Diffuse optical tomography

We have known that the main absorber in biological tissue is HbO2 and Hb.

Therefore, the optical characteristics of absorption or scattering ability are affected by chromophores. The DOT uses another algorithm to approach the optical characters of tissue. In order to generate a mapping image of spatial variations optical parameters, we need to measure the photon fluence with multiple sources and allocate detectors to

back-project the image essentially. This section introduces the theory and approach ways of DOT system.

2.3.1 Diffuse equation

To describe how the near-infrared photon migration through biological tissue has been developed based on the radiative transfer equation (RTE) about the 1990s. The scattering probability is much greater than absorption probability in turbid medium.

Therefore diffusion approximation to the transport equation can be used. The diffusion equation is showed as Eq. (6).

2 ( , ) _a ( , ) ( , ) ( , )

D r t r t r t S r t

νμ ^∂t ν

− ∇ Φ + Φ + Φ =

∂ (11)

The Φ( , )r t is the photon fluence at position r and at time t. S r t( , ) is the light intensity of the light source. D is the scattering factor which distinct from the optical characteristics and can be presented as Eq. (11).

' '

3 _{s a} 3 _s

D ν ν

μ αμ μ

= ≅

+ ⁽¹²⁾

The μ_s^'and μ_a are reduce scattering and absorption coefficient of objective. In

turbid medium, μ_s^' much greater than μ_a so D can be reduced to the right side of Eq. (11). The optical properties of biological tissue can be found in reference [16]. ν is light speed of the medium. Note that the parameters in Eq. (11) are dependency to wavelength of light source. The relation between μ_a and concentration of HbO2 and Hb is showed in Eq. (12).

2, [ 2] , [ ]

a HbO _λ HbO Hb_λ Hb

μ =ε +ε (13)

To get the variation of absorption coefficient the Φ( , )r t should be measure first.

Eq. (11) is an implicit equation and it demand to do the approximation and linearization to simplify the diffusion equation.

There are some applications to know the changed of the biological tissue, such as

early tumor detection, brain function image, and early discrimination between ischemic and hemorrhagic stroke. There are several technical solutions to realize DOT system, including time domain (TD), frequency domain (FD), and continuous wave (CW) techniques.

2.3.2 Application and implementation of DOT

TD-DOT use ultra high speed laser (picoseconds) to incident pulses of light into the tissue. After the pulses incident the tissue, various tissue made them board and attenuate which is mean reshape the pulse. TD system detects amplitude and temporal distribution when they penetrate out of the surface of tissue. In figure 2.4, the head of the long pulse is the photons which don’t undergo many scattering effect and are called ballistic photon. While the photons reach the detectors slower they also contain more information about the depth, optical characteristic and others. TD systems have some advantage, the scattering coefficient of tissue can be get by calculate the slope of the long pulse and TD-DOT also have relatively high spatial resolution to FD-DOT and CW-DOT.

On other hand, TD systems are very expensive, large dimension and long acquisition times to receive reasonable signal- to-noise ration. The high speed optical detectors are also needed to implement the systems such as streak camera, avalanche photon-diode and photomultiplier.

  Figure 2.4 The modality of TD-DOT systems.

In FD systems, amplitude of optical sources are modulated at frequency about tens to hundreds megahertz which is between TD and CW systems. This system reconstruct the information of tissue by detect the amplitude decline and the phase delay of the photon. After modulating, the light includes AC and DC component. The AC part has phase and the amplitude component and the DC part also has the information of amplitude. Fig. 2.5 shows the modality of FD-DOT system. The phase delay is hard to detect because of modulate of the optical sources. Therefore, when the signals are detected, the cross-correlation also is done at the same time. The frequency of signal is modulated to below 1 kHz to obtain the ration of AC and DC amplitude and the phase delay.

Compare to TD system the photon penetrate depth of FD system is shallow, but temporal revolution is much higher than TD systems. The optical source of CW-DOT system is very low frequency and steady compare to “pulse” in TD systems. The optical sources can view as on continuously. The information obtains from optodes is only the DC amplitude so scattering parameter can’t obtain in CW systems. Scattering coefficient is usually set to be constant in CW-DOT. The reconstruction algorithm is relative simple and computation overhead is lower than other two systems.

  Figure 2.5 The modality of FD-DOT systems.

The main characteristics of CW-DOT systems are the high potential to achieve the goals of low-power, low-cost and portable. The optical sources and detectors have less criteria and easy to assemble. The power consumption of CW is lower which 3.6V Li-ion battery can drive. So, CW-DOT systems have the highest potential to commercialize and massive produce. The relatively poor penetration and localization are the shortcoming of CW-DOT systems. The ability to precise the localization is influenced by the power of optical sources, the sensitivity of sensors and the reconstruction method. How to tradeoff between spatial resolution and makes it portable is a challenge. Table 3 reveals the pros and cons of different systems.

  Figure 2.6 The modality of CW-DOT systems.

Table 3 Pros and cons of different types of DOT systems. 

Type Advantages Disadvantages

TD 1. Spatial resolution 2. Penetration depth

3. Most accurate separation of absorption and scattering

1. High Sampling rate 2. Instrument size and weight 3. Stabilization and cooling 4. Cost

Example Uses: Imaging cerebral oxygenation and hemorrhage in neonates, breast imaging.

FD 1. Relatively low sampling rate 2. Relatively accurate separation of

absorption and scattering

1. Penetration depth

2. Instrument size and weight 3. Cost

Example Uses: Cerebral and muscle oximetry, breast imaging CW 1. Low sampling rate

2. Instrument size, weight and simplicity 3. Low cost

1. Penetration depth

2. Difficult to separate absorption and scattering.

Example Uses: Finger pulse oximeter and Functional brain experiments