Technology - Principles of Optical Tomography

• Light Propagation in Tissue
• Principles of Image Reconstruction
• Optical Quantities
• Wavelength λ
• Absorption Coefficient μa
• Scattering Coefficient μs
• Diffusion coefficient D

Light Propagation in Tissue

In most medical imaging techniques, the main portion of the probing energy form (e.g., x-rays, gamma-rays, ultrasound waves) can be assumed to travel through biological tissue along straight paths.

The propagation of light in tissue, however, is more complex. The reason for this is that the light particles (photons) do not travel along a straight path as they do in a clear medium like air or glass but bounce of f of the many boundaries of tissue substructures on a cellular and sub-cellular level. This phenomenon of light scattering causes the photon propagation direction to change randomly.

In most biological tissues, photons are scattered many times even within relatively short distances (on the order of 10 times per cm) so that photon propagation is quickly randomized. This results in strong blurring of optical contrasts and is the reason that simple transillumination of tissue usually does not work well. The problem faced in diffuse optical tomography (DOT) is similar to the challenge of trying to see a spoon in a glass of milk; light is strongly scattered by the milk fat droplets, preventing clear view of the interior.

The difference between straight beam traveling and scattered (or diffuse) propagation is depicted above. In the case of a clear medium (left), collimated illumination causes a sharp shadow, also called a projection, of the inclusion. For a strongly scattering medium, as on the right side, this shadow is blurred because photons passing through any one region in the medium are randomly dispersed causing them to fall on many locations on the image screen. Because random reorientation occurs at all locations in the medium, the image formed at each point on the image plane contains information from every point in the medium.

Principles of Image Reconstruction

To many, on first take, image blurring caused by random scattering would seem to render hopeless any effort to recover internal features of the target. This can be accomplished, however, with refined measurement methods and image reconstruction techniques based on physical models of random light scatter. Detailed description of these methods can be found in the reference section. Here we present a more easily understood intuitive description.

Although the exact path of a multiply scattered photon cannot be known, the physics of light propagation in a turbid medium dictates which region it most likely has come through. Consider a source that launches photons into the medium at one point on the surface point and a detector located at a different point that measures the amount of photons exiting the medium at that location (see figure).

For each of those photons, the likelihood for having traveled through a certain tissue region can be graphed in a contour plot. Because of their shape, the areas enclosed by these isosurfaces have been dubbed "photon bananas". For a given source-detector pair, the detected photons are known to more likely have traveled through the central area of the banana shape (indicated in dark red) than through its outer portions (lighter shades of pink). The likelihood values over the entire cross-section of the medium add up to one because the measured photons must have come through the medium somewhere. Because photons are more likely to pass through the central regions of the "banana", the measurement is most sensitive to objects found in that area. For example, the measurement depicted in above figure would be more sensitive to an object in location 1 (inside the main light path) than in location 2 (outside the main light path). The exact shape of "photon bananas" depends on the optical properties of a medium and can be computed using physical models of light propagation. These computations result in a table - the weight matrix - that shows the influence of each point in the medium on a measurement for a given source and detector location.

Using the knowledge about photon travel, an image of the interior of a dense scattering medium can be generated when a sufficient number of optical measurements from different views are obtained (see figure). The arrows indicate different source and detector positions on the medium surface. For a given source, multiple measurements are made on the target's surface. By combining the information from these datasets, a tomographic image of the interior of the medium can be reconstructed. Generally speaking, the more source-detector combinations are used in a DOT measurement and the larger the angle enclosed by the optical sensors is, the better is the achievable image quality.

The simplified description of light transport in scattering media given above assumes the light source to emit a constant light power and neglects any effects due to temporal variations in light intensity. Optical measurements employing light sources that emit a constant power or that are intensity modulated at low frequencies (Hz-kHz range) are referred to as continuous wave (C.W.) or DC methods. This is the imaging approach taken with NIRx imaging systems. Other methods that make use of time-dependent effects in light propagation are time-domain measurements, which use ultra short light pulses, and frequency-domain measurements using radio frequency modulated light intensity.

Optical Quantities

The following is a brief introduction to some of the physical quantities that are used to describe the interaction of light with a medium. Because the images reconstructed from OT measurements represent contrasts in light absorption and scattering, a basic understanding of those quantities is important to understand these images.

Wavelength λ

Although it is appropriate to model light as a stream of moving particles, light can also be treated as an electromagnetic wave in the visible part of the electromagnetic spectrum (see the chart below) and as such is characterized by its wavelength, λ and its frequency, ν.

The wavelength is the spatial length of one wave period, i.e. the distance from one wave trough to the next. The frequency describes the number of oscillations of the wave per second. It is common to characterize light by its wavelength measured in nanometers (nm, 1 nm = 109 m). Light of different wavelengths - corresponding to different light wave energies - is perceived by the human eye as different colors. The visible part of the electromagnetic spectrum ranges from ~400 nm (violet/blue, high energetic radiation) to ~700 nm (red, low energetic radiation). White light is a mixture of many different colors or wavelengths.

A special light source is the laser, whose light is monochromatic, i.e., its radiation spectrum is a very narrow distribution around one wavelength. Our systems use laser diodes and emit light in the near infrared region (700 - 1000 nm), which is slightly beyond what the human eye is able to see. The wavelength and the power levels emitted by the system are completely harmless for skin exposure as long as the system is used appropriately. No cumulative radiation effects are known.

Absorption Coefficient μa

photon absorption process - This quantity describes the likelihood of a photon for being absorbed over a given distance of travel inside a specific medium. The absorption coefficient is the statistical average number of absorption events per distance and is usually given in units of 1/cm = cm-1. The longer the optical path in a material and the higher its μa value, the more light is absorbed inside of it.

Light absorption occurs due to excitation of atoms or molecules - so-called chromophores - to higher energetic states by a photon, which is destroyed in the process (see figure above). The absorption coefficient of a material varies for different wavelengths, leading to a so-called absorption spectrum for that material. Each molecule or atom has its own characteristic absorption spectrum ("spectroscopic fingerprint"). The spectra of two of the most important chromophores for diffuse optical tomography in biomedical applications are oxy and de-oxy hemoglobin. Both absorption spectra are shown in the figure to the right.

absobtions curves for hemoglobin - A material containing a certain chromophore possesses a μa value that depends on the chromophore's concentration. This concentration can be determined by measuring the amount of light absorbed along a known thickness of the material.

Scattering Coefficient μs

Light scattering is the process of a photon elastically bouncing off a microscopic obstacle. The photon is not destroyed in the process; only its direction of propagation is changed. The scattering coefficient μs is the statistical average number of scattering events over the light travel distance in a material. It is usually given in units of 1/cm = cm-1. Scattering occurs on microscopic boundaries inside a heterogeneous material, for instance on the cellular and subcellular components in tissue or on water droplets in fog. Because scattering events redirect the photon paths randomly, the process causes blur and reduces contrast.

In general, the scattering coefficient is wavelength dependent, but usually much less so than the absorption coefficient.

Because scattering occurs randomly, only statistical predictions about the outcome of a scattering process can be made. For example, the likelihood for a large change in the propagation direction of a scattered photon depends on material and wavelength of the light. Scattering events that tend to cause large changes in direction have a larger impact on light propagation than those that most likely redirect the photon by a small amount. A quantity incorporating this influence of the scattering characteristics is the reduced scattering coefficient μ's (μs-prime), which is obtained by multiplying µs by a material-specific correction factor.

Diffusion Coefficient D

As is usually practiced, DOT is applied to media wherein light scattering dominates absorption, i.e. μ's >> μa. It has been shown that the distribution of light intensity in this regime follows a mathematical model that is analog to that for diffusion processes, such as heat propagation or particle diffusion. Light propagation in diffusion theory is influenced by two material parameters, the absorption coefficient μa and the diffusion coefficient D, which quantifies the scattering properties of the material.  Our image reconstruction model is based on diffusion theory. Therefore, reconstructed images show local variations in μa (absorption) and D (scattering).