Contemporary Mathematics
Multiple Illumination Quantitative Photoacoustic
Tomography using Transport and Diffusion Models
Ben Cox, Tanja Tarvainen, and Simon Arridge
Abstract. The task in quantitative photoacoustic imaging is to recover the
optical properties of the imaged region from the product of the absorption
coefficient and the light fluence. As the light fluence depends on both the
absorption and the scattering this is a nonlinear and ill-posed inverse prob-
lem and is non-unique when only one illumination pattern and wavelength of
light is used. Model-based least squares inversions have proved highly success-
ful for similar problems in diffuse optical tomography (DOT) where, for the
most part, the diffusion approximation to the radiative transfer equation is a
sufficiently accurate model. However, as the domain of photoacoustic images
typically reaches well into the non-diffusive region close to the tissue surface,
a model that can take into account the strongly forward scattering nature of
real tissue may be required. A simulated two-dimensional example inverting
for absorption and scattering simultaneously using data from four illumination
directions is shown using finite element models of both the radiative transfer
equation and the diffusion approximation. The reasons for the differences are
1. Introduction
1.1. Photoacoustic Tomography. Photoacoustic tomography (PAT) is em-
erging as a useful soft tissue imaging modality for both clinical and preclinical imag-
ing. It combines the contrast advantages of purely optical imaging techniques such
as diffuse optical tomography with the high spatial resolution achievable with high
frequency ultrasound. A short (ns) pulse of light is used to illuminate the region
of tissue of interest. As the tissue is optically scattering, the light floods the tissue
where it is then absorbed by absorbing molecules (chromophores). The total energy
absorbed at a point is given by the product of the local absorption coefficient and
fluence. Following its absorption, the optical energy is rapidly thermalised lead-
ing to an increase in pressure and a small accompanying increase in temperature.
Because of the elastic nature of tissue the pressure increase propagates through
the tissue as an acoustic wave to be detected by an array of ultrasound sensors
1991 Mathematics Subject Classification. Primary 92C55; Secondary 49M15.
Key words and phrases. quantitative photoacoustic imaging, light transport, radiative trans-
fer, nonlinear inversion.
This work was supported by the Academy of Finland (projects 122499 and 213476) and by the
Engineering and Physical Sciences Research Council, UK (EP/E034950/1 and EP/E050980/1).
c 0000 (copyright holder)
Contemporary Mathematics
Volume 559, 2011
c 2011 American Mathematical Society
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