Time-resolved absorption and hemoglobin concentration difference maps: a method to retrieve depth-related information on cerebral hemodynamics.

Bruno Montcel; Renée Chabrier; Patrick Poulet

doi:10.1364/OE.14.012271

1 Introduction

Non-invasive functional brain mapping explores either the neuronal response associated to a stimulus or the vascular response associated to neural activation. Usual imaging modalities include single-photon emission tomography, positron emission tomography and magnetic resonance imaging. A new neuroimaging technique, completely non-invasive and without requiring complete motion restriction is desirable. Near-infrared spectroscopy (NIRS) has this potential for non-invasive, lesser motion restrictive neuroimaging and a wide range of different NIRS instruments are commercially available. Instruments with continuous intensity measurements allow following dynamic changes in cerebral blood flow. However, quantification of brain functions is almost impossible with this kind of instruments. Other NIRS approaches have been tried to obtain quantitative data, they used time-resolved or frequency-domain instrumentation.

Variations in brain perfusion and oxygen saturation of hemoglobin associated with cortical activation can be detected through the skull by NIRS [1]. Other optical parameters can also reflect brain activity, like light scattering and cytochrome-c-oxidase absorption, but at a lower level [2]. The NIRS technique suffers from two main limitations: it has a poor spatial resolution and is hardly quantitative. It has been argued that the use of a short picosecond-laser pulse and of the detection of photons as a function of time, in a time resolved spectroscopic (TRS) instrumentation, allows the quantitative measurement of hemoglobin concentration changes [3].

Moreover, such time resolved methods are especially powerful for achieving the spatial localization of optical properties in diffuse optical tomography (DOT). 3D images of absorption and scattering changes have been obtained in different application areas such as small animal imaging [4, 5] or newborn infant heads [6]. However the inversion process in DOT requires a lot of data [7, 8], and volumetric neuro-functional imaging through the intact adult head is still on the agenda.

On the other hand optical topography is another approach, which uses multi-channel NIRS instrumentation and does not require any inversion method for reconstruction processing [9]. Multiple regions are simultaneously measured by optical topography, but quantitative data can not be reconstructed. This is due to two main assumptions which have to be done for reconstruction. Firstly, the effective optical pathlength is β times as long as the separation between illuminating and detecting light guides. It is often assumed that the optical pathlength factor β is constant, but this assumption is not correct [10]. Secondly, the variations of the absorption properties, associated with the hemoglobin concentration changes, should be considered as constant over the whole effective optical path, from the skin to the brain.

In TRS, the optical pathlength factor can be measured from the mean time of flight of detected photons; the modified Beer- Lambert law can then be used to compute the mean optical absorption coefficient [3]. It is also necessary to implement experimental methods to achieve depth discrimination of this coefficient, by using the whole time profile of detected photons and/or multidistance measurements.

Considering a TRS experiment at one position of the source and of the detector, it has been demonstrated that the information of depth is encoded in the time delay [11]. It has also been shown that TRS has a better sensitivity to brain activation and a better immunity to superficial events as compared to continuous wave measurements [12]. These properties allowed differentiating between modifications in the absorption properties which occur superficially or at a deeper level [13]. Depth-resolved measurements of the absorption variation linked to the activation of the motor cortex have been obtained with a reconstruction method based on a simplified multilayer model and on time dependant mean partial pathlength in each layer [14]. This method has been improved by TRS multidistance measurements and allowed the depth-resolved measurement of the variation of absorption in human adult heads after the injection of an ICG bolus [15].

This article describes a method to retrieve depth-related information on brain activity on the basis of time-resolved measurements of absorption variations and which requires no reconstruction step or any prior information. The theoretical justification of this method is based on the microscopic, or time-resolved, Beer-Lambert law [16, 17]. Experimental validation was performed with resin phantoms. We also present the condition which allows extending the method and gaining access to functional parameters, through the calculation of variations in oxyhemoglobin (HbO₂) and deoxyhemoglobin (Hb) concentrations. The experimental results of the hemodynamic response measured over the motor cortex, and during Valsalva manoeuvre paradigm will be subsequently presented and discussed.

2 Materials and methods

2.1 Time-resolved absorption difference maps

2.1.1 Method

The time-resolved or microscopic Beer-Lambert law [16] describes the distribution I_λ(t,T) of the photons detected after the time of flight t, at the wavelength λ and at the experiment time T as a function of the optical properties of the propagation medium.

I_{λ} (t, T) = I_{0 λ} (t) \exp (- μ_{aλ} (t, T) vt)

I_λ(t) and I_0λ(t) are the distributions of the times of flight of photons with and without absorber. μ_aλ is the absorption coefficient at the wavelength λ. v is the velocity of light in the medium.

If this law is to be used, one should assume that the distribution of photon pathlengths does not depend on optical absorption variations [18]. For measurements series, the absorbance difference ΔA_λ(t,T-T₀) between a given state observed at the time T and the reference state at the time T₀ is given [19] by:

Δ A_{λ} (t, T - T_{0}) = \log (\frac{I_{λ} (t, T_{0})}{I_{λ} (t, T)}) = \frac{Δ μ_{aλ} (t, T - T_{0}) vt}{\ln (10)}

where Δμ_aλ(t,T-T₀) is the absorption difference between the two states. The absorbance difference can be computed if the events measured only introduce small absorption variations and leave the scattering properties unchanged. In the following, T, the time of the experiment, will be called the macroscopic time whereas t, the time of flight of photons, will be named the microscopic time. This method has already been used to evaluate the mean absorption variation by a linear fitting of the slope ΔA_λ(t,T-T₀)/vt [17, 19]. In that case one has to consider that the variation in the absorber concentration is uniform throughout the medium measured. In this article we consider cases where the absorbance difference is not a linear function of the microscopic time that is to say when the variation in the absorber concentration is non-uniform throughout the medium measured. We aim to relate the general behaviour of the time-resolved absorption difference to the depth of the variation of absorption. In such experimental conditions, we consider time-resolved absorption differences relative to a reference state as a 2-dimensional function of the “macroscopic” and “microscopic” times, and we represent them as 2-D maps.

2.1.2 Depth dependence of time resolved absorption variations

The depth dependence of the behaviour of the time resolved absorption difference is investigated thanks to simulations based on a homogeneous semi-infinite medium of absorption coefficient μ_a=0.2 cm^-1 and reduced scattering coefficient μ’_s=15 cm^-1 [12] and with a typical refractive index n=1.4 for biological tissues [20]. The model is intentionaly simple and does not correspond to the head layered structure. However it is only used to investigate the general behaviour of the time resolved absorption difference and it is not used for fitting of experimental data. An absorbing inclusion (absorption coefficient μ_a+Δμ_abs, volume V) is introduced into the medium at a depth z_pert below the surface between the source and the detector positions. Considering a small inclusion, its effects can be estimated by using the Born approximation. Therefore an analytical expression of the time resolved absorption difference due to this inclusion can be obtained from the solution of the diffusion equation for a homogeneous semi-infinite medium, bounded by z=0, using the method of images [21]. For a source at position r_s and a detector at position r_d, both on the boundary, the temporal profile of detected photons, also named temporal point spread function (TPSF), is equal to [21]:

I (r_{s}, r_{d}, t) = {(4 π D v)}^{- \frac{3}{2}} z_{0} t^{- \frac{5}{2}} \exp (- \frac{ρ_{s}^{d^{2}} + z_{0}^{2}}{4 D v t} - μ_{a} vt)

where z₀=(μ’_s)^-1 is the depth of the image source, $ρ_{s}^{d}$ =|r_d-r_s| is the distance between the source and the detector and D=1/3μ’_s is the diffusion coefficient. The contribution of μ_a to the diffusion coefficient was neglected to take into account the necessity for the distribution of photon pathlengths to be independent of absorption variations. Therefore only the contribution of μ’_s was taken into account, which is a fair approximation considering the optical properties of the media studied.

The change in the temporal profile due to the absorbing inclusion, whose total contribution is given by the product Δμ_absV, can be calculated from the diffusion equation by applying the Born approximation. It was given by [22]:

Δ I (r_{s}, r_{d}, r_{pert}, t) = \frac{z_{pert} (Δ μ_{abs} V)}{{(2 π)}^{\frac{3}{2}} ρ_{pert}^{d}} [S (ρ_{s -}^{pert}, ρ_{pert}^{d}, t) - S (ρ_{s +}^{pert}, ρ_{pert}^{d}, t)]

where $ρ_{i}^{j}$ =|r_j-r_i| and r_pert is the position of the absorbing inclusion, r_s- and r_s+ are the positions of the image sources. S is equal to [22]:

S (x, y, t) = (\frac{1}{y^{2}} + \frac{x + y}{2 Dvt} (\frac{1}{x} + \frac{1}{y})) G (x + y, t)

where G is the Green function for an infinite medium [21]:

G (r, t) = v {(4 π D v t)}^{- \frac{3}{2}} \exp (- \frac{r^{2}}{4 D v t} - μ_{a} v t)

The above equations allow the computation of the relative variations of the recorded signal, due to the (Δμ_absV) absorbing inclusion at depth z_pert. They are equal to:

\frac{Δ I}{I} = \frac{{vtz}_{pert} (Δ μ_{abs} V)}{{(2 π)}^{\frac{3}{2}} ρ_{pert}^{d} z_{0}} [f (ρ_{s -}^{pert}, ρ_{pert}^{d}, t) - f (ρ_{s +}^{pert}, ρ_{pert}^{d}, t)]

with:

f (x, y, t) = (\frac{1}{y^{2}} + \frac{x + y}{2 D v t} (\frac{1}{x} + \frac{1}{y})) \exp [\frac{r^{2} + z_{0}^{2} - {(x + y)}^{2}}{4 D v t}]

The time resolved absorption difference can be expressed from Eq. 1 and Eq. 7:

Δ μ_{a} (t) = \frac{- \ln (1 - \frac{Δ I}{I})}{vt}

The time resolved absorption differences Δμ_a(t) plotted as a function of the microscopic time t, for a depth of the unit (Δμ_absV=1) inclusion varying from 1 to 25 mm, are shown on Fig. 1(a). for a source-detector separation of 30 mm. The simulation indicates a weak influence of the source-detector distance on the behaviour of the time resolved absorption difference. For example the monitoring of the position of the maximum of the time-resolved absorption difference on the microscopic time axis for a depth of the inclusion of 25 mm show a shift of this maximum smaller than 15 ps between the typical range of source-detector distances of 25 mm to 35 mm. Furthermore, even between the extremal source-detector distances of 10 mm to 40 mm, the shift is still smaller than 40 ps. For increasing microscopic time, Δμ_a(t) increases until a maximum and decreases until the end of the simulation at 5 ns for an inclusion depth lower that 20 mm. For greater depths, the behaviour is identical but the maxima occur after 5 ns. The time position of the maximum is plotted as a function of the depth of the absorbing inclusion on Fig. 1(b). Considering experimental limitation in the ability to retrieve the exact position of the maximum of the time resolved absorption difference, these results will only be considered as a way to differentiate a deep (continuous increase of Δμ_a(t)) or superficial (increase followed by a continuous decrease of Δμ_a(t)) absorbing events.

2.1.3 Time resolved absorption difference and cerebral activation

Numerous physiological events are associated with cerebral activation, but the optical signal is mainly sensitive to the local variations in cerebral blood volume and in the oxygen saturation of hemoglobin. These events introduce absorption variations in the brain gray matter and in the associated vasculature, but the scattering properties can be considered as constant during a cerebral activation experiment. As a consequence the absorbance difference method can be implemented.

On the other hand we cannot consider that such variations in hemoglobin-concentration are homogeneous throughout the head, because the superficial layers that mainly contribute to the optical signal are not affected by cerebral activation.

Fig.1. (a). Time-resolved absorption difference for 9 different depths of the inclusion (1, 4, 7, 10, 13, 16, 19, 22 and 25 mm below the surface). Source-detector separation 30mm. The simulated TPSF is also plotted, with a different vertical scale, for easier reading. The arrow indicates the different time-resolved absorption difference curves from 1 to 25 mm. (b). Time position of the maximum of the time-resolved absorption difference as a function of the depth of the inclusion. The values for depth greater than 20 mm are saturated to 5 ns only because of the limited time window of the simulations.

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In a previous study [13], we simulated time-resolved photon measurement density functions (PMDFs) by a finite element method (FEM) on a model of the head. Obtained results have shown that the contribution of cerebral tissues to the measurement for a given source – detector configuration increases as a function of the photon arrival time. Then the variations measured in the TPSFs, over a microscopic time interval, should be associated to a mean variation in absorption of a defined sampled region of the head. These regions have the well known “banana” shape of the PMDFs. Each of the regions sampled is highly weighted by superficial layers, but the weight of the cerebral layer increases as a function of the microscopic time interval considered.

We also have to consider that modifications in the optical properties related to the brain hemodynamic response have negligible effects on the boundaries of each region scanned. Finally, it should be emphasized that even if the cerebral contribution to the absorption variations increases as a function of the microscopic time. Therefore, this time cannot be considered as a depth scale. Indeed every temporal strip is highly weighted by superficial events.

2.1.4 Time-resolved concentration difference maps

From multi-wavelength measurements it is possible to compute functional parameters such as the time-resolved differences in HbO₂ and Hb concentrations. However it is necessary to consider that each temporal step at each wavelength corresponds to the same sampled zone. This means that the time-resolved distributions of photons at each wavelength are identical. This can be assumed if the different wavelengths used correspond to total absorption and scattering coefficients of the same order of magnitude. Moreover, because the impulse response functions of the instrument (IRF) are different at all wavelengths, deconvolution of the TPSFs is mandatory. This was not the case for the computation of time resolved absorption differences map described in the previous paragraph because the convolution by the IRF only changes the relation between the microscopic time and the photon pathlength, inducing some kind of geometrical aberration. This is not an additional problem, as we already stated in paragraph 2.1.3 that the microscopic time scale could not be considered as a depth scale.

The deconvolution was implemented through inversion of the linear convolution matrix, with a Tichonov regularization method. After computing the time resolved absorption differences Δμ_aλ1(t,T-T₀) and Δμ_aλ2(t,T-T₀) at both wavelengths, the time-resolved differences in HbO₂-, ΔC_HbO2(t,T-T₀), and Hb-, ΔC_Hb(t,T-T₀), concentrations, can be calculated by solving the following system:

[\begin{matrix} ε_{{HbO}_{2}}^{λ 1} & ε_{Hb}^{λ 1} \\ ε_{{HbO}_{2}}^{λ 2} & ε_{Hb}^{λ 2} \end{matrix}] [\begin{matrix} Δ C_{{HbO}_{2}} (t, T - T_{0}) \\ Δ C_{Hb} (t, T - T_{0}) \end{matrix}] = [\begin{matrix} Δ μ_{aλ 1} (t, T - T_{0}) \\ Δ μ_{aλ 2} (t, T - T_{0}) \end{matrix}]

where ${ε^{λ i}}_{{HbO}_{2}}$ and ${ε^{λ i}}_{Hb}$ are the molar extinction coefficients of HbO₂ and Hb respectively at the wavelength λi.

2.2 Phantoms

We performed experiments with a layered, “head” -like, phantom (35 mm high and 100 mm in diameter cylinder) made of polyester resin (Roth-Sochiel, France), with a refractive index of 1.54, mixed with titanium dioxide particles (Sigma-Aldrich, France), black India ink (Conté, France), Luxol blue (BDH Chemicals, UK) and Projet 900 (Avecia Inc., UK). This phantom consisted of four layers corresponding to the scalp, the skull, gray and white matter of the brain, with thicknesses and optical properties at 690 nm adjusted to those reported in Table 1. Its optical properties were chosen to match real tissues values at 800 nm according to literature [23]. These optical properties at 800 nm were calibrated by fitting of the TPSF measured on homogeneous phantoms and of a semi-infinite model [22]. The values at 690 nm were evaluated with the same calibration method. We drilled out a hole, 28 mm in diameter in the centre of the cylinder, nearly all the way through except for a 1.8-mm layer, corresponding to the outermost part of the scalp layer. We also made polyester rods fitted to the size of the hole, with the same layer configuration as the phantom but with different absorption properties in the layer of interest. With this configuration, the interface between the phantom and the optodes remained stable while the different inclusions were swapped. This condition is essential, the observed instability of the interface conditions from one setting to another does not allow any change of the interface between a solid phantom and the optodes if results should be compared. An aqueous solution of black India ink and calibrated polystyrene micro-spheres with the same optical properties as the scalp layer has to be inserted between the phantom and the rod, to insure a good interface between them. This liquid film introduces a refractive index mismatch which could introduce unwanted reflections. Nevertheless we observed a good reproducibility when moving on and off a given inclusion, this was not the case when changing the optodes on the phantom surface.. We made three rods fitting the hole, the first one with the same absorption properties as the external cylinder, simulating rest (case 1), and the two others with one more absorbing layer at two different depths. In the second rod (case 2), a more-absorbing inclusion was introduced into the “gray matter” layer (15 mm deep beneath the phantom surface, 7-mm thick and 28 mm in diameter, μ_a=3.6 cm^-1) to simulate brain activation. In the third rod (case 3), an absorbing inclusion was introduced into the “scalp” layer (1.8 mm deep beneath the phantom surface, 2.2-mm thick and 28 mm in diameter, μ_a=0.27 cm^-1) to simulate a superficial increase in absorption.

Table 1. Absorption coefficient μ_a, transport scattering coefficient μ’_s and thickness of each tissue layer of the headlike phantom, for a wavelength equal to 690 nm.

View Table

2.3 Experimental set up

The apparatus assembled uses a multi-channel picosecond laser diode system (Sepia, Picoquant Germany) which can drive up to 8 laser heads under synchronous or sequential operation modes, with a repetition rate ranging from 5 to 80 MHz. Two sets of four laser heads, operating at 4 wavelengths (690, 785, 830 and 870 nm), are fitted with 4-furcated optical fibers (Ocean Optics, USA) providing 2 space-separated sources of light, each of them consisting of up to 4 sequential sources spectrally separated. In the experiments described in the following, we only use one local source with 2 wavelengths. The specified pulse Full Width at Half Maximum (FWHM) is less than 70 ps for an average power not exceeding 1 mW at a repetition rate of 80 MHz. An 8-anode Micro-Channel Plate Photo-Multiplier Tube (MCP-PMT, R4110U, Hamamatsu, Japan) followed by 2 stacks of four Time-Correlated Single Photon Counting (TCSPC) modules (SPC 134, Becker & Hickl, Germany). Multimode optical fibers, 1000-µm in core diameter (Fiber1000-VIS/NIR, Ocean Optics, USA) can be used to detect light emerging from eight points of the surface of the heads or of the phantoms. These fibers are connected to a bundle assembly (Hamamatsu, Japan) whose end is shaped to match the geometry of the MCP-PMT photocathode. Only one fiber was used in the present work.

The contact between the head and the optodes is a critical issue. The source and the detector were maintained by a helmet which was adapted from an Electro-Encephalography cap (Medical Equipement International, France), widely used in the clinical environment. This helmet ensures correct stability of the optodes throughout the experiment. It also makes access to the fiber tips easier and therefore allows a good positioning of the fibers among the hair.

The scanner has proven its ability to retrieve optical properties maps of phantoms [24] and to detect small absorption variations linked to cerebral activation [13]. The light pulses generated by the picosecond laser diodes have very low energy in the 10–100 pJ range. The signal to noise ratio of the system tends towards the shot noise theoretical limit. The overall Instrument Response Function (IRF) was measured by placing the corresponding collecting fiber in the direction of the illumination fiber (180° position) and by recording the temporal profiles of photons transmitted through a light-scattering piece of white paper. A typical IRF recorded with one 785-nm picosecond laser diode at 1 mW and one PMT+TCSPC detection channel has a FWMH of about 260 ps. Using a second laser diode and a second detection channel, with a black ink absorber to reduce light intensity impinging on the MCP-PMT, provides a time reference for the experiments. The variations in the mean time of the “experimental” channel minus the “reference” channel have a mean standard deviation of 5 ps. Such stability can be obtained after a short warm-up, less than 10 minutes. A second aspect of the temporal stability concerns the laser diode energy. It was measured through the variations in integral intensity of the temporal profiles. Variations by about 2% per hour were observed. This temporal drift of the light intensity can be compensated for by using a “reference” channel and the “experimental” to “reference” integral intensity ratio. For these two reasons, a “reference” channel was always used in our experiments.

2.4 FEM simulations

A 2-D FEM simulation method is used to compare the simulated and experimental time-resolved absorption difference of the phantoms. The FEM model was described in detail in a previous paper [13]. The model is a 2D cut off of the previously described phantoms in the source-detector plane. The TPSF at both states (with and without the absorbing inclusion) are simulated and convoluted by the experimental IRF and the time-resolved absorption difference is calculated thanks to Eq. (2).

The validity of the diffusion approximation is critical at early times, for the zones scanned close to the source and to the surface. Furthermore, the artefacts are amplified, at early times, in the simulated time-resolved absorption difference because of the very short photon pathlength. This is the reason why data obtained for early times should be considered with caution. As a consequence, these simulated results are to be considered only for temporal steps with a real significance (where the diffusion approximation is valid and where the experimental signal-to-noise ratio is sufficient).

3 Results and discussion

3.1 Phantoms experiments; time resolved absorption differences

All experiments were conducted at a wavelength of 690 nm and two optodes, one source and one detector, were positioned over the phantom surface, 30 mm apart from each other. The time-resolved absorption difference between “rest” (case 1) and “gray matter activation” (case 2) is shown on Fig. 2. The experimental results are very noised at the beginning and at the end of the TPSF, but the main part of the curves, for times between 1 and 2.4 ns, where the TPSFs are significantly higher than the noise, confirms that the time-resolved absorption difference is not constant, but increases continuously over the microscopic time. For comparison purposes, FEM simulation results of the time-resolved absorption difference are also shown on Fig. 2.

Considering the experiments involving the “scalp” inclusion (case 3), the time-resolved absorption difference between rest and activation is shown on Fig. 3. The experimental results are also very noisy at the beginning and at the end of the TPSF, but the main part of the curve, from 0.6 to 2.8 ns, confirms that the time-resolved absorption difference decreases continuously over the microscopic time. For comparison purposes, FEM simulations of the time-resolved absorption difference are also shown on Fig. 3. The mismatch between experiment and simulation at early times could be explained by the limitation of the diffusion equation, as discussed in paragraph 2.4. These results confirm the validity of the time-resolved absorption difference principle, and its ability to provide information about the depth at which absorption variations occur.

Fig. 2. FEM simulation (solid line) and experimentally measured (dots) time-resolved absorption difference between rest and activation for an absorbing inclusion in the “gray matter” layer of the head-like phantom. Measurements at 690 nm for a source-detector distance of 30 mm.

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Fig. 3. FEM simulation (solid line) and experimentally measured (dots) time-resolved absorption difference between rest and activation for an absorbing inclusion in the “scalp layer” of the head-like phantom. Measurements at 690 nm for a source-detector distance of 30 mm.

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Comparison of the vertical scales of Fig. 2 and Fig. 3 demonstrates that absorption differences produced by superficial changes are much greater than those produced by deep changes, at any microscopic time. A simultaneous change in both regions would make the detection of deep changes difficult or impossible, even with time resolved methods. Nevertheless, the ratio of absorption differences due to deep to superficial changes increases with the microscopic time, demonstrating a lower sensitivity of time resolved techniques to superficial changes, as compared with continuous wave (CW) techniques. Another practical advantage of time resolved detection over CW methods is that it allows for the detection of a superficial change, and in this case, gives the possibility to reject these experimental data and consider a further experiment.

3.2 In vivo experiments: Time-resolved absorption differences and maps

3.2.1 Experimental paradigms

Stimulation of the motor cortex was achieved through a short finger tapping movement (< 1 s) followed by a rest period (~ 20 s). This paradigm produces less intense activation than continuous stimulation but allows the temporal measurement of the hemodynamic response. Because of the low level of the recorded variations, 46 cycles were acquired and accumulated. Prior to NIRS experiments, the motor cortex of the subject was localized using fMRI during a finger tapping task. The optodes were then positioned 30 mm apart on the scalp over the activated area thus determined. The TPSFs at 690 and 830 nm were acquired during the experiments with microscopic time steps of 60 ps and macroscopic time steps of 150 ms (6.7 Hz).

For comparison purposes, we conducted experiments involving a Valsalva manoeuvre (held for 5 s) followed by a rest period (~ 30 s), with the optodes maintained in the same position. 10 cycles were acquired and accumulated. TPSFs at 690 and 830 nm were acquired during the experiments with microscopic time steps of 12 ps and macroscopic steps of 250 ms (4 Hz). The Valsalva manoeuvre consists in a prolonged expiratory effort resulting in an increased intrathoracic pressure which compresses the great vessels, resulting in a transient increase in arterial pressure (AP). As increased thoracic pressures continues, venous return decreases, reducing the AP. When the strain is released, a transient fall in AP below baseline occurs, followed by an overshoot. In an attempt to offset the fall in AP, the autonomic nervous system is recruited, the time-course of neural recruitment was studied by functional-MRI. Significant signal changes have been observed within multiple brain areas, including the amygdale, hippocampus, cerebellum, insular and lateral frontal cortices. No change was observed on the motor cortex [25].

Fig. 4. (a). Finger tapping stimulus, (b). Valsalva manoeuvre. Statistical significance of the differences between the two time-resolved absorption differences at 830 nm, computed after binning the data by 2. The first sample is for the activation period and the second one for the rest period. The retained time window corresponding to a threshold of 5 % (p-value < 0.05) is indicated by the vertical dotted lines.

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3.2.2 Data analysis

The intensity-to-noise ratio of the TPSFs and consequently the significance of the time-resolved absorption differences were not constant along the whole microscopic time. For this reason, we evaluated the statistical significance of the time-resolved absorption differences. Their means, during rest and stimulation periods, were computed at all microscopic time steps and compared through a Wilcoxon signed rank test for zero median (Matlab 7.1). This test returns the significance probability that the medians of two matched distributions are equal. A typical threshold of 5 % was chosen and the time window where the p-values were lower than 0.05 was retained for computation of the time-resolved absorption difference maps. The statistical differences were then filtered in order to eliminate high-frequency noise. We used a Chebyshev filter with an 8 samples time window (Matlab 7.1).

3.2.3 In vivo experiments: motor cortex activation

The TPSFs at 690 and 830 nm was recorded as describe above, and the time origin was arbitrarily taken at the maximum of the IRF, measured as described in the paragraph 2.3. This is not the real time origin, but its knowledge is not mandatory, as the TPSFs were not deconvoluted. The stimulation period was chosen to correspond to the known hemodynamic response to a finger tapping stimulus (1.5 to 9 s). The rest period was chosen prior to the stimulus (-7.5 to 0 s). The data were binned along the microscopic time to increase the signal to noise ratio. The results of the statistical hypothesis test at 830 nm are shown on Fig. 4(a). They are formulated in terms of the statistical significance (p-value) of the time-resolved absorption differences during the stimulation period along the microscopic time. On the example of Fig. 4(a), the retained time window was 0.67 to 2.2 ns.

Fig. 5. Finger tapping stimulus: Experimental absorption differences at 690 nm (x) and 830 nm (dots). Filtered absorption differences at 690 nm (dashed line) and 830 nm (solid line). The short finger tapping period started at the time 0 (vertical dashed line).

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The reference state used for the calculation of absorption differences was the mean value over a 2-s period before the short finger tapping stimulus. For comparison purposes, absorption differences for the total intensity, obtained by integration of the time differences over all microscopic times, and corresponding to CW measurements, are presented on Fig. 5. The experimental data and filtered data, Chebyshev, 8 samples time window (1.2 s), are shown. Measurements at 690 and 830 nm were mainly influenced by Hb- and HbO₂-concentrations, respectively. This is why absorption differences showed this different behaviour with an increase at 830 nm and a decrease at 690 nm. At 690 nm, the filtered absorption difference reached a minimum equal to -4.7 10^-4 cm^-1 at a macroscopic time equal to 4.8 s. At 830 nm, this difference rose up to a maximum equal to 6.3 10^-4 cm^-1 at 4.65 s. These values are in accordance with the known characteristics of the hemodynamic response.

The time-resolved absorption difference maps at both wavelengths are shown in Fig. 6(a) and Fig. 6(b). These experimental data were filtered in order to eliminate the high-frequency noise along both time axes in two steps. The same filter was used for the macroscopic axes as for the filtering of non-time–resolved absorption differences (Fig. 5) to allow comparisons.

These maps clearly show that absorption was not significantly modified at early microscopic times, corresponding to superficial tissues. On the contrary, it increased and followed the behaviour of the hemodynamic response at later times, when the contribution of deep tissues was increased. At 690 nm, the filtered time-resolved absorption difference reached a minimum equal to -0.9.4 10^-4 cm^-1. This occurred at a macroscopic time equal to 4.8 s, and a microscopic time of 2 ns. An important decrease in the time-resolved absorption difference is observed at microscopic times greater than 1.4 ns and at macroscopic times ranging from 2 to 8 s. At 830 nm, the filtered time-resolved absorption difference rose up to a maximum equal to 10 10^-4 cm^-1, at a 5.1s macroscopic time and at a 2 ns microscopic time.

Fig. 6. Finger tapping stimulus: Time-resolved absorption difference maps at 690 nm (a) and 830 nm (b). The short finger tapping period started at the time 0 (vertical dashed line). Valsalva manoeuvre: Time-resolved absorption difference maps at 690 nm (c) and 830 nm (d). The Valsalva manoeuvre was performed between 0 and 5 s (vertical dashed lines).

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3.2.4 In vivo experiments: Valsalva manoeuvre

The same process was applied to the data from the Valsalva manoeuvre experiment. The statistical tests at 830 nm, Fig. 4(b), showed the difference between the significant time window for motor cortex stimulation (0.67 to 2.2 ns) and for Valsalva manoeuvre (0.51 to 1.88 ns). The stimulation period was chosen to correspond to the Valsalva manoeuvre (0 to 5 s) and the rest period was chosen prior to the stimulus (-5 to 0 s). The data were binned along the microscopic time for the same reasons as previously. The time-resolved absorption difference maps were then calculated within the time range 0.51 to 1.88 ns, after filtering of the experimental data [Chebyshev filter, 8 samples time window (96 ps)].

The total absorption differences shown for comparison on Fig. 7 were also filtered [Chebyshev, 8 samples time window (2 s)]. They reflected the behaviour known to be induced by a Valsalva manoeuvre. During the manoeuvre there was an accumulation of HbO₂ in superficial layers which produced a large increase in absorption at 830 nm and a smaller increase at 690 nm. After the intra-thoracic pressure was released, there was a decrease in both Hb and HbO₂. This produced a large decrease in absorption at both wavelengths. The filtered absorption difference rose up to a maximum (1.2 10^-3 cm^-1 at 690 nm and 3.6 10^-3 cm^-1 at 830 nm) after about 3 s. It then reached a minimum (-2.7 10^-3 cm^-1 at 690 nm and -4.1 10^-3 cm^-1 at 830 nm) after about 8.5 s, therefore about 3.5 s after the end of the Valsalva manoeuvre. Finally absorption values returned to their initial state.

The time-resolved absorption difference maps at both wavelengths are shown in Fig. 6(c). and Fig. 6(d). (same filter for the macroscopic axes as for the non-time–resolved absorption differences). These maps exhibit a behaviour which is completely different from that observed on brain activation maps [Fig. 6(a). and Fig. 6(b)]. Absorption was significantly modified at early microscopic times, corresponding to superficial tissues. Whereas at later microscopic times, variations were less pronounced and almost disappeared at the latest times. At 690 nm, the filtered time-resolved absorption difference reached a maximum equal to 3.3 10^-3 cm-1 (3.7 s macroscopic time, 0.55 ns microscopic time), followed by a minimum equal to -6.1 10^-3 cm^-1 (8 s, 0.57 ns). At 830 nm, it reached a maximum equal to 9.4 10^-3 cm^-1 (3.7 s, 0.56 ns) followed by a minimum equal to -7.7 10^-3 cm^-1 (8.2 s, 0.62 ns). It should be noted that all the maxima of the time resolved absorption differences are much greater than the maxima of the total absorption difference, demonstrating some first advantages of time resolved experiments over continuous wave detection.

Fig. 7. Valsalva manoeuvre: Absorption differences at 690 nm (x) and 830 nm (dots). Filtered absorption differences at 690 nm (dashed line) and 830 nm (solid line). The Valsalva manoeuvre was performed between 0 and 5 s (vertical dashed lines).

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In addition, time resolved experiments are not only able to retrieve depth-related information, but time-resolved absorption difference maps also allow to testify, in a very reliable way, on the origin of absorption variations, by displaying the very different behaviours inherent to deep and superficial absorption variations.

3.3 Time-resolved HbO₂- and Hb-concentration difference maps

3.3.1 Experimental paradigms

Stimulation of the motor cortex was achieved through continuous finger tapping movements. 10 cycles were acquired and accumulated, each of them consisted in a 32-s rest period, followed by stimulation for 32 s, and by another 32-s rest period. The optodes were positioned 30 mm apart as previously determined. The TPSFs at 690 and 830 nm were acquired during the experiments with microscopic time steps equal to 12 ps and macroscopic steps equal to 1 s. This paradigm (continuous tapping) was different from the previous one (single tapping) and produces a more important vascular response. It allows obtaining data with better signal to noise ratio, in order to deconvolute them. The macroscopic time origin was set to coincide with the beginning of the finger tapping period to facilitate comprehension.

3.3.2 Results

The TPSFs at 690 and 830 nm were deconvoluted as described in paragraph 2.1.4 and the time-resolved HbO₂- and Hb-concentration differences were calculated according to Eq. 10. The statistical treatment previously described was applied. A review of the published absorption and scattering coefficients of the various tissues encountered by the photons demonstrate that for our wavelengths of interest they do not differ by more than 20 %, except for the scalp [26]. The assumption that the time resolved distributions of photons are the same at both wavelengths should therefore be considered carefully. The stimulation period was the finger tapping period (1 to 32 s) and the rest period was chosen prior to this period (-31 to 0 s). The results of the statistical test performed on HbO₂ data are shown on Fig. 8. The chosen time window corresponds to p-values lower than 0.01 (a significance level of 1 % was chosen because of the better signal to noise ratio). As a consequence time-resolved HbO₂- and Hb-concentration difference maps were calculated within the time range from 0.3 to 1.4 ns.

Fig. 8. Finger tapping experiment: Bottom: Time-resolved HbO₂-concentration differences for the stimulation period and for the rest period (error bars=2 times the standard error). Up: Statistical significance of the difference between these two time-resolved HbO₂-concentration differences. The retained time window (0.3 to 1.4 ns) corresponding to a threshold of 1 % (p-value < 0.01) is indicated by the vertical dotted lines.

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The reference state used to calculate concentration differences was the mean value over the 32-s rest period before the finger tapping task. For comparison purposes, HbO₂- and Hbconcentration differences computed from the total intensity are presented in Fig. 9. These experimental data and filtered data [Chebyshev time window with a length of 8 samples (8 s)] are shown. The filtered Hb-concentration difference reached a minimum of -0.43 μmol at 8 s, but was fairly constant over the stimulation period. The filtered HbO₂-concentration difference rose up to a maximum equal to 0.73 μmol at 8 s and then slowly decreased over the subsequent part of the stimulation period.

Fig. 9. Finger tapping period: HbO₂- (dot) and Hb- (+) concentration differences. Filtered HbO₂- (dashed line) and Hb- (solid line) concentration differences. The finger tapping period started at the time 0 and ended at 31 s (vertical dashed lines).

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The time-resolved HbO₂- and Hb-concentration difference maps are shown in Fig. 10(a). and Fig. 10(b). These experimental data were also filtered along the macroscopic time axes with the same filter as that used for the non-time–resolved absorption differences (Fig. 9) to allow comparison. These maps exhibit the same behaviour as the time-resolved absorption difference maps. The filtered time-resolved Hb-concentration difference reached a minimum equal to -3.5 μmol (31 s macroscopic time, 1.36 ns microscopic time). The filtered time-resolved HbO₂-concentration difference rose up to a maximum equal to +5.1 μmol (31 s, 1.37 ns). The maxima and minima of the HbO₂ and Hb time resolved concentration difference maps are about ten times greater than the corresponding maxima and minima of the non time resolved concentration differences.

Fig. 10. Finger tapping period: Time-resolved HbO₂- (a) and Hb- (b) concentration difference maps. The finger tapping period started at the time 0 and ended at 31 s (vertical dashed lines).

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4 Conclusion

We implemented an experimental NIRS method, based on time-resolved absorption and concentration difference maps, from which depth-related information can be retrieved with a single measurement at a given position and without any reconstruction process. We first showed with the simple analytical model of an inclusion embedded in a homogeneous semi-infinite medium that these maps can discriminate between absorption variations occurring at superficial or at deeper levels. These results have been confirmed with resin phantoms experiments. Applied to functional brain studies, we have shown that time resolved absorption difference maxima are about two times greater than CW difference maxima. An integration of time resolved absorption differences over a specified microscopic time (for example 1.5 to 2 ns) will improve the signal to noise ratio if necessary. So the experimental method we proposed not only testifies that absorption variations originate from brain tissues, but also amplifies the differences between rest and activation period, improving the ability of NIRS methods for brain function studies.

Signals recorded at late temporal steps still contain a high contribution from superficial tissues. Since early steps contain only information specific to superficial layers, it would be possible to eliminate this background, superficial, contribution from brain activation signal. Such a procedure has already been described, using multi-layers models of the head. It has been demonstrated that time resolved data allows two-dimensional mapping of absorption changes with depth localization [12, 14], with a quite simple reconstruction scheme. This could be considered as an intermediate step between our method, which does not require any reconstruction, and a more precise optical 3D brain mapping which should take into account the more complex geometry of the various layers separating white matter from the head surface and will require the use of a multi-channel time-resolved system [27, 28]. The multi-channel system assembled in our laboratory, having 8 sources and 8 detectors, will give us the possibility to go further in this direction.

Acknowledgments

This work was supported by the Hopitaux Universitaires de Strasbourg, the French Ministere de la Recherche and the Region Alsace. The authors wish to thank Ms M. Torregrossa for simulation algorithms and Ms N. Heider for thoroughly reading the manuscript.

References and links

1. B. Chance, Z. Zhuang, C. Unah, C. Alter, and L. Lipton, “Cognition-activated low-frequency modulation of light absorption in human brain,” Proc. Natl. Acad. Sci. USA 90, 3770–3774 (1993). [CrossRef] [PubMed]

2. A. Villringer and B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends in Neurosciences 20, 435–442 (1997). [CrossRef] [PubMed]

3. D. T. Delpy, M. Cope, P. Van der Zee, S. Arridge, S. Wray, and J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988). [CrossRef] [PubMed]

4. J. P. Culver, A. M. Siegel, J. J. Stott, and D. A. Boas, “Volumetric diffuse optical tomography of brain activity,” Opt. Lett. 28, 2061–2063 (2003). [CrossRef] [PubMed]

5. A.Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, and A. H. Hielscher, “Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia,” J. Biomed. Opt. 9, 1046–1062 (2004). [CrossRef] [PubMed]

6. J. C. Hebden, A. Gibson, T. Austin, R. Yusof, N. Everdell, D. T. Delpy, S. R. Arridge, J. H. Meek, and J. S. Wyatt, “Imaging changes in blood volume and oxygenation in the newborn infant brain using threedimensional optical tomography,” Phys. Med. Biol. 49, 1117–1130 (2004). [CrossRef] [PubMed]

7. B. W. Pogue, T. O. McBride, O. L. Osterberg, and K. D. Paulsen, “Comparison of imaging geometries for diffuse optical tomography of tissue,” Opt. Express 4, 270–286 (1999). [CrossRef] [PubMed]

8. C. H. Schmitz, H. L. Graber, Y. L. Pei, M. Farber, M. Stewart, R. D. Levina, M. B. Levin, Y. Xu, and R. L. Barbour, “Dynamic studies of small animals with a four-color diffuse optical tomography imager,” Rev. Sci. Instrum. 76, 094302 (2005). [CrossRef]

9. H. Koizumi, T. Yamamoto, A. Maki, Y. Yamashita, H. Sato, H. Kawaguchi, and N. Ichikawa, “Optical topography: practical problems and new applications,” Appl. Opt. 42, 3054–3062 (2003). [CrossRef] [PubMed]

10. Y. Hoshi, “Functional near-infrared optical imaging: Utility and limitations in human brain mapping,” Psychophysiology 40, 511–520 (2003). [CrossRef] [PubMed]

11. S. Del Bianco, F. Martelli, and G. Zaccanti, “Penetration depth of light re-emitted by a diffusive medium: theoretical and experimental investigation,” Phys. Med. Biol. 47, 4131–4144 (2002). [CrossRef] [PubMed]

12. J. Selb, J. J. Stott, M. A. Franceschini, A. G. Sorensen, and D. A. Boas, “Improved sensitivity to cerebral hemodynamics during brain activation with a time-gated optical system: analytical model and experimental validation,” J. Biomed. Opt. 10, 011013 (2005). [CrossRef]

13. B. Montcel, R. Chabrier, and P. Poulet, “Detection of cortical activation with time-resolved diffuse optical methods,” Appl. Opt. 44, 1942–1947 (2005). [CrossRef] [PubMed]

14. J. Steinbrink, H. Wabnitz, H. Obrig, A. Villringer, and H. Rinneberg, “Determining changes in NIR absorption using a layered model of the human head,” Phys. Med. Biol. 46, 879–896 (2001). [CrossRef] [PubMed]

15. A. Liebert, H. Wabnitz, J. Steinbrink, H. Obrig, M. Möller, R. Macdonald, A. Villringer, and H. Rinneberg, “Time-resolved multidistance near-infrared spectroscopy of the adult head: intracerebral and extracerebral absorption changes from moments of distribution of times of flight of photons,” Appl. Opt. 43, 3037–3047 (2004). [CrossRef] [PubMed]

16. Y. Nomura, O. Hazeki, and M. Tamura, “Exponential attenuation of light along nonlinear path through the biological model,” Adv. Exp. Med. Biol. 248, 77–80 (1989). [CrossRef] [PubMed]

17. M. Oda, Y. Yamashita, G. Nishimura, and M. Tamura, “A simple and novel algorithm for time resolved multiwavelength oximetry,” Phys. Med. Biol. 41, 551–562 (1996). [CrossRef] [PubMed]

18. Y. Tsuchiya, “Photon path distribution and optical responses of turbid media: theoretical analysis based on the microscopic Beer-Lambert law,” Phys. Med. Biol. 46, 2067–2084 (2001). [CrossRef] [PubMed]

19. Y. Nomura, O. Hazeki, and M. Tamura, “Relationship between time-resolved and non-time-resolved Beer-Lambert law in turbid media,” Phys. Med. Biol. 42, 1009–1022 (1997). [CrossRef] [PubMed]

20. F. P. Bolin, L. E. Preuss, C. Taylor, and R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28, 2297–2303 (1989). [CrossRef] [PubMed]

21. M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989). [CrossRef] [PubMed]

22. S. R. Arridge, “Photon-measurement density functions Part I: Analytical forms,” Appl. Opt. 34, 7395–7409 (1995). [CrossRef] [PubMed]

23. Y. Fukui, Y. Ajichi, and E. Okada “Monte Carlo prediction of near-infrared light propagation in realistic adult and neonatal head models,” Appl. Opt. 42, 2881–2887 (2003). [CrossRef] [PubMed]

24. P. Poulet, C. V. Zint, M. Torregrossa, W. Uhring, and B. Cunin, “Comparison of two time-resolved detectors for diffuse optical tomography: photomultiplier tube-time-correlated single photon counting and multichannel streak camera,” in Optical Tomography and Spectroscopy of Tissue VB. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, and E. M. Sevick-Muraca, eds., Proc. SPIE4955, 154–163 (2003). [CrossRef]

25. L. A. Henderson, P. M. Macey, K. E. Macey, R. C. Frysinger, M. A. Woo, R. K. Harper, J. R. Alger, F. L. Yan-Go, and R. M. Harper, “Brain responses associated with the Valsalva maneuver revealed by functional magnetic resonance imaging,” J Neurophysiol. 88, 3477–3486 (2002). [CrossRef] [PubMed]

26. J. Mobley and T. Vo-Dinh, “Optical properties of tissue,” in Biomedical Photonics Handbook, T. Vo-Dinh ed. (CRC Press, Boca Raton, Fla., 2003).

27. A. P. Gibson, T. Austin, N. L. Everdell, M. Schweiger, S. R. Arridge, J. H. Meek, J. S. Wyatt, D. T. Delpy, and J. C. Hebden, “Three-dimensional whole-head optical tomography of passive motor evoked responses in the neonate,” Neuroimage 30, 521–528 (2006). [CrossRef]

28. D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, F. Paglia, and R. Cubeddu, “Multi-channel time-resolved system for functional near infrared spectroscopy,” Opt. Express 14, 5418–5432 (2006). [CrossRef] [PubMed]

Tissue type	μ′_s (cm^-1)	μ _a (cm^-1)	Thickness (mm)
Scalp	21	0.21	4
Skull	18	0.15	11
Gray matter	24	0.46	7
White matter	100	0.14	13

Time-resolved absorption and hemoglobin concentration difference maps: a method to retrieve depth-related information on cerebral hemodynamics.

Abstract

1 Introduction