Hyperspectral optical tomography of
intrinsic signals in the rat cortex
Soren D. Konecky
Robert H. Wilson
Nathan Hagen
Amaan Mazhar
Tomasz S. Tkaczyk
Ron D. Frostig
Bruce J. Tromberg

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Neurophotonics 2(4), 045003 (Oct–Dec 2015)

Hyperspectral optical tomography of intrinsic
signals in the rat cortex
Soren D. Konecky,a Robert H. Wilson,a Nathan Hagen,b Amaan Mazhar,a,d Tomasz S. Tkaczyk,bRon D. Frostig,c,d and Bruce J. Tromberga,d,*a
University of California, Irvine, Beckman Laser Institute and Medical Clinic, Laser Microbeam and Medical Program,
1002 Health Sciences Road, Irvine, California 92612, United Statesb
Rice University, Department of Biomedical Engineering, 6500 Main Street, Houston, Texas 77030, United StatescUniversity of California, Irvine, Department of Neurobiology and Behavior, 2205 McGaugh Hall, Irvine, California 92697, United StatesdUniversity of California, Irvine, Department of Biomedical Engineering, 5200 Engineering Hall, Irvine, California 92697, United States

Abstract. We introduce a tomographic approach for three-dimensional imaging of evoked hemodynamic activity, using broadband illumination and diffuse optical tomography (DOT) image reconstruction. Changes in diffuse
reflectance in the rat somatosensory cortex due to stimulation of a single whisker were imaged at a frame rate of
5 Hz using a hyperspectral image mapping spectrometer. In each frame, images in 38 wavelength bands from
484 to 652 nm were acquired simultaneously. For data analysis, we developed a hyperspectral DOT algorithm
that used the Rytov approximation to quantify changes in tissue concentration of oxyhemoglobin (ctHbO2 ) anddeoxyhemoglobin (ctHb) in three dimensions. Using this algorithm, the maximum changes in ctHbO2 and ctHb
were found to occur at 0.29  0.02 and 0.66  0.04 mm beneath the surface of the cortex, respectively. Rytov
tomographic reconstructions revealed maximal spatially localized increases and decreases in ctHbO2 and ctHbof 321  53 and 555  96 nM, respectively, with these maximum changes occurring at 4  0.2 s poststimulus.
The localized optical signals from the Rytov approximation were greater than those from modified Beer–Lambert,
likely due in part to the inability of planar reflectance to account for partial volume effects. © 2015 Society of Photo-Optical
Instrumentation Engineers (SPIE) [DOI: 10.1117/1.NPh.2.4.045003]

Keywords: optical brain imaging; hyperspectral imaging; optical tomography; hemodynamic imaging; neurovascular coupling;
wide-field optical imaging.
Paper 15021R received Apr. 29, 2015; accepted for publication Oct. 19, 2015; published online Nov. 12, 2015.

1

Introduction

The study of cerebral hemodynamics is important for treating
brain pathologies, neuroimaging, and fundamental neuroscience. Cerebral hemodynamics plays a critical role not only in
cerebrovascular diseases such as stroke1 but also in neurodegenerative diseases such as Alzheimer’s disease2 and age-related
neurodegeneration.3 Hemodynamic activity is also the basis
for functional magnetic resonance imaging (fMRI), which
does not measure neuronal activity directly but instead measures
the hyperemic response that accompanies neuronal activity.4,5
Hemodynamics may play a direct role in information processing
itself, in addition to its supportive role of delivering glucose andoxygen.6 Thus, the ability to quantitatively measure cerebral
hemodynamics with high temporal and spatial resolution isimportant for fundamental neuroscience research and fordeveloping new treatments and therapeutic targets for brain
pathologies.
Intrinsic signal optical imaging (ISOI) is a powerful tool for
imaging the hemodynamic responses to evoked activity of thebrain in animal models.7,8 ISOI is a camera-based technique that
relies on the fact that hemodynamic activity changes the lightintensity remitted from an illuminated brain. It allows forhigh spatial (∼10 μm) and temporal (<0.1 s) resolution overa wide field of view. It is low cost, noninvasive, and can beused in chronic imaging studies in animal models. However,despite its widespread use, ISOI only provides two-dimensional(2-D) planar images, and thus cannot localize the depth in thecortex at which hemodynamic changes occur.
The need for three-dimensional (3-D) determination ofhemoglobin concentration and oxygenation state has been amajor factor driving the growth of the field of diffuse optical
tomography (DOT).9 Researchers have used the temporal profile
of pulsed sources10–14 and large arrays of fibers15–19 to localize
the depth of hemodynamic activity in humans. Optical tomography of cerebral hemodynamics of small animals has also been
performed using optical fibers20,21 and fast scanning.22 However,fiber-based approaches tend to be constrained by the number of
discrete (fiber optic) source and detector probes that are used,
and by the vast dynamic range required for different source–
detector separations.
For small-animal imaging experiments in which only the first∼1 − 2 mm of tissue needs to be probed, hyperspectal camerabased imaging may provide a simple approach to acquire depthresolved images with high spatial and temporal resolution. This
would provide ISOI with the ability to determine whether optical signals originate from vasculature in the parenchyma or at
the surface of the cortex.23,24 Quantifying these signals would
provide a more complete picture of the spatiotemporal featuresof the hemodynamic response and may help to determine thesignaling mechanisms underlying the coupling between neuronal and vascular activity.23,25 While several studies have usedconfocal and multiphoton microscopy to look at the flow of*Address all correspondence to: Bruce J. Tromberg, E-mail: bjtrombe@uci.edu

2329-423X/2015/$25.00 © 2015 SPIE

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Konecky et al.: Hyperspectral optical tomography of intrinsic signals in the rat cortex

red blood cells,26,27 the dilation of individual vessels,23 and the
distribution of oxygen tension,28 these approaches are based on
exogenous probes and are generally only viable for depths up to∼500 μm. In addition, microscopy-based methods necessarily
probe a limited number of microvascular structures in a small
field of view.
Many researchers have performed ISOI at multiple wavelengths and used the differing spectral features of oxy- anddeoxyhemoglobin to produce 2-D maps of changes in oxyand deoxyhemoglobin concentration. Practical constraints typically limit the ability of serial spectral scanning to simultaneously provide both spatial and spectroscopic information.
Spectroscopic approaches generally sacrifice imaging performance by either collecting data at a single point or diffracting
light passing through a slit in order to obtain a one-dimensional(1-D) “image.”29–31 Other methods have used a filter wheel or
flashing LEDs to serially obtain images at multiple
wavelengths.32–34 While effective, these methods are limitedby the trade-off between the number of wavelengths measured
and temporal resolution. Recent attempts to overcome these limitations include approaches using a combination of beam splitters and filters to image at four wavelengths simultaneously35
and methods using concurrent CCD-based imaging and fiberbased spectroscopy in a single experiment.36 Ideally, one
would like to acquire high-resolution images that contain full
spectral information at every location on the cortex, and use
this data to reconstruct 3-D maps of the changes in tissue
hemodynamics.
In this paper, we describe image mapping spectroscopy (IMS)
to image intrinsic optical signals following sensory stimulation in
the rat. IMS is a new method for hyperspectral imaging capable offorming planar 2-D images in multiple distinct wavelength
bins.37–39 In this work, we employed an IMS camera operating
at 5 Hz to image with 38 spectral bands from 484 to 652 nm
in a single snapshot. Unlike other hyperspectral imaging methods,
IMS has high optical throughput and does not require scanning or
image reconstruction to produce a set of spectrally binned images.
As a result, IMS can acquire hyperspectral images at the frame
rate of the camera. Thus, IMS is ideal for high-resolution hyperspectral imaging of the small and transient changes in light intensity following sensory stimulation.
To take advantage of the IMS spectral content, we developed a hyperspectral optical tomography algorithm to generate
3-D images of poststimulus changes in oxy- and deoxyhemoglobin concentrations from the acquired reflectance data.
Multiwavelength depth localization has recently been studied
by several groups for subsurface fluorescence imaging,40–42 inwhich distortions in the emission profiles resulting from theabsorption of the emitted light as it travels to the surface
are used to estimate the depth of the fluorescent object. Our
tomographic reconstruction algorithm, based on the Rytov
approximation, takes advantage of the distortion of the reflectance spectra to localize the depth at which the concentrationsof tissue absorbers (i.e., oxy- and deoxyhemoglobin) change.
Previous studies have employed the Rytov approximation for
tomographic reconstruction of data taken at multiple spatial
points43,44 or with light of multiple spatial frequencies.45,46
However, to our knowledge, this work is the first to employ
the Rytov algorithm for tomographic reconstruction of hyperspectral optical imaging data. A key feature of the algorithm is
its speed, as each hemodynamic time course consists of manytime points (72 in the present study). By performing the
Neurophotonics

calculation in the spatial Fourier domain and directly solving
for the concentrations of oxy- and deoxyhemoglobin, the algorithm takes <15 s to compute 3-D images at each time point
using the large (∼2.5 × 106 data points) hyperspectral data
sets. The combination of hyperspectral data collection methods
and DOT algorithms potentially enhances ISOI by providing
new information for localization and quantification of hemodynamic signals. To compare our results with establishedapproaches and utilize the power of broadband spectral content, we have also calculated hemodynamic signal changes
using the modified Beer–Lambert law, where the widely varying photon path length was accounted for using Monte Carlomodeling.

2

Methods

2.1

Animal Preparation

Rats were prepared for imaging using our standard protocol thathas been described previously.47,48 Briefly, five male SpragueDawley rats were anesthetized with an intraperitoneal injectionof Nembutal (55 mg∕kg b.w.). Rats were also given an intramuscular injection of atropine (0.05 mg∕kg b.w.) into thehind leg, and a subcutaneous injection of 5% glucose(3 mL). Supplemental injections of Nembutal (27.5 mg∕kg b.
w.) were given as necessary (approximately 1∕h). Body temperature was monitored by a rectal probe and maintained at 37°C
using a self-regulating heating blanket. Skin and muscle were
removed from the area over the left primary somatosensory
cortex, and a 6 × 8 mm imaging window was made by thinning
the skull to a thickness of ∼150 μm using a dental drill.
Petroleum jelly was built around the thinned skull region, filledwith saline, and capped with a glass coverslip, keeping thethinned skull moist and translucent during the imaging procedure. All performed procedures were in compliance with
National Institutes of Health guidelines and approved by the
University of California Animal Care and Use Committee.

2.2

Imaging Protocol

In each imaging trial, sensory stimulation consisted of fivedeflections at 5 Hz to the right C2 whisker. For each deflection,a copper wire displaced the whisker 0.8 mm along the rostral–
caudal axis at a distance of 5 mm from the C2 follicle for a duration of 100 ms. Images were acquired with an exposure time of
50 ms at a rate of 5 Hz beginning 1.5 s before stimulus onset andlasting 15 s. For each rat, two blocks of 64 trials each wereacquired with an intertrial interval of 15 s plus a random
delay between 0 and 5 s. The imaging window was evenly illuminated by broadband light from a tungsten-halogen quartz
lamp.

2.3

Hyperspectral Imaging

We have described our IMS system previously.37–39 Briefly, light
remitted from the cortex is focused on a custom-made redirecting mirror composed of many long strips. Each strip hasa slightly different 2-D tilt angle that reflects light in a different
direction. A prism subsequently disperses the light from each
strip before it arrives at a large-format CCD array. Each pixelon the CCD array corresponds to the light within a narrow wavelength band remitted from a point on the cortex. Therefore,
images at the various wavelength bands are obtained by a simple
mapping procedure, eliminating the need to reconstruct images

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Konecky et al.: Hyperspectral optical tomography of intrinsic signals in the rat cortex

as is done with other hyperspectral snapshot techniques such as
computed tomography imaging spectrometry49 and coded aperture snapshot spectral imaging.50 For this paper, we acquired
intrinsic signal images simultaneously at 38 separate wavelengths between 484 and 652 nm over a grid of 350 × 350 pixels
using the image mapping spectrometer system. Our field of view
was approximately 6 × 6 mm such that each pixel corresponded
to a 17 × 17 μm area of the cortex. The width of each wavelength band ΔλðλÞ varied continuously from Δλ ¼ 3 nm at λ ¼
484 nm to Δλ ¼ 8 nm at λ ¼ 652 nm. A representative hyperspectral snapshot of a rat cortex acquired with a single 50-ms
exposure appears in Fig. 1. The key advantage provided by
the IMS is that it simultaneously acquires images at all 38 wavelengths, enabling brain imaging at multiple frames per second, acritical feature for resolving the rapid hemodynamic signaturesof neurovascular coupling in response to stimulus.

2.4

Data Analysis

2.4.1

Intrinsic signal

For each block of 64 trials, we averaged the imaged reflectanceat each time point over the 64 trials. For each time point, theaveraged data set consisted of a data cube consisting of 38 350 ×
350 pixel images, with each image corresponding to one wavelength bin. We averaged the three exposures immediately preceding stimulation onset to calculate the baseline intensity. The
intrinsic signal for each time point was then calculated for eachpixel and wavelength separately as ϕðtÞ ¼ log½RðtÞ∕R0 , whereRðtÞ and R0 are the measured light intensity at time t and thebaseline intensity, respectively. We related the intrinsic signal
ϕðtÞ to the changes in oxy- and deoxyhemoglobin in the cortex

resulting from sensory stimulation using both the modified
Beer–Lambert law and the Rytov approximation.
2.4.2

Modified Beer–Lambert law

In order to generate 2-D images of the changes in hemoglobin
concentrations, we used the modified Beer–Lambert law, whichappears asϕðtÞ ¼ −½εHbO2 ðλÞδctHbO2 ðtÞ þ εHb ðλÞδctHbðtÞLðλÞ:

EQ-TARGET;temp:intralink-;e001;326;667(1)Here, εHbO2 and εHb are the extinction coefficients for oxy- anddeoxyhemoglobin,51 δctHbO2 ðtÞ and δctHbðtÞ are the changes
in tissue concentration of those chromophores relative to theirbaseline values, and LðλÞ is the mean photon path length in thecortex as a function of wavelength. Monte Carlo simulations
were used to determine the mean path lengths traveled by photons of differing wavelengths. In our Monte Carlo simulations,
we began by using tissue oxy- and deoxyhemoglobin concentrations of ctHbO2 ¼ 60 μM and ctHb ¼ 40 μM, respectively,
tissue-scattering coefficient of μs ¼ 10 mm−1 , and tissue-scattering anisotropy of g ¼ 0.9, similar to values we have measured
previously in this animal model using quantitative spatial frequency domain imaging.52
2.4.3

Rytov approximation

While the modified Beer–Lambert law has been used extensively to produce images of changes in hemoglobin concentration, Eq. (1) assumes that the changes occur uniformly
throughout the brain. The Rytov approximation is a generalization of the modified Beer–Lambert law that allows one to solve
for spatially varying changes in chromophore concentrations.53

Fig. 1 Snapshot of the rat cortex at 38 wavelengths simultaneously with the image mapping spectrometer during a single 50-ms exposure. Light remitted from the cortex is imaged onto the mapping mirror,
which is composed of many strips. Each strip reflects the light focused on it to a different location. The
light from each strip is dispersed by a prism before reaching the CCD array. Each location on the CCD
array corresponds to a wavelength of light and a point on the cortex. A simple mapping procedure reorganizes the data to produce the spectrally resolved images.

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Konecky et al.: Hyperspectral optical tomography of intrinsic signals in the rat cortex

By taking advantage of the differing penetration depths of visible and near-infrared light in the cortex, we can implement the
Rytov approximation to generate 3-D images of the changes in
Hb and HbO2 concentrations.
The propagation of multiple-scattered incoherent light in tissue is governed by the radiative transport equation (RTE)Zs^ · ∇Iðr; s^ Þ þ μt Iðr; s^ Þ ¼ μs

EQ-TARGET;temp:intralink-;e002;63;686

We solve Eq. (4) using a correction to the standard diffusion
approximation that accounts for the fact that near boundaries,
the specific intensity is not isotropic.54,55 Using this correction,
we can rewrite Eq. (4) asϕðλ; ρd Þ ¼
d2 sAð^s; s^ 0 ÞIðr; s^ Þ þ Sðr; s^ Þ;(2)where Iðr; s^ Þ is the specific intensity, μa and μs are the absorption and scattering coefficients, respectively, μt ¼ μa þ μs is theextinction coefficient, Að^s; s^ 0 Þ is the phase function, and Sðr; s^ Þdescribes the source. The RTE allows us to relate the changes inlight intensity detected at location ρd in direction sd to changes
in the concentrations of Hb and HbO2 , by use of the Rytov
approximationl2∇Iðλ; zÞd3 r Iðλ; zÞGðλ; r; rd Þ −3· ∇Gðλ; r; rd Þ cδμa ðλ; rÞ:Z

EQ-TARGET;temp:intralink-;e006;326;708

Here, Iðλ; zÞ is the photon density, l ¼ 1∕ðμa þ μs0 Þ is thetransport mean free path, c is the speed of light, ρd is a 2-D
vector specifying the detector location, and the Green’s function
Gðλ; r; r 0 Þ satisfies the diffusion equation½DðλÞ∇2 þ cμa ðλÞGðλ; r; r 0 Þ ¼ δðr − r 0 Þ;

EQ-TARGET;temp:intralink-;e007;326;590

Z
ϕðλ; ρd ; s^ d Þ ¼ −EQ-TARGET;temp:intralink-;e003;63;553

d3 r d2 sIðλ; z; s^ ÞGðλ; r; s; rd ; s^ d Þδμa ðλ; rÞ;
(3)

where



Rðλ; ρd ; s^ d Þ
ϕðλ; ρd ; s^ d Þ ¼ Iðλ; z ¼ 0; s^ Þ log
R0 ðλ; ρd ; s^ d Þ(4)

EQ-TARGET;temp:intralink-;e004;63;485

is the data function, Iðλ; z; s^ Þ is the specific intensity of the planar illumination in the cortex, Gðλ; r; s; rd ; nÞ is the Green’s
function for the RTE, and the change in absorption is decomposed into a sum of the contributions from changes in ctHb
and ctHbO2

δμa ðλ; rÞ ¼ εHb ðλÞδctHbðrÞ þ εHbO2 ðλÞδctHbO2 ðrÞ:(5)

EQ-TARGET;temp:intralink-;e005;63;391

(6)

(7)

with the diffusion coefficient D ¼ cl  ∕3. In Eq. (6), we haveassumed that the source and detected light are orientated normal
to the tissue surface.
Equation (7) is the most easily inverted in the Fourier domain
where it is block diagonal. Taking a 2-D Fourier transform withrespect to the detector position ρd yields a 1-D integral for eachvalue of the Fourier coefficient qZ
ϕ̃ðλ; qÞ ¼

EQ-TARGET;temp:intralink-;e008;326;482dzκðλ; q; zÞδμ̃a ðλ; q; zÞ:(8)

The function κðλ; q; zÞ can be calculated from Eq. (7) using
known expressions for the Green’s functions of the diffusion
equation. 55 In the semi-infinite geometry, we have

Mean concentration over ROI,
normalized to peak value

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1

Actual extent of simulated inclusion

0
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Depth beneath surface (mm)Fig. 2 Absorber concentration [averaged over a region of interest (ROI) and normalized to peak] as afunction of depth, calculated for simulated data using the Rytov-approximation-based optical tomographyalgorithm described in Sec. 2.4.2. The data functions were generated by using Monte Carlo software57 tosimulate the two-dimensional surface reflectance at different wavelengths for a tissue model with a subsurface absorbing inclusion (10× the absorption of the surroundings) buried beneath 0.5 mm of tissue
and having an extent of 2 mm in the z-direction (as denoted by the blue box overlaid on the figure). The
reconstructed center depth of the inclusion was defined as the z-value at which the reconstructed concentration had its highest value. The reconstructed extent of the inclusion was defined as the full-width at
half-maximum of the curve describing the concentration as a function of depth. For this case, the multispectral tomography algorithm reconstructed the center depth and thickness of the inclusion to within
23% and 18%, respectively.

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Konecky et al.: Hyperspectral optical tomography of intrinsic signals in the rat cortex

EQ-TARGET;temp:intralink-;e009;63;752

κðλ; q; zÞ ¼


 2 ll2Qðλ; qÞQðλ; 0Þ
1−
D
3


expf½Qðλ; qÞ þ Qðλ; 0Þzg×;½Qðλ; qÞl þ 1½Qðλ; 0Þl þ 1Z
EQ-TARGET;temp:intralink-;e010;326;752

δctHbðρ; zÞ ¼

 ðλm ; q; zÞM−1m;n ðqÞϕ̃ðλn ; qÞ;(9)Z

EQ-TARGET;temp:intralink-;e011;326;699

δctHbO2 ðρ; zÞ ¼
where l is the extrapolation length, defined as the distancefrom the boundary at which the energy density reaches
zero,56 and Qðλ; qÞ ¼ ðcμa ∕D þ q2 Þ1∕2 . The changes in
ctHb and ctHbO2 , relative to baseline, are then calculated
according toX
d2 qexpð−iq · ρÞ εHb ðλm Þκ
2
ð2πÞ
m;n
(10)

X
d2 q
expð−iq·ρÞ
εHbO2 ðλm Þκ
ð2πÞ2
m;n

 ðλm ; q; zÞM−1m;n ðqÞϕ̃ðλn ; qÞ:(11)

We compute the matrix elements of MðqÞ analytically according to

Fig. 3 Imaging changes in light intensity. (a) Images of the cortex using 570 nm light are overlaid withcolor images representing the change in remitted light at 529 nm (isosbestic point sensitive to total hemoglobin concentration) and 630 nm (primarily sensitive to deoxyhemoglobin). Time points correspond to
the initial decrease in signal at 630 nm, the decrease at 529 nm, and the overshoot at 630 nm. The purple/
yellow color scale indicates an increase in remitted light, while the green/blue scale represents a
decrease. (b) Time course of remitted light intensity for the ROI (see Sec. 2) at an isosbestic point(529 nm), deoxyhemoglobin peak (557 nm), oxyhemoglobin peak (576 nm), and at 630 nm.
(c) Spectra of the intrinsic signal during the time points pictured in (a). (d) False color representationof intrinsic signal as a function of both time and wavelength. (e) Spectra of oxy- and deoxyhemoglobin.
(b, c) Error bars represent the standard error over all pixels in the ROI. Regions of interest were determined by selecting a pixel in the 630 nm image where a maximum drop in measured light intensity
occurred, and then averaging over a 500 mm × 500 mm area surrounding that pixel.
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Konecky et al.: Hyperspectral optical tomography of intrinsic signals in the rat cortex

M m;n ðqÞ ¼

Z ∞EQ-TARGET;temp:intralink-;e012;63;752

3dz½εHb ðλm ÞεHb ðλn Þ0

þ εHbO2 ðλm ÞεHbO2 ðλn Þκðλm ; q; zÞκ  ðλn ; q; zÞ;(12)and then find its inverse by solving its eigenvalue problem.
The inversion is regularized by setting eigenvalues below a
threshold to zero.
The framework of this Rytov-approximation-based algorithm has previously been shown to provide accurate estimatesof depth of buried fluorescent inclusions in small animals.46 In
addition, we have recently performed a validation of the hyperspectral tomography algorithm on data generated using Monte
Carlo simulations57 with a 2-mm thick absorbing inclusion
buried 0.5 mm beneath the surface. For this case (Fig. 2), themultispectral tomography algorithm was able to accurately
reconstruct the center depth of the inclusion to within 23%
and the inclusion thickness to within 18%. A more detailed
discussion of tomography validation studies, employing bothtissue-simulating phantoms and computational models of theforward problem, will be the subject of a future report (currently
in preparation).

Results and Discussion

Figure 3 demonstrates our ability to image the changes in lightintensity due to functional activation with high spatial and temporal resolution simultaneously at many wavelengths through athinned skull in a representative rat. Figure 3(a) shows images ofchanges in light remitted from the cortex at 529 nm (isosbestic
point equally sensitive to oxy- and deoxyhemoglobin) and
630 nm (about 9× more sensitive to deoxyhemoglobin thanoxyhemoglobin).
Color maps of the change in light intensity are superimposedover black and white images at 576 nm, which clearly show theunderlying vasculature. As can be seen by looking at the timedependence of the signal over the area of peak activation shownin Fig. 3(b), the time points chosen in Fig. 1(a) correspond to theinitial decrease in the 630 nm signal, the time at which the isosbestic wavelength (529 nm) has its largest signal, and theincrease of signal at 630 nm. Complete spectral information
for these three time points is shown in Fig. 3(c), and the intrinsic
signal is represented in Fig. 3(d) in false color as a function ofboth wavelength and time. These results are in agreement with
our previous ISOI imaging at a single wavelength.48
Representative images of the changes in ctHb and ctHbO2
along with traces of the region of interest calculated using
the modified Beer–Lambert law appear in Figs. 4(a) and 4(b).

Fig. 4 Representative images of changes in concentration and with varied wavelengths. (a) Images of
the change in tissue concentration of deoxy- and oxyhemoglobin for a representative rat at time points
corresponding to the initial ctHb increase (1.1 s), the ctHbO2 increase (3.1 s), and the ctHb decrease(3.7 s), obtained using the modified Beer–Lambert law. Color maps of the hemoglobin changes are overlaid above an image of the cortex at 570 nm. The purple/yellow color scale indicates an increase inconcentration, while the green/blue scale represents a decrease. (b, c) Time-resolved changes in
ctHb and ctHbO2 for the ROI on the cortex, obtained using the modified Beer–Lambert law, for(b) all wavelengths and (c) only for the wavelengths 529 and 630 nm. Error bars represent the standard
error for all pixels in the ROI.

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Konecky et al.: Hyperspectral optical tomography of intrinsic signals in the rat cortex
Table 1 Peak times and maximum changes in the concentrations ofoxyhemoglobin (ctHbO2 ) and deoxyhemoglobin (ctHb) using themodified Beer–Lambert law and the Rytov approximation.

Modified Beer–Lambert law
ctHbO2 increase

ctHb decrease

Time to peak (s)3.1  0.3

4.3  0.3

Magnitude (nM)

248  80−84  19

Time to peak (s)4  0.2

4  0.2

Magnitude (nM)

321  53−555  96

Rytov approximation

Changes in concentration (Table 1, averaged over all rats) were
determined using the modified Beer–Lambert law, where
optical path lengths were determined using Monte Carlo simulations of photon transport. The peak increase in ctHbO2(δctHbO2 ¼ 248  80 nM) was ∼3× greater than the ctHb
decrease (δctHb ¼ −84  20 nM). The peak changes in concentration did not occur at the same time; the peak change intotal hemoglobin arose first (tHbT ¼ 2.6  0.4 s), followed by
the peak in ctHbO2 (tHbO2 ¼ 3.1  0.3 s), and the maximum
decrease in ctHb (tHb ¼ 4.3  0.3 s).
We varied the number of wavelengths used to fit for ctHb andctHbO2 to determine the effect on the recovered changes inhemoglobin concentration. We found that using fewer wavelengths led to additional noise in the recovered hemoglobin values. For example, Figs. 4(b) and 4(c) shows the hemoglobin
time courses for a single rat using all 38 wavelengths [Fig. 4(b)],and only using two wavelengths [Fig. 4(c)]: an isosbetic wavelength (529 nm) and a deoxyhemoglobin sensitive wavelength(630 nm). When reducing the number of wavelengths from 38 to2, the standard error of hemoglobin concentration changes in theregions of interest increased from 6 to 20 nM for ctHbO2 andfrom 3.5 to 5.6 nM for ctHb. However, despite the increase innoise, removing wavelengths did not significantly alter the timing or peak magnitudes of the hemodynamic time courses.
We also conducted Monte Carlo simulations over a wide
range of parameters to determine the effect of path length on
the calculated values for changes in ctHb and ctHbO2 .
Figure 5 illustrates the variability in the magnitude of hemoglobin changes calculated when different baseline optical properties
are assumed. The variability of the initial ctHb increase, thectHbO2 increase, and the subsequent ctHb decrease are reported
in Table 2. Increasing the baseline value of total hemoglobin or

scattering leads to an increase in the magnitude of all parameters. This occurs because an increase in absorption or scattering
decreases the mean photon path length. Since the data remain
fixed, this leads to an increase in the calculated hemoglobin concentrations (see Sec. 2). All changes due to varying the wavelength dependence of scattering, described by Aλ−b where the A
and b parameters refer to scattering amplitude and power,
respectively,46,52 were less than 15% despite changing scattering
power, b, over a large range (b ¼ 0–2.5).
Future work will include a quantitative comparison between
the tomography model used in this paper and a Monte Carlobased tomography model that uses photon path length information stored in the simulations to provide accurate quantificationof absorber depth and concentration. Future work will also
include a detailed computational investigation into the influenceof tissue background absorption and scattering properties on thedepth sensitivity of the optical tomography algorithm. This
future study will also include a systematic investigation into
how the background optical properties and the set of wavelengths employed affects the ability of the algorithm to fully
separate oxygenated hemoglobin absorption from deoxygenatedhemoglobin absorption. This future work will include a quantitative comparison between the tomography model used inthis paper and a Monte Carlo-based tomography model thatuses photon pathlength information stored in the simulations
to provide accurate quantification of absorber depth andconcentration.
Figure 6 shows representative depth-resolved snapshots ofthe changes in oxy- and deoxyhemoglobin at 4 s poststimulus
for one rat. These images were calculated according to the Rytov
approximation method described in Sec. 2.4.2. Eleven wavelengths from 586 to 652 nm were employed in the reconstructions. Slices of the 3-D images of ctHb and ctHbO2 are shown at
six depths from 100 μm to 1.1 mm beneath the surface of thecortex. Depth profiles of the changes in oxy- and deoxyhemoglobin, as a function of depth beneath the surface of the cortex,
are shown in Fig. 7(a) for the same rat as in Fig. 6. Figure 7(b)shows time courses of these changes in oxy- and deoxyhemoglobin, at a depth of 0.3 mm beneath the surface of the cortex,
averaged over four rats.
The time courses shown in Fig. 7(b) illustrate an initial
decrease in the concentration of oxyhemoglobin and an initial
increase in the concentration of deoxyhemoglobin over the first2 s poststimulus, followed by an increase in the oxyhemoglobin
concentration and a decrease in the deoxyhemoglobin concentration over the subsequent 5 s. Using the Rytov tomographyalgorithm, the maximum changes in ctHbO2 and ctHb were
found to occur at depths of 0.29  0.02 and 0.66  0.04 mm
beneath the surface of the cortex, respectively. The peak

Table 2 Magnitude of changes in hemoglobin concentrations for the differing optical properties used in the Monte Carlo simulations.
Parameter varied in Monte Carlo simulation
HbT (ctHbO2 þ ctHb)

StO2(ctHbO2 ∕HbT)

μs (Aλ−b )

b

50 μM

20 μM

50%

100%

5 mm−120 mm−10

2.5

ctHbO2 increase (nM)

142

450

237

247

225

283

241

259

ctHb decrease (nM)

−52

−143

−84

−67

−71

−103

−83

−86

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Konecky et al.: Hyperspectral optical tomography of intrinsic signals in the rat cortex

Fig. 5 Time courses for the concentrations of oxy- and deoxyhemoglobin, averaged over all rats, where
the optical properties have been varied when determining the mean photon path length used in the modified Beer–Lambert law. The values of (a) total tissue hemoglobin concentration (HbT), (b) tissue hemoglobin oxygenation (StO2 ), (c) scattering coefficient (μs ), and (d) scattering power (b parameter, see text)
were varied. Error bars indicate the standard error for all rats.

Fig. 6 Representative three-dimensional reconstructed images of changes in oxy- and deoxyhemoglobin for one rat in response to stimulus, obtained at time t ¼ 4 s poststimulus using the Rytov approximation. Each panel represents a cross section at a given depth beneath the surface of the cortex. The
concentration maps have been overlaid on 571-nm reflectance images of a 4.35 mm × 4.35 mm regionof the cortex.

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Konecky et al.: Hyperspectral optical tomography of intrinsic signals in the rat cortex

Fig. 7 Depth profiles of changes in oxy- and deoxyhemoglobin concentrations in response to stimulus(a) at time t ¼ 4 s poststimulus, for the same rat as in Fig. 6, shown alongside a schematic of the rat
cortical layers (based on Ref. 58), on the same scale as the depth profile plot. The changes in oxy- anddeoxyhemoglobin were primarily confined to layers 2 to 4 of the cortex. (b) Time courses of changes in
ctHbO2 and ctHb poststimulus, obtained at a depth of 0.3 mm beneath the surface of the cortex (thedepth of peak change in oxyhemoglobin concentration), using the Rytov approximation, averaged
over four rats (error bars represent the standard error).

times and magnitudes of concentration changes for the 3-D
image reconstructions are summarized in Table 1. For the
Rytov tomography algorithm, the point of peak concentration
change (Table 1) was defined as the peak time point at thedepth (z ¼ 0.3 mm beneath the surface of the cortex) at
which the peak change in oxyhemoglobin concentration
occurred. The magnitudes of the peak changes in oxy- and deoxyhemoglobin concentration shown in Table 1 are larger for the
Rytov tomography algorithm than the Beer–Lambert method;
this finding is expected because the Rytov tomography algorithm localizes the changes in 3-D space.
The results shown in Figs. 6 and 7 are indicative of thedepletion of oxygen by the cortex in response to the stimulus,
followed by the reperfusion of oxygenated blood into the region.
Figures 6 and 7 also suggest that the relative magnitudes of thechanges in oxy- and deoxyhemoglobin may vary with depth.
This effect could possibly be explained by differences in
depth of diving arterioles and venuoles, with the extractionof oxygen occurring deeper in the cortex and the reperfusionof oxygenated blood occurring closer to the surface.
However, this effect may also represent a limitation of the abilityof the measurement technique and/or mathematical model tofully resolve the depths of two different absorbers (oxy- anddeoxyhemoglobin), whose spectral features are close together
in the interrogated wavelength range.
It is important to note that the peak magnitudes of concentration change were higher in the 3-D tomographic images
Neurophotonics(using the Rytov approximation) than for the modified Beer–
Lambert law analysis. This is not surprising since the modified
Beer–Lambert law results represent a depth-averaged hemodynamic change, while the tomographic results localize thisinformation. When the reconstructed 3-D maps of concentration
changes were averaged over depths from 0.1 to 1.3 mm beneaththe surface of the cortex to create 2-D maps of changes in oxyand deoxyhemoglobin, the magnitude of the change in oxyhemoglobin concentration decreased to 154  29 nM, but thechange in deoxyhemoglobin concentration remained essentiallythe same as in the 3-D map (555  99 nM). This result is related
to the inability of the Rytov tomography algorithm to localize
the changes in deoxyhemoglobin concentration as precisely as
the changes in oxyhemoglobin concentration (Figs. 6 and 7).
This discrepancy could be due in part to the fact that the absorption features of oxy- and deoxyhemoglobin were not completely
decoupled from each other due to the size of the wavelength
bands detected by the image mapping spectrometer. Future studies will quantitatively examine this issue by convolving the oxyand deoxyhemoglobin absorption spectra with the bandwidth
profile ΔλðλÞ of the detector.

4

Conclusion

We have employed a parallel hyperspectral imaging technique,
IMS, to record intrinsic optical signals in the rat somatosensory
cortex over 38 wavelength bands (from 484 to 652 nm) at 5 Hz
following mechanical movement of a single whisker. This

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Konecky et al.: Hyperspectral optical tomography of intrinsic signals in the rat cortex

approach was combined with a hyperspectral optical tomography algorithm to quantify and localize time-dependent concentration changes in oxygenated and deoxygenated hemoglobinthat are characteristic of the response to the evoked stimulus.
Our image reconstruction algorithm uses the Rytov approximation and takes advantage of the fact that the measured spectralchanges in reflectance have a strong depth-dependent distortion.
Data were also analyzed using a modified Beer–Lambert law inwhich the photon pathlength was accounted for using Monte
Carlo modeling.
The Rytov approach revealed that the maximum measuredchanges in ctHbO2 and ctHb were primarily confined to layers
II–IV of the cortex. However, the depth distribution of the
Rytov-calculated ctHb change had a broader tail than thatof the ctHbO2 change. Rytov tomographic reconstructions
revealed spatially localized increases and decreases in
ctHbO2 and ctHb of 321  53 and 555  96 nM, respectively,
at 4  0.2 s poststimulus. The modified Beer–Lambert model
revealed a 248  80 nM increase in ctHbO2 at 3.1  0.3 s poststimulus and an 84  19 nM decrease in ctHb at 4.3  0.3 s
poststimulus.
Localized optical BOLD signals for both ctHbO2 and ctHb
were greater using the Rytov approximation than those estimated using the modified Beer–Lambert approach. One contribution to these differences in signal magnitude likely comesfrom the inability of planar reflectance methods to accountfor partial volume effects. The additional discrepancy between
the ctHb values calculated with the Rytov and Beer–Lambertapproaches is likely an artifact of the inability of the algorithm
to completely separate the signal contributions from oxy- anddeoxyhemoglobin. This is due, in part, to the fact that we
did not rigorously characterize the effect of the wavelength
dependence of detector bandwidth ΔλðλÞ. Future studies will
investigate potential improvements to the Rytov model aswell as imposing further optical path length constraints throughthe use of structured light projection patterns.45,46 Despite theselimitations, this study provides, for the first time, a generalframework for localizing and characterizing hemodynamic signals in the cortex with ∼mm resolution over a wide, scalable
field of view. One application of great potential biomedical
importance is to employ multispectral optical tomography incombination with spatial frequency domain and laser speckle
contrast imaging methods in order to separate the hemodynamic
effects of blood flow from metabolism in the brain. These studies are currently in progress in our laboratory, with emphasis on
characterization of the brain’s response to traumatic perturbations such as cardiac arrest and stroke in preclinical animalmodels.

Acknowledgments
Support for this work was provided by the NIH Laser
Microbeam and Medical Program (LAMMP, P41-EB015890),
NIH R21 NS078634, R21 EB014440, R21EB009186, and
R01CA124319, and NINDS NS 066001 and NS 055832. We
acknowledge the use of Virtual Photonics software resources(http://virtualphotonics.org/) supported by LAMMP. Soren D.
Konecky was supported by a postdoctoral fellowship fromthe Hewitt Foundation for Medical Research. Robert H.
Wilson is also supported by a postdoctoral fellowship fromthe Hewitt Foundation for Medical Research. Beckman Laser
Institute programmatic support from the Beckman Foundationis also acknowledged.
Neurophotonics

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