The challenges for quantitative photoacoustic imaging B. T. Cox, J. G. Laufer and P. C. Beard Department of Medical Physics and Bioengineering, University College London, Gower Street, London WC1E 6BT, UK www.medphys.ucl.ac.uk/research/mle ABSTRACT In recent years, some of the promised potential of biomedical photoacoustic imaging has begun to be realised. It has been used to produce good, three-dimensional, images of blood vasculature in mice and other small animals, and in human skin in vivo, to depths of several mm, while maintaining a spatial resolution of 100 ��m. Furthermore, photoacoustic imaging depends for contrast on the optical absorption distribution of the tissue under study, so, in the same way that the measurement of optical spectra has traditionally provided a means of determining the molecular constituents of an object, there is hope that multiwavelength photoa- coustic imaging will provide a way to distinguish and quantify the component molecules of optically-scattering biological tissue (which may include exogeneous, targeted, chromophores). In simple situations with only a few significant absorbers and some prior knowledge of the geometry of the arrangement, this has been shown to be possible, but significant hurdles remain before the general problem can be solved. The general problem may be stated as follows: is it possible, in general, to take a set of photoacoustic images obtained at multiple optical wavelengths, and process them in a way that results in a set of quantitatively accurate images of the concen- tration distributions of the constituent chromophores of the imaged tissue? If such an ���inversion��� procedure - not specific to any particular situation and free of restrictive suppositions - were designed, then photoacoustic imaging would offer the possibility of high resolution ���molecular��� imaging of optically scattering tissue: a very powerful technique that would find uses in many areas of the life sciences and in clinical practice. This paper describes the principal challenges that must be overcome for such a general procedure to be successful. Keywords: photoacoustic tomography, quantitative, chromphores, multiwavelength 1. INTRODUCTION Consider a photoacoustic image of a region of tissue obtained using a single optical wavelength and showing a network of blood vessels. As a photoacoustic image is related to the absorption coefficient within the tissue, and recalling that a co-oximeter uses measurements of the absorption coefficient of blood at four wavelengths in order to estimate its oxygenation, it would seem a small step to obtain a map of blood oxygenation using photoacoustic imaging. More generally, if the absorption spectrum of a sample is known then it is often possible to work out the concentrations of the constituent molecules using a spectroscopic analysis. Surely multiwavelength photoacoustic imaging can, by analogy, provide maps of the concentrations of the constituent chromophores? It is starting to be understood that spectroscopic problems like this are more challenging in photoacoustic imaging than the above analogies would suggest, and there is one principal reason for this: photoacoustic images are not images of the absorption coefficient. A set of photoacoustic images obtained at multiple wavelengths does not, therefore, give the absorption spectrum of each pixel in the image, not even to within a multiplicative constant, and na����ve spectroscopic approaches are bound to fail, as has been demonstrated experimentally.1 Nevertheless, despite these difficulties, a technique that could deliver quantitatively accurate images of chro- mophore concentrations, or equivalently of absorption coefficient distributions, would have so many uses2 both in basic science (eg. molecular imaging of small animals) and clinically (eg. spatially resolved measurements of hemoglobin and oxygen saturation, sO2) that this is a goal worth working towards. This paper describes which aspects of this problem have been tackled and the challenges that remain. Send correspondence to B. T. Cox. bencox@mpb.ucl.ac.uk Photons Plus Ultrasound: Imaging and Sensing 2009: The Tenth Conference on Biomedical Thermoacoustics, Optoacoustics, and Acousto-optics, edited by Alexander Oraevsky, Lihong V. Wang, Proc. of SPIE Vol. 7177, paper 717713

2. WHAT DOES A PHOTOACOUSTIC IMAGE ACTUALLY REPRESENT? As a first step in tackling the problem of quantitative photoacoustics it is worth reminding ourselves what a photoacoustic image is an image of. In other words, what is the source of contrast in a photoacoustic image? A photoacoustic image is related to the optical absorption in the tissue, as the incident photons must be absorbed to have any effect, but this relationship is rather less direct than is often assumed. A photoacoustic image is an estimate (typically to within a constant scaling factor) of the distribution of acoustic pressure that arises following the absorption of a pulse of light. To see clearly what it is that a photoacoustic image depends on, we will briefly summarise the physics of photoacoustic signal generation. Consider a region of tissue that has an optical absorption coefficient distribution of ��a(x). If the tissue is irradiated with a light pulse of duration tp then the distribution of optical energy, h(x) Jm-3, absorbed in the tissue during the pulse is h(x) = integraldisplay tp 0 ��a(x)��(x, t)dt = ��a(x)��(x) (1) where ��(x, t) Wm-2 is the fluence rate describing the light distribution at a point x in the tissue at time t, and �� Jm-2 is its integral over time, often called simply the fluence. The fluence will depend on the optical properties of the medium, which in a highly scattering medium such as tissue can usually be characterised by the absorption and scattering coefficients, ��a and ��s, and the anisotropy factor, g. As the incident fluence rate is of low power, in order to avoid tissue damage, and as the wavelength of the light is typically chosen to be in the near-infrared, in order to benefit from the optical ���window��� at these wavelengths, the vast majority of the absorbed photons will be converted via vibrational relaxation to heat. The temperature rise, ���T , following the light pulse is related to the amount of ���deposited��� heat by the specific heat capacity of the tissue. If it is assumed that the duration of the light pulse, tp, is much shorter than the time is takes the density to change significantly, ie. the mechanical relaxation time of the tissue, then the relevant heat capacity is that for constant volume heating, Cv: ���T = h/��0Cv (2) where ��0 is the mass density of the tissue. If the amount of heat energy deposited is small, it will cause small changes to the local density, pressure, �����, ���p, as well as the temperature, in proportions given by the thermodynamic identity ����� = ��0KT ���p ��� ��0�����T (3) where KT is the isothermal compressibility and �� is the volume thermal expansivity of the tissue. If, as above, it is assumed that the duration of the light pulse is much shorter than the time is takes the density to change significantly, ie. ����� = 0, then Eq. (3) gives a relationship between the pressure and temperature changes in the tissue following the light pulse: ���p = (��/KT )���T (4) Combining Eqs. (2) and (4) gives an expression for the increase in pressure as ���p = (��/KT ��0Cv) h = ( ��c2/Cp ) h = ��h (5) where the first equality uses the substitution c2 = Cp/KT ��0Cv (with Cp the specific heat capacity at constant presssure), and �� = ��c2/Cp is a dimensionless thermodynamic property of the tissue called the Gr��uneisen parameter. The small - and spatially varying - increase in pressure that we have so far called ���p will initiate an acoustic pressure wave because tissue is elastic and inertial and so supports propagating acoustic waves. In this sense, ���p can be considered to be an initial condition of an acoustic (or ultrasonic) radiation problem. If in general the acoustic pressure at a point x and time t is denoted by p(x, t), then p0(x) ��� p(x, 0) = ���p. The ultrasonic waves that propagate out are called photoacoustic waves, and they can be described by the following initial value problem: Lwp(x, t) = 0 (6) p0(x) = ��(x)h(x) ���p/���t(x, 0) = 0 Proc. of SPIE Vol. 7177, 717713-2