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Phil. Trans. R. Soc. A (2011) 369, 4531–4557
doi:10.1098/rsta.2011.0228
REVIEW
Implicit and explicit prior information in
near-infrared spectral imaging: accuracy,
quantification and diagnostic value
B Y B RIAN W. P OGUE*, S COTT C. D AVIS, F REDERIC L EBLOND,
M ICHAEL A. M ASTANDUNO, H AMID D EHGHANI AND K EITH D. P AULSEN
Thayer School of Engineering, Dartmouth College, Hanover, NH 03755, USA
Near-infrared spectroscopy (NIRS) of tissue provides quantification of absorbers,
scattering and luminescent agents in bulk tissue through the use of measurement data
and assumptions. Prior knowledge can be critical about things such as (i) the tissue shape
and/or structure, (ii) spectral constituents, (iii) limits on parameters, (iv) demographic
or biomarker data, and (v) biophysical models of the temporal signal shapes. A general
framework of NIRS imaging with prior information is presented, showing that prior
information datasets could be incorporated at any step in the NIRS process, with the
general workflow being: (i) data acquisition, (ii) pre-processing, (iii) forward model,
(iv) inversion/reconstruction, (v) post-processing, and (vi) interpretation/diagnosis.
Most of the development in NIRS has used ad hoc or empirical implementations of prior
information such as pre-measured absorber or fluorophore spectra, or tissue shapes as
estimated by additional imaging tools. A comprehensive analysis would examine what
prior information maximizes the accuracy in recovery and value for medical diagnosis,
when implemented at separate stages of the NIRS sequence. Individual applications
of prior information can show increases in accuracy or improved ability to estimate
biochemical features of tissue, while other approaches may not. Most beneficial inclusion
of prior information has been in the inversion/reconstruction process, because it solves
the mathematical intractability. However, it is not clear that this is always the most
beneficial stage.
Keywords: spectroscopy; molecular; tomography; reconstruction; near-infrared; optical
1. Introduction
Imaging using near-infrared spectroscopy (NIRS) has diversified and expanded
into several fields of medical research and science, and pre-packaged biomedical
instruments are now commonplace. While the rate at which new instruments have
been introduced outpaces their utility, research in this field continues to expand.
This expansion is driven by a rapidly increasing pace of discoveries in molecular
*Author for correspondence ([email protected]).
One contribution of 20 to a Theo Murphy Meeting Issue ‘Illuminating the future of biomedical
optics’.
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B. W. Pogue et al.
diagnostic imaging at the pre-clinical stage, with potential to profoundly impact
basic biology and clinical medicine. Most implementations of NIRS use a modelbased estimation strategy for quantifying tissue parameters based upon spectral
features and thus incorporate some form of prior information. For example, NIRS
applications include diffuse optical tomography as well as a wide variety of other
tissue interrogation approaches where biochemical information is derived using
approaches in which spatial tissue sampling is more limited. One aspect that
is shared by all NIRS methodologies is that they rely on the acquisition of
diffuse near-infrared (NIR) light signals followed by the solution of an inverse
problem in the form of either a tomography problem or a simpler type of
least-squares problem, such as curve fitting. In recent years, many sources of
prior information have been examined, taking several different forms and being
analysed quantitatively in terms of their potential to make NIRS amenable to
a level of accuracy that is closer to, if not better than, that achievable with
concurrent imaging modalities that are providing functional and/or molecular
tissue information. The conceptual framework examined in this study is to
identify explicit prior information as a multi-parametric factor that can be
inserted into the NIRS process at several stages. This is illustrated in the
schematic of figure 1. The use of prior information in measuring, processing and
interpreting NIRS data is examined with the goal of identifying key examples in
which explicit prior information benefits the ability to quantify and/or diagnose.
The general framework illustrated in figure 1 is conceptual and can be used
to systematically examine at what stages prior information improves NIRS. The
NIRS process consists of the following steps: (i) data acquisition, (ii) calibration
and pre-processing of the data, (iii) forward light transport modelling, (iv)
inverse problem, (v) post-processing, and (vi) interpretation of the parameters.
Not all of these steps are necessarily used, but this generically describes the
possible steps, and into each of these steps it is feasible to involve prior
information from any number of data streams. These possible streams may consist
of (i) spatial structure information obtained from other imaging modalities,
(ii) spectral information of the molecules being assayed, (iii) physical constraints
on parameters in the model and data, (iv) subject or tissue biomarkers and/or
demographic information, and (v) biophysical models to modify or interpret
the NIRS process data. These are not fundamentally separate prior information
features but rather general categories.
Historically, a majority of NIRS systems rely on spectral prior information as
a basis for interpreting the signals in the process of using this for diagnosis.
NIRS spectral features measured in most cases are broad, provide a direct
transformation to physiological parameters, and the prior measurement of them is
possible without any change in system hardware. Because of these characteristics,
spectral priors arguably have the most effective impact on NIRS quantification
for medical applications. Implementation of spatial prior information as either
region definitions, soft priors or shape-based priors has been a steady area of
investigation, albeit with niche conclusions for specific examples that provide
synergy between NIRS and another imaging system. In the sections below,
prior information streams for NIRS are identified, and the details of their
implementation and potential to impact NIRS quantification and possible
diagnosis are discussed. An attempt is also made to quantify the proven and
potential benefits presented by different prior–NIRS convolutions.
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NIRS process
prior
information
effect upon image
interpretation
acquire data
spatial
structures
pre-process
molecular
spectra
diagnosis
forward
model
parameter
limits
sensitivity
inversion/
reconstruct
biomarkers and
demographics
post-process
biophysical
models
ROC
1-specificity
interpret
[P]
×
(N)
=
(D)
Figure 1. The inclusion of prior information of several different types into the NIRS imaging process
has been implicit in most applications. The reason for using prior information is to improve the final
interpretation of the results, through more accurate quantification, and in medical applications to
improve the sensitivity or specificity of the technique. In a process manner, this can be thought of as
a prior information, P, being convolved into the NIRS steps, N, resulting in a different interpretation
and diagnosis, D. Most of the tests are added either to improve sensitivity or specificity, or to reach
a better compromise of both, as illustrated by the receiver operating characteristic (ROC) curve.
2. Prior information: structure
(a) External shape and internal fluence
Without question, the most dominant factors in NIRS measurement accuracy are
the tissue shape and source–detector coupling to the tissue [1,2]. The external
shape affects the internal light transport distribution and thereby affects the
amplitude of the detected light signal at points on the surface. See figure 2a for
an illustration of how the shape of the tissue may influence the light distribution.
A large number of papers have been published describing logistical approaches to
modelling light in tissues of different shapes and source–detector arrangements
[3], and it is generally thought that using as accurate a light propagation model
as possible is required in order to interpret the data or accurately estimate optical
properties through an inversion of the measurements. In this case, the prior
information is implicit in the design of the system and the forward modelling.
Prior information can be used in the pre-processing of data in order to make
the data more accurately match the model. For example, the first committed
step for light transport modelling is determining, for each optical measurement,
the spatial locations of where light enters tissue and where it is detected. This
is achieved by first reconstructing the outer surface of the specimen using, for
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B. W. Pogue et al.
external biophysical factors
(a)
internal tissue factors
(b)
spatial
and
tissue
exterior shape changes internal fluence
(c)
(d)
0.5
600
900
wavelength (nm)
0.5
600
1.0
absorption
luminescence
fluorescence
elastic
scatter
absorption
coefficient (mm–1)
2.5
reduced scattering
–1
coefficient (mm )
2.5
biochemical
and
biological
internal heterogeneity is averaged over
950
wavelength (nm)
0
600
750
wavelength (nm)
biochemical features have broad spectra
molecular reporters not informing on
microenvironment, such as binding
Figure 2. Major limitations of NIRS imaging. There are biophysical factors and internal tissue
factors that limit the capability of NIRS imaging. (a,b) With respect to spatial issues, it is well
known that the shape of the tissue changes the internal fluence (a) and must be accounted for in
most cases, requiring prior knowledge of the shape of the tissue. The sensitivity profile of the NIR
signal is illustrated in (b) and shows how the details of this internal optical structure may be lost
due to the blurring and partial volume averaging that dominate the recovery of internal values.
(c,d) In terms of biochemical effects, the spectral features of most biological species are broad (c),
leading to an increased value with spectral prior information. Finally, at the microenvironment
level (d), the NIRS data are often not sufficient to understand the binding or partition status of
biochemical species, requiring biomarker or biological modelling prior information. (Online version
in colour.)
example, an optical profilometer or by co-registering the coordinate system
of the NIRS system with that of an imaging modality providing structural
images from which the outer surface of the tissue can be extracted. Then, a
light transport modelling approach must be devised and strategies designed
for finding numerical or analytical solutions that are subsequently used in the
scope of the inverse problem allowing interpretation of the data. Improving
the fidelity of the match between model and data through the use of prior
information for source and detector positioning generally relies on algorithm
designs that combine geometrical hardware considerations for the NIRS system
design with co-registration tools allowing registration with the coordinate system
of the instrument from which the prior information is obtained. As discussed in
more detail in §2b, another important factor in the modelling chain that can
significantly affect the match between model and data is the light propagation
model itself.
The modelling stage of the NIRS process is critical because it is reasonably
well established that model–data mismatch errors can dominate the inversion
process and lead to large bias errors [2,4–6]. However, measurement approaches
can be used that minimize the need for accurate modelling. Such approaches
can be categorized into several different data types, as outlined in table 1. These
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Table 1. The types of data acquisition implemented that implicitly reduce the need for model
accuracy or can utilize simpler empirical models.
acquisition data
example
application
references
wavelength ratio
data
two transmitted
wavelengths
spectral derivative data
fluorescence/excitation ratio
pulse oximetry and tissue
oximetry
multiple analyte analysis
fluorescence imaging
[7–9]
multi-distance
data
estimation of slopes with
linear approximations
robust tissue spectroscopy
systems insensitive to slight
shape changes
[16–18]
small-volume
sampling
scatter spectroscopy
fibre probes with size less than
effective scatter distance
fibre probes sensitive to
absorption only
fibre probes sensitive to
fluorescence and not tissue
[19–22]
absorption spectroscopy
fluorescence spectroscopy
temporal signals
millisecond variations in
tissue
microsecond sampling
picosecond sampling
high-frequency phase shift
derivative with distance
lifetime-based signals
oxygen saturation and
haemodynamic sampling
flash photolysis analysis of
biochemical changes in vivo
ultrafast signals to reduce
model dependence
frequency-domain spectroscopy
of tissue
fluorophore identification or
microenvironment analysis
[10–12]
[13–15]
[23,24]
[25,26]
[8,27,28]
[29,30]
[31–35]
[36,37]
[38]
include: (i) ratiometric or derivative data at two or more different wavelengths, (ii)
multiple-distance ratio or derivative data, (iii) small spatial volumes that either
limit the effect of physical boundaries through scatter and/or absorption, or allow
simpler empirical modelling, and (iv) temporal signals that are less sensitive to
boundaries and/or more robustly insensitive to shape changes. The use of prior
information about the tissue to be sampled is still essential in the design process
with these systems, but can be implemented in the very first step of the NIRS
process, namely data acquisition and calibration. This type of prior information
is often used to eliminate the need for modelling completely, allowing simpler and
perhaps more robust analysis of just the raw data or some processed version of
the data. Examples of and references to these are shown in table 1.
Approaches to analytically model NIRS light transport and allow direct
inversion or fast inversion have dominated the successful commercial applications
and led to several practical biological discoveries [39–42]. Many advanced
solutions to the diffusion equation have been developed for regular geometries
[43] and are widely used in practical systems, although contact variation or
tissue shape, which cannot be accurately accounted for through modelling, can
be a major problem for quantitative parameter estimation. The ideal systems use
data types that are robust and less sensitive to boundary shape changes and fibre
contact issues [35,44], as described in table 1.
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X-ray CT
surgical
microscopy
ultrasound
spatial prior info.
MRI
NIR spectroscopy
wavelength (nm)
1.0
900
0.5
600
wavelength (nm)
luminescence
fluorescence
absorption
950
Raman intensity (a.u)
0.5
600
2.5
elastic
scatter
absorption
coefficient (mm–1)
reduced scattering
coefficient (mm–1)
spectral prior info.
2.5
0
600
wavelength (nm)
750
1.0
Raman
0
900
Raman shift (cm–1)
1500
better specificity through more spectral features
more signal through higher interaction probability
Figure 3. The use of spatial and spectral prior information has been widely studied. Spatial
information can come from imaging systems such as X-ray, magnetic resonance imaging (MRI),
ultrasound or surgical imaging. The integration of NIRS into these systems has been developed
technologically, and the effect of prior spatial information upon imaging accuracy has been studied
in niche cases. The application of spectral priors is thought to be quite beneficial, and has been
widely adopted. In general, it is believed that using more spectral features, and sampling more
wavelengths, improves the specificity of the inversion. Unfortunately, the most specific spectroscopy
methods, such as Raman spectroscopy, also tend to correlate inversely with interaction cross section,
leading to degraded signal-to-noise ratio. (Online version in colour.)
Systems that encode shape, location and external boundaries have been
developed in many research and commercial systems. Figure 3 illustrates a
handful of possible combinations, showing how inclusion of spatial information is
done with additional hardware, and spectral prior inclusion is done with careful
choice of the wavelength and source–detector bands.
One of the earliest hybrid systems was demonstrated by Ntziachristos et al. [45],
where concurrent magnetic resonance imaging (MRI) and NIRS of breast tumours
were used to improve the estimation of indocyanine green uptake concentration
in tumours. The examples shown in this study stimulated substantial interest in
this approach.
(b) Internal shapes and physical limitations of light transport
One of the largest limitations of NIRS in tissue is the physical spread of
light during transmission as a result of multiple scattering effects. This multiple
scattering over large distances leads to diffuse propagation and the inability
to resolve structures near the size of the transport scattering length (near
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Table 2. The different models that have been used for optical radiation transport modelling are
listed (left column) with relative rankings (using + marks) of their applicability and utility for
accurate use with different levels of prior information: −, not feasible; +, permitted but difficult;
++, permitted; and + + +, approach is ideally suited.
radiation transport
model
Boltzmann equation
neutral particles
SPn approximation to
the Boltzmann
Monte Carlo stochastic
diffusion—analytic
diffusion—finite
difference
diffusion—boundary
element
diffusion—finite element
complex complex refractive
hard spatial soft spatial
external boundary index
internal
inversion
inversion
shape
conditions variation heterogeneity constraint constraint
+
+++
+++
+++
++
++
+
+
++
+
++
++
+++
+
++
+++
++
+++
+++
++
+++
++
++
++
++
+++
+++
++
+++
+++
+++
+++
+++
−
+++
−
+++
+++
+++
+++
+++
+++
1 mm). While recovery of heterogeneous regions on the surface can approach the
resolution of microscopy systems, the resolution degrades by orders of magnitude
with depth into the tissue, and so measurements taken over several centimetres
of tissue effectively become averages over larger volumes of tissue. See figure
2b for an illustration of this effect. This phenomenon places size limits on
objects that can be resolved with NIRS [46,47]. Moon et al. [46] developed a
useful metric that estimates that the photon bundle path width, as illustrated in
figure 2b, is approximately 20 per cent of the distance between the source and
detector, when sources and detectors are arranged in transmission geometry. This
suggests that the sensitivity profile (sometimes called the photon measurement
density function, or photon path width) is 2 mm for a 1 cm separation, and
2 cm for a 10 cm separation. These numbers provide a rough guide to the type
of resolution that could be achieved, although it is generally accepted that
regularized inversion solvers can improve this by nearly four times, such that a
fundamental resolution for optical tomography in a 10 cm domain might be closer
to 5 mm. This improvement in resolution comes in part from multiple overlapping
source–detector projections through the domain.
The forward light transport model must have the flexibility to accurately model
any spatial heterogeneity. There are several approaches used to solve this problem,
largely separated into deterministic models, such as the Boltzmann equation for
neutral particle transport, or stochastic approaches, such as a Monte Carlo model.
Table 2 summarizes the major modelling approaches used, with a relative ranking
of their ability to incorporate heterogeneity. Several solutions for Monte Carlo
models exist, and the ability to incorporate arbitrary geometries and arbitrary
internal heterogeneities with ease has improved dramatically in recent years, as
developed by Fang [48]. The inversion of Monte Carlo data is still somewhat
crippled by the need to run repeated forward solutions, which takes significant
amounts of time unless very regular geometries are used [49,50]. However,
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the recent developments in graphics card processing units have made this a
more realistic potential even for complex geometries [48,51]. A more common
approach is the deterministic modelling of the diffusion equation, a second-order
differential equation that is an approximation to the Boltzmann equation (a more
complicated integro-differential equation). The transport equation itself can be
directly solved with discrete ordinates solvers but requires substantial specialized
computer resources and programming. As a consequence, the diffusion equation
is simpler to solve than the transport equation in terms of both the mathematical
complexity and the computational burden involved. Moreover, the diffusion
equation depends on two rather than three phenomenological tissue parameters,
namely, the absorption coefficient and the reduced scattering parameter. In fact,
in the mathematical derivation leading to the diffusion equation, the scattering
coefficient and the so-called phase function are absorbed into one parameter called
the reduced scattering parameter. A critical point here, though, is that it is
even more difficult, if not impossible, to devise generic approaches that would
allow disentangling phase and scattering. However, accomplishing this would be
the minimal step required for using the full benefits of the transport equation
for forward modelling in NIRS. Moreover, the ability to incorporate accurate
boundary conditions and internal heterogeneities also comes at a much greater
difficulty level for approaches based on the Boltzmann equation.
An aspect that is sometimes regarded as an advantage for using the diffusion
equation is the fact that many useful analytical solutions can be derived from
it, while the number of solutions associated with the transport equation is much
more limited. The transport solutions also typically involve several mathematical
simplifying assumptions that limit the scope of their application. However, even
in the case of the diffusion-based analytical equations, solving the internal
heterogeneity must be accomplished using perturbation theory approaches, where
the perturbed optical backgrounds are usually defined from analytical solutions,
making such approaches reliable only for simple imaging geometries (e.g. tissue
slabs in transmission, semi-infinite turbid media for epi-illumination imaging).
These linear perturbation approaches are associated with the other drawback
that the actual optical signal contrast rarely corresponds to optical property
variations that satisfy the linear approximation from which the model is derived.
Nevertheless, this has formed the basis for many reconstruction algorithms,
allowing fast inversion with large datasets. The inclusion of arbitrary boundaries
and arbitrary internal heterogeneity is arguably best achieved with a numerical
model such as the finite element approach, where the domain is solved as a discrete
defined set of points, linked by a mesh of finite basis functions. This approach
was introduced for NIRS about 15 years ago, and has formed the basis of several
available solvers. Some of these solvers have been developed to facilitate the use
of a variety of priors, such as structural priors from MRI or X-ray tomosynthesis
[52,53], spectral priors and biochemical priors.
(c) Explicit prior shape inclusion applications and analysis
The incorporation of internal structures in the inversion problem has been
an area of increased academic interest in recent years. The prior information
approach that is the less involved from both computational and mathematical
complexity standpoints consists in pre-defining the imaging domain into a small
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(a)
(b)
[HbT]
FEM mesh
H2O
StO2
A
b
40
20
MRI of
phantom
0
–20
–40
–40 –20
0
20 40
µs¢
µa
9
true optical
properties
43 40
100 30
100 0.2
1.4 0
3.7
A
b
(c)
[HbT]
StO2
H2O
no prior
11
two layers
of prior info.
100
three layers
of prior info.
0.006
0.02 0.5
1.6
adipose
tissue
glandular
tissue
35 30
80 40 100 0.24 3
adipose
tissue
0
1.5
glandular
tissue
3
2.5
80
2
60
1.5
40
1
20
0.5
0.0
0
Sc A Sc P Sc A
[HbT] StO2 water [HbT] StO2 water
(µM) (%) (%) (µM) (%) (%)
Sc P
Figure 4. (a) Spatial prior inclusion can improve quantitative recovery, as shown in this MRIguided phantom study, where images show the increasing level of spatial prior information used
in the reconstruction algorithm. (b) Spectral prior inclusion can improve both spatial resolution
and quantitative recovery, even without explicit tissue structure, as shown in these images.
(c) Combining NIRS, spatial and spectral priors maximizes recovery accuracy in large regions,
here providing the most benefit for quantifying haemoglobin (HbT), oxygen saturation (StO2 ),
water and scattering values for adipose tissue and fibroglandular tissue in vivo. (Online version
in colour.)
number of specific regions. In this case, reduction of the dimensionality of the
inversion is achieved by assuming the regions to be optically homogeneous.
This approach is often called ‘hard prior’ information and was demonstrated
in breast imaging by Ntziachristos et al. [45]. The composite approach to this
consists in relaxing the homogeneity assumption in order to retain the original
large dimensionality of the inversion domain. However, increased flexibility is
conferred to the inversion problem by applying appropriately penalized inversion
methods that are encoding the prior information but still allow optical property
gradients to exist within each composite region of the domain. A common
implementation of this latter approach used by several groups is to use a
Laplacian-type regularization matrix that smoothes the parameter values within
the pre-defined regions, but allows separate regularization between different
tissue types [54,55]. This has been used in breast imaging with MRI-guided
NIRS by Brooksby et al. [56] to more accurately estimate the concentrations of
haemoglobin, oxygen saturation, water and scattering values in fibroglandular and
adipose tissues in the normal breast. This ‘soft priors’ approach was validated in
multiple tissue-simulating phantom studies as shown in figure 4 and demonstrated
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for tumour imaging by Carpenter et al. [57]. The fluorescence tomography version
of this has been adopted by several groups [58], and has been used in several
pre-clinical murine tumour imaging studies of contrast agent uptake [59,60].
The posterior incorporation of imaging shapes can be done in the analysis
of NIRS data, and this is perhaps the most conventional way to approach
combined modality data. A commercial prototype NIRS breast imager was
shown to have significant discriminatory power between benign and malignant
tumours [61]. The system was designed to be used in concert with mammogram
analysis, thereby allowing posterior added information, for the improvement
of the diagnostic reading, similar to the way ultrasound and mammography
are interpreted together [62]. This added specificity has been confirmed in the
summaries of two academic studies that show promise for interpretation of NIRS
imaging in posterior combination with mammography [63,64]. Poplack et al.
[64] showed that the combination of NIRS and mammography could increase
the positive predictive power significantly. The explicit use of X-ray structure
in NIRS inversion was demonstrated by Fang et al. [65] with a hybrid X-ray
tomosynthesis system. This approach could be used to increase the sensitivity
and/or specificity of the tomosynthesis exam depending upon the approach to
use the prior information. Similarly, NIRS breast tumour imaging to quantify
response from neoadjuvant chemotherapy with a posterior comparison to MRI
by Choe et al. [66] demonstrated that contrast reduction from NIRS added to
the diagnostic value of MRI. Additionally, Jiang et al. [67] examined the role
of defining the region of interest based upon the size of the lesion in the initial
pre-treatment image, and concluded that the quantitative estimate of tumour
haemoglobin is significantly affected by the posterior estimate of lesion size. Thus,
while posterior analysis is perhaps the least complex combination of NIRS and
imaging data, it may become the most utilized as NIRS systems enter the clinic.
(d) Summary of benefits and limits
Several approaches were presented for which the inclusion of prior spatial
information can increase the biological information content that can be derived
from data acquired with NIRS instruments. Significant gains can be realized
by using methodologies where the impact of tissue shape, source and detector
coupling and light transport are minimized by an appropriate choice of data type,
while still ensuring that sufficient tissue sampling is achieved to provide useful
spatial resolution and quantification. Moreover, three approaches for inclusion
of spatial information have been extensively examined to include internal tissue
structures into the inverse problem, referred to here as (i) hard prior, (ii) soft
prior and (iii) posterior use of the structural information. Of these, the one
that is less technically involved is the third one, since it does not require that
the prior information be fed directly to the NIRS reconstruction algorithm,
thereby eliminating any potential reconstruction bias or the propagation of
registration errors in the NIRS images. However, a significant limitation of this
approach is that the information it can convey is limited by the intrinsic spatial
resolution of diffuse optical imaging, namely from a few millimetres to a few
centimetres depending on the interrogated volume size. In other words, although
a tomography dataset might encode the information associated with a small
area of optical contrast (i.e. smaller than the spatial resolution), NIRS images
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Review. Prior information in NIR imaging
4541
might not reveal it, although contrast can be resolved on the structural image.
Alternatively, ‘hard prior’ and ‘soft prior’ methods can potentially reveal the
biological information contained in the NIRS dataset precisely because the prior
spatial information is directly encoded in the inverse problem. Of those two
approaches, the method based on soft priors is preferable because of the reduced
likelihood that spatial biases will be introduced during the inversion process. The
implementation of soft prior constraints requires that it be tested carefully and
the approach be well calibrated, otherwise the use of hard priors is perhaps a safer
implementation. Yet, even with hard priors, it is critical to know that the regions
identified are accurate, otherwise it is easy to recover false values in the regions.
3. Prior information: molecular and biochemical limits
(a) Molecular and biochemical limits
The inclusion of spectral fitting into data analysis has been ubiquitous throughout
most of NIRS’s development owing to its ability to recover concentrations
of biochemical species rather than relative values or absorption coefficients.
Systems with multiple wavelengths have the ability to directly measure the
spectral constituent contributions to the signal independently, and it often
does not require additional hardware. The value of spectral fitting has been
established in many studies, and in bulk tissue spectroscopy without model-based
inversion, this is often done either at the pre-processing stage or at the postprocessing stage, without a significant difference in quantification between the two
approaches. This is because of the linear relationship between the concentration
of chromophores and optical absorption coefficients measured by NIRS in a bulk
tissue measurement paradigm. However, in the NIRS imaging problem based
on matrix inversion, the explicit inclusion of the pre-determined spectra in the
inversion algorithm, rather than in a post-processing step, has been shown to
dramatically improve the quantification and final interpretation. This is generally
considered to be important because the spectral constraint inversion limits the
solution space of the ill-posed problem [68–70] and thereby improves accuracy
spatially. This can be seen in figure 4b where a phantom containing higher blood
concentration was imaged with high noise, resulting in blotchy image features
when spectral information was applied after the absorption coefficient images
had been recovered. The inclusion of the spectral prior constraint directly in
the imaging algorithm improved the recovery significantly for this noisy dataset
[71]. When compared with a spatial prior implementation, it was determined that
spectral prior information was superior in terms of quantitative accuracy, but that
the inclusion of both provided the most accurate quantification, in the setting of
breast imaging [56,69]. Some optimally fitted values for breast tissues are shown
in figure 4c.
The type and quality of prior information should be a key consideration in the
design phase of NIRS systems. In addition to the obvious design considerations
necessary for building hybrid systems, the use of an optimal wavelength set for
particular chromophores should also factor strongly in the system design [72,73].
While this is a subject of ongoing analysis, it is probable that systems that
can adaptively change wavelengths or map to key wavelengths will allow more
accurate quantification of chromophores in tissue.
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Spectral constraints in fluorescence imaging have been widely adopted in
both research and commercial luminescence NIRS systems. Prior knowledge of
the luminescent spectra can be used to separate the signals from the analyte
of interest from contaminating background molecules or to image multiple
analytes simultaneously. Major commercial systems incorporate algorithms to
fit images at multiple wavelength bands to recover fluorophore concentrations,
or use the approach to suppress or remove non-specific background signals [74].
These approaches are essential tools for low-concentration imaging, or multiple
analyte imaging in vivo. Additionally, a large body of work has been produced
to either correct for or exploit the distortion of luminescent spectra by the
absorbing spectra of the tissue. This can correct quantification of signals that
would otherwise be incorrect [75–77] or be used to make an intractable problem
solvable, such as in the case of bioluminescence tomography where spectral
constraints are used to reduce the ill-posedness of the problem [77–82]. However,
an inherent limitation of such approaches is that quantification improvements
heavily rely on prior knowledge not only of the absorption spectra of the tissue
chromophores but also of the magnitude of their relative contributions. In cases
where this information is not available, modelling errors can propagate into the
inversion process, potentially negating any gains attributable to the spectral
constraints. Research attempting to quantify this effect and minimize its impact
in applications such as diffuse fluorescence tomography is ongoing.
The inclusion of physiological limits in the fitting or estimation process is often
essential in the presence of noise, either from stochastic processes (e.g. photondetection shot noise) or from modelling errors (e.g. neglecting to account for
the presence of a chromophore in spectral fitting applications). Such constraints
are often included in fitting algorithms without mention, yet it can be the
key factor in obtaining accurate estimates, especially when multiple overlapping
species are being estimated, such as in endogenous NIRS imaging. Most systems
explicitly incorporate this in the inversion process, requiring a constrained
inversion algorithm. The importance of this problem can be traced to the fact
that, for any inversion problem, there generally exist several equivalent solutions
that match the data for a given set of convergence criteria determined by a
residual expression (e.g. the two-norm of the difference between experimental
data and model) or a generalized norm that includes explicit prior information.
In tomography, this problem is often referred to as ill-posedness and, because of
noise, leads to the paradoxical situation that solutions that fit the measurements
perfectly are always non-physical. Often, these non-physical solutions will, for
example, include negative values for parameters that can only be positive (e.g.
concentration of molecules) and lead to blood concentrations beyond or below
what is physiologically possible. In such cases, inversion algorithms must be
implemented where prior information in the form of bound constraints (e.g.
non-negativity, lower and upper limits for recovered parameters) are introduced.
Endogenous NIRS in vivo breast imaging requires sparse sampling to cover the
large volume of tissue, creating the ill-posedness problem discussed previously.
From a practical standpoint, prior information has become commonplace
in diffuse optical breast imaging, and is quintessential for the recovery of
prognostically valuable images. Figure 5 gives an illustrative example of a
reconstruction of data from a hybrid MRI–optical imaging system. In this
example, both the hardware design and the reconstruction algorithm use
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(a)
45
(d)
23
(b)
34
18
85
(e)
75
(f)
4543
(c)
0.44
0.34
1.49
(g)
1.41
Figure 5. Images of a single tumour imaged with NIR spectroscopy within the MRI: (a) axial MR
image used for segmentation of fat, fibroglandular and tumour regions; (b) total haemoglobin
overlay; (c) three-dimensional image of (b); (d) water image overlay on the MRI; (e) oxygen
saturation percentage; (f ) scatter amplitude; and (g) scatter power. (Online version in colour.)
spatial and spectral prior information. This system incorporates MRI images
by collecting optical and MRI data simultaneously, providing a high-resolution
spatial image from which to generate a boundary mesh. Additionally, adipose
and fibroglandular tissue can be separated and assigned to specific nodes in the
optical domain. By generating the optical solution space from the MRI images, the
datasets are easily co-registered and a ‘hard priors’ reconstruction can be applied.
Figure 5a shows an axial MRI image, which would be used to separate tissue
types. The imaging system also uses spectral prior information in two ways. The
six imaging wavelengths are optimized in the NIR window to maximize sensitivity
to spectral features. As a result, each of the five chromophores seen in figure 5b–g
can be more robustly decoupled during image reconstruction. The reconstruction
algorithm in this case also constrains the solution to be physiologically valid, as
discussed earlier. In this example, the use of spectral and spatial priors reduces
the number of unknowns significantly and allows the optical solution to more
accurately quantify the tissue properties.
Posterior or post-processing analysis of spectra has been suggested in the
interpretation of pathlength based upon assumed concentrations of absorbers,
such as water, in tissue [83]. While this approach is not widely used, it is
possible that such post-processing based upon spectra could provide easier or
more accurate quantification.
(b) Summary of benefits and limits
For the situation of single source–detector measurements it is unclear whether
prior knowledge in pre- versus post-processing is more beneficial, and it seems
probable that the two are substantially similar, owing to the linearity of the data
during processing. For imaging applications where matrix inversion is involved,
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which is ill-posed, there seems to be a significant benefit in the inversion step,
owing to the magnitude of the regularization parameter relative to the matrix
diagonal values. The evidence to date would support the fact that spectral prior
information is perhaps even more important than spatial structure, but this is
probably case-specific. More development and analysis in this area is warranted.
4. Prior information: patient demographics and biomarkers
(a) Patient demographics and biomarkers
Few studies have investigated incorporating demographic information about
patients in NIRS; however, there are some niche applications where it may prove
to be beneficial. NIRS data in breast imaging has shown strong correlations
with demographic factors such as age, body mass index (BMI), radiographic
breast density and menopausal/hormonal status. This correlation implies that
there could be some benefit in using this prior information, perhaps to make
systems simpler or more reliable. Examples of this approach include the use
of radiographic density or BMI to estimate lipid concentration in the breast.
Radiographic density is also highly correlated to optical scattering, indicating
that this dominant factor affecting optical signals may be derived from a
clinical radiograph. In the event that this was shown to be feasible, this
would reduce or eliminate the need for accurate frequency- or time-domain
NIRS measurement systems required for recovering optical scattering properties.
Simpler, less expensive continuous-wave systems would be adequate to quantify
absorbing and/or luminescent NIR signals.
The use of explicit biomarker prior information was recently demonstrated with
a hybrid MRI–NIRS system [84]. This study demonstrated that incorporating
fat/water values estimated with MRI fat–water imaging into the NIRS image
recovery algorithm improved the accuracy of haemoglobin and oxygen saturation
fitting. This hybrid information combination has been largely untested but will
probably have increasing relevance as systems are developed to have mutual,
complementary information sets. Additional data that would be synergistic with
NIRS include blood haematocrit level and concentration of tracers in the blood.
Risk prediction of breast cancer is a recent example of how the intersection
of patient demographics with NIRS has the potential for clinical impact. Lilge
and colleagues (e.g. [85]) have systematically examined the potential for NIRS to
quantify the parenchymal density of the breast. The density is a known correlate
to the risk of incidence of breast cancer, and so NIRS is being examined as a
research tool to help understand the nature of the correlation, and to determine
if NIRS measurement systems could provide a low-cost screening platform for
population risk analysis. In this paradigm, NIRS may be used to test and
analyse the demographic community with a known genetic predisposition to
high incidence of cancer, particularly younger women in whom higher numbers
of mammograms might have adverse effects [86]. In addition to parenchymal
density, biochemical and structural changes related to NIRS data have been
shown to be associated with the risk of cancer [87], further indicating that NIRS
data combined with patient demographic information might provide diagnostic
information about breast cancer risk. This work is still ongoing, but serves as a
key example of the potential synergy that might exist with the right application.
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Table 3. Some of the major biophysical models used in conjunction with NIRS, with applications
and key references.
biophysical model examples
application
reference(s)
molecular diffusion and
degradation models
dissolved oxygen metabolism interpretation
drug photobleaching and transport
drug partitioning and localization
molecular consumption during therapy
[88–91]
[92]
[93]
[94]
compartment rate model
pharmacokinetic analysis of drugs
[95,96]
vascular convection model
blood flow quantification
drug vascular leakage and kinetic identification
[96–100]
[101–105]
viscoelastic model
interpreting response to tissue pressure and
displacement
vascular resistance estimation
[106–112]
[113,114]
enzyme activation
vascular permeability versus cellular binding
receptor internalization and renewal modelling
[115–117]
[118–120]
[121,122]
receptor, ligand and
activatable probe models
(b) Summary of benefits and limits
Strong correlations exist between NIRS data and demographics. Datasets from
different diagnostic modalities may be exchanged or used to reduce uncertainty
in quantification, when applied a priori rather than analysed posterior. The prior
implementation of demographic or biomarker data is largely undeveloped in the
NIRS prior implementation.
5. Prior information: biophysical models
(a) Biophysical models
Biophysical models to interpret the NIRS data have been used widely for a range
of applications. While these could also be incorporated into the NIRS process
at earlier steps, it is most common at the post-processing or interpretation
stage. Examples of biophysical models are listed in table 3. Tissue oxygen
extraction models have perhaps been most widely incorporated into NIRS
endogenous imaging of oxygen saturation because of the potential to estimate
tissue consumption of oxygen in key organs such as the brain or in diseases
such as cancerous tumours. Generally, biophysical model information that could
be included is in three different temporal domains: (i) static information (i.e.
fat, water, blood volumes), (ii) harmonic information (i.e. blood pulsation or
breathing or hormonal cycling), or (iii) dynamic inflow/outflow data (i.e. contrast
agent injection and clearance). The latter two are illustrated in figure 6.
Post-processing of fluorescence data has been widely analysed to study
pharmacokinetics in vivo as a way to improve data interpretation and extract
additional information from the measured signals. Temporal fitting can be used
with compartmental models to estimate the pharmacokinetics of injected dyes
[101,123,124], drug production or bleaching rates [125,126], or drug-binding rates
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(a)
(b)
dynamic/transient
signal
signal
harmonic/pulsatile
time
time
compartment model
1
Ke
recover SaO2 and pulsatile flows
K23
K12
avg. cycles/Fourier filter/lock in
2
K21
3
K32
vascular leakage and binding rate
Figure 6. The type of data collected for transmitted or emitted signals are illustrated as either
(a) harmonic or (b) dynamic transient. If these patterns are known and can be modelled with an
explicit numerical function, then it can be incorporated into the prefiltering, inversion or postprocessing of the data, leading to output of the model biophysical parameters instead of raw data
such as absorption, fluorescence yield or scattering. (Online version in colour.)
in vivo [118]. Temporal analysis was used to illustrate how fluorescence signals can
identify different organs in vivo by Hillman et al. [102]. This is a post-processing
approach to include prior information about the molecules. Incorporation of the
drug kinetics in the forward or inverse photon propagation models has been shown
in just one or two studies [95], and there is a promise that including an accurate
kinetic model in the inversion problem may improve accuracy in quantification.
More complex kinetic or tissue modelling procedures have been studied by some
groups [103]. Additionally, several studies have indicated that better knowledge
of the drug concentration a priori would improve the ability to define the best
acquisition parameters [127], indicating that inclusion in the data acquisition or
system design level could also be beneficial.
Incorporating viscoelastic tissue modelling in NIRS is an approach that has
seen some recent activity. Dynamic measurements induced by changes in pressure
applied to the tissue can provide a rich dataset for robust, often ratiometric,
interpretation of oxygen saturation and total haemoglobin values [106–111]. These
mechanical models are almost uniformly applied in post-processing or forward
modelling [112], owing to the complexity of solving the viscoelastic problem
in irregular domains. While they may introduce additional uncertainty in the
inversion process, if implemented in the right way, they have the potential to
reduce the ill-posedness of the problem and thus offer more accurate diagnostic
performance.
Model-based interpretation of injected tracers is one area where there may
be substantial gains, which would allow NIRS to provide fundamentally new
information that cannot be obtained by other modalities. The key factor in this
is that NIRS imaging allows quantification of more than one analyte in vivo so
multiple species can be used to reference against one another. This has been
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shown for vascular permeability studies [119] and for drug-binding studies [118].
In this type of analysis, the binding rate constant of the targeted probe is directly
related to the drug affinity and the concentration of binding sites within the
tissue. Thus, by combining NIRS measurements or images with compartmentbinding modelling, it is feasible to quantify molecular receptor expression and
affinity in vivo. The processing of this information has been in post-processing to
date, but explicit incorporation of these linear models into the inversion algorithm
with a temporal dataset is readily done. An example of explicit incorporation of
a forward model is in the way spectral constraints are added into a multiplewavelength inversion problem, to reduce the ill-posedness of the inversion and
provide more accurate recovery properties. A similar approach could be tried
with forward physical models, in the inversion problem.
(b) Summary of benefits and limits
Proven benefits have been widespread in post-processing of NIRS data.
Inclusion of biophysical modelling into forward NIRS modelling is probably
somewhat beneficial. However, similar to spectral constraints, there is probably
a major benefit in inclusion into the inverse algorithms.
6. Prior information: impact on diagnosis
Ultimately, any convolution of prior information data streams with NIRS must be
assessed for diagnostic performance. This is a critical component of the innovation
process often missing from NIRS studies. The prior–NIRS convolution must be
assessed against other convolution schemes as well as against clinical and preclinical diagnostic standards. An important consideration in this analysis is the
trade-off between performance and technical complexity. The value of modest
gains in diagnostic power realized through extensive, difficult and time-consuming
imaging strategies must be considered carefully.
Figure 7 illustrates how a receiver operating characteristic (ROC) curve can be
used to compare the diagnostic performance of different prior implementations
that can be used for MRI-guided NIRS imaging. In this example, a coronal MRI
image of a human breast lightly compressed between two plates (figure 7a) was
segmented and used to produce a finite element mesh containing two distinct
tissue regions, an adipose and a fibroglandular region. Each compression plate
is lined with eight optical source–detector fibres for transmitting and receiving
light through the tissue, as illustrated by grey rectangles in figure 7b. The ROC
curve analysis began by generating simulated test domains from the finite element
mesh. A suspicious circular legion was numerically added to the mesh in one of two
locations, either near the centre of the tissue, as shown in figure 7b, or a specified
distance from one edge, as illustrated in figure 7c. The lesion simulates a region
of gadolinium (Gd) enhancement in the MRI image, but may not necessarily be
malignant. The radius of this lesion was varied over the range illustrated in figure
7b,c, and the optical absorption contrast was varied from 0 to 5 : 1 for each lesion
size. Lesions with zero contrast in optical absorption represented an MRI false
positive. For each lesion size/contrast, forward data were generated numerically
and noise added to the measurements. A total of 600 datasets were considered in
this example.
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(a)
(b)
(c)
true positive rate (sensitivity)
(e) 1.0
(d)
(f)
0.8
0.6
0.4
0.2
0
0.5
false positive rate (1-specificity)
1.0
0
0.5
false positive rate (1-specificity)
1.0
Figure 7. (a) A T1-weighted coronal MRI image of a breast compressed between two plates. Tissue
types were segmented and used to generate a two-tissue-region finite element mesh for NIRS
modelling as shown in (b,c). Sixteen fibre probes contact the tissue surface in a transmission
geometry, as illustrated in (b). Regions that simulate suspicious lesions defined by Gd-MRI were
added numerically to the mesh, simulating a positive reading in the MRI image. The size, position
and optical contrast of these lesions were varied over a wide range (the lesion sizes and positions
are illustrated in (b,c)). The ROC curve in (e) demonstrates the improvement in diagnostic
performance when the hard prior approach is used (red curve) versus the approach that uses
the MRI information only in the interpretation step of the imaging process (blue curve). If the
segmentation of the fibroglandular region is incorrect, as shown in (d), the hard prior approach
(red curve) loses much of its diagnostic advantage over the other method (blue curve), as shown
in (f ). (Online version in colour.)
The synthetic optical data were then used to recover and interpret absorption
images using one of two prior-imaging convolutions. The first method applied the
structural prior in the interpretation step, while the second approach considered
the hard-prior method, which incorporated the MRI information directly in the
image reconstruction step. In the former approach, the optical data were used
to perform a ‘no-priors’ image formation. Once the image was recovered, the
average value in the region defined by the lesion in the corresponding MRI image
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was extracted as the diagnostic parameter. The hard-prior approach, on the
other hand, encodes the internal structure of the tissue in optically homogeneous
regions. Thus, the value recovered in this lesion was extracted directly from the
image.
The value of optical absorption in the lesion region was used as the diagnostic
parameter in the ROC curve analysis for both methods shown in figure 7e.
This result demonstrates an improvement in ROC curve performance when the
prior was applied in the reconstruction step as opposed to the interpretation
step. Area-under-the-curve metrics were 0.85 and 0.73 for the hard-prior and
interpretation-only approaches, respectively. However, this analysis assumed
perfect image segmentation of the fibroglandular region. Errors in segmenting
this region will affect the performance of the hard-prior approach but should not
affect the approach that uses the MRI information only in the interpretation step.
To explore to what degree the performance is degraded, the segmentation of the
fibroglandular region used in the hard-prior image reconstruction was dilated, as
shown in figure 7d, and the analysis repeated. ROC curves for the two approaches
under imperfect segmentation conditions are shown in figure 7f , and demonstrate
a significant decrease in diagnostic performance for the hard-prior approach due
to the segmentation error. Analyses such as this can help determine what imaging
strategies are most beneficial under different experimental conditions.
The strategy described above is an effective way to evaluate and compare
different implementations of prior information. ROC curve analysis is the
preferred method for assessing diagnostic performance in most cases (though
specific applications, such as glucose monitoring, have their own standard
diagnostic scales). Other types of analyses are commonly reported for NIRS
imaging, such as spatial resolution, contrast resolution and contrast detail
analysis. While useful for assessing system performance, these analyses should be
considered an intermediate step on the path towards a full diagnostic assessment
using an ROC curve, which also accounts for biological variability. Establishing
truth can be challenging and must be accomplished using accurate gold standards
of conventional medicine. Also, the metrics assessed should match the objectives
of the diagnostic test. In some cases, the aim of the NIRS technique is to quantify
rather than detect diseased tissue, and thus an assessment of detectability would
be inappropriate. This is especially true for paradigms in which structural imaging
modalities are used to identify suspicious lesions and a prior–NIRS convolution
strategy is used to characterize and diagnose the abnormalities. In most cases,
a comprehensive ROC curve study should be the ultimate goal of the NIRS
researcher to determine whether adoption of the technique in the clinic or research
setting is warranted.
7. Conclusions
The observations of improved quantification or improved diagnostic values are a
complex range of niche examples. A few applications show clear and significant
benefits, others demonstrate only modest improvements in diagnosis, and many
have not been tested using the conventions of diagnostic assessment. Table 4
provides a listing of the prior information types from figure 1, along with the NIRS
process steps. The table includes a qualitative ranking of which prior information
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Table 4. Listing of the prior information options and NIRS process steps outlined in figure 1, with
relative scoring of the proven benefit, where notation is as follows: −, no benefit; +, possible benefit;
++, demonstrated some benefit; and + + +, demonstrated major benefit.
types of prior information used
NIRS process step
spatial
structures
molecular
spectra
parameter
limits
biomarkers and
demographics
biophysical
models
data acquisition
pre-processing
forward model
inversion model
post-processing
interpretation
+++
++
+++
++
−
+++
++
+++
−
+++
++
−
+
−
−
+++
++
−
−
−
−
+
++
+++
++
++
+
++
+++
+++
streams have benefits in each of the NIRS steps, using − to indicate no clear
benefit, + to indicate possible benefit, ++ to indicate probable benefit with some
demonstrated evidence, and + + + to indicate a major demonstrated benefit in
quantification or diagnosis.
While these scores are admittedly relative and somewhat subjective, this chart
is an initial attempt to think about this framework for determining how the
benefit from prior information might be maximized in the NIRS process, and
how systems can be designed to maximize quantitative accuracy and ultimately
diagnostic value in terms of the sensitivity and specificity trade-off.
This work was funded by the National Cancer Institute research grants RO1CA069544,
RO1CA109558, K25CA138578 and R01CA120368.
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