2.1.

Source

The system uses a pulsed Titanium:Sapphire laser (Mai Tai, Spectra Physics) with a $80\mathrm{MHz}$ repetition rate, emitting in the near infrared with a tunable wavelength between 750 and $850\mathrm{nm}$ and a spectral bandwidth of $\sim 10\mathrm{nm}$ . The emitted pulses are approximately $100\mathrm{fs}$ wide. The maximum average exit power is $1\mathrm{W}$ , which can be attenuated by a rotating polarizer. The laser beam enters a multiplexer, which redirects the beam in two dimensions with two mirrors driven by a software-controlled bi-axial galvanometer. In this way, the laser beam is directed into one of an array of fibers (42 fibers in the present configuration) through a telecentric focusing lens.

The pulsed laser we use offers the advantages of wavelength tunability over $100\mathrm{nm}$ , and high output power enabling time-multiplexing of the source over multiple positions. On the other hand, it has the main drawback of being limited to a single wavelength. It is thus not possible to extract concentrations of oxy- and deoxy-hemoglobin from our measurements, as dual- (or multiple-) wavelength systems provide. At $830\mathrm{nm}$ , the changes in intensity that we detect result from a combination of changes in blood volume and oxygenation. By working at $800\mathrm{nm}$ , we can monitor changes in local blood volume, but we lack the information on oxygen saturation changes. In the future, we expect the technological development of laser sources to enable us more flexibility. For instance, the source could be updated to a dual-wavelength pulsed fiber laser, as in the MONSTIR system used by Hebden ²²

2.2.

Detector

While most existing time-domain systems are based on a time-correlated single-photon counting (TCSPC) detection, ^{16, 17, 19, 20, 21, 23, 24, 25, 26} the use of time-gated detectors has also been reported by a few teams for early photon detection or diffuse optical tomography. ^{18, 27, 28, 29} Our system performs a gated detection of the temporal point spread function (TPSF) through narrow temporal windows. The detector is an Intensified Charge Coupled Device (ICCD) camera (PicoStar HR, LaVision), which comprises an image intensifier followed by a 12-bit CCD camera of 1370 by 1040 pixels. The ICCD acts as a very fast shutter synchronized with the laser pulses through a delay unit (PS-Delay Unit, LaVision). The delay between the laser pulses and their gated detection can be adjusted with a 25-ps step. The gate width is adjustable by steps of $100\mathrm{ps}$ from $300\mathrm{ps}$ to $1000\mathrm{ps}$ . After the image intensifier, the CCD camera integrates light over a typical exposure time of $100\mathrm{ms}$ , i.e., 8 million successive laser pulses. Because of the transfer time to the PC, the actual CCD acquisition frame is a bit lower than $8\mathrm{Hz}$ for this exposure time.

We use 3-meter-long, step-index, multimode, silica optical fibers (core diameter $400\mathrm{\mu }\mathrm{m}$ , NA 0.39, Tecs, Thorlabs) to bring light from the laser multiplexer to the studied medium and from the medium to the ICCD (core diameter $300\mathrm{\mu }\mathrm{m}$ and $400\mathrm{\mu }\mathrm{m}$ ). An objective lens of unit magnification images the tips of the fibers onto the photocathode of the ICCD. In the present configuration, we have a total of 175 fibers imaged in parallel onto the CCD.

2.3.

TPSF Measurement

The temporal point spread functions (TPSF) are measured through the temporal gate provided by the image intensifier. To record the whole TPSF, this gate is electronically scanned, providing a measure of the true TPSF convolved by the instrument response function, whose width is a combination of the gate width and the dispersion in the fibers. However, this electronic delay scanning is too slow for functional imaging, where we desire acquisition frequencies higher than $1\mathrm{Hz}$ . The time to change the delay is $370\mathrm{ms}$ , which leads to measurement times from a few seconds up to a couple of minutes depending on the number of measurement points of the TPSF we choose to record. Alternatively to the electronic delay, we implemented “hardware” optical delays enabling simultaneous measurements in various temporal gates. For each detector position, we use 7 fibers of different lengths, which introduce different delays to the measurement (see pictures of the fibers on Figs. 2a, 2b, 2c ). With 10-cm increments in each fiber length, we create 500-ps delays between fibers. On the head, the 7 fibers at each position are arranged in a hexagonal pattern (Fig. 2b) and cover an area of about 2-mm diameter. These 7 individual fibers are then resolved by the CCD such that the different time delays are simultaneously imaged.

Fig. 2

Detector fibers. (a) Seven fibers of different lengths for one detector position. (b) The same 7 fibers after being looped together. The small scheme shows the 7 fiber geometry on the head side. (c) The 25 detector bundles. (d) TPSF recorded on a scattering phantom by the 7 fibers of a same detector bundle.

We therefore have two modes of operation of our instrument. The first mode is the electronic scan of the delay, which provides a slow (up to 2 minutes) but finely resolved (down to 25-ps steps) measure of a TPSF. This is the mode we use for characterizing the static optical properties of a medium. In that mode, the 7 fibers at each position measure the same signal, simply delayed from one fiber to another (see Fig. 2d). Although they do not offer extra information, they can be used to increase the signal-to-noise ratio. The second operation mode is a continuous grabbing of CCD frames at a fixed temporal delay. In that mode, the 7 fibers at each position enable us to achieve parallel acquisition in 7 different time gates. We record the evolution of the TPSF at all sampling delays simultaneously. Since it has better temporal resolution, this mode is used for functional imaging.

3.1.

Warm-up Time

All parts of the equipment require time to reach steady-state thermal equilibrium. After initial warm-up, both the ICCD and the multiplexer stay within 0.2% of their asymptotic value within a 30-minute period. The laser requires about an hour to reach the same level. It also requires approximately 30 minutes of pre-warm-up before turning the pump diodes on. The characterizations presented ahead were performed after all elements of the time domain system were turned on for at least 1.5 hours to avoid any system drift associated with warm-up.

3.2.

ICCD Sensitivity and Signal-to-Noise Ratio

In this part, we summarize the theoretical description of the signal-to-noise ratio (SNR) of an ICCD presented by Brukilacchio in his Ph.D. thesis,³⁰ and we present our own experimental SNR characterization of our system.

We first briefly summarize the principle of operation of the ICCD. The image intensifier consists of a photocathode, a microchannel plate (MCP), and a phosphor layer. The photons incident on the photocathode are converted into photoelectrons (quantum efficiency ${\eta }_{PC}\sim 3.8\%$ at $750\mathrm{nm}$ down to $\sim 0.46\%$ at $850\mathrm{nm}$ , with a decay close to exponential, as specified for the photocathode material S20). A fraction $\Omega \sim 60\%$ of these photoelectrons actually enter the MCP active area. Secondary photoelectrons are produced and multiplied in the MCP with a gain $G_{MCP}$ depending on the high voltage $V=260\text{–}800\mathrm{V}$ applied to the MCP. They are then accelerated toward a phosphor layer where they produce green photons. A 2:1 lens system insures the relay to the CCD array (efficiency ${\eta }_{Relay}\sim 5\%$ ), where the green photons are converted into photoelectrons (quantum efficiency ${\eta }_{CCD}\sim 70\%$ ) and stored in wells for the specified integration time $\tau$ . The total sensitivity of the ICCD was calculated using the photocathode quantum efficiency and the MCP sensitivity provided by the manufacturer and is shown in Fig. 3a at $\lambda =800\mathrm{nm}$ . The actual sensitivity depends on additional parameters, such as the incident wavelength and the CCD pixel binning, and is affected by saturation effects at high powers and MCP gains (up to 50% loss athigh power for $V=800\mathrm{V}$ ). See Ref. 30 for a more systematic description of all the mentioned effects.

Fig. 3

(a) ICCD sensitivity at $800\mathrm{nm}$ as a function of the MCP voltage, deduced from the manufacturer indications. (b) Experimental SNR vs. number of CCD counts, for different MCP voltages. (c) Signal to noise ratio vs. number of incident photons, as deduced from the two previous curves.

The signal is affected by noise from the image intensifier and from the CCD camera, with a strong dependence on the ICCD gain. Sources of noise include intensifier shot noise, dark noise, noise resulting from the gain process in the MCP, phosphor photon shot noise, CCD dark noise, and CCD read-out noise. Brukilacchio shows a dependence of the SNR on the signal as being close to a square root,³⁰ with saturation effects appearing at high signal levels.

We measured experimentally the SNR as a function of the number of CCD counts for different values of the intensifier gain (see Fig. 3b). The probe was set on a solid scattering phantom with optical properties ${\mu }_{\mathrm{a}}\sim 0.085{\mathrm{cm}}^{-1}$ and ${\mu }_{\mathrm{s}}\sim 4.9{\mathrm{cm}}^{-1}$ at $800\mathrm{nm}$ , and CCD frames with 100-ms integration time were acquired at $\sim 8\mathrm{Hz}$ for 1 minute. Two hundred dark frames were also recorded with the laser beam blocked, and the averaged dark image was subtracted from the previous signal images. The dark signals from the MCP and the CCD are around 40 to 50 counts per frame. The process was repeated for various intensities of the source by varying the attenuation of the incident beam. We defined the signal as the number of CCD counts on one pixel for each detector fiber corrected by the dark image, averaged over all the recorded frames. The noise was defined as the standard deviation of this value. The evolution of the SNR with the number of counts is very close to a square root. For typical signal values encountered in our functional imaging experiments ( $\tau =100\mathrm{ms}$ ; $V=500\text{–}800\mathrm{V}$ ) with pixel counts close to saturation, we thus expect the SNR to vary between 3 and 50. These values can be improved by integrating the signal over more pixels. A factor of 2 in the SNR can be gained by averaging the signal over 10 pixels, after which the SNR reaches saturation. We would expect an improvement of the SNR as the square root of the number of averaged pixels if the signal and noise were of the same magnitude on each pixel, and the noise was uncorrelated. However, not all pixels from the region of interest have the same signal level, which explains the saturation in SNR as we increase the number of pixels in the estimate of the signal.

From the ICCD sensitivity and the experimental SNR, we deduced the evolution of the SNR with the number of incident photons (Fig. 3c). For a given number of incident photons, the SNR increases with increased gain, within the saturation limit of the CCD.

3.3.

Instrument Response Function

When measuring an experimental TPSF on a phantom or a head, the system records the true TPSF due to the optical properties of the medium, convolved by the instrument response function (IRF). The IRF accounts for the laser pulse width, the width and shape of the detector gate, the pulse broadening in the source and detector fibers, and additional electronic delays. It is therefore important to empirically determine the width and shape of the IRF. We estimated this by placing a source fiber and a detector fiber facing each other $1\mathrm{cm}$ apart with a diffusive paper between them, as was suggested by Liebert to fill all the fiber modes.³¹ The source intensity was greatly attenuated with the exit polarizer to avoid detector saturation. A resulting IRF is shown in Fig. 4a for a gate width set to $300\mathrm{ps}$ . The measured FWHM is about $500\mathrm{ps}$ , which can be explained by the dispersion in the fibers (in this case, 3 meters of source fiber and 3 meters of detector fiber). A characteristic secondary amplitude peak of about 1% of the maximum is visible about $1800\mathrm{ps}$ after the primary peak. This secondary peak is due to reflection of light on the photocathode and back on the fiber array. The 1800-ps delay corresponds to an optical path of about $36\mathrm{cm}$ in glass, which is twice the length of the camera lens.

Fig. 4

(a) Typical instrumental response function (IRF) of the instrument, measured for one source fiber and one detector fiber facing each other with a diffusive paper between them. A typical secondary peak due to glass reflection from the camera is visible $\sim 1800\mathrm{ps}$ after the main peak. (b) Typical cross-talk between detector fibers. The decimal logarithm of the intensity on the CCD is shown for a single illuminated fiber. The square indicates the position of the nearest detector fiber. The insert shows the signal evolution for the region of interest corresponding to the central fiber, and for the nearest fiber.

3.4.

Cross-Talk

The cross-talk between detectors or between sources and detectors is a crucial point to characterize as it can affect the measurements greatly. There are two main possible mechanisms for cross-talk in our system: source to detector, and detector to detector. The source to detector fiber cross-talk has to be carefully controlled, as the light intensity in the source fibers can be 9 to 12 orders of magnitude higher than the light intensity in the detector fibers. Even an extremely small fraction of light leaking from source to detector fiber would cause high distortion of the signal. To prevent that effect, we shielded all sources and detector fibers in black PVC insulating tubing. This also prevents detector to detector cross-talk along the fibers. However, all fibers are imaged in parallel on the same CCD array, which we identified as the main cause for detector cross-talk. Fig. 4b shows the spot created by one illuminated fiber on the CCD array after background subtraction. Intensity is displayed in decimal log to visualize low CCD counts. The spot extends to a larger area than the pixels taken into account for this fiber, and in particular it covers the area of the next closer fiber (indicated by the square). The TPSF measured on the central fiber and on the closest one are presented in the figure insert. A cross-talk of about 0.3% is visible at the peak of the TPSF. At later delays, the difference between the two curves decreases as we reach the background noise level.

3.5.

Stability and Reproducibility

We characterized the stability and reproducibility of our system by measuring the evolution of the IRF over time for a single source–detector.

The stability of the signal was measured over 10 minutes, which is the typical duration of a single run for functional imaging. Two kinds of variations are observed simultaneously when studying the stability: the intensity stability and the stability of the temporal delay. To minimize the effects of a delay drift, we first made a measurement at the peak of the IRF, where the slope of intensity vs. delay is close to zero (see Fig. 5a , fiber 2 at delay 1). In that case, the intensity variations were found to be less than 0.6% over 10 minutes (Fig. 5b, fiber 2). When the measurement is made at a delay where the IRF slope is high, this stability can deteriorate to 5–10% variation over 10 minutes (Fig. 5b, fiber 1, and Fig. 5c). The instabilities shown in Fig. 5c are clearly due to variations in the delay, evidenced by the correlated signal changes of opposite directions in the two delay windows where the slopes have opposite directions. Taking into account the slope of the IRF at this delay, the 10% variation corresponds to a delay variation of about $30\mathrm{ps}$ . Even though the delay drift is small, it causes significant intensity variations, much larger than the intensity changes we expect to detect during functional brain imaging. However these variations related to delay drifts are slow (typical time scale $\sim 1$ minute) and can be removed by our standard $0.02\mathrm{Hz}$ high-pass filtering of brain activation data.

Fig. 5

Stability measurements. (a) TPSF recorded at the two fibers where the stability was measured (same detector bundle, two fibers of different lengths). The two gray areas show the delay gates at which the stability was assessed. The actual gate width is wider than represented. (b) Stability over $10\min$ measured at delay 1. Note in particular fiber 2 for which the slope of intensity vs. delay is close to zero, and which presents very little intensity variation over time. On the contrary, the intensity from fiber 1 (high slope intensity vs. delay) presents several percent variation over $10\min$ , due to delay drifts. (c) Stability over $10\min$ measured at delay 2, for fibers 1 and 2.

The reproducibility was estimated by repeating measurements at intervals of several hours. The delay variations were found to be less than $100\mathrm{ps}$ over several days. However, the drifts in intensity or delay in this case is not a very relevant parameter, since such drifts would not interfere with the measurements as functional imaging experiments typically last for no more than several minutes. As for characterization of optical properties of a medium, we always first measure a reference phantom to calibrate the system. To estimate the reproducibility of the system, we thus proceeded differently: we repeated the measurement of the absolute optical properties of a scattering phantom as described in Section 4 (see ahead). For each characterization, we first measured a reference phantom to determine the IRF, we then measured the target phantom. Over five hours, the maximum variation in the measured ${\mu }_{\mathrm{a}}$ was 5%, and 13% for ${\mu }_s^{\prime }$ .

5.1.

Head Probe

The head probe is divided in two parts, one for each hemisphere (see Fig. 7a ). Each half consists of $4\times 4$ sources and $3\times 3$ detectors (7 delays each) in a square geometry, with a source–detector separation of $2.5\mathrm{cm}$ . This separation was chosen to enable good coverage of the whole head while maintaining an acceptable SNR. The fixation of the fibers on the head is achieved in a way common to most functional brain imaging equipment in our laboratory. For the detector fibers, the tips of each group of 7 fibers are inserted in a 3-cm-long metallic ferrule bent at 90 degrees with a smooth curvature (custom made). For the source fiber, the same process is used with only one fiber per ferrule. The ferrule is spring-loaded in a plastic optode cap. These plastic optodes in turn plug into the slots made on the head probe. The probe itself is made out of soft plastic and Velcro bands to attach onto a headband fixed around the head. The whole probe can be further secured with a chinstrap. On the detector side, all 175 fibers were epoxied together in a circular plug and polished simultaneously. The plug is inserted in front of the lens that forms its image onto the ICCD.

Fig. 7

Two-hemisphere imaging. (a) Two-part probe picture. (b) TPSFs detected on detector 5 for successive illumination of sources 1 to 16. (c) Schematic showing the principle of the source scanning.

5.2.

Source Scanning

On the source side, we only have one light source: we need to time-multiplex it to illuminate the 32 source fibers sequentially. We thus divided the 32 source positions into 4 subsets of 8 sources that can be illuminated during the same camera frame while minimizing cross-talk from second nearest sources (see first line of Fig. 7c). For each subset, each detector only sees one of its nearest neighbor sources, the other sources being turned off. During one camera frame lasting $100\mathrm{ms}$ , we scan the galvanometer mirror through the 8 positions, staying approximately $10\mathrm{ms}$ on each, then switching to a reference fiber. The timing scheme of this scanning is illustrated in Fig. 7c. The reference fiber goes to a photodiode whose output is low-pass filtered and compared to a reference signal. The comparator controls a switch that closes the laser interlock in case the scanning fails and thus avoids excessive integrated laser power on the subject’s scalp. The source scanning and safety device enable us to increase the power at the end of the source fibers. The mean power at the end of each fiber was set to $100\mathrm{mW}$ , which corresponds to an average power of $2\mathrm{mW}$ because of the 2% duty cycle (each fiber shines light during $11\mathrm{ms}$ every $556\mathrm{ms}$ ). Because of scattering, the effective diameter of the light illumination can be considered to be $3\mathrm{mm}$ at this wavelength, leading to a power density of $\sim 28\mathrm{mW}∕{\mathrm{cm}}^2$ , well below the ANSI safety standards for skin exposure at these wavelengths (250 to $400\mathrm{mW}∕{\mathrm{cm}}^2$ from 750 to 850-nm). By defining 4 illumination states corresponding to one camera frame each, we reduce the acquisition frequency by a factor of 4. This yields an effective acquisition frequency for the whole head of $\sim 1.8\mathrm{Hz}$ , which is reasonable for functional imaging.

When the source scanning is implemented, the system stability over 10 minutes deteriorates to approximately 1%, when care is taken not to measure the delay drifts (see the procedure for stability measurement above). We studied the cross-talk from second nearest sources by placing the probe on a scattering phantom of optical properties ${\mu }_a\sim 0.085{\mathrm{cm}}^{-1}$ and ${\mu }_s^{\prime }\sim 4.9{\mathrm{cm}}^{-1}$ . We turned each source on alternatively, and recorded the complete TPSF for all detectors. One result is presented for detector 5 in Fig. 7b. For better clarity we show only the signal recorded by one of the 7 detector fibers. Note that the curves were plotted without any delay or amplitude correction, showing very good precision in the probe construction. Second-nearest-neighbor sources are visible with an amplitude about 1% of that of the nearest neighbor. For simultaneous illumination of all sources of a particular state, this distinction between nearest and second-nearest sources could not be made, leading to some cross-talk between sources. However, this cross-talk was smaller when measured on the head of a volunteer, between 0.2% and 1% depending on the detector position. This smaller cross-talk is probably due to the fact that the head is more absorbing and scattering than the phantom. The variation between detectors can be explained by the fact that the source–detector separations are less accurate on the curved head.

5.3.

Dynamic Imaging on Phantoms

The real-time acquisition capability of the system was tested on dynamic liquid phantoms. The setup is shown Fig. 8a . The phantom consisted of a $19\mathrm{cm}\times 19\mathrm{cm}\times 9\mathrm{cm}$ tank filled with a solution of intralipid and ink. A 15-mm diameter hollow glass sphere connected to horizontal tubes was embedded in the middle of the tank and filled with the same solution. A mechanical pump allowed circulation of the solution through the tubes via a $2\mathrm{L}$ reservoir. At one extremity, one of the tubes was also connected through a derivation to a 50-mL syringe containing the same intralipid solution but with increased ink concentration to create a higher absorption coefficient. Every $40\sec$ , $10\mathrm{mL}$ of the darker solution was injected in the tube over a period of $10\sec$ . The pump circulated this ink bolus into the sphere, after which it was diluted in the reservoir. The ink bolus created a transient absorption contrast in the sphere roughly similar to brain activation. Five boli were injected successively, enabling a block-averaging of the data as usually done in brain function experiments. We performed this experiment with the sphere at two different depths: top of the sphere at $6\mathrm{mm}$ and $17.5\mathrm{mm}$ below the surface.

Fig. 8

(a) Dynamic phantom setup. (b) Block-averaged time course of the intensity changes for the source-detector pair of maximal contrast, for a superficial (left) and a deep (right) inclusion.

By fitting the TPSFs measured before the dynamic experiment to an analytical model, as described in part 4 above, we estimated the following optical properties for the liquid phantom at $830\mathrm{nm}$ : ${\mu }_{\mathrm{a}}=0.14{\mathrm{cm}}^{-1}$ and ${\mu }_{\mathrm{s}}^{\prime }=10.2{\mathrm{cm}}^{-1}$ . We did not estimate the optical properties of the solution used for the bolus, which had a very high absorption coefficient. The ink concentration was about 70 times higher in the bolus than in the background.

Figure 8b shows the evolution of intensity with time at five different delays for the source–detector pair above the sphere, after averaging over the five successive blocks, for the superficial inclusion (top) and the deep inclusion (bottom). The curves at the last two delays are not shown because of a high noise level. Even though we are only showing one source–detector pair measurement, note that data from all 36 source–detector pairs (72 if we use both sides of the probe) were acquired in parallel at $1.8\mathrm{Hz}$ . For the superficial inclusion, the curves are very similar at every delay, the contrast increasing only very slightly for late delays. We attribute the secondary dip in the intensity time course to incomplete mixing of the ink bolus in the reservoir: the ink bolus therefore goes twice through the sphere, though with a lower absorption the second time. Also, note that the block averaged signal does not recover to zero level at $35\sec$ after bolus injection in the case of the superficial inclusion, because the successive injected boli, even though diluted in the reservoir, gradually increased the average absorption coefficient of the solution in the sphere, resulting in an overall decrease in intensity. For the deep inclusion, the change in the intensity increases as we increase the delay as expected and described in Ref. 18.

From each time course, we define the contrast as the change in intensity between the off state (before ink injection) and the on state (during ink injection). This contrast is calculated for each source–detector pair and each delay window. Figure 9 shows the resulting contrast maps for 5 different delay windows represented on the first line. For a superficial inclusion (2nd row), the inclusion is visible from the first delay window, and its contrast only increases mildly with delay. On the contrary, for a deep inclusion (3rd row), the contrast of the inclusion is almost null in the first window, and its contrast increases to become maximum in the fourth delay window. In both cases, the tubes themselves are also visible, due to their rather large diameter $\left(3\mathrm{mm}\right)$ . Also, note that the scales of the contrast maps are different in the two cases: the superficial inclusion yields a higher contrast than the deep one. As we had previously predicted theoretically,¹⁸ the two depths of inclusion give rise to very different behavior for the evolution of contrast with delay (see last curve of each line on Fig. 9).

Fig. 9

Contrast maps of the dynamic phantoms. The first line shows the delay window in which each map was made. The second and third lines show the averaged contrast maps for a superficial and deep inclusion, respectively (each pixel corresponds to a source–detector pair). The last curve of each line presents the evolution of the contrast with the delay for the pixel of maximum contrast.

5.4.

Human Results

As a last step of validation, we tested the imaging system on a healthy 34-year-old volunteer during a motor stimulus. The study was approved by the Institutional Review Board of Massachusetts General Hospital, and the subject gave informed written consent. The stimulus was a self-paced finger-tapping of the right hand. The subject was reclined, and instructed to touch the thumb with all other fingers of the hand alternatively. The protocol consisted of 20 blocks of alternate finger-tapping $\left(10\sec \right)$ and resting $\left(20\sec \right)$ , for a total run time of $10\min$ . We repeated the whole run three times. For this preliminary experiment, we used a simplified version of the probe, to make its positioning easier. Each half of the probe consisted of only $3\times 3$ sources and $2\times 2$ detectors, for a total of 18 sources and 8 detectors on the head, and a source–detector separation of $3\mathrm{cm}$ . The imaging was done at $\lambda =830\mathrm{nm}$ . The raw intensities were low-pass filtered (moving average filter over a 2-sec window) to remove heart beat oscillations and high-frequency noise, and slow drifts of the signal were subtracted (moving average filter over a 50-sec window). Block averaging over 18 successive blocks of each run was then performed, the first and last block of each run being removed to avoid artifacts due to the filtering process.

Figure 10a shows the time course of the block-averaged intensity for the first run, obtained on the source-detector pair of maximum contrast, on the hemisphere contralateral to the hand tapping, at 5 different delays. The tapping duration is indicated by the gray area. We observe a response to the stimulus (decrease in intensity) from the first delay window, indicating some contribution from the superficial layers. However, the contrast increases with delay, and the time course of the response varies with delay, showing that a deeper response is also present. When considering the time courses of all source–detector pairs (data not shown), we observe the small response in the early windows on most of them, but the strong increase of the contrast with delay is only present locally.

Fig. 10

Functional brain imaging on an adult volunteer. (a) Time course of the block-averaged intensity changes for the source–detector pair of maximal contrast. (b) Contrast maps for the left and right hemispheres, at the delay windows shown in the first column.

To present the results over both hemispheres, we calculated the contrast maps as done with the dynamic phantom (see Fig. 10b). The “on” time is defined between $5\sec$ and $10\sec$ after the stimulus onset, the “off” time between $17\sec$ and $25\sec$ . In the left hemisphere, contralateral to the tapping hand, a localized response is observed in-depth, as indicated by the strong increase in contrast with delay. A smaller ipsilateral response is also observed. Note that almost all pixels show some contrast, though much smaller than the localized response, and almost constant with delay. We interpret this as a systemic response, yielding a change in the skin, thus visible over the whole head. Previous theoretical and experimental work shows that superficial response yields almost uniform contrast with delay.¹⁸