Appendix 1. Principles of photoacoustic tomography
1. Photoacoustic (or optoacoustic) imaging
Optoacoustic (or photoacoustic) imaging is a hybrid method where the image contrast is
determined primarily by optical absorption, while image resolution is determined by
ultrasound [1,2]. Optoacoustic tomography is becoming useful for small animal imaging in
preclinical studies [3,4]. It might also help in assessing human breast cancer where it could be
used for high-resolution anatomical and molecular imaging [3,4].
The optoacoustic (or photoacoustic) effect was first described by Adam Graham Bell in
1880 [1]. Wilhelm Conrad Röntgen has also published about this theme [2]. In principle, if a
short near-infrared (NIR) light pulse is absorbed by a small target, then the target's initial
thermoelastic expansion generates exponentially decaying broadband acoustic pressure waves
that can be measured by ultrasound detectors for generating images (Appendix Fig. 1).
Appendix Fig. 1: Principle of photoacoustic imaging
A short light pulse from a pulsed Laser is partially absorbed by a target within the tissue. Due to the
photoacoustic effect this target slightly expands. This thermoelastic expansion causes broadband
ultrasound waves that can be measured by a broadband ultrasound detector. This principle allows for
molecular imaging, where high-resolution ultrasound images carry information about the target's light
absorption characteristics. These spectral characteristics depend on the target's molecular composition.
The NIR-light pulses in optoacoustic imaging are usually generated by a pulsed laser with
pulse durations of about 10 nanoseconds, which fulfills the stress confinement [5]. The higher
the target's NIR-light absorption, the higher is the amplitude of the emitted acoustic wave [5].
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In biological tissue any NIR-light imaging is complicated by light scattering. The NIR
photons are diffusively scattered by small tissue particles (Mie-scattering) and therefore need
more time to travel through a volume element (voxel) [6,7]. This prolongation of the mean
photon pathway causes that the voxel's molecules can absorb more NIR-light than if the NIRlight would pass straight through that voxel only once. Noteworthy, within the range of
6501100 nm the scattering decreases smoothly at increasing wavelength, which may be
utilized in reconstruction algorithms [6,7]. The effective NIR-light absorption depends on
absorption, scattering, and anisotropy of the tissue [5]:
eff = (3 a (a + s'))1/2,
with s' = s (1  g)
(formula 1)
where
eff is the effective absorption (cm1); a is the absorption coefficient (cm1);
's is the reduced scattering coefficient (cm1); s is the scattering coefficient (cm1);
g is the anisotropy factor (dimensionless, about 0.9 in biological tissue).
Typical values in the breast are a = 0.05 cm1 and s' = 10 cm1 at 800 nm [8]. The reduced
scattering coefficient 's is much larger than the absorption coefficient a, allowing for a
simplification:
eff = (3 a s')1/2,
with s' = s (1  g)
(formula 2)
For imaging purposes the optoacoustic measurements must be performed spatially-resolved.
Light (speed ~3108 m/s) travels much faster through the tissue than acoustic waves (speed
~1.54103 m/s), so that the propagation time of the NIR-light is negligible when measuring
acoustic waves. The time delay between the laser pulse and the arrival of the sound wave at
the ultrasound detector is used to estimate the depth of the tissue voxel where the optoacoustic
effect occurred. The three-dimensional position of this voxel is determined by using a
sufficiently large two-dimensional array of acoustic detectors and tomographic reconstruction.
Among the reconstruction algorithms for the three-dimensional map of optoacoustic sources
are filtered back-projection and iterative image reconstruction [9,10]. The latter requires more
computation time but can result in more accurate images [11]. Similar to all other noninvasive
imaging methods, some imaging artifacts must be considered. For example, artifacts may be
caused by internal reflection or scattering of acoustic waves but can be reduced by the
reconstruction algorithm [10].
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2. Reconstruction of absorption coefficients from photoacoustic tomographic
measurements
In scattering media the light transport at wavelength  is modeled by the light diffusion
equation [12]:
D(r) U(r) + a(r) U(r) = q0
(formula 3)
where
r is the tomographic position of interest;
D(r) = 3 (s' + a) is the spatially-dependent diffusion coefficient of the medium;
s' is the reduced scattering coefficient at position r;
a is the absorption coefficient at position r;
U(r) is the photon fluence rate at position r;
q0 is the source term of the isotropic light source.
Optoacoustic tomography provides images of the NIR-light energy that was converted to the
ultrasound energy by the optoacoustic effect. At each wavelength  and at each voxel r, the
locally absorbed light energy H(,r) is proportional to the local absorption coefficient a(,r)
and the local light fluence U(,r) [13,14]:
H(,r) ~ a(,r) U(,r)
(formula 4)
As an example for U, according to DIN EN 60 825-1 the maximum permissible light fluence
at the skin surface is U = 20 mJ/cm2 at 700 nm and U = 100 mJ/cm2 at 1050 nm [15]. In tissue
the light fluence U diminishes exponentially with depth due to attenuation of the NIR-light. In
formula (3) two variables (a and U) must be determined by one equation, which requires
further information about a and/or U. While a solely depends on the measured object, the
tomographic map of U depends on several factors such as intensity of the incident light,
measurement geometry, way of light propagation, and the effects of scattering and absorption
on the photon pathway from the light source to the place of the optoacoustic effect. Different
methods have been developed for modeling the spatial distribution of U, such as iterative
approaches [12], sparse signal decomposition [13], and analytical normalization [16]. Sparse
signal decomposition utilizes that U varies at a larger spatial frequency than a [13].
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3. Multispectral optoacoustic tomography (MSOT)
In-vivo imaging with NIR light utilizes the 650900 nm spectral range where the light can
travel several centimeters through biological tissues due to the relatively low light absorption
in this spectral window. A further smaller spectral window exists around 1064 nm, where the
scattering is about 30% lower and the maximum permitted laser illumination is 5-fold higher
than at 700 nm (see section 4 below) [6,7,15]. In the wavelength range of 6501100 nm the
dominant natural NIR-light absorbers in the human breast are water, lipids, oxyhemoglobin
and deoxyhemoglobin[1719]. There also is some background absorption from other tissue
components. The spectral range of 650900 nm is most useful for differentiation of
oxyhemoglobin and deoxyhemoglobin. Also, most exogenous optical contrast agents such as
indocyanine green have their characteristic spectral signatures in this wavelength range. The
spectral range of 9001100 nm is suitable for differentiating water and lipids [17,18]. In
multi-spectral optoacoustic tomography (MSOT) several optoacoustic measurements are
performed sequentially at multiple wavelengths. The major NIR light absorbers within each
tomographic voxel are then obtained by spectral decomposing [20,21].
4. Maximum permitted laser illumination of the skin
The skin's maximum permitted laser illumination according to DIN EN 60 825-1 is
summarized in Table 1. Per second a single laser pulse (in mJ/cm2) may contribute up to 10%
to the average illumination (in mW/cm2), i.e. it may be repeated at a frequency of 10 Hz. At
higher repetition frequencies the single pulse's maximum illumination is reduced
correspondingly for considering the skin's maximum average illumination.
Table 1: Maximum permitted laser illumination of the skin 1 in the near-infrared (NIR) range
of 6501100 nm
Single
Average
laser pulse, illumination,
duration
duration
wavelength,
1100 ns,
 500 min,
nm
mJ / cm2
mW / cm2
650
20
200
700
20
200
750
25
251
800
31
316
850
39
399
900
50
502
950
63
632
1000
79
796
1050
100
1000
1100
100
1000
1 according to DIN EN 60 825-1 [15]
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