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Tomographic bioluminescence imaging by use of a combined
optical-PET (OPET) system: a computer simulation feasibility
study
George Alexandrakis
1
, Fernando R Rannou
2
, and Arion F Chatziioannou
1
1 David Geffen School of Medicine at UCLA, Crump Institute for Molecular Imaging, University of
California, 700 Westwood Plaza, Los Angeles, CA 90095, USA
2 Departamento de Ingenieria Informatica, Universidad de Santiago de Chile (USACH), Av. Ecuador
3659, Santiago, Chile
Abstract
The feasibility and limits in performing tomographic bioluminescence imaging with a combined
optical-PET (OPET) system was explored by simulating its image formation process. A micro-MRI
based virtual mouse phantom was assigned appropriate tissue optical properties to each of its
segmented internal organs at wavelengths spanning the emission spectrum of the firefly luciferase
at 37 °C. The TOAST finite-element code was employed to simulate the diffuse transport of photons
emitted from bioluminescence sources in the mouse. OPET measurements were simulated for single-
point, two-point and distributed bioluminescence sources located in different organs such as the liver,
the kidneys and the gut. An expectation maximization code was employed to recover the intensity
and location of these simulated sources. It was found that spectrally resolved measurements were
necessary in order to perform tomographic bioluminescence imaging. The true location of emission
sources could be recovered if the mouse background optical properties were known a priori.
Assumption of a homogeneous optical property background proved inadequate for describing photon
transport in optically heterogeneous tissues and lead to inaccurate source localization in the
reconstructed images. The simulation results pointed out specific methodological challenges that
need to be addressed before a practical implementation of OPET-based bioluminescence tomography
is achieved.
1. Introduction
The translation of putative cancer therapy agents to the clinic can greatly be facilitated by non-
invasive imaging methods that allow high throughput screening in animal models.
Additionally, time-lapse whole body imaging of animals bearing xenografts of appropriately
labelled cancer cells can provide new information on tumour growth dynamics and metastasis
patterns that is not possible to obtain by invasive experimental approaches. Bioluminescence
imaging has recently emerged as a modality that can meet these research needs by use of low
cost and easy to operate equipment (Contag et al 1998). The capacity to detect optical photons
with high efficiency and the intrinsically low autoluminescence background of mice make
bioluminescence detection a very sensitive technique if photon sources are located near the
tissue surface. However, most bioluminescence probes currently in use emit the bulk of their
optical signal at green wavelengths and are therefore attenuated very strongly if they are located
deep in tissues (Troy et al 2004). In addition, planar images of weak sources near the surface
E-mail: ArChatziioann@mednet.ucla.edu.
(1)
Author: Please provide journal title in ‘Arridge et al 1993’ and ‘Contag et al 1998’.
NIH Public Access
Author Manuscript
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Published in final edited form as:
Phys Med Biol. 2005 September 7; 50(17): 4225–4241.
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could look identical to ones produced by stronger sources deeper in tissue (Kuo et al 2004).
Tomographic imaging is therefore required for source localization. The capacity of
bioluminescence imaging in producing accurate tomographic reconstructions is a topic of
ongoing investigation (Kuo et al 2004, Wang et al 2004, Chaudhari et al 2005).
Positron emission tomography (PET) is a well-established modality for small animal imaging
(Tai et al 2001, Chatziioannou 2002) and several commercial systems are now available. PET
can perform functional imaging of physiological processes with exquisite specificity if an
appropriate radiolabeled tracer analogue exists. New PET tracers that allow monitoring of
previously inaccessible physiological processes or simply ones that confer increased specificity
of detection in small animals can subsequently be tested on humans in the clinic without
modification (Ray et al 2004). Despite this direct translational advantage PET is hindered by
the need to use positron emitting tracers, which usually requires the presence of a nearby
cyclotron. This makes PET methodology a valuable but expensive and lower throughput tool.
A single device that will perform simultaneously both optical and PET (OPET) imaging on
the same animal is currently under development in our laboratory (Prout et al 2004, Rannou
et al 2004). The OPET radial field of view is only slightly larger than the mouse torso (figure
1). Both bioluminescence and scintillation photons from the converted annihilation gammas
are detected by photomultiplier tubes at the back end of the PET crystals and the two signal
types are distinguished by their very different pulse amplitudes (Prout et al 2004). Use of fusion
reporter gene probes co-expressing optical and PET signals under the same promoter (Ray et
al 2003) will produce images that are intrinsically co-registered in space. This unique advantage
of the OPET device will enable direct comparison of how well the optical and PET modalities
can localize and how sensitively they can detect emission sources existing at different tissue
depths.
The purpose of this work is to explore the feasibility and limits in performing bioluminescence
tomographic measurements with the proposed OPET system, by simulating its image formation
process. A mouse micro-MRI image volume (Segars et al 2004) provided the anatomical
features for a virtual phantom. Each of the segmented tissues was assigned appropriate optical
properties which were collected from the literature and were adjusted for blood content and
oxygenation levels (see the methods). OPET measurements were simulated for single-point,
two-point and distributed bioluminescence sources located in different organs such as the liver,
the kidneys and the gut. An expectation maximization (EM) code was employed to recover the
intensity and location of these simulated sources. The effects of spectrally-resolved
measurements, detector spatial sampling and the adequacy of approximating the mouse
background optical properties by a uniform medium were explored.
2. Methods
In order to assess the effect of background optical properties on the OPET image formation
process, photon propagation calculations were performed in an optically heterogeneous virtual
mouse phantom. The anatomical definitions of the different tissues in this phantom were
provided by a publicly available time-gated high resolution MRI image volume known as the
mouse phantom for molecular imaging research (Segars et al 2004) (MOBY). Different time
instances of the mouse image volume could be generated by use of a program utilizing the
natural spline definitions of its segmented organ volumes (Segars et al 2004). For our
simulations we used the first time gate of that image volume and we implemented some further
alterations in order to simplify computations: only the mouse torso was simulated, from the
neck to the base of the tail, the tissue surface was padded out to a perfect cylinder of 27 mm
diameter and the image volume was re-sampled to 2 mm size voxels (figure 2). The amount
of padding did not exceed 2 mm in the radial direction at any location near the torso surface.
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As the original MOBY image did not include the mouse skin, the latter was defined as the first
2 mm (one voxel) in from the cylinder’s surface. As a result, the padded volume voxels were
defined to be occupied by skin. The MOBY-defined organ volumes for the gall-bladder, vas
deferens, and testes were left out due to insufficient knowledge of their optical properties from
current literature data. The space occupied by these organs as well as any space between organs
in the modified mouse torso was defined as adipose tissue.
All of the organs included in the modified phantom were assigned optical properties for
wavelengths spanning the firefly luciferase emission spectrum (500–800 nm) reported by Kuo
et al. The absorption (μ
a
) and transport scattering (μ′) coefficients assigned to each organ, as
a function of photon wavelength (λ), were estimated on the basis of a compilation of relevant
tissue optical property data reported in the literature (tables 1 and 2). An empirical function
was employed to approximate μ′
s
(λ):
μ
′
s
(
λ
) =
a
×
λ
−
b
mm
−1
,
λ
in nm (1)
where a and b were constants controlling the spectral variation in each tissue (table 1).
The amount of light absorption taking place in all tissues was assumed to depend only on the
resident oxy-haemoglobin (HbO
2
), deoxy-haemoglobin (Hb) and water (W) concentrations.
The spectral absorption coefficient (μ
a
(λ)) was then approximated as a weighted sum of the
three constituent absorption coefficients (μ
aHbO
s
(λ), μ
aHb
(λ) and μ
aW
(λ)), which were
calculated from the corresponding absorbance spectra reported by Prahl (2001):
μ
a
(
λ
) =
S
B
(
xμ
aHb
(
λ
) + (1 −
x
)
μ
aHbO
2
(
λ
)) +
S
W
μ
aW
(
λ
)
(2)
where x = (HbO
2
)/((HbO
2
)+(Hb)) and S
B
and S
W
were heuristic scaling factors adjusted to
match the absorption data currently available in the literature for each tissue (table 2). S
B
and
S
W
were consistent with the known blood and water volume fractions respectively in the
different mouse organs (Brown et al 1997) with the exception of the kidneys and the lungs.
The blood volume fractions in these two organs predicted higher μ
a
(λ) values than those
reported in the literature.
It is important to emphasize that the tissue optical property literature data are sparse and
incomplete. The publications compiled in table 1 report on measurements performed on tissues
from different species, in vitro or in vivo, and at a great variety of other experimental conditions.
In addition, the optical properties of the mouse stomach and bowel contents were unknown
and this material could possibly shift around and mix with air pockets during image acquisition.
In this work, the stomach and bowel contents were assumed to be homogeneous and static.
They were assigned the abdomen optical properties as inferred from bulk tissue measurements
(Torricelli et al 2001). Given the above shortcomings, it should be stated that the parametric
descriptions that we assumed for equations (1) and (2) could only be interpreted as reasonable
but rough estimates of the true mouse tissue optical properties.
The propagation of bioluminescence photons in the mouse torso phantom was first simulated
by Monte Carlo (MC) methods. An open source MC code, originally intended for computing
the time-resolved reflectance from photon sources located on the surface of optically
heterogeneous media (Boas et al 2002), was modified to simulate the migration of photons
emanating from sources at the mouse torso interior. The modified MC code required as inputs
the discretized bioluminescence emission spectra, the voxelized distributed photon sources and
the mouse torso optical property phantom. Although the background optical properties were a
continuous function of photon wavelength, we have approximated the firefly luciferase
emission spectrum (Kuo et al 2004) as five discrete intensity bins of 25 nm width each, centred
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at 600, 625, 650, 675 and 700 nm respectively. Photons emitted at longer wavelengths
comprised <1% of the total emission intensity and were ignored. Though photons from the
firefly luciferase spectrum could be emitted at wavelengths as low as 500 nm, we found that
these underwent extreme attenuation in all tissues and were therefore not included in the
simulations. The mouse torso optical property phantom was defined as a cylindrical volume
of 2 mm side cubic voxels. This rather coarse voxel size was employed in order to reduce
memory and computation time requirements. Though the phantom’s interior was voxelized,
its air–tissue boundary was modelled as a smooth cylindrical surface. This was done to ensure
that photons were refracting out of the phantom at the appropriate surface geometry, free of
voxelation artefacts. Photons were subsequently scored at virtual detectors, of 2 mm × 2 mm
size, which were located on the phantom’s surface.
As MC simulations were time consuming (15 minutes on a 1.6 GHz PC for 10
6
photon histories)
and their estimates for the photon flux reaching the phantom’s surface inevitably contained
statistical noise, we explored the alternative of using a deterministic code to perform these
calculations. The publicly available time-resolved optical absorption and scattering
tomography (TOAST) finite-element code (Arridge et al 1993, Schweiger et al 1995), which
solves the diffusion approximation to the radiative transfer equation, was employed to compute
the boundary fluxes resulting from point sources located in the mouse torso interior. The same
optical property mouse phantom was used to match the MC simulation conditions. Though not
used in this work, a smaller voxel size or even a non-segmented image volume of continuously
varying optical properties could have been used to assign optical properties to the finite-element
nodes defined in the TOAST code. A mesh generation tool which was part of the TOAST
package was employed to discretize the mouse torso volume into tetrahedrons of an average
0.65 mm side size. This was sufficiently small to confer numerical stability to the diffusion
computations. By comparing TOAST predictions with corresponding MC simulations we
verified that, with the exception of sources located at <1 mm from the torso surface, the
diffusion approximation was adequate. Figure 3 demonstrates the agreement between MC and
TOAST in the case of a point source in the mouse gut, located 3 mm from the torso surface
and emitting photons at 650 nm, for detector locations on the same transverse plane as the
source. Similar results were found for all other bioluminescence emission wavelengths, source
and detector locations considered in this work. However, in contrast to the MC code, TOAST
could not handle non-scattering regions located within the geometric tissue boundaries. This
presented a problem for modelling photon transport through the bladder. We verified by MC
simulation that, for the detector field-of-view (FOV) locations examined in this work, the
photon fluxes detected from point sources located at the edge of the FOV, and nearest to the
bladder, were independent of the bladder’s presence. Given this observation, the volume
occupied by the bladder was filled with a scattering medium, chosen to be adipose tissue.
TOAST was advantageous to use over MC because it could calculate boundary photon fluxes
with similar accuracy but in addition, its computations were free of statistical noise and were
completed faster by a factor of 7, or more, on the same computer. Therefore, the TOAST code
was employed to compute the photon fluxes from emission sources, located in internal organs,
reaching each of the boundary elements of the mouse torso surface. These computations were
the first step in simulating the virtual OPET detector measurements. A controlled amount of
Gaussian noise, having zero mean and variance amplitude equal to the square root of photons
crossing each boundary element, was then added to the noiseless flux calculations. In addition,
a wavelength-dependent autoluminescence background flux (Troy et al 2004) was added to
each of those photon counts as spatially invariant Gaussian noise. It was a reasonable
approximation to assume that the angular distribution of diffuse photons exiting the mouse
torso was isotropic (Martelli et al 1999). The noise-added photon counts from each torso
boundary element were then geometrically projected onto the virtual OPET detectors by use
of appropriate solid angle factors (Gotoh and Yagi 1971, Wielopolski 1984). Finally a
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wavelength independent detection efficiency and dark noise, estimated at 10% and 35 counts
s
−1
respectively (Prout et al 2004), were also modelled into the virtual OPET measurements.
Source contributions from each of the five wavelength bins in which the firefly luciferase
spectrum was discretized were weighed by the fractional spectrum area that they subtended.
The intensity of source voxels was adjusted to achieve any desired overall signal-to-noise ratio
(SNR) at the detectors.
In addition to performing virtual measurements with the OPET detectors (2.2 mm × 2.2 mm,
384 in total) high resolution detectors spanning OPET’s geometrical FOV and having an area
equal to that of boundary finite elements (HiResOPET, 0.68 mm × 0.65 mm, 1740 in total)
were also utilized. These idealized HiResOPET virtual detectors were located on the mouse
torso surface and had 100% detection efficiency. Thus the performance of OPET detectors
could be compared to that of superior ones capable of higher spatial sampling and ideal
detection efficiency.
Bioluminescent source distributions were reconstructed by use of an EM algorithm for
emission tomography (Shepp and Vardi 1982). One of the required inputs for the EM code was
the P-matrix—the collection of probabilities that a photon emitted from any source location
in the image volume would reach any given detector. The P-matrix needs to be computed once
for any particular choice of tissue optical properties and organ topologies. We employed
TOAST to compute the P-matrix for point sources located at the centre of all 2 mm size voxels
of the virtual mouse torso phantom for all five wavelengths approximating the luciferase
emission spectrum. These were very time-consuming calculations that collectively took
approximately 3 weeks to complete on a cluster of 27 CPUs (2 GHz, 4 GB RAM each) which
were available at our institute. The EM algorithm utilized the P-matrix to reconstruct the most
likely distributed source that generated the simulated measurement data. A weakness of the
EM algorithm was that there was no official stopping criterion (Hebert and Leahy 1989) and
the latter had to be determined empirically. For our virtual mouse torso phantom and the OPET
detection geometry (Rannou et al 2004) we found that the reconstructed images did not change
significantly after 2500 iterations. All of the images presented in this work were reconstructed
with 5000 iterations, which were completed in approximately 1 h on a single CPU.
3. Results
The need for tomographic bioluminescence measurements was first demonstrated by
simulating the OPET detector data for the case of a point source located at the mouse torso
centre (figure 4(a)). Even for noise-free detection, there is no intuitive way to infer the true
depth of the point source, or even that it is indeed a point source, by simply looking at the
detector data image (figure 4(b)). It is even harder to infer any conclusions about the true
localization of the source when its intensity is not much larger than the detected background
noise (figure 4(c)). An additional difficulty is that tissue optical properties vary with photon
wavelength. Thus both photon propagation and detection need to be considered in a spectrally-
resolved fashion.
It was first investigated whether the proposed OPET system could attain tomographic images
from simulated monochromatic detector measurements. In these test cases the tissue optical
properties were assumed to be known and the simulated detector data were noise free. For a
point source located at the mouse torso centre emitting at 650 nm (figure 4(a)) the reconstructed
source was placed near the torso surface (figure 5(a)), which was clearly not its true location.
The apparent near-surface reconstructed source placement was also observed for simulated
sources located at different tissue depths emitting monochromatically at any wavelength in the
firefly luciferase spectrum. An attempt to improve point source localization by employing the
higher resolution virtual detectors (see the methods) was unsuccessful. In fact, the total photon
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counts reaching each detector from the reconstructed source intensity distribution were always
nearly identical to those reaching these same detectors from the true point source location. The
similarity in detected intensity profiles from two different monochromatic emission source
distributions demonstrated the ill-posed nature of the problem which has been previously
reported (Kuo et al 2004).
The ability to reconstruct the true location of point emission sources by use of measurements
at two wavelengths was then investigated. When noiseless detector data were simulated for the
point source in figure 4(a), now emitting both at 600 nm and 650 nm, the EM reconstruction
recovered its true location (figure 5(b)). Similarly, the true locations of point sources anywhere
in the mouse torso could be recovered when detector data from any two of the five wavelengths
used in this work (see the methods) were used in the reconstructions. Inclusion of noiseless
detector data at additional wavelengths did not substantially improve the quality of
reconstructed images. Furthermore, it was examined whether noisy detector data at two
wavelengths would still be sufficient for the EM reconstructions to recover the true locations
of point sources. The same point source as in figure 4(a) was simulated to have an emission
intensity sufficient to produce a total of OPET detector counts which was three standard
deviations above the sum of the overall autoluminescence background and detector dark noise.
Measurements at any two wavelengths yielded reconstructed images of a diffuse source
distribution which encompassed the true source location (e.g. figure 5(c)). Measurements at
three wavelengths improved the point source localization (figure 5(d)). Incremental inclusion
of additional measurements at up to five wavelengths (figure 5(e)) further improved
reconstructions though ever less so. Similar results were found for most point source locations
within the detectors’ geometrical FOV. Exceptions to these observations were any sources
located deep within highly attenuating tissues, e.g. at the liver centre. In the latter case and for
physiologically relevant source intensities (Troy et al 2004), photon count contributions from
wavelengths below 650 nm were lower than background noise.
The above simulations were performed under the assumption that the mouse optical properties
were known exactly. This is difficult to achieve by prior non-invasive optical measurements
even when additional anatomical information is provided by some other high resolution
imaging modality (Barnett et al 2003). In addition, time-consuming P-matrix calculations
would need to be repeated for every mouse, which is impractical. We have examined the
possibility of assuming a uniform optical property background for the mouse torso while
reconstructing the measurements obtained from the heterogeneous torso phantom. We found
that assigning the volume average optical properties of the whole mouse torso to the
homogeneous phantom did not describe photon transport well in all regions of the optically
heterogeneous torso. The reason was that the volume average properties were close to those
of liver, which were too attenuating to accurately describe the photon transport in less
attenuating tissues such as the gut. We decided to examine more closely the favourable case
of having the OPET geometrical FOV encompass the less heterogeneous middle part of the
torso which mostly contained adipose tissue and the gut (μ
a
(λ) and μ′
s
(λ) volume averages
shown in table 3). Noiseless detector data from three separate point source locations, all located
on an axial plane which was centred in the OPET FOV, were reconstructed. In the radial
direction one source was located at the cylinder’s centre, one at half-radius and one at the edge
voxel (figure 6(a)). The reconstruction of the source at the centre was poor (figure 6(b)). The
reconstructed source distribution at half-radius (figure 6(c)) was slightly mis-positioned
relative to the true point source location and was somewhat diffuse. The point source at the
cylinder’s edge (figure 6(d)) was reconstructed at its correct location. These findings
demonstrated that assumption of a uniform optical property background was appropriate only
when point sources were superficial.
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The capacity of OPET measurements to tomographically resolve two neighbouring-point
sources at different tissue depths and in different organs was then explored for the case where
the mouse optical properties were known exactly. The arbitrary criterion for considering the
two sources resolved was that in a line profile through the image a trough, dipping at >15% of
the two peak amplitudes’ mean, would exist between the two source peak intensities. First, it
was examined whether two point sources separated by a distance of 2 voxels (or 4 mm) could
be resolved. When two such sources of equal intensity were placed on either side of the mouse
torso centre in either the gut or the liver, they could not be resolved in the reconstructed images
(figure 7(a), SNR = 5). In addition, these sources could also not be resolved for unequal relative
intensity ratios (data not shown). When those source pairs were moved on either side of the
torso half-radius, they could still not be resolved if they were of equal intensities (figure 7(b)).
However, they could be resolved in the liver if their relative intensities were in the vicinity of
2:1 (figure 7(b)) but did not exceed 3:1. Finally, the two sources were moved near the torso
edge so that the one nearest to the surface was located at 1 mm depth. Even at these superficial
tissue depths two equal intensity sources in the gut could not be resolved but they could be
resolved in the liver (figure 7(c)). Nevertheless, these two sources could actually be resolved
for unequal intensity ratios ranging from 2:1 to 5:1 in the gut and for up to 10:1 in the liver
(data not shown). When the two sources were separated by a centre-to-centre distance of 3
voxels, or 6 mm, they were always resolved at all tissue locations if the true tissue optical
properties were assumed to be known. For example, two equal intensity point sources located
in the gut and the spleen respectively could be resolved under these circumstances (figure 7
(d)). However, when a uniform optical property background was assumed the two point sources
were reconstructed as a single source located half-way between the two true source locations
(figure 7(d)). In all of the above cases where the two equal intensity point sources were resolved
they were typically not reconstructed at equal intensities though they were within a factor of
4 of each other.
Interestingly, image reconstruction artefacts in the form of additional ‘phantom’ emission
sources appeared at mouse torso locations from where emitted photons had a small probability
of reaching the OPET detectors. For example in the case of two point sources, separated by 4
mm, in the gut (figure 8(a)) a phantom source appeared at the edge of the FOV and near the
liver centre (figure 8(b), SNR = 5). The artefact persisted even for noiseless detector data (figure
8(c)) though its intensity was much weaker. A similar image artefact was observed in the heart
blood pool area when the OPET FOV was shifted to the upper half of the mouse torso (data
not shown). As photons emitted from these artefactual sources were highly attenuated, they
did not contribute significantly to the total detected signal. Interestingly, these artefacts
disappeared and the two point sources were better localized when virtual measurements were
performed by the more numerous HiResOPET detectors located on the torso surface (figure 8
(d), SNR = 5). Nevertheless, even with measurements performed by these higher resolution
detectors the two equal intensity sources at the torso centre were neither resolved nor were they
reconstructed at equal intensities.
Finally the capacity to reconstruct distributed emission sources from OPET detector data was
investigated. In two test cases the segmented volumes occupied by the kidneys (encircled green
voxels in figure 9(a)) and the gut (green–yellow voxels in figure 9(d)) were each defined as
distributed sources. The same emission intensity was assigned to all source voxels with each
one contributing an overall SNR ≽ 5 at the OPET detectors. When the true torso optical
properties were utilized in the reconstructions, the true spatial extents of the distributed sources
defined by the kidneys (figure 9(b)) and the gut (figure 9(e)) were both recovered. As found
previously, assumption of a uniform optical property background resulted in artefacts. The
reconstructed kidneys volumes were shifted relative to their true locations and an apparent
exclusion of source emission activity, similar to that seen in figure 6(b), could also be observed
(figure 9(c)). The problem of emission source exclusion from the torso centre was seen more
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clearly when the gut was reconstructed while assuming a uniform optical property background
(figure 9(f )).
4. Discussion and conclusions
Simulations were performed to assess the capacity of a proposed OPET system to perform
tomographic bioluminescence imaging. Measurements at a single wavelength were found to
be inadequate for achieving three-dimensional source localization. The latter was not even
obtained when the idealized HiResOPET detectors were employed, even though these were
located on the phantom surface. Therefore the need for spectrally resolved detection to achieve
tomographic bioluminescence imaging was independent of the imaging system specifics.
Though OPET measurements at two wavelengths did produce tomographic images, source
localization improved when additional spectral measurements were included. With the
exception of sources located on the skin surface, photons emitted at wavelengths <600 nm
suffered extreme attenuation in all tissues. In addition sources located deep in highly
attenuating tissues, such as the liver centre, did not have significant signal contributions to the
detectors for wavelengths <650 nm. Therefore, image reconstructions for experimental data
from these source locations are expected to suffer not only from fewer photon counts but also
from having a smaller fraction of the firefly luciferase spectrum available for spectrally
resolved measurements.
The capacity of the OPET system to resolve two neighbouring point sources was a function of
their locations in different tissues and decreased with tissue depth. It was also observed that
two neighbouring sources were better resolved in the liver than in the gut even though the
former was a more absorbing tissue. It is hypothesized that this was a result of the higher spatial
gradient of spectral attenuation in the more absorbing tissues which would favour depth
resolution. When two equal intensity point sources were resolved, they were typically not
reconstructed at equal intensities. In addition, the range of relative intensity ratios for which
two point sources could be resolved was a function of their locations in tissues. The overall
dynamic range for resolving two neighbouring sources separated by 2 voxels (4 mm) was rather
limited, not exceeding 4:1, unless these were located within a few mm of the tissue surface. It
should nevertheless be noted that the limits in resolving neighbouring sources will not have
been fully explored until image reconstructions utilizing P-matrices of 1 mm voxel size, or
less, are performed. Given that the computation of the 2 mm voxel P-matrices used in this work
was time consuming, use of higher resolution P-matrices is presently impractical.
The spatial distribution of photon fluence reaching the tissue surface depends both on the tissue
optical properties and the size and shape of the mouse organs in which bioluminescence sources
are embedded. Exact knowledge of the tissue optical properties in every mouse being imaged
may not be practical or even possible. In addition the optical property map in the mouse changes
with breathing and food digestion. Even if that dynamic optical property map was known it
would be impractical to compute a new P-matrix for every mouse. On the other hand, the
attempted simplification of assuming a uniform optical property background was shown to be
inadequate unless emission sources were superficial. The above findings imply that
development of computationally efficient methods taking into account the differences between
individual mouse optical properties would be the key to any practical implementation of
bioluminescence tomography. In future work we plan to explore image artefacts arising from
assigning inaccurate optical properties to tissues whose anatomical boundaries are obtained by
an independent high resolution imaging modality.
The detector spatial resolution was shown to play an important role in the quality of the resulting
reconstructed images. The OPET detector spatial resolution was restricted to 2.2 mm. The latter
was equal to the centre-to-centre distance between neighbouring PET crystals (block of 8 × 8,
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2 mm × 2 mm each, 0.2 mm inter-crystal gap) which were designed to match the physical size
of the channels on a 64-channel photomultiplier tube. Unfortunately, bioluminescence
detection at 2.2 mm resolution resulted in reconstructed image artefacts in areas of high photon
attenuation in the mouse. These artifacts were eliminated when the OPET detectors were
replaced by the HiResOPET ones, which were simulated to have a width of approximately 650
μm—a resolution easily achievable by CCD cameras. These considerations indicate some of
the compromises one is faced with when designing a hybrid imaging modality system.
The proposed OPET system presents a unique opportunity to determine the relative
bioluminescence and PET tracer detection sensitivities as a function of source depth in the
mouse in a spatially co-registered setting. Optical photons undergo both strong and spatially
variable attenuation as they travel through tissues. Based on calculations performed in this
work, typical OPET detection probabilities per bioluminescence photon emitted are 0.15% for
a point source located at the mouse torso centre in the gut and 0.01% for one at the liver centre.
Near the torso surface, bioluminescence photon detection probabilities are about 2%. In
contrast, annihilation gamma photons undergo little (~20%) attenuation as they travel through
the mouse but they are also hard to stop even by high-density detector materials. As a result
small animal PET systems have an absolute sensitivity of the order of 4% (Chatziioannou
2002). It is important to remember though that the detected emission intensities from both PET
and bioluminescence sources are also the functions of their respective tracer kinetics in vivo
as well as the underlying cell biology of each tracer. Future comparisons between simultaneous
optical and PET images will enable exploring the detection sensitivity of bioluminescence
tomography under the design constraints of a dual modality system.
Acknowledgements
We would like to thank Dr Richard Taschereau for providing us with the schematic shown in figure 1. We would also
like to thank Dr Martin Schweiger and Jason Riley of University College, London, for their advice on the use of the
TOAST code. We would like to acknowledge Dr Richard Leahy, Dr Felix Darvas, and Abhijit Chaudhari of the
University of Southern California for fruitful discussions and advice on finite-element bioluminescence computations.
Finally, we would like to thank Dr Michael Patterson of McMaster University, Canada, for his comments on the
manuscript. This work was supported by the NIBIB R01-EB001458, NIH/NCI R25 CA098010:01 and DE-
FC02-02ER63520 grants.
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Figure 1.
A schematic of the proposed OPET system. Its gantry size is only slightly larger than the mouse
torso diameter.
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Figure 2.
(a) Sagittal view of the MOBY mouse. (b) Corresponding sagittal view for the modified mouse
torso phantom. Different colours correspond to different tissue types (dark blue: adipose tissue,
light blue: liver, turquoise: lungs, yellow: bone, red: whole blood, orange: heart wall, light
green: gut, and purple: skin).
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Figure 3.
Comparison between MC and TOAST boundary flux predictions for a 3 mm deep point source
in the mouse gut emitting at 650 nm. Results are shown for a single ring of HiResOPET
detectors centred on the axial plane containing the point source.
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Figure 4.
(a) Transverse view of the mouse torso gut area with a point source located at its centre (star).
(b) Noise-free and spectrally blind OPET detector measurements for the point source described
in (a), emitting at wavelengths and spectral intensities defined by the luciferase spectrum. (c)
As in (b) but with the point source emitting at an intensity that is three times higher than the
standard deviation of background noise as measured at the mouse torso surface. The six OPET
detector blocks can be discerned.
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Figure 5.
(a) Reconstructed source distribution based on noiseless boundary flux data generated by the
point source in figure 4(a) emitting at 650 nm. (b) As in (a) but for spectrally distinct detection
of photons emitted simultaneously at 625 nm and 650 nm. (c) Reconstructed source distribution
for spectrally distinct detection of noise-added boundary flux data generated by the point source
in figure 4(a) emitting at 625 nm and 650 nm. (d) As in (c) but with the source emitting at 600,
625 and 650 nm. (e) As in (c) but with the source emitting at 600, 625, 650, 675 and 700 nm.
Alexandrakis et al. Page 16
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Figure 6.
(a) Transverse view of the homogeneous mouse torso with three individually simulated point
sources sequentially placed at its centre, at half-radius and at 1 mm from the surface. (b)
Reconstructed source distribution based on noiseless boundary flux data generated by the point
source at the torso centre emitting at all five wavelengths. (c) As in (a) but for a source located
at half-radius; the red cross indicates the correct position of the point source. (d) As in (a) but
for a source located at 1 mm from the surface.
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Figure 7.
Line profiles through the two source peak intensities in reconstructed images of source pairs
in different anatomical locations. (a) Equal intensity sources separated by 4 mm in the gut
(solid curve) and the liver (short dashed curve). (b) As in (a) but with the two sources located
symmetrically around the torso half-radius. The two sources could be resolved in the liver for
a relative intensity ratio of 2:1 (grey long dashed curve). (c) As in (a) but with the two sources
located at 1 mm and 5 mm from the torso surface. (d) Two equal intensity point sources, 6.3
mm apart, when the true tissue optical properties (solid curve) and a uniform optical property
background (short dashed curve) were utilized in the image reconstructions.
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Figure 8.
(a) Coronal view of the mouse torso phantom with two equal intensity point sources (red stars)
located on either side of the torso centre in the gut. The artefactual source (orange oval) was
located at the liver centre and near the OPET FOV (red dashed lines) edge. (b) Reconstructed
image of the two point sources based on the OPET detector measurements at SNR = 5. (c) As
in (b) but for noiseless detector data. (d) Reconstructed image based on the virtual HiResOPET
detector measurements at SNR = 5.
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Figure 9.
(a) Transverse view of the mouse torso for an axial slice through the kidneys (encircled green
voxels). (b) Transverse view of the kidneys reconstructed as a uniform distributed source. The
red crosses indicate the peak intensity value in each kidney. (c) As in (b) but assuming a uniform
optical property background. The red crosses indicate a shift in the reconstructed kidney source
locations. (d) Transverse view of the mouse torso for an axial slice through the gut (yellow–
green voxels). (e) Transverse view of the gut reconstructed as a uniform distributed source.
(f ) As in (e) but assuming a uniform optical property background.
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Alexandrakis et al. Page 21
Table 1
Values for the parameters a and b used to estimate μ′
s
(λ) for each tissue by use of equation (1). Definitions of
these parameters are provided in the text.
Tissue type a (mm
−1
) b (no units) References
Adipose 38.0 0.53 (Mitic et al 1994, Kienle et al 1996, Holboke et al 2000, Srinivasan et al
2003)
Bone 35600 1.47 (Firbank et al 1993, Beek et al 1997a, 1997b, Pifferi et al 2004, Ugryumova
et al 2004)
Bowel 3670 1.24 (Matern et al 1996, Torricelli et al 2001, Solonenko et al 2002, Wei et al
2003)
Heart wall 10600 1.43 (Swartling et al 2003)
Kidneys 41700 1.51 (Solonenko et al 2002)
Liver and spleen 629 1.05 (Karagiannes et al 1989, Marchesini et al 1989, Parsa et al 1989, Kienle et
al 1996, Beek et al 1997a, 1997b, Ritz et al 2001, Srinivasan et al 2003)
Lung 68.4 0.53 (Beek et al 1997a, Beek et al 1997b, Srinivasan et al 2003)
Muscle 4.e7 2.82 (Cheong et al 1990, Kienle et al 1996, Beek et al 1997a, 1997b, Zijp and ten
Bosch 1998, Torricelli et al 2004)
Skin 2850 1.1 (Jacques and Prahl 1987, Marchesini et al 1989, Beek et al 1997a, 1997b,
Doornbos et al 1999, Lualdi et al 2001)
Stomach wall 792 0.97 (Thueler et al 2003)
Whole blood 133 0.66 (Enejder et al 2003)
Phys Med Biol. Author manuscript; available in PMC 2005 December 20.
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Alexandrakis et al. Page 22
Table 2
Values for the parameters S, x, and y used to estimate μ
a
(λ) for each tissue by use of equation (2). Definitions of
these parameters are provided in the text. The literature references employed for these estimates are identical to
those in table 1.
Tissue type S
B
x S
W
Adipose 0.0033 0.7 0.5
Bone 0.049 0.8 0.15
Bowel 0.0093 0.8 0.5
Heart wall 0.05 0.75 0.5
Kidneys 0.056 0.75 0.8
Liver and spleen 0.30 0.75 0.7
Lung 0.15 0.85 0.85
Muscle 0.07 0.8 0.5
Skin 0.06 0.75 0.5
Stomach wall 0.01 0.7 0.8
Whole blood 1.0 0.75 0.0
Phys Med Biol. Author manuscript; available in PMC 2005 December 20.
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Alexandrakis et al. Page 23
Table 3
The uniform mouse torso optical property values at the five wavelengths used in this work.
Emission wavelength μ
a
(λ) (mm
−1
) μ′
s
(λ) (mm
−1
)
600 0.19 1.66
625 0.062 1.59
650 0.038 1.53
675 0.028 1.47
700 0.022 1.41
Phys Med Biol. Author manuscript; available in PMC 2005 December 20.
