using near-infrared diffuse optical tomography (DOT) after the administration of indocyanine green (ICG) for contrast enhancement. The optical examination was performed concurrently with a magnetic resonance imaging (MRI) exam on patients scheduled for excisional biopsy or surgery so that accurate image coregistration and histopathological information of the suspicious lesions was available. The ICG-enhanced optical images coregistered accurately with Gadolinium-enhanced magnetic resonance images validating the ability of DOT to image breast tissue. In contrast to simple transillumination, we found that DOT provides for localization and quantification of exogenous tissue chromophore concentrations. Additionally our use of ICG, an albumin bound absorbing dye in plasma, demonstrates the potential to differentiate disease based on the quantified enhancement of suspicious lesions.