A quantitative assessment of the depth sensitivity of an

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IOP PUBLISHING
PHYSICS IN MEDICINE AND BIOLOGY
Phys. Med. Biol. 54 (2009) 6277–6286
doi:10.1088/0031-9155/54/20/016
A quantitative assessment of the depth sensitivity of an
optical topography system using a solid dynamic
tissue-phantom
Teresa Correia, Anil Banga, N L Everdell, Adam P Gibson
and Jeremy C Hebden
Department of Medical Physics and Bioengineering, University College London, Gower Street,
London WC1E 6BT, UK
E-mail: [email protected]
Received 17 June 2009, in final form 15 August 2009
Published 1 October 2009
Online at stacks.iop.org/PMB/54/6277
Abstract
A solid dynamic phantom with tissue-like optical properties is presented,
which contains seven discrete targets impregnated with thermochromic pigment
located at different depths from the surface. Changes in absorption are obtained
in response to localized heating of the targets, simulating haemodynamic
changes occurring in the brain and other tissues. The depth sensitivity of a
continuous wave optical topography system was assessed successfully using
the phantom. Images of the targets have been reconstructed using a spatially
variant regularization, and the determined spatial localization in the depth
direction is shown to be accurate within an uncertainty of about 3 mm down to
a depth of about 30 mm.
1. Introduction
Diffuse optical imaging (DOI) is a non-invasive technique for monitoring haemodynamic
activity in biological tissues (Leef et al 2008, Zeff et al 2007, Gibson et al 2005). It provides
three-dimensional (3D) maps of the spatial distribution of optical properties of tissue, which
can reveal changes in the concentration of oxygenated and deoxygenated haemoglobin, from
measurements of light attenuation at near-infrared wavelengths. An array of sources and
detectors is placed on the surface of the object of study. Where measurements of transmitted
light are involved, the technique is usually known as optical tomography, whereas if reflectance
measurements are made, it is often referred to as optical topography (Gibson et al 2005). For
the latter the source–detector separations are relatively small (<3 cm), which restricts imaging
to relatively superficial signals resulting in a degradation in spatial resolution with increasing
depth. However, it is usually based on continuous-wave (CW) technology that permits fast
acquisition times, which makes it optimal for real-time imaging applications. Nevertheless,
0031-9155/09/206277+10$30.00
© 2009 Institute of Physics and Engineering in Medicine
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T Correia et al
for these types of systems, depth resolution can be improved by using a high-density array
of optical fibres (Zeff et al 2007), overlapping measurements at different source–detector
separations (Boas et al 2004) and a spatially variant regularization parameter (Culver et al
2003).
Zhao et al (2007) used a depth variant regularization, which follows a sigmoidal decay
function with depth, to reconstruct images from simulated data. They showed that depth
contrast is improved and position errors of less than 3 mm could be obtained for objects
located at depths from the surface of 1–3 cm. A similar study, using a regularization parameter
proportional to the maximum singular value of the forward matrix for each depth layer, yielded
identical results (Niu et al 2008). Endoh et al (2008) assigned a different regularization
parameter to each voxel by setting the regularization parameter proportional to the square root
of the diagonal elements of the forward matrix times its transpose (refer to section 3.1), hence
compensating for both depth and lateral sensitivity decrease. They successfully reconstructed
simultaneously two simulated objects located at different depths. Simulations, if correctly
implemented, are good approximations to reality, and are inexpensive, relatively easy and fast
to perform. However, they usually reproduce an ideal and simplified system performance,
where, for example, all sources have identical noise levels. To fully characterize a specific
imaging system, appropriate phantom measurements are essential.
Over the last decade, the increasing popularity of DOI prompted the development of
tissue-like optical phantoms to evaluate the performance of optical imaging systems, optimize
existing systems and compare between systems and image reconstruction algorithms (Pogue
and Patterson 2006). Most optical phantoms employ liquids, commonly based on an intralipid
emulsion mixed with an absorbing element, such as near-infrared dyes (Flock et al 1992).
Dynamic liquid phantoms have been used to mimic blood flow, or localized changes in
haemoglobin concentration by flowing liquid through tubes embedded within a scattering
solution (Franceschini et al 2006, Selb et al 2006, Kurth et al 1995). The disadvantages
of using such phantoms are the relatively poor stability over time, the lack of repeatability
with high accuracy, and the fact that they are not easily transportable. Hence, comparison
between the different optical systems in different laboratories is difficult using this type of
phantom. A solid dynamic phantom containing a reversible, electrically activated region has
been developed by NIRx Medical Technologies (USA). Their phantom consists of realistic
head and breast geometries with embedded electrochromic cells, whose optical properties can
be programmed to vary over time (Barbour et al 2006). Koh et al (2009) proposed a phantom
based on a liquid crystal display (LCD) inserted in a multi-layer resin phantom. Each pixel in
the LCD can be activated individually, meaning that it can reproduce highly localized optical
dynamic changes.
Recently we presented an electrically activated tissue-like solid phantom, based on a
thermochromic substance that changes colour in response to a change in temperature, which
consequently produces changes in absorption (Hebden et al 2008a). A portable, batteryoperated prototype phantom containing two thermochromic targets was described, and its
optical and temporal characteristics were investigated. An alternative design, based on an
array of semiconductor diodes, allows the sequential activation of an arbitrary number of
different thermochromic regions within a phantom (Hebden et al 2008b).
This type of phantom can provide controlled and localized changes in the optical
properties, and can mimic, for example, haemodynamic changes in the brain, which is essential
to assess the performance of optical topography systems. One of the main limitations of optical
topography is the low spatial accuracy, i.e. poor ability to accurately locate a change in the
optical properties, in particular in the depth direction. In this paper we introduce a new
design of electrically activated phantom, which has been developed to evaluate the ability of
A quantitative assessment of the depth sensitivity of an optical topography system
6279
4.5mm
5mm
z
4.7 k
thermistor
4
3
5mm
115mm
(a)
(b)
z
2
5mm
23mm
6
5
10
0m
m
y
5m
m
12
resistor
7
41mm
50mm
x
x
1
5mm
(c)
Figure 1. (a) A target with thermistor and resistor embedded. The resistor is connected to one
of the wires of the thermistor; (b) schematic of the phantom containing seven targets impregnated
with thermochromic dye located at different depths. The targets are electrically activated through
the sockets on top of the phantom; (c) top view of the phantom showing the target arrangement.
Targets are at depths from 5 mm to 35 mm in intervals of 5 mm.
an optical topography system to detect and localize discrete regions of absorption at different
depths below the surface. The phantom is described, and its use to characterize the performance
of an imaging system is reported.
2. Phantom design
The phantom is based on a recipe described in detail in Hebden et al (2008a). It
consists of a solid block of polyester resin (Alec Tiranti Ltd, UK) mixed with titanium
dioxide (TiO2 ) particles, which provide tissue-like optical scattering, with embedded discrete
R
powder, Thermographic
targets containing a black thermochromic pigment (ChromaZone
Measurements Co. Ltd, UK). When heated, the pigment changes from black to white, with a
nominal activation temperature of 47 ◦ C.
Seven targets were generated by inserting a 12 surface mount resistor together with
a 4.7 k bead thermistor (to monitor the temperature) inside a small plastic cylindrical tube
and filling it with a mixture of thermochromic dye and polyester resin. The concentration of
pigment was 16 mg cm−3, which produces a change in absorption of approximately 0.6 mm−1
when heated above the activation temperature, according to our previous measurements at
690 nm. When extracted from the tube, each target was a 4.5 mm diameter cylinder with a
length of 41 mm. To reduce the number of wires and therefore the possibility of a short circuit
within the narrow targets, the thermistor and heating resistor shared a common wire, as shown
in figure 1(a). The thermistor was placed 5 mm from one end, to allow heat to flow along the
length of the target without being blocked by the thermistor.
The phantom was constructed in four stages. The first stage involved filling a polyethylene
box with a 23 mm thick layer of polyester resin mixed with TiO2 powder to produce
a transport scattering coefficient μs = 0.8 ± 0.05 mm−1, absorption coefficient μa =
0.001 ± 0.0002 mm−1 and dimensions of 115 mm × 100 mm. Once hardened, the block
was removed from the box and the targets were attached to it with the arrangement illustrated
in figure 1(b). This target arrangement minimizes the imaging array dimensions necessary
to cover all targets simultaneously and confines the targets to a central position, which takes
advantage of the higher sensitivity in the centre of the imaging array. The smallest spacing
T Correia et al
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Figure 2. Imaging array with eight sources and eight detectors. D1–D15 are the source–detector
separations.
(This figure is in colour only in the electronic version)
between targets is 11.2 mm, which is sufficient to ensure that heating of a target does not cause
a colour change in its neighbours. The block with attached targets was placed in the box again,
and the remaining space (50 mm) was filled with the same resin mixture described previously.
Finally, the block was removed from the box and machined to provide a flat imaging surface,
where the target nearest the surface was at depth 5 mm and the deepest at 35 mm, as shown in
figure 1(c). The target closest to the surface will be referred to as target 1, the second target
closest to the surface as target 2 and so on. Sockets were attached to the wires and mounted on
a plastic plate fixed on the top of the phantom. Tests on a target embedded in a small volume
of clear resin indicate that 3.5 V delivers a heating power of approximately 1.2 W, which is
sufficient to produce a change in the absorption of the target after approximately 70 seconds,
at room temperature.
3. Phantom measurements
3.1. Optical imaging
The UCL continuous-wave optical topography system described by Everdell et al (2005),
was used to image changes in absorption for each target within the phantom. The sources are
frequency modulated and illuminated simultaneously, so that the contribution from each can be
isolated from the detected signal, sampled at 10 Hz, by Fourier transform. The imaging array
consists of eight detectors and eight sources operating at a wavelength of 670 nm. Data were
collected for all 15 possible source–detector distances, making a total of 64 measurements.
The array configuration is shown in figure 2.
The probe was placed on the centre of the xy surface at z = 0 (using the coordinate system
shown in figure 1(b)), with the centre of the array immediately above the centre of target 2.
Data were acquired for 20 s with the targets at room temperature, and then each target was
heated in turn for approximately 70 s, followed by a cooling period of 120 s to allow the targets
to return to room temperature. For each target and each source–detector channel, a reference
measurement was calculated from the mean signal of the 20 s recorded at room temperature.
Similarly, the activation measurement was obtained by averaging over the 20 s segment of data
centred on the time at which the maximum temperature was reached. Differences between
A quantitative assessment of the depth sensitivity of an optical topography system
(g)
(e)
(c)
6281
(f)
(d)
(b)
(a)
Figure 3. Optical topography images of each target in the xz plane. Bottom images from right to
left correspond to (a) target 1 located at true depth ztrue = 5 mm, (b) target 2 at ztrue = 10 mm and
(c) target 3 at ztrue = 15 mm. Middle images from right to left show (d) target 4 at ztrue = 20 mm
and (e) target 5 at ztrue = 25 mm. Top images from right to left show (f) target 6 at ztrue = 30 mm
and (g) target 7 at ztrue = 35 mm.
the reference measurements and the corresponding activation measurements were used to
generate 3D images representing absorption changes occurring within the phantom. The
linear image reconstruction approach relates the changes in the measured data, y, to changes
in the optical absorption x through y = J x, where J is the Jacobian or sensitivity matrix.
The Jacobian was calculated using the software package TOAST (temporal optical absorption
and scattering tomography), which has been developed by Professor Arridge and Dr Schweiger
at UCL, by solving the diffusion equation using the finite element method (FEM), for both the
forward and adjoint solutions (Arridge et al 2000), assuming uniform optical properties (μs =
0.8 mm−1 and μa = 0.001 mm−1). In order to find x one needs to solve an ill-posed and
under-determined inverse problem, and Tikhonov regularization of the Moore–Penrose inverse
is used in order to obtain a stable solution. This is expressed as x = L−1 J̃ T (J̃ J̃ T +λI )−1 y,
where I is the identity matrix, λ is the regularization parameter, which was set to 0.5% of
the maximum singular value of J J T , σmax (found using the L-curve method (Correia et al
−1 1/2
2009)), and J̃ = J L−1 , where the spatial variant regularization L = diag J J T + σmax
. As
mentioned previously, this type of regularization has been shown to improve the depth spatial
accuracy for images reconstructed from simulated data (Endoh et al 2008).
Figure 3 shows the images for each target in the xz plane at y = 33 mm. The targets
in the image have different relative locations, and visually they seem to be approximately
T Correia et al
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Figure 4. Graph showing how resolution varies with depth.
accurate. It is also clear that the spatial resolution and contrast decreases with depth.
A quantitative analysis necessary to assess the imaging performance is described in the
following section.
3.2. Image analysis
For the purpose of this analysis only the xz cross-sectional images of each target were used.
This gives us information regarding apparent depth and lateral positions of the targets.
Spatial resolution is often characterized by the full width at half maximum (FWHM)
of the point spread function (PSF). The true PSF represents the image of an object of an
infinitesimal size. The image cross-section in the xz plane for each target is, in fact, the
convolution of the true target structure with the PSF. Therefore, the squared FWHM of the
target image is approximately equal to the squared width of the true target (4.5 mm) added
to the squared width of the PSF, i.e. FWHM2target = FWHM2PSF + (4.5)2 . Profiles containing
the highest intensity pixel in the image were generated for both the x and z directions and the
FWHM was calculated
in each case. The estimates of the PSF width were calculated using
FWHMPSF = FWHM2target − (4.5)2 . The error is given by the pixel size, which is 3.33 mm
for the z direction and 3.54 mm for the x direction. Figure 4 shows the mean values of the PSF
width for each target plotted as a function of depth, and as expected the resolution decreases
with depth, except for the discrepancy in the general trend between targets 3 and 4. The lower
resolution of target 3 is almost certainly due to the lower sensitivity of the imaging array
to perturbations located near the edges, as opposed to higher sensitivity to perturbations in
central locations.
Contrast is a measure of the ability to distinguish a feature based on its brightness in
the image
relative to
the background. Image contrast in terms of μa can be expressed as
C = μamax − μabkg μabkg , where μamax refers to the maximum absorption coefficient value
in the image and μabkg is the mean background absorption coefficient. The error associated
with derived contrast values corresponds to the propagation of the uncertainty
associated with
σμ , where σμ is the
the calculation of the background absorption coefficient, i.e., ∂μ∂C
abkg
ab kg
a
bkg
A quantitative assessment of the depth sensitivity of an optical topography system
6283
Figure 5. Graph showing how contrast varies with depth.
standard deviation of μabkg . As shown in figure 5, contrast decreases with increasing depth
up to 20 mm depth, and beyond this point contrast values are very low. This means that the
reconstructed absorption changes become less accurate with depth. The error increases from
4% of the background value for the first target to 15% for the deepest target.
The spatial accuracy is defined as a measure of the error between the true and the apparent
positions of the target. It is assumed that the target closest to the surface was in the correct
location, and therefore the positions of the other targets were calculated relative to this. The
derived from
weighted mean position along the PSF profiles, which
apparent position xm is the
n
μ
is calculated as xm = ni μai xi
ai . Again, the uncertainty in position corresponds to
i
the intrinsic uncertainty of the pixel size. As shown in figure 6, the lateral spatial accuracy
reduces with depth, due to the lower sensitivity of the measurements and the smaller number
of overlapping measurements at deeper regions. As shown in figure 7, the calculated apparent
position in the z axis reveals a very good agreement with the true depth of the target. From the
results described before, one would expect the depth accuracy to be reasonable up to 20 mm
depth. However, the apparent depth agrees with the true depth within the associated error, at
all depths up to at least 30 mm.
4. Discussion
One of the limitations of optical tomography as a brain imaging tool is the low sensitivity to
haemodynamic activity occurring within deeper tissues compared to that occurring nearer the
surface. This is due to the fact that larger source–detector separations are required to sample
at greater depths, and large separation implies more attenuation and less diffusely reflected
light. The volume of tissue sampled also increases with larger separation, and consequently
spatial resolution and contrast also decrease with depth. Nevertheless, considerable effort has
been devoted to the development of image reconstruction algorithms capable of generating 3D
images from diffuse reflectance data, and schemes have been devised which aim to improve
the ability of optical tomography to discriminate along the depth direction [18].
6284
T Correia et al
Figure 6. Graph showing the difference between the real target position and apparent position in
the image, assuming that the target closest to the surface is in the correct position.
Figure 7. Graph showing how the depth of the target in the image varies with true depth. The
expected depth is represented by the straight line.
In this paper we have described a dynamic tissue phantom for quantitative assessment of
the depth sensitivities of optical topography systems. The phantom is easy to use, compact,
involves no moving parts, and gives reliable and repeatable changes in absorption properties.
Its portability enables it to be easily exchanged between users of similar systems, enabling
appropriate comparisons of imaging performance to be made. The background absorption
is deliberately relatively low (representing that of fatty tissue at near-infrared wavelengths),
enabling depth sensitivity to be evaluated at large depths. The optical properties of the resin
block are stable over many years, while the thermochromic pigment is known to maintain
A quantitative assessment of the depth sensitivity of an optical topography system
6285
its properties for at least 12 months (unless subjected to excessive heating, well above the
activation temperature).
The study presented here indicates that while spatial resolution degrades roughly linearly
with depth, contrast falls exponentially. It is also shown that, with an appropriate choice of
regularization parameter, the apparent depth of a feature can match the true depth within the
statistical uncertainty of the measurement. Relatively good resolution, contrast and spatial
accuracy were obtained for images reconstructed of targets up to 20 mm depth. For targets
located deeper, our system was still able to reconstruct sensible images but with lower quality.
An increase in the number of overlapping measurements at deeper regions could potentially
improve the quality of the images of deeper located targets.
There are three factors which contribute towards the poor recovery of true contrast values
shown in figure 5. First, the linear reconstruction algorithm inherently assumes that all
changes in optical properties are small (infinitesimal). Second, the Jacobian matrix used
in the reconstruction algorithm assumes homogeneous optical properties (as is common
practice in scientific applications of optical topography), while the phantom is actually
highly heterogeneous. Although nonlinear methods (where the Jacobian is updated iteratively
(Arridge 1999)) have been shown to provide more quantitatively accurate results, they are
computationally complex and slow, and not suitable for real-time imaging of haemodynamic
activity. Third, the decrease in spatial resolution with depth (shown in figure 4) implies that
the contrast is spread over a greater volume at larger depths, and thus the maximum absorption
value in the image is lower (hence the decrease observed in figure 5).
Although the phantom presented here is of a generic design, the recipe can be adapted to
produce phantoms with any background optical properties and incorporating different shapes
and arrangements of targets. This offers the facility to develop dynamic, fully portable
phantoms for a range of different tests of diffuse optical imaging systems.
Acknowledgments
The work has been supported in part by the EPSRC, and by a scholarship awarded to TC
by Fundação para a Ciência e a Tecnologia, Portugal. This work has also been supported
in part by funding from the EC’s seventh framework programme under grant agreement
FP7-HEALTH-2007-201076.
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