review implicit and explicit prior information in near...

Phil. Trans. R. Soc. A (2011) 369, 4531–4557doi:10.1098/rsta.2011.0228

REVIEW

Implicit and explicit prior information innear-infrared spectral imaging: accuracy,

quantification and diagnostic valueBY BRIAN W. POGUE*, SCOTT C. DAVIS, FREDERIC LEBLOND,

MICHAEL A. MASTANDUNO, HAMID DEHGHANI AND KEITH D. PAULSEN

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 dataand assumptions. Prior knowledge can be critical about things such as (i) the tissue shapeand/or structure, (ii) spectral constituents, (iii) limits on parameters, (iv) demographicor biomarker data, and (v) biophysical models of the temporal signal shapes. A generalframework of NIRS imaging with prior information is presented, showing that priorinformation datasets could be incorporated at any step in the NIRS process, with thegeneral 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 priorinformation such as pre-measured absorber or fluorophore spectra, or tissue shapes asestimated by additional imaging tools. A comprehensive analysis would examine whatprior information maximizes the accuracy in recovery and value for medical diagnosis,when implemented at separate stages of the NIRS sequence. Individual applicationsof prior information can show increases in accuracy or improved ability to estimatebiochemical features of tissue, while other approaches may not. Most beneficial inclusionof prior information has been in the inversion/reconstruction process, because it solvesthe mathematical intractability. However, it is not clear that this is always the mostbeneficial stage.

Keywords: spectroscopy; molecular; tomography; reconstruction; near-infrared; optical

1. Introduction

Imaging using near-infrared spectroscopy (NIRS) has diversified and expandedinto several fields of medical research and science, and pre-packaged biomedicalinstruments are now commonplace. While the rate at which new instruments havebeen 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 biomedicaloptics’.

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4532 B. W. Pogue et al.

diagnostic imaging at the pre-clinical stage, with potential to profoundly impactbasic biology and clinical medicine. Most implementations of NIRS use a model-based estimation strategy for quantifying tissue parameters based upon spectralfeatures and thus incorporate some form of prior information. For example, NIRSapplications include diffuse optical tomography as well as a wide variety of othertissue interrogation approaches where biochemical information is derived usingapproaches in which spatial tissue sampling is more limited. One aspect thatis shared by all NIRS methodologies is that they rely on the acquisition ofdiffuse near-infrared (NIR) light signals followed by the solution of an inverseproblem in the form of either a tomography problem or a simpler type ofleast-squares problem, such as curve fitting. In recent years, many sources ofprior information have been examined, taking several different forms and beinganalysed quantitatively in terms of their potential to make NIRS amenable toa level of accuracy that is closer to, if not better than, that achievable withconcurrent imaging modalities that are providing functional and/or moleculartissue information. The conceptual framework examined in this study is toidentify explicit prior information as a multi-parametric factor that can beinserted into the NIRS process at several stages. This is illustrated in theschematic of figure 1. The use of prior information in measuring, processing andinterpreting NIRS data is examined with the goal of identifying key examples inwhich explicit prior information benefits the ability to quantify and/or diagnose.

The general framework illustrated in figure 1 is conceptual and can be usedto systematically examine at what stages prior information improves NIRS. TheNIRS process consists of the following steps: (i) data acquisition, (ii) calibrationand 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 thepossible steps, and into each of these steps it is feasible to involve priorinformation from any number of data streams. These possible streams may consistof (i) spatial structure information obtained from other imaging modalities,(ii) spectral information of the molecules being assayed, (iii) physical constraintson parameters in the model and data, (iv) subject or tissue biomarkers and/ordemographic information, and (v) biophysical models to modify or interpretthe NIRS process data. These are not fundamentally separate prior informationfeatures but rather general categories.

Historically, a majority of NIRS systems rely on spectral prior information asa basis for interpreting the signals in the process of using this for diagnosis.NIRS spectral features measured in most cases are broad, provide a directtransformation to physiological parameters, and the prior measurement of them ispossible without any change in system hardware. Because of these characteristics,spectral priors arguably have the most effective impact on NIRS quantificationfor medical applications. Implementation of spatial prior information as eitherregion definitions, soft priors or shape-based priors has been a steady area ofinvestigation, albeit with niche conclusions for specific examples that providesynergy between NIRS and another imaging system. In the sections below,prior information streams for NIRS are identified, and the details of theirimplementation and potential to impact NIRS quantification and possiblediagnosis are discussed. An attempt is also made to quantify the proven andpotential benefits presented by different prior–NIRS convolutions.

Phil. Trans. R. Soc. A (2011)



Review. Prior information in NIR imaging 4533

priorinformation

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interpretation

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[P] (N)× (D)=

Figure 1. The inclusion of prior information of several different types into the NIRS imaging processhas been implicit in most applications. The reason for using prior information is to improve the finalinterpretation of the results, through more accurate quantification, and in medical applications toimprove the sensitivity or specificity of the technique. In a process manner, this can be thought of asa prior information, P, being convolved into the NIRS steps, N, resulting in a different interpretationand diagnosis, D. Most of the tests are added either to improve sensitivity or specificity, or to reacha 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 arethe tissue shape and source–detector coupling to the tissue [1,2]. The externalshape affects the internal light transport distribution and thereby affects theamplitude of the detected light signal at points on the surface. See figure 2a foran illustration of how the shape of the tissue may influence the light distribution.A large number of papers have been published describing logistical approaches tomodelling light in tissues of different shapes and source–detector arrangements[3], and it is generally thought that using as accurate a light propagation modelas possible is required in order to interpret the data or accurately estimate opticalproperties through an inversion of the measurements. In this case, the priorinformation 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 makethe data more accurately match the model. For example, the first committedstep for light transport modelling is determining, for each optical measurement,the spatial locations of where light enters tissue and where it is detected. Thisis achieved by first reconstructing the outer surface of the specimen using, for





external biophysical factors

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exterior shape changes internal fluence internal heterogeneity is averaged over

biochemical features have broad spectra

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microenvironment, such as bindingmolecular reporters not informing on

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Figure 2. Major limitations of NIRS imaging. There are biophysical factors and internal tissuefactors that limit the capability of NIRS imaging. (a,b) With respect to spatial issues, it is wellknown that the shape of the tissue changes the internal fluence (a) and must be accounted for inmost cases, requiring prior knowledge of the shape of the tissue. The sensitivity profile of the NIRsignal is illustrated in (b) and shows how the details of this internal optical structure may be lostdue 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 microenvironmentlevel (d), the NIRS data are often not sufficient to understand the binding or partition status ofbiochemical species, requiring biomarker or biological modelling prior information. (Online versionin colour.)

example, an optical profilometer or by co-registering the coordinate systemof the NIRS system with that of an imaging modality providing structuralimages from which the outer surface of the tissue can be extracted. Then, alight transport modelling approach must be devised and strategies designedfor finding numerical or analytical solutions that are subsequently used in thescope of the inverse problem allowing interpretation of the data. Improvingthe fidelity of the match between model and data through the use of priorinformation for source and detector positioning generally relies on algorithmdesigns that combine geometrical hardware considerations for the NIRS systemdesign with co-registration tools allowing registration with the coordinate systemof the instrument from which the prior information is obtained. As discussed inmore detail in §2b, another important factor in the modelling chain that cansignificantly affect the match between model and data is the light propagationmodel itself.

The modelling stage of the NIRS process is critical because it is reasonablywell established that model–data mismatch errors can dominate the inversionprocess and lead to large bias errors [2,4–6]. However, measurement approachescan be used that minimize the need for accurate modelling. Such approachescan be categorized into several different data types, as outlined in table 1. These





Table 1. The types of data acquisition implemented that implicitly reduce the need for modelaccuracy or can utilize simpler empirical models.

acquisition data example application references

wavelength ratiodata

two transmittedwavelengths

pulse oximetry and tissueoximetry

[7–9]

spectral derivative data multiple analyte analysis [10–12]fluorescence/excitation ratio fluorescence imaging [13–15]

multi-distancedata

estimation of slopes withlinear approximations

robust tissue spectroscopysystems insensitive to slightshape changes

[16–18]

small-volumesampling

scatter spectroscopy fibre probes with size less thaneffective scatter distance

[19–22]

absorption spectroscopy fibre probes sensitive toabsorption only

[23,24]

fluorescence spectroscopy fibre probes sensitive tofluorescence and not tissue

[25,26]

temporal signals millisecond variations intissue

oxygen saturation andhaemodynamic sampling

[8,27,28]

microsecond sampling flash photolysis analysis ofbiochemical changes in vivo

[29,30]

picosecond sampling ultrafast signals to reducemodel dependence

[31–35]

high-frequency phase shiftderivative with distance

frequency-domain spectroscopyof tissue

[36,37]

lifetime-based signals fluorophore identification ormicroenvironment analysis

[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 eitherlimit the effect of physical boundaries through scatter and/or absorption, or allowsimpler empirical modelling, and (iv) temporal signals that are less sensitive toboundaries and/or more robustly insensitive to shape changes. The use of priorinformation about the tissue to be sampled is still essential in the design processwith these systems, but can be implemented in the very first step of the NIRSprocess, namely data acquisition and calibration. This type of prior informationis often used to eliminate the need for modelling completely, allowing simpler andperhaps more robust analysis of just the raw data or some processed version ofthe data. Examples of and references to these are shown in table 1.

Approaches to analytically model NIRS light transport and allow directinversion or fast inversion have dominated the successful commercial applicationsand led to several practical biological discoveries [39–42]. Many advancedsolutions to the diffusion equation have been developed for regular geometries[43] and are widely used in practical systems, although contact variation ortissue shape, which cannot be accurately accounted for through modelling, canbe a major problem for quantitative parameter estimation. The ideal systems usedata types that are robust and less sensitive to boundary shape changes and fibrecontact issues [35,44], as described in table 1.





X-ray CTsp

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more signal through higher interaction probability

MRIsurgical

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900 600 wavelength (nm) 950 600 wavelength (nm) Raman shift (cm–1)750 900 1500

NIR spectroscopy

Figure 3. The use of spatial and spectral prior information has been widely studied. Spatialinformation 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 developedtechnologically, and the effect of prior spatial information upon imaging accuracy has been studiedin niche cases. The application of spectral priors is thought to be quite beneficial, and has beenwidely adopted. In general, it is believed that using more spectral features, and sampling morewavelengths, improves the specificity of the inversion. Unfortunately, the most specific spectroscopymethods, 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 beendeveloped in many research and commercial systems. Figure 3 illustrates ahandful of possible combinations, showing how inclusion of spatial information isdone with additional hardware, and spectral prior inclusion is done with carefulchoice 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 tumourswere used to improve the estimation of indocyanine green uptake concentrationin tumours. The examples shown in this study stimulated substantial interest inthis approach.

(b) Internal shapes and physical limitations of light transport

One of the largest limitations of NIRS in tissue is the physical spread oflight during transmission as a result of multiple scattering effects. This multiplescattering over large distances leads to diffuse propagation and the inabilityto resolve structures near the size of the transport scattering length (near





Table 2. The different models that have been used for optical radiation transport modelling arelisted (left column) with relative rankings (using + marks) of their applicability and utility foraccurate use with different levels of prior information: −, not feasible; +, permitted but difficult;++, permitted; and + + +, approach is ideally suited.

complex complex refractive hard spatial soft spatialradiation transport external boundary index internal inversion inversionmodel shape conditions variation heterogeneity constraint constraint

Boltzmann equationneutral particles

+ + + + + + + + + + ++ ++

SPn approximation tothe Boltzmann

+ + ++ + ++ ++

Monte Carlo stochastic + + + + + + + + + ++ ++ ++diffusion—analytic + ++ ++ ++ + + + + + +diffusion—finite

difference++ + + + + + + ++ + + + + + +

diffusion—boundaryelement

+ + + + + + + + + − + + + −

diffusion—finite element + + + + + + + + + + + + + + + + + +

1 mm). While recovery of heterogeneous regions on the surface can approach theresolution of microscopy systems, the resolution degrades by orders of magnitudewith depth into the tissue, and so measurements taken over several centimetresof tissue effectively become averages over larger volumes of tissue. See figure2b for an illustration of this effect. This phenomenon places size limits onobjects that can be resolved with NIRS [46,47]. Moon et al. [46] developed auseful metric that estimates that the photon bundle path width, as illustrated infigure 2b, is approximately 20 per cent of the distance between the source anddetector, when sources and detectors are arranged in transmission geometry. Thissuggests that the sensitivity profile (sometimes called the photon measurementdensity function, or photon path width) is 2 mm for a 1 cm separation, and2 cm for a 10 cm separation. These numbers provide a rough guide to the typeof resolution that could be achieved, although it is generally accepted thatregularized inversion solvers can improve this by nearly four times, such that afundamental resolution for optical tomography in a 10 cm domain might be closerto 5 mm. This improvement in resolution comes in part from multiple overlappingsource–detector projections through the domain.

The forward light transport model must have the flexibility to accurately modelany spatial heterogeneity. There are several approaches used to solve this problem,largely separated into deterministic models, such as the Boltzmann equation forneutral particle transport, or stochastic approaches, such as a Monte Carlo model.Table 2 summarizes the major modelling approaches used, with a relative rankingof their ability to incorporate heterogeneity. Several solutions for Monte Carlomodels exist, and the ability to incorporate arbitrary geometries and arbitraryinternal heterogeneities with ease has improved dramatically in recent years, asdeveloped by Fang [48]. The inversion of Monte Carlo data is still somewhatcrippled by the need to run repeated forward solutions, which takes significantamounts of time unless very regular geometries are used [49,50]. However,





the recent developments in graphics card processing units have made this amore realistic potential even for complex geometries [48,51]. A more commonapproach is the deterministic modelling of the diffusion equation, a second-orderdifferential equation that is an approximation to the Boltzmann equation (a morecomplicated integro-differential equation). The transport equation itself can bedirectly solved with discrete ordinates solvers but requires substantial specializedcomputer resources and programming. As a consequence, the diffusion equationis simpler to solve than the transport equation in terms of both the mathematicalcomplexity and the computational burden involved. Moreover, the diffusionequation 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 scatteringcoefficient and the so-called phase function are absorbed into one parameter calledthe reduced scattering parameter. A critical point here, though, is that it iseven more difficult, if not impossible, to devise generic approaches that wouldallow disentangling phase and scattering. However, accomplishing this would bethe minimal step required for using the full benefits of the transport equationfor forward modelling in NIRS. Moreover, the ability to incorporate accurateboundary conditions and internal heterogeneities also comes at a much greaterdifficulty level for approaches based on the Boltzmann equation.

An aspect that is sometimes regarded as an advantage for using the diffusionequation is the fact that many useful analytical solutions can be derived fromit, while the number of solutions associated with the transport equation is muchmore limited. The transport solutions also typically involve several mathematicalsimplifying assumptions that limit the scope of their application. However, evenin the case of the diffusion-based analytical equations, solving the internalheterogeneity must be accomplished using perturbation theory approaches, wherethe perturbed optical backgrounds are usually defined from analytical solutions,making such approaches reliable only for simple imaging geometries (e.g. tissueslabs in transmission, semi-infinite turbid media for epi-illumination imaging).These linear perturbation approaches are associated with the other drawbackthat the actual optical signal contrast rarely corresponds to optical propertyvariations 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 boundariesand arbitrary internal heterogeneity is arguably best achieved with a numericalmodel such as the finite element approach, where the domain is solved as a discretedefined set of points, linked by a mesh of finite basis functions. This approachwas introduced for NIRS about 15 years ago, and has formed the basis of severalavailable solvers. Some of these solvers have been developed to facilitate the useof 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 beenan area of increased academic interest in recent years. The prior informationapproach that is the less involved from both computational and mathematicalcomplexity standpoints consists in pre-defining the imaging domain into a small





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Figure 4. (a) Spatial prior inclusion can improve quantitative recovery, as shown in this MRI-guided phantom study, where images show the increasing level of spatial prior information usedin the reconstruction algorithm. (b) Spectral prior inclusion can improve both spatial resolutionand 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 versionin colour.)

number of specific regions. In this case, reduction of the dimensionality of theinversion is achieved by assuming the regions to be optically homogeneous.This approach is often called ‘hard prior’ information and was demonstratedin breast imaging by Ntziachristos et al. [45]. The composite approach to thisconsists in relaxing the homogeneity assumption in order to retain the originallarge dimensionality of the inversion domain. However, increased flexibility isconferred to the inversion problem by applying appropriately penalized inversionmethods that are encoding the prior information but still allow optical propertygradients to exist within each composite region of the domain. A commonimplementation of this latter approach used by several groups is to use aLaplacian-type regularization matrix that smoothes the parameter values withinthe pre-defined regions, but allows separate regularization between differenttissue types [54,55]. This has been used in breast imaging with MRI-guidedNIRS by Brooksby et al. [56] to more accurately estimate the concentrations ofhaemoglobin, oxygen saturation, water and scattering values in fibroglandular andadipose tissues in the normal breast. This ‘soft priors’ approach was validated inmultiple tissue-simulating phantom studies as shown in figure 4 and demonstrated





for tumour imaging by Carpenter et al. [57]. The fluorescence tomography versionof this has been adopted by several groups [58], and has been used in severalpre-clinical murine tumour imaging studies of contrast agent uptake [59,60].

The posterior incorporation of imaging shapes can be done in the analysisof NIRS data, and this is perhaps the most conventional way to approachcombined modality data. A commercial prototype NIRS breast imager wasshown to have significant discriminatory power between benign and malignanttumours [61]. The system was designed to be used in concert with mammogramanalysis, thereby allowing posterior added information, for the improvementof the diagnostic reading, similar to the way ultrasound and mammographyare interpreted together [62]. This added specificity has been confirmed in thesummaries of two academic studies that show promise for interpretation of NIRSimaging in posterior combination with mammography [63,64]. Poplack et al.[64] showed that the combination of NIRS and mammography could increasethe positive predictive power significantly. The explicit use of X-ray structurein NIRS inversion was demonstrated by Fang et al. [65] with a hybrid X-raytomosynthesis system. This approach could be used to increase the sensitivityand/or specificity of the tomosynthesis exam depending upon the approach touse the prior information. Similarly, NIRS breast tumour imaging to quantifyresponse from neoadjuvant chemotherapy with a posterior comparison to MRIby Choe et al. [66] demonstrated that contrast reduction from NIRS added tothe diagnostic value of MRI. Additionally, Jiang et al. [67] examined the roleof defining the region of interest based upon the size of the lesion in the initialpre-treatment image, and concluded that the quantitative estimate of tumourhaemoglobin is significantly affected by the posterior estimate of lesion size. Thus,while posterior analysis is perhaps the least complex combination of NIRS andimaging 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 spatialinformation can increase the biological information content that can be derivedfrom data acquired with NIRS instruments. Significant gains can be realizedby using methodologies where the impact of tissue shape, source and detectorcoupling and light transport are minimized by an appropriate choice of data type,while still ensuring that sufficient tissue sampling is achieved to provide usefulspatial resolution and quantification. Moreover, three approaches for inclusionof spatial information have been extensively examined to include internal tissuestructures into the inverse problem, referred to here as (i) hard prior, (ii) softprior and (iii) posterior use of the structural information. Of these, the onethat is less technically involved is the third one, since it does not require thatthe prior information be fed directly to the NIRS reconstruction algorithm,thereby eliminating any potential reconstruction bias or the propagation ofregistration errors in the NIRS images. However, a significant limitation of thisapproach is that the information it can convey is limited by the intrinsic spatialresolution of diffuse optical imaging, namely from a few millimetres to a fewcentimetres depending on the interrogated volume size. In other words, althougha tomography dataset might encode the information associated with a smallarea of optical contrast (i.e. smaller than the spatial resolution), NIRS images





might not reveal it, although contrast can be resolved on the structural image.Alternatively, ‘hard prior’ and ‘soft prior’ methods can potentially reveal thebiological information contained in the NIRS dataset precisely because the priorspatial information is directly encoded in the inverse problem. Of those twoapproaches, the method based on soft priors is preferable because of the reducedlikelihood that spatial biases will be introduced during the inversion process. Theimplementation of soft prior constraints requires that it be tested carefully andthe approach be well calibrated, otherwise the use of hard priors is perhaps a saferimplementation. Yet, even with hard priors, it is critical to know that the regionsidentified 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 throughoutmost of NIRS’s development owing to its ability to recover concentrationsof biochemical species rather than relative values or absorption coefficients.Systems with multiple wavelengths have the ability to directly measure thespectral constituent contributions to the signal independently, and it oftendoes not require additional hardware. The value of spectral fitting has beenestablished in many studies, and in bulk tissue spectroscopy without model-basedinversion, this is often done either at the pre-processing stage or at the post-processing stage, without a significant difference in quantification between the twoapproaches. This is because of the linear relationship between the concentrationof chromophores and optical absorption coefficients measured by NIRS in a bulktissue measurement paradigm. However, in the NIRS imaging problem basedon matrix inversion, the explicit inclusion of the pre-determined spectra in theinversion algorithm, rather than in a post-processing step, has been shown todramatically improve the quantification and final interpretation. This is generallyconsidered to be important because the spectral constraint inversion limits thesolution space of the ill-posed problem [68–70] and thereby improves accuracyspatially. This can be seen in figure 4b where a phantom containing higher bloodconcentration was imaged with high noise, resulting in blotchy image featureswhen spectral information was applied after the absorption coefficient imageshad been recovered. The inclusion of the spectral prior constraint directly inthe imaging algorithm improved the recovery significantly for this noisy dataset[71]. When compared with a spatial prior implementation, it was determined thatspectral prior information was superior in terms of quantitative accuracy, but thatthe inclusion of both provided the most accurate quantification, in the setting ofbreast imaging [56,69]. Some optimally fitted values for breast tissues are shownin figure 4c.

The type and quality of prior information should be a key consideration in thedesign phase of NIRS systems. In addition to the obvious design considerationsnecessary for building hybrid systems, the use of an optimal wavelength set forparticular chromophores should also factor strongly in the system design [72,73].While this is a subject of ongoing analysis, it is probable that systems thatcan adaptively change wavelengths or map to key wavelengths will allow moreaccurate quantification of chromophores in tissue.





Spectral constraints in fluorescence imaging have been widely adopted inboth research and commercial luminescence NIRS systems. Prior knowledge ofthe luminescent spectra can be used to separate the signals from the analyteof interest from contaminating background molecules or to image multipleanalytes simultaneously. Major commercial systems incorporate algorithms tofit 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 multipleanalyte imaging in vivo. Additionally, a large body of work has been producedto either correct for or exploit the distortion of luminescent spectra by theabsorbing spectra of the tissue. This can correct quantification of signals thatwould otherwise be incorrect [75–77] or be used to make an intractable problemsolvable, such as in the case of bioluminescence tomography where spectralconstraints are used to reduce the ill-posedness of the problem [77–82]. However,an inherent limitation of such approaches is that quantification improvementsheavily rely on prior knowledge not only of the absorption spectra of the tissuechromophores but also of the magnitude of their relative contributions. In caseswhere this information is not available, modelling errors can propagate into theinversion process, potentially negating any gains attributable to the spectralconstraints. Research attempting to quantify this effect and minimize its impactin applications such as diffuse fluorescence tomography is ongoing.

The inclusion of physiological limits in the fitting or estimation process is oftenessential in the presence of noise, either from stochastic processes (e.g. photon-detection shot noise) or from modelling errors (e.g. neglecting to account forthe presence of a chromophore in spectral fitting applications). Such constraintsare often included in fitting algorithms without mention, yet it can be thekey factor in obtaining accurate estimates, especially when multiple overlappingspecies are being estimated, such as in endogenous NIRS imaging. Most systemsexplicitly incorporate this in the inversion process, requiring a constrainedinversion algorithm. The importance of this problem can be traced to the factthat, for any inversion problem, there generally exist several equivalent solutionsthat match the data for a given set of convergence criteria determined by aresidual expression (e.g. the two-norm of the difference between experimentaldata and model) or a generalized norm that includes explicit prior information.In tomography, this problem is often referred to as ill-posedness and, because ofnoise, leads to the paradoxical situation that solutions that fit the measurementsperfectly are always non-physical. Often, these non-physical solutions will, forexample, include negative values for parameters that can only be positive (e.g.concentration of molecules) and lead to blood concentrations beyond or belowwhat is physiologically possible. In such cases, inversion algorithms must beimplemented 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 thelarge volume of tissue, creating the ill-posedness problem discussed previously.From a practical standpoint, prior information has become commonplacein diffuse optical breast imaging, and is quintessential for the recovery ofprognostically valuable images. Figure 5 gives an illustrative example of areconstruction of data from a hybrid MRI–optical imaging system. In thisexample, both the hardware design and the reconstruction algorithm use





(a)

(d) (e) ( f ) (g)

(b) 23

1845 85 0.44 1.49

34 75 0.34 1.41

(c)

Figure 5. Images of a single tumour imaged with NIR spectroscopy within the MRI: (a) axial MRimage used for segmentation of fat, fibroglandular and tumour regions; (b) total haemoglobinoverlay; (c) three-dimensional image of (b); (d) water image overlay on the MRI; (e) oxygensaturation percentage; (f ) scatter amplitude; and (g) scatter power. (Online version in colour.)

spatial and spectral prior information. This system incorporates MRI imagesby collecting optical and MRI data simultaneously, providing a high-resolutionspatial image from which to generate a boundary mesh. Additionally, adiposeand fibroglandular tissue can be separated and assigned to specific nodes in theoptical domain. By generating the optical solution space from the MRI images, thedatasets 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 tissuetypes. The imaging system also uses spectral prior information in two ways. Thesix imaging wavelengths are optimized in the NIR window to maximize sensitivityto spectral features. As a result, each of the five chromophores seen in figure 5b–gcan be more robustly decoupled during image reconstruction. The reconstructionalgorithm in this case also constrains the solution to be physiologically valid, asdiscussed earlier. In this example, the use of spectral and spatial priors reducesthe number of unknowns significantly and allows the optical solution to moreaccurately quantify the tissue properties.

Posterior or post-processing analysis of spectra has been suggested in theinterpretation of pathlength based upon assumed concentrations of absorbers,such as water, in tissue [83]. While this approach is not widely used, it ispossible that such post-processing based upon spectra could provide easier ormore accurate quantification.

(b) Summary of benefits and limits

For the situation of single source–detector measurements it is unclear whetherprior knowledge in pre- versus post-processing is more beneficial, and it seemsprobable that the two are substantially similar, owing to the linearity of the dataduring processing. For imaging applications where matrix inversion is involved,





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 matrixdiagonal values. The evidence to date would support the fact that spectral priorinformation is perhaps even more important than spatial structure, but this isprobably 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 aboutpatients in NIRS; however, there are some niche applications where it may proveto be beneficial. NIRS data in breast imaging has shown strong correlationswith demographic factors such as age, body mass index (BMI), radiographicbreast density and menopausal/hormonal status. This correlation implies thatthere could be some benefit in using this prior information, perhaps to makesystems simpler or more reliable. Examples of this approach include the useof radiographic density or BMI to estimate lipid concentration in the breast.Radiographic density is also highly correlated to optical scattering, indicatingthat this dominant factor affecting optical signals may be derived from aclinical radiograph. In the event that this was shown to be feasible, thiswould reduce or eliminate the need for accurate frequency- or time-domainNIRS measurement systems required for recovering optical scattering properties.Simpler, less expensive continuous-wave systems would be adequate to quantifyabsorbing and/or luminescent NIR signals.

The use of explicit biomarker prior information was recently demonstrated witha hybrid MRI–NIRS system [84]. This study demonstrated that incorporatingfat/water values estimated with MRI fat–water imaging into the NIRS imagerecovery algorithm improved the accuracy of haemoglobin and oxygen saturationfitting. This hybrid information combination has been largely untested but willprobably have increasing relevance as systems are developed to have mutual,complementary information sets. Additional data that would be synergistic withNIRS include blood haematocrit level and concentration of tracers in the blood.

Risk prediction of breast cancer is a recent example of how the intersectionof patient demographics with NIRS has the potential for clinical impact. Lilgeand colleagues (e.g. [85]) have systematically examined the potential for NIRS toquantify the parenchymal density of the breast. The density is a known correlateto the risk of incidence of breast cancer, and so NIRS is being examined as aresearch tool to help understand the nature of the correlation, and to determineif NIRS measurement systems could provide a low-cost screening platform forpopulation risk analysis. In this paradigm, NIRS may be used to test andanalyse the demographic community with a known genetic predisposition tohigh incidence of cancer, particularly younger women in whom higher numbersof mammograms might have adverse effects [86]. In addition to parenchymaldensity, biochemical and structural changes related to NIRS data have beenshown to be associated with the risk of cancer [87], further indicating that NIRSdata combined with patient demographic information might provide diagnosticinformation about breast cancer risk. This work is still ongoing, but serves as akey example of the potential synergy that might exist with the right application.





Table 3. Some of the major biophysical models used in conjunction with NIRS, with applicationsand key references.

biophysical model examples application reference(s)

molecular diffusion and dissolved oxygen metabolism interpretation [88–91]degradation models drug photobleaching and transport [92]

drug partitioning and localization [93]molecular consumption during therapy [94]

compartment rate model pharmacokinetic analysis of drugs [95,96]

vascular convection model blood flow quantification [96–100]drug vascular leakage and kinetic identification [101–105]

viscoelastic model interpreting response to tissue pressure anddisplacement

[106–112]

vascular resistance estimation [113,114]

receptor, ligand and enzyme activation [115–117]activatable probe models vascular permeability versus cellular binding [118–120]

receptor internalization and renewal modelling [121,122]


Strong correlations exist between NIRS data and demographics. Datasets fromdifferent diagnostic modalities may be exchanged or used to reduce uncertaintyin quantification, when applied a priori rather than analysed posterior. The priorimplementation of demographic or biomarker data is largely undeveloped in theNIRS prior implementation.

5. Prior information: biophysical models

(a) Biophysical models

Biophysical models to interpret the NIRS data have been used widely for a rangeof applications. While these could also be incorporated into the NIRS processat earlier steps, it is most common at the post-processing or interpretationstage. Examples of biophysical models are listed in table 3. Tissue oxygenextraction models have perhaps been most widely incorporated into NIRSendogenous imaging of oxygen saturation because of the potential to estimatetissue consumption of oxygen in key organs such as the brain or in diseasessuch as cancerous tumours. Generally, biophysical model information that couldbe included is in three different temporal domains: (i) static information (i.e.fat, water, blood volumes), (ii) harmonic information (i.e. blood pulsation orbreathing or hormonal cycling), or (iii) dynamic inflow/outflow data (i.e. contrastagent injection and clearance). The latter two are illustrated in figure 6.

Post-processing of fluorescence data has been widely analysed to studypharmacokinetics in vivo as a way to improve data interpretation and extractadditional information from the measured signals. Temporal fitting can be usedwith compartmental models to estimate the pharmacokinetics of injected dyes[101,123,124], drug production or bleaching rates [125,126], or drug-binding rates





harmonic/pulsatile dynamic/transient

time

(a) (b)

time

K12

K21KeK32

K23

compartment model

1 2 3avg. cycles/Fourier filter/lock in

vascular leakage and binding raterecover SaO2 and pulsatile flows

sign

al

sign

al

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 anexplicit numerical function, then it can be incorporated into the prefiltering, inversion or post-processing of the data, leading to output of the model biophysical parameters instead of raw datasuch as absorption, fluorescence yield or scattering. (Online version in colour.)

in vivo [118]. Temporal analysis was used to illustrate how fluorescence signals canidentify different organs in vivo by Hillman et al. [102]. This is a post-processingapproach to include prior information about the molecules. Incorporation of thedrug kinetics in the forward or inverse photon propagation models has been shownin just one or two studies [95], and there is a promise that including an accuratekinetic model in the inversion problem may improve accuracy in quantification.More complex kinetic or tissue modelling procedures have been studied by somegroups [103]. Additionally, several studies have indicated that better knowledgeof the drug concentration a priori would improve the ability to define the bestacquisition parameters [127], indicating that inclusion in the data acquisition orsystem design level could also be beneficial.

Incorporating viscoelastic tissue modelling in NIRS is an approach that hasseen some recent activity. Dynamic measurements induced by changes in pressureapplied to the tissue can provide a rich dataset for robust, often ratiometric,interpretation of oxygen saturation and total haemoglobin values [106–111]. Thesemechanical models are almost uniformly applied in post-processing or forwardmodelling [112], owing to the complexity of solving the viscoelastic problemin irregular domains. While they may introduce additional uncertainty in theinversion process, if implemented in the right way, they have the potential toreduce the ill-posedness of the problem and thus offer more accurate diagnosticperformance.

Model-based interpretation of injected tracers is one area where there maybe substantial gains, which would allow NIRS to provide fundamentally newinformation that cannot be obtained by other modalities. The key factor in thisis that NIRS imaging allows quantification of more than one analyte in vivo somultiple species can be used to reference against one another. This has been





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 directlyrelated to the drug affinity and the concentration of binding sites within thetissue. Thus, by combining NIRS measurements or images with compartment-binding modelling, it is feasible to quantify molecular receptor expression andaffinity in vivo. The processing of this information has been in post-processing todate, but explicit incorporation of these linear models into the inversion algorithmwith a temporal dataset is readily done. An example of explicit incorporation ofa forward model is in the way spectral constraints are added into a multiple-wavelength inversion problem, to reduce the ill-posedness of the inversion andprovide more accurate recovery properties. A similar approach could be triedwith forward physical models, in the inversion problem.


Proven benefits have been widespread in post-processing of NIRS data.Inclusion of biophysical modelling into forward NIRS modelling is probablysomewhat beneficial. However, similar to spectral constraints, there is probablya 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 beassessed for diagnostic performance. This is a critical component of the innovationprocess often missing from NIRS studies. The prior–NIRS convolution must beassessed against other convolution schemes as well as against clinical and pre-clinical diagnostic standards. An important consideration in this analysis is thetrade-off between performance and technical complexity. The value of modestgains in diagnostic power realized through extensive, difficult and time-consumingimaging strategies must be considered carefully.

Figure 7 illustrates how a receiver operating characteristic (ROC) curve can beused to compare the diagnostic performance of different prior implementationsthat can be used for MRI-guided NIRS imaging. In this example, a coronal MRIimage of a human breast lightly compressed between two plates (figure 7a) wassegmented and used to produce a finite element mesh containing two distincttissue regions, an adipose and a fibroglandular region. Each compression plateis lined with eight optical source–detector fibres for transmitting and receivinglight through the tissue, as illustrated by grey rectangles in figure 7b. The ROCcurve analysis began by generating simulated test domains from the finite elementmesh. A suspicious circular legion was numerically added to the mesh in one of twolocations, either near the centre of the tissue, as shown in figure 7b, or a specifieddistance from one edge, as illustrated in figure 7c. The lesion simulates a regionof gadolinium (Gd) enhancement in the MRI image, but may not necessarily bemalignant. The radius of this lesion was varied over the range illustrated in figure7b,c, and the optical absorption contrast was varied from 0 to 5 : 1 for each lesionsize. Lesions with zero contrast in optical absorption represented an MRI falsepositive. For each lesion size/contrast, forward data were generated numericallyand noise added to the measurements. A total of 600 datasets were considered inthis example.





1.0

0.8

true

pos

itive

rat

e (s

ensi

tivity

)

0.6

0.4

0.2

0 00.5false positive rate (1-specificity)

1.0 0.5false positive rate (1-specificity)

1.0

(a) (b)

(e) ( f )

(c) (d)

Figure 7. (a) A T1-weighted coronal MRI image of a breast compressed between two plates. Tissuetypes were segmented and used to generate a two-tissue-region finite element mesh for NIRSmodelling as shown in (b,c). Sixteen fibre probes contact the tissue surface in a transmissiongeometry, as illustrated in (b). Regions that simulate suspicious lesions defined by Gd-MRI wereadded numerically to the mesh, simulating a positive reading in the MRI image. The size, positionand optical contrast of these lesions were varied over a wide range (the lesion sizes and positionsare illustrated in (b,c)). The ROC curve in (e) demonstrates the improvement in diagnosticperformance when the hard prior approach is used (red curve) versus the approach that usesthe MRI information only in the interpretation step of the imaging process (blue curve). If thesegmentation 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 shownin (f ). (Online version in colour.)

The synthetic optical data were then used to recover and interpret absorptionimages using one of two prior-imaging convolutions. The first method applied thestructural prior in the interpretation step, while the second approach consideredthe hard-prior method, which incorporated the MRI information directly in theimage reconstruction step. In the former approach, the optical data were usedto perform a ‘no-priors’ image formation. Once the image was recovered, theaverage value in the region defined by the lesion in the corresponding MRI image





was extracted as the diagnostic parameter. The hard-prior approach, on theother hand, encodes the internal structure of the tissue in optically homogeneousregions. Thus, the value recovered in this lesion was extracted directly from theimage.

The value of optical absorption in the lesion region was used as the diagnosticparameter in the ROC curve analysis for both methods shown in figure 7e.This result demonstrates an improvement in ROC curve performance when theprior was applied in the reconstruction step as opposed to the interpretationstep. Area-under-the-curve metrics were 0.85 and 0.73 for the hard-prior andinterpretation-only approaches, respectively. However, this analysis assumedperfect image segmentation of the fibroglandular region. Errors in segmentingthis region will affect the performance of the hard-prior approach but should notaffect the approach that uses the MRI information only in the interpretation step.To explore to what degree the performance is degraded, the segmentation of thefibroglandular region used in the hard-prior image reconstruction was dilated, asshown in figure 7d, and the analysis repeated. ROC curves for the two approachesunder imperfect segmentation conditions are shown in figure 7f , and demonstratea significant decrease in diagnostic performance for the hard-prior approach dueto the segmentation error. Analyses such as this can help determine what imagingstrategies are most beneficial under different experimental conditions.

The strategy described above is an effective way to evaluate and comparedifferent implementations of prior information. ROC curve analysis is thepreferred method for assessing diagnostic performance in most cases (thoughspecific applications, such as glucose monitoring, have their own standarddiagnostic scales). Other types of analyses are commonly reported for NIRSimaging, such as spatial resolution, contrast resolution and contrast detailanalysis. While useful for assessing system performance, these analyses should beconsidered an intermediate step on the path towards a full diagnostic assessmentusing an ROC curve, which also accounts for biological variability. Establishingtruth can be challenging and must be accomplished using accurate gold standardsof conventional medicine. Also, the metrics assessed should match the objectivesof the diagnostic test. In some cases, the aim of the NIRS technique is to quantifyrather than detect diseased tissue, and thus an assessment of detectability wouldbe inappropriate. This is especially true for paradigms in which structural imagingmodalities are used to identify suspicious lesions and a prior–NIRS convolutionstrategy is used to characterize and diagnose the abnormalities. In most cases,a comprehensive ROC curve study should be the ultimate goal of the NIRSresearcher to determine whether adoption of the technique in the clinic or researchsetting is warranted.

7. Conclusions

The observations of improved quantification or improved diagnostic values are acomplex range of niche examples. A few applications show clear and significantbenefits, others demonstrate only modest improvements in diagnosis, and manyhave not been tested using the conventions of diagnostic assessment. Table 4provides a listing of the prior information types from figure 1, along with the NIRSprocess steps. The table includes a qualitative ranking of which prior information





Table 4. Listing of the prior information options and NIRS process steps outlined in figure 1, withrelative 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

spatial molecular parameter biomarkers and biophysicalNIRS process step structures spectra limits demographics 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 clearbenefit, + to indicate possible benefit, ++ to indicate probable benefit with somedemonstrated evidence, and + + + to indicate a major demonstrated benefit inquantification or diagnosis.

While these scores are admittedly relative and somewhat subjective, this chartis an initial attempt to think about this framework for determining how thebenefit from prior information might be maximized in the NIRS process, andhow systems can be designed to maximize quantitative accuracy and ultimatelydiagnostic 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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