Near-field diffraction tomography with diffuse photon density waves

L1-norm based nonlinear reconstruction improves quantitative accuracy of spectral diffuse optical tomography

Spectrally constrained diffuse optical tomography (SCDOT) is known to improve reconstruction in diffuse optical imaging; constraining the reconstruction by coupling the optical properties across multiple wavelengths suppresses artefacts in the resulting reconstructed images. In other work, L1-norm regularization has been shown to improve certain types of image reconstruction problems as its sparsity-promoting properties render it robust against noise and enable the preservation of edges in images, but because the L1-norm is non-differentiable, it is not always simple to implement. In this work, we show how to incorporate L1 regularization into SCDOT. Three popular algorithms for L1 regularization are assessed for application in SCDOT: iteratively reweighted least square algorithm (IRLS), alternating directional method of multipliers (ADMM), and fast iterative shrinkage-thresholding algorithm (FISTA). We introduce an objective procedure for determining the regularization parameter in these algorithms and compare their performance in simulated experiments, and in real data acquired from a tissue phantom. Our results show that L1 regularization consistently outperforms Tikhonov regularization in this application, particularly in the presence of noise.

Near-Infrared Fluorescence-Enhanced Optical Tomography

Fluorescence-enhanced optical imaging using near-infrared (NIR) light developed for in vivo molecular targeting and reporting of cancer provides promising opportunities for diagnostic imaging. The current state of the art of NIR fluorescence-enhanced optical tomography is reviewed in the context of the principle of fluorescence, the different measurement schemes employed, and the mathematical tools established to tomographically reconstruct the fluorescence optical properties in various tissue domains. Finally, we discuss the recent advances in forward modeling and distributed memory parallel computation to provide robust, accurate, and fast fluorescence-enhanced optical tomography.

Diffuse Optics for Tissue Monitoring and Tomography

This review describes the diffusion model for light transport in tissues and the medical applications of diffuse light. Diffuse optics is particularly useful for measurement of tissue hemodynamics, wherein quantitative assessment of oxy- and deoxy-hemoglobin concentrations and blood flow are desired. The theoretical basis for near-infrared or diffuse optical spectroscopy (NIRS or DOS, respectively) is developed, and the basic elements of diffuse optical tomography (DOT) are outlined. We also discuss diffuse correlation spectroscopy (DCS), a technique whereby temporal correlation functions of diffusing light are transported through tissue and are used to measure blood flow. Essential instrumentation is described, and representative brain and breast functional imaging and monitoring results illustrate the workings of these new tissue diagnostics.

Quantitation and mapping of tissue optical properties using modulated imaging

We describe the development of a rapid, noncontact imaging method, modulated imaging (MI), for quantitative, wide-field characterization of optical absorption and scattering properties of turbid media. MI utilizes principles of frequency-domain sampling and model-based analysis of the spatial modulation transfer function (s-MTF). We present and compare analytic diffusion and probabilistic Monte Carlo models of diffuse reflectance in the spatial frequency domain. Next, we perform MI measurements on tissue-simulating phantoms exhibiting a wide range of l values (0.5 mm to 3 mm) and (micro(s) (')micro(a)) ratios (8 to 500), reporting an overall accuracy of approximately 6% and 3% in absorption and reduced scattering parameters, respectively. Sampling of only two spatial frequencies, achieved with only three camera images, is found to be sufficient for accurate determination of the optical properties. We then perform MI measurements in an in vivo tissue system, demonstrating spatial mapping of the absorption and scattering optical contrast in a human forearm and dynamic measurements of a forearm during venous occlusion. Last, metrics of spatial resolution are assessed through both simulations and measurements of spatially heterogeneous phantoms.

Theory and analysis of frequency-domain photoacoustic tomography

A new frequency-domain approach to photoacoustic tomography has recently been proposed, promising to overcome some of the shortcomings associated with the pulsed photoacoustic approach. This approach offers many of the benefits of pulsed photoacoustics but requires a different set of equations for modeling of the forward and inverse problems due to the longer time scales involved in the optical input signal. The theory of photoacoustic tomography with an optical input that is not necessarily a short pulse is considered in this paper. The full optical, thermal, and acoustic governing equations are derived. A transfer function approach is taken for the solution and analysis of this problem. The results and implications are compared with those of pulsed photoacoustics and traditional ultrasonic diffraction tomography. A Fourier diffraction theorem is also presented, which could be used as a basis for the development of tomographic imaging algorithms.

Evaluation of higher-order time-domain perturbation theory of photon diffusion on breast-equivalent phantoms and optical mammograms

Time-domain perturbation theory of photon diffusion up to third order was evaluated for its accuracy in deducing optical properties of breast tumors using simulated and physical phantoms and by analyzing 141 projection mammograms of 87 patients with histology-validated tumors that had been recorded by scanning time-domain optical mammography. The slightly compressed breast was modeled as (partially) homogeneous diffusely scattering infinite slab containing a scattering and absorbing spherical heterogeneity representing the tumor. Photon flux densities were calculated from densities of transmitted photons, assuming extended boundary conditions. Explicit formulas are provided for second-order changes in transmitted photon density due to the presence of absorbers or scatterers. The results on phantoms obtained by perturbation theory carried up to third order were compared with measured temporal point spread functions, with numerical finite-element method (FEM) simulations of transmitted photon flux density, with results obtained from the diffraction of diffuse photon density waves, and from Padé approximants. The breakdown of first-, second-, and third-order perturbation theory is discussed for absorbers and a general expression was derived for the convergence of the Born series in this case. Taking tumor optical properties derived by the diffraction model as reference we conclude that estimates of tumor absorption coefficients by perturbation theory agree with reference values within +/-25% in only 65% (first order), 66% (second order), and 77% (third order) of all mammograms analyzed. In the remaining cases tumor absorption is generally underestimated due to the breakdown of perturbation theory. On average the empirical Padé approximants yield tumor absorption coefficients similar to third-order perturbation theory, yet at noticeable lower computational efforts.

Reconstruction of optical properties of phantom and breast lesion in vivo from paraxial scanning data

We report on the reconstruction of absorption and reduced scattering coefficients of breast tissue in vivo of a patient with mastopathic disease. Distributions of times of flight of photons through the compressed breast were recorded by paraxial scanning. From data measured at four different source-detector offsets optical properties were reconstructed within the linear Rytov approximation by a fast inverse Fourier space method. Low-pass filtering in Fourier space was employed to remove excessive noise from high spatial frequency components and to reduce the computational efforts by a factor of 3, typically. The mammograms displaying reconstructed absorption and reduced scattering coefficients were compared with projection mammograms either obtained by time-window analysis of experimental data or based on average absorption and reduced scattering coefficients which were derived from measured temporal point spread functions within a simple homogeneous model. All inhomogeneities which were visible in the projection mammograms and which could be associated with specific breast tissue compartments could be correlated with inhomogeneities in the reconstructed absorption coefficient. In particular, the mastopathic disease was detected in the reconstructed absorption mammogram. In order to assess reliability of optical properties reconstructed from data obtained by paraxial scanning, corresponding phantom experiments and reconstructions of phantom optical properties were carried out. Because of the limited angular range sampled by the in vivo and phantom measurements, considerable blurring of the absorption coefficient occurs along the compression direction, compromising longitudinal resolution.

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.

Signal-to-noise-ratio expressions in optical diffusion tomography

Optical diffusion tomography is a technology that is employed to obtain images of the heterogeneous nature of turbid media by using optical radiation. Noise ultimately limits the achievable spatial resolution in these reconstructed images; therefore it is of interest to develop signal-to-noise-ratio expressions that relate spatial resolution in the images to the underlying system and material properties. In this study, Fourier-domain signal-to-noise-ratio expressions are derived for two types of optical diffusion tomography systems: those that use amplitude-modulated illumination sources and those that use continuous-wave illumination sources. The signal-to-noise-ratio expressions are compared for these two types of systems and are validated by laboratory data.

Propagation of single-cycle terahertz pulses in random media

We describe what are to our knowledge the first measurements of the propagation of coherent, single-cycle pulses of terahertz radiation in a scattering medium. By measuring the transmission as a function of the length L of the medium, we extract the scattering mean free path l(s)(omega) over a broad bandwidth. We observe variations in l(s) ranging over nearly 2 orders of magnitude and covering the entire thin sample regime from L/l(s)<<1 to L/l(s)~10 . We also observe scattering-induced dispersive effects, which can be attributed to the additional path traveled by photons scattered at small angles.

Validity of the diffusion approximation in bio-optical imaging

Accurate numerical simulations based on rigorous radiative transfer theory are used to assess the validity of the diffusion approximation that is frequently used in bio-optical imaging. These simulations show that the error is large for a non-index-matched boundary between air and tissue. This weakness of the diffusion approximation underscores the need to understand how diffusion theory can be used to extract accurate values of tissue optical properties. A validity criterion for the diffusion approximation is established on the basis of the single-scattering albedo a and the asymmetry factor g for a slab with index-matched boundaries.

Deconvolution-based spatial resolution in optical diffusion tomography

The role that deconvolution plays in the achievable spatial resolution in optical diffusion tomography is examined for the case of imaging an inhomogeneity in an otherwise homogeneous medium. It is shown that, in the measured data, it is the shape of the turbid medium modulation transfer function that determines the maximum spatial resolution. When the turbid medium transfer function is deconvolved from the measured data, it is the signal-to-noise ratio properties of the Fourier-transformed measured data that determine the maximum spatial resolution. It is shown that deconvolution-based methods can improve the spatial resolution in measured data up to a factor of 5 for realistic noise levels. These results are demonstrated with computer-simulated data.

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 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.