Photoacoustic imaging

The photoacoustic effect is the physical phenomenon where light absorbed by a sample leads to its emission of ultrasound waves. For this to occur, the light source must be discontinuous: this is usually achieved using a pulsed laser. A continuous wave laser with intensity modulation at some constant or variable frequency can also be used, although this usually has a poorer signal-to-noise ratio. The photoacoustic effect involves the conversion of optical energy to thermal, kinetic and acoustic energy. [1]

The optical absorber is referred to as a chromophore: typically, endogenous tissue chromophores include haemoglobin, melanin and water. Since the optical absorption coefficients of the chromophores are dependent upon the wavelength of the absorbed light, the concentration of each chromophore can be determined via spectroscopic inversion. [3]

Figure 1: Graph showing absorption coefficients at different wavelengths of light for chromophores.

Source: ncbi.nlm.nih.gov

Photothermal expansion

For PAT signal generation, the duration of the laser pulse is usually several nanoseconds. The pulse leads to the excitation and expansion of the chromophore according to the following equation:

where 𝛋 is the isothermal compressibility, 𝛃 is the thermal coefficient of volume expansion, and p(r) and T(r) are changes in pressure and temperature respectively. [1]

Since the laser pulse duration is so small, it is generally within the thermal and stress confinement periods of the material. This condition yields the following conclusions:

Thermal diffusion during laser illumination can be neglected
Volume expansion during the illumination period can be neglected

Thermal confinement occurs when the laser pulse width is much shorter than the thermal relaxation time. Thermal relaxation time is the time taken for a structure to return to thermal equilibrium. Stress confinement occurs when the laser pulse width is much shorter than the stress relaxation time. Stress relaxation is the observed decrease in stress in response to strain generated in a structure. [2]

What is the isothermal compressibility of a material?

The isothermal compressibility is a measure of the relative volume change of a material due to a pressure change. It is the reciprocal of the bulk modulus.

Equations for conditions of the photothermal expansion differential

The confinement conditions allow the following equations to be produced:

For PAT signal generation, the duration of the laser pulse is usually several nanoseconds. The pulse leads to the excitation and expansion of the chromophore according to the following equation:

where A_e is the absorbed energy density, 𝛒 is the mass density, C_V is the specific heat capacity for constant volume, 𝛍_a is the absorption coefficient and 𝛤 (r) is the Grueneisen parameter, which increases with temperature. [1]

Once the pressure p_0 has been generated, it splits into two waves of equal magnitude propagating in opposite directions. The shape of the wavefront depends on the object's geometry, and the distance between the two wavefronts is proportional to the size of the object.

The aim of photoacoustic imaging techniques is to recover the distribution of p_0 from the time-resolved ultrasonic signals in order to produce a map of the chromophores at the specific loci.

References:

[1] Xia, J. et al., 'Photoacoustic tomography: principles and advances' Electromagnetic Waves Cambridge, 2014; 147: 1–22.

[2] https://en.wikipedia.org/wiki/Photoacoustic_effect#Photothermal_mechanism [Accessed: 26/02/19]

[3] Rosencwaig, A. 'Photoacoustics and photoacoustic spectroscopy', New York: John Wiley & Sons, 1980