We present a review of methods for the forward and inverse problems in optical tomography. We limit ourselves to the highly scattering case found in applications in medical imaging, and to the problem of absorption and scattering reconstruction. We discuss the derivation of the diffusion approximation and other simplifications of the full transport problem. We develop sensitivity relations in both the continuous and discrete case with special concentration on the use of the finite element method. A classification of algorithms is presented, and some suggestions for open problems to be addressed in future research are made.

https://iopscience.iop.org/article/10.1088/0266-5611/15/2/022/pdf

Optical tomography in medical imaging

When a picosecond light pulse is incident on biological tissue, the temporal characteristics of the light backscattered from, or transmitted through, the sample carry information about the optical absorption and scattering coefficients of the tissue. We develop a simple model, based on the diffusion approximation to radiative transfer theory, which yields analytic expressions for the pulse shape in terms of the interaction coefficients of a homogeneous slab. The model predictions are in good agreement with the results of preliminary in vivo experiments and Monte Carlo simulations.

Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties.

The interaction of light within tissue has been used to recognize disease since the mid-1800s. The recent developments of small light sources, detectors, and fiber optic probes provide opportunities to quantitatively measure these interactions, which yield information for diagnosis at the biochemical, structural, or (patho)physiological level within intact tissues. However, because of the strong scattering properties of tissues, the reemitted optical signal is often influenced by changes in biochemistry (as detected by these spectroscopic approaches) and by physiological and pathophysiological changes in tissue scattering. One challenge of biomedical optics is to uncouple the signals influenced by biochemistry, which themselves provide specificity for identifying diseased states, from those influenced by tissue scattering, which are typically unspecific to a pathology. In this review, we describe optical interactions pursued for biomedical applications (fluorescence, fluorescence lifetime, phosphorescence, and Raman from cells, cultures, and tissues) and then provide a descriptive framework for light interaction based upon tissue absorption and scattering properties. Finally, we review important endogenous and exogenous biological chromophores and describe current work to employ these signals for detection and diagnosis of disease.

Quantitative optical spectroscopy for tissue diagnosis

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 is developed, and the basic elements of diffuse optical tomography are outlined. We also discuss diffuse correlation spectroscopy, 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.

/pdf/diffuse-optics-for-tissue-monitoring-and-tomography-curjv2s4p6.pdf

Diffuse optics for tissue monitoring and tomography

This paper introduces a simple model for subsurface light transport in translucent materials. The model enables efficient simulation of effects that BRDF models cannot capture, such as color bleeding within materials and diffusion of light across shadow boundaries. The technique is efficient even for anisotropic, highly scattering media that are expensive to simulate using existing methods. The model combines an exact solution for single scattering with a dipole point source diffusion approximation for multiple scattering. We also have designed a new, rapid image-based measurement technique for determining the optical properties of translucent materials. We validate the model by comparing predicted and measured values and show how the technique can be used to recover the optical properties of a variety of materials, including milk, marble, and skin. Finally, we describe sampling techniques that allow the model to be used within a conventional ray tracer.

/pdf/a-practical-model-for-subsurface-light-transport-53mwxbibui.pdf

A practical model for subsurface light transport

To allow the determination of scattering and absorption parameters of a turbid material from reflection measurements the relation of these parameters to the reflection has been described by two theoretical approaches. One approach is based on the diffusion theory which has been extended to include anisotropic scattering. This results in a reflection formula in which the scattering and absorption are described by one parameter each. As a second more general approach a Monte Carlo model is applied. Comparison of the results indicates the range of values of the scattering and absorption parameters where the computationally fast diffusion approach is applicable.

Scattering and absorption of turbid materials determined from reflection measurements. 1: theory.

A new experimental method has been developed to determine the scattering and absorption characteristics of a turbid material. Existing methods usually require transmission and reflection measurements carried out on a thin slab of the material under study; this method is based on reflection measurements carried out on bulk material. This will be of great advantage in many applications. This paper describes the measuring system and indicates the area of application of the method. Calibration measurements have been carried out to substantiate the approach.

Scattering and absorption of turbid materials determined from reflection measurements. 2: measuring method and calibration.

Knowledge of the optical properties of tooth enamel and an understanding of the origin of these properties are necessary for the development of new optical methods for caries diagnosis and the measurement of tooth color. We measured the scattering intensity functions for HeNe-laser light of 80- to 100- micrometers-thick human dental enamel slabs. The asymmetry factors were calculated to be g = 0.68 at 633 nm. By measuring the collimated beam attenuation, we determined the scattering coefficient to be s = 6.6mm(-1). From Fraunhofer diffraction patterns, obtained from transmission of the laser beam, we calculated the periodicity of the prismatic structure as 5.4 micrometers. We present a model containing scattering by crystals and by prisms. It shows that the prisms are the most important scatterers but that the crystals are responsible for the back-scattering.

/pdf/hene-laser-light-scattering-by-human-dental-enamel-6gyh5nvhyd.pdf

HeNe-Laser Light Scattering by Human Dental Enamel

During demineralization and remineralization of dental enamel its structure changes resulting in a change of the absorption and scattering coefficients of the enamel. By measuring these coefficients during demineralization and remineralization these processes can be monitored in a non-destructive way. For this purpose an experimental arrangement was made: a fibre illuminates a spot on the sample with monochromatic light with a wave-length between 400 nm and 700 nm; a photomultiplier measures the luminance of the light back-scattered by the sample as a function of the distance from the measuring snot to the spot of illumination. In a Monte Carlo-model this luminance is simulated using the same geometry given the scattering and absorption coefficients in a sample. Then the scattering and absorption coefficients in the sample are determined by selecting the theoretical curve fitting the experimental one. Scattering coefficients below 10 mm-1 and absorption coefficients obtained with this method on calibration samples correspond well with those obtained with another method. Scattering coefficients above 10 mm-1 (paper samples) were measured ton low. This perhaps is caused by the anisotropic structure of paper sheets. The method is very suitable to measure the scattering and absorption coefficients of bulk materials.© (1981) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

R. A. J. Groenhuis

Papers

Scattering and absorption of turbid materials determined from reflection measurements. 1: theory.

Scattering and absorption of turbid materials determined from reflection measurements. 2: measuring method and calibration.

HeNe-Laser Light Scattering by Human Dental Enamel

Nondestructive Method For Measuring The Scattering Coefficient Of Bulk Material