1.

Introduction

Diffuse optical imaging is a brain imaging technique used to study the temporal and spatial neuronal activity in the brain.¹ Near infrared spectroscopy takes advantages of light absorption in the tissue of interest, which is dominated by water, oxy- and deoxyhemoglobin in the near infrared, and can be linearly linked to changes in chromophore concentrations. In continuous-wave near infrared spectroscopy (CW-NIRS), continuous monochromatic light emitted by sources located at the surface of the scalp, is both scattered and absorbed by cortical tissues and superficial tissue layers so that changes in measured intensities can provide information about cerebral hemodynamics from surface measurements. However, due to its inability to separate absorption and scattering and to provide absolute measures of optical parameters, CW-NIRS is unable to generate quantitative values of hemoglobin concentrations.² Thus assumptions are required about tissue properties.

As with other hemodynamic techniques, neuronal activation is indirectly monitored through the neurovascular coupling.³ Following neuronal activity, possibly due to local information processing, a local hemodynamic response occurs enhancing the supply in oxyhemoglobin and glucose and the removal of carbon dioxide. The hypothesis of linearity between neural and hemodynamic changes, associated with accurate measures of the latter can be used to generate activation maps, akin to the ones developed in functional magnetic resonance imaging (fMRI).⁴ Recent work toward robust statistical parametric mapping for near infrared spectroscopy (NIRS) provided a framework to compare groups and populations based on measured responses.⁵ Further advances using multimodality to provide anatomical a priori information extended early topographical studies to three-dimensional (3-D) tomographic reconstruction of activity in both space and time.^6,7

These progresses in data analysis, the instruments, portability, flexibility, and minimal invasiveness led to increased interest in finding clinical scenarios where CW-NIRS could be applied. The elderly population presents easy access to the brain as they have pale or even no hair and benefit from the noninvasiveness of the technique. For example, in the context of cognition and aging neuroscience studies, CW-NIRS has been used to investigate focalisation and lateralization of brain activity.^8–11

However, with aging, changes in the measured hemodynamic response and associated activation maps are related to changes in neuronal processing but also to modifications of physiology with age. There is evidence that cerebral blood flow and cerebral oxygenation decrease^12,13 and that the capability to respond to strong demands in oxygen declines with age.¹⁴ Leveque et al. proposed the idea that capillary circulation significantly decreases in the skin around 60 years causing the strong changes in light propagation properties in skin observed at the same age.¹⁵ Other changes associated with the process of normal aging are associated with anatomy: Bones become more porous,¹⁶ whereas elasticity properties of the skin decline. Both have decreasing thicknesses even if there is no consensus about the onset age from which this phenomena affects the skin. Some authors claim the onset age to be around 45 years.¹⁵

The above changes in the properties of tissues and how they interact with light may affect CW-NIRS observations. Whereas long term/lifetime evolution of light absorption is of interest since it contains information about hemodynamics, changes in the diffusion properties can bias measurements and ensuing statistical analyses comparing young and old populations. The simplest formulation to characterize these changes is the modified Beer Lambert law, Eq. (1), where $d$ is the distance separating the source and the detector, $I/I_0$ describe the intensity changes with respect to baseline, $\mathrm{\Delta }{\mu }_a(\lambda )$ the associated change in absorption (at illumination wavelength $\lambda$), and $D(\lambda )$ the differential pathlength factor, i.e., the term correcting the pathlength value so that the Beer-Lambert law can be applied to turbid media such as biological tissues:

A power law between the DPF and the age of the subjects ranging from 1 day old to 50 years old has been empirically established previously by Duncan et al.¹⁸ using intensity modulated optical spectrophotometer measurements in 283 subjects. In that work, the setup consisted of a single source and detector pair placed on the left side of the forehead just below the hairline (for adults). Even if Duncan et al. specified that DPF estimations showed important variation among subjects belonging to the same age bin, the high repeatability of the measures on the forearm – $0.8\%$ – has won unanimity among the NIRS community. However, by current standards, the oldest subjects acquired in this study remain young. Changes in anatomy and physiology described above with aging are expected to appear later in life and measured data evaluating the DPF in older subjects is lacking. Assessing the validity of the power law beyond 50 years is required in view of the increasing number of NIRS aging studies.

A separate question is to identify the main causes for the observed changes in the DPF. Several studies have demonstrated the prominence of the cerebrospinal fluid (CSF) layer in modulating the value of the DPF. With Monte Carlo simulations and experiments on phantoms, Okada et al.¹⁹ have shown a large influence of CSF on the DPF estimations in both simulations and in measures. The specific impact of the value of the reduced scattering coefficient, ${{\mu }_s}^{\prime }$, in that layer has also been studied. As long as the inverse of the coefficient was larger than the average thickness of the CSF layer, its value did not have a large influence on the results as was demonstrated with Monte Carlo simulations.²⁰ However, the CSF thickness is variable around the head. As a result the position of sources and detectors is of prime importance as are source-detector distances.^19,20 Observations show that the DPF increases until source-detector distances reach about 2.5 cm where they reach a plateau. In contradistinction, sulci geometry and gray and white matter boundaries are not expected to have much influence on the DPF.¹⁹ Thus measuring the DPF at a number of source-detector distances may be required for accuracy.

With aging, two main factors are expected to modulate the DPF. First, the morphology changes, e.g., brain shrinkage,^21,22 will impact measures. Second, changes in skin and skull optical properties are also expected to modulate the DPF. The high variability of the DPF among subjects of the same age supports the hypothesis that morphology and optode placement have a key role. Our primary goal in this work was to extend Duncan et al.’s¹⁸ findings and measure the DPF between 60 and 70 years of age, contributing experimental data to support aging NIRS studies. This was performed using two methods: simulations and time-domain measures. Realistic head models using individual anatomical magnetic resonance images (MRIs) and Monte-Carlo simulations were used to evaluate the impact of layer geometry on DPF changes. Separately, measures using time resolved spectroscopy acquisitions (TRS) at multi-distances were performed. Additional simulations to test the influence of layer thickness (other than CSF) and optical coefficients on phantoms were also done. Results confirm a slight increase of the DPF with age, showing that Duncan’s result can be extended to older adults. We also show a larger dependence of these estimations on optical coefficients than on geometry.

2.

Methodology

Forty-three healthy adult right-handed volunteers participated in this study, divided in two age groups: 19 young adults (age $24.4\pm 2.5$, 10 females) and 23 older adults (age $67.6\pm 2.9$, 17 females). In either age group, there was no significant difference between the ages of the males compared to those of the females (2-sampled $t$-test, $P>0.1$). Exclusion criteria included any history of neurological, cardiovascular or respiratory disease, color-blindness, functional analphabetism, smoking, drug or alcohol problem, signs of early dementia as assessed by the Mini-Mental State Examination, and any serious contraindication to MR imaging. This study was approved by the institutional review board of the Unité de Neuroimagerie Fonctionnelle of the Center de Recherche de l’Institut Universitaire de Gériatrie de Montréal (UNF/CRIUGM) and that of École Polytechnique de Montréal. Written consent was obtained from all subjects prior to the study. Subjects underwent two tests on the same day described in the next sections.

2.1.

Time Resolved Spectroscopy

The TRS system consisted of four pulsed lasers operating at 690, 750, 800, and 850 nm and four single-photon counting avalanche detectors (SPADs). Whereas all four lasers were illuminating the same optical fiber, each of the SPADs were connected to a distinct fiber used to collect light. As shown in Fig. 1, the source and the four detection fibers were fastened to a rubber patch placed on the left side of the forehead of each subject. The source was positioned above the Fp1 point of the 10 to 20 system. Source-detector distances were, respectively 10, 15, 25, and 30 mm.

Fig. 1

Diagram of the TRS rubber patch (a) and its positioning on one of the study subjects (b). Source-detector distances specified in millimeters.

The experiment took place in a dark room to reduce the SPADs noise. The subjects were seated on a comfortable chair and were asked to stay calm during the acquisition. Photons were collected for a period of 5 min to generate sufficient statistics. The fitting procedure used a nonlinear optimization routine (MATLAB function lsqcurvefit) with parameters ${\mu }_a$, ${{\mu }_s}^{\prime }$, and an amplitude factor to get the best fit of the theoretical model for a homogeneous medium to the experimental temporal point spread functions (TPSFs). The 16 TPSFs (four distances times four wavelengths) were fit individually with a homogeneous model with the same three parameters: ${\mu }_a$, ${{\mu }_s}^{\prime }$, and the amplitude factor.

To extract optical parameters $({\mu }_a,{\mu }_s^{\prime })$ for each wavelength, each theoretical TPSF function of the medium was convolved with the experimental instrument response function (IRF) before comparison with the experimental TPSF. Finally, hemoglobin concentrations were recovered by inverting Eq. (3) with a least-square fit for the only layer of this homogeneous model. We assumed that tissues contained 70% water.

Eq. (3)

$$\left[\begin{array}{c}{\mu }_a({\lambda }_1)\\ {\mu }_a({\lambda }_2)\\ {\mu }_a({\lambda }_3)\\ {\mu }_a({\lambda }_4)\end{array}\right]=\left[\begin{array}{ccc}{ϵ}_{\mathrm{Hb}{\mathrm{O}}_2}^{{\lambda }_1}& {ϵ}_{\mathrm{HbR}}^{{\lambda }_1}& {ϵ}_{{\mathrm{H}}_2\mathrm{O}}^{{\lambda }_1}\\ {ϵ}_{\mathrm{Hb}{\mathrm{O}}_2}^{{\lambda }_2}& {ϵ}_{\mathrm{HbR}}^{{\lambda }_2}& {ϵ}_{{\mathrm{H}}_2\mathrm{O}}^{{\lambda }_2}\\ {ϵ}_{\mathrm{Hb}{\mathrm{O}}_2}^{{\lambda }_3}& {ϵ}_{\mathrm{HbR}}^{{\lambda }_3}& {ϵ}_{{\mathrm{H}}_2\mathrm{O}}^{{\lambda }_3}\\ {ϵ}_{\mathrm{Hb}{\mathrm{O}}_2}^{{\lambda }_4}& {ϵ}_{\mathrm{HbR}}^{{\lambda }_4}& {ϵ}_{{\mathrm{H}}_2\mathrm{O}}^{{\lambda }_4}\end{array}\right]\left[\begin{array}{c}{C}_{\mathrm{Hb}{\mathrm{O}}_2}\\ C_{\mathrm{HbR}}\\ C_{{\mathrm{H}}_2\mathrm{O}}\end{array}\right].$$

The following formula from²³ was used to compute the DPF from TRS:

Eq. (4)

$$D(\lambda )=\frac{1}{2}{\left(3\frac{{\mu }_s^{\prime }}{{\mu }_a}\right)}^2{[1+\frac{1}{{d(3{\mu }_s^{\prime }{\mu }_a)}^{1/2}}]}^{-1}.$$

3.

Results

3.1.

Effect of Layer Thickness on Monte Carlo Simulations

The five layer phantom is presented in Fig. 2(a), and Monte-Carlo based DPF estimations were done for both 10 mm and 30 mm source-detector distances. Figure 2(b) shows the effect of CSF thickness when varied between 1 and 4 mm with ${\mu }_s^{\prime }=0.1\mathrm{mm}$. Figure 2(c) and 2(d) shows, respectively the impact of the most superficial layers (scalp and skull) on the DPF as their thicknesses varied from 3 to 6 mm.

Fig. 2

(a) Reference phantom used for simulations, (b) effect of changes in CSF thickness (1 to 4 mm) on the DPF and (c), (d) effects of skull and scalp thicknesses, respectively (3 to 6 mm) on the DPF. In (b–d), the top panels show results for the 10 mm source-detector distance, the bottom panel for the 30 mm pair. DPFs were computed for 690 nm (crosses) and 830 nm (squares).

Results showed an increase in the estimated DPF of the 30 mm distance channel with the thickening of scalp or skull but no significant effect with changes in CSF thickness (mean DPF $6.14\pm 0.02$ for 690 nm and $5.24\pm 0.03$ for 830 nm over the thickness range 1 to 5 mm). With a source detector separation of 10 mm, the DPF was observed to be less sensitive to layer thickness. For this distance, the averaged largest difference in the DPF had a mean of $0.045\pm 0.003$ for 690 nm and $0.032\pm 0.014$ for 830 nm. These results show that with respect to changes in thickness, the longer distance pairs were more sensitive, while the short distance pairs saw small changes as the DPF values were dominated by the first layer.

3.2.

Effect of Source or Detector Positions on Monte Carlo Simulations

To assess the impact of optode positioning errors on simulations in realistic geometries, we computed DPF on all subjects by introducing an offset of 1 cm to translate the probe toward the right or the top of the head. Group results are shown in Fig. 3 for 690 nm and in Fig. 4 for 830 nm. No significant change was found between the different positions at 690 nm or 830 nm despite mean DPF variations reaching 14%.

Fig. 3

DPF at 690 nm for groups of young (left side of each subfigure) and old adult (right side of each subfigure) groups with Fp1 positioning (Fp1), offset to the right (R) or to the top (T) for each source-detector pairs S-D1(a), S-D2(b), S-D3(c), S-D4(d). Boxes extend to the first and third quartiles, central horizontal lines are the medians, whereas the eyes represent means. Outliers are represented as crosses.

Fig. 4

DPF at 830 nm for groups of young (left side of each subfigure) and old adults (right side of each subfigure) groups with Fp1 positioning (Fp1), offset to the right (R) or to the top (T) for each source-detector pairs S-D1(a), S-D2(b), S-D3(c), S-D4(d). Boxes extend to the first and third quartiles, central horizontal lines are the medians, whereas the eyes represent means. Outliers are represented as crosses.

3.3.

Estimation of Layer Thickness with Respect to Age

Layer thickness estimations from Monte-Carlo following the procedure described in Sec. 2.3.2 were performed in the layered phantom and confirmed the reliability of this method with a simple geometry. The same procedure was thus used with T1 segmented images. Computed layer thicknesses were then averaged over all subjects and fiber positions. Figure 5(a) displays the averaged layer thicknesses of the first three layers (CSF, skull, and scalp) over all fibers positions in young and old adults. The largest range was found for the CSF layer in older adults due to increased inaccuracies in CSF segmentation. Two sample $t$-tests indicated no significant difference between young and old groups. However, the comparison of the average values indicated that on average, the brain was situated deeper from the surface of the head in the elderly population.

Fig. 5

(a) Computed thicknesses of CSF, Skull and Scalp below the source and four detectors on the TRS patch for young (y) and old adults (o). (b) These three thicknesses have been summed to obtain the depth of the brain inside the head for young (y) and old adults (o). Boxes extend to the first and third quartiles, central horizontal lines are the medians whereas the eyes represent means.

3.4.

DPF Change with Age

DPF estimates were computed both from measured data and from Monte-Carlo simulations based on individual MRI images. The rationale for this was to evaluate whether Monte-Carlo based estimations scaled with measurements which would form a basis for ongoing work in image reconstruction. A typical Monte-Carlo simulation is shown in Fig. 6.

Fig. 6

Monte-Carlo simulation in individual anatomy. Sensitivity matrix is displayed on the right whereas the corresponding segmented anatomical image is on the left.

A similar simulation was done for all subjects and source/detector positions resulting in a total of $N=4\times 42=168$ simulations per wavelength. Optical parameters used for these simulations are provided in Table 1. Figures 7 (690 nm) and 8 (830 nm) show the estimated values of DPF for all source-detector distances (S-D3) for both the TRS measurements and the estimations performed with Monte-Carlo simulations. The variability observed in Monte-Carlo simulations is not due to simulation statistics, but rather, to realistic differences between subjects’ anatomies. In measured data, variability originates from anatomy, optical property, and measurement errors (estimated at 5% in test-retest experiments on phantoms). In the case of the largest source-detector distance [Figs. 7(d) and 8(d)], results found by the heuristic formula developed by Duncan et al.¹⁸ is also overlaid on the data. Since the latter formula was found with a range ending at 50 years, we extrapolated above this age for the older subjects.

Fig. 7

DPF at 690 nm measured with TRS (TRS), Monte Carlo simulations (MC) for each source-detector pairs S-D1(a), S-D2(b), S-D3(c), S-D4(d) for young (left side of each subfigure) and old adults (right side of each subfigure). Values proposed by Duncan et al.¹⁸ with a source-detector distance of 4.5 cm (d) are also displayed with the TRS largest source-detector pair (d). The boxes extend to the first and third quartiles, central horizontal lines are the medians whereas the eyes represent means.

Fig. 8

DPF at 830 nm measured with TRS (TRS), Monte Carlo simulations (MC) for each source-detector pairs S-D1(a), S-D2(b), S-D3(c), S-D4(d) for young (left side of each subfigure) and old adults (right side of each subfigure) groups. Values proposed by Duncan et al.¹⁸ with a source-detector distance of 4.5 cm (d) are also displayed with the TRS largest source-detector pair (d). The boxes extend to the first and third quartiles, central horizontal lines are the medians whereas the eyes represent means.

DPF evaluated with simulations were lower for both wavelengths and age when compared to TRS measurements or Duncan’s values. A two sample $t$-test showed that the difference between Monte-Carlo and TRS measurements was significant ($P<0.05$) except for the young subjects measured at 690 nm on the two largest source-detector distances. This underestimation remained even when correcting literature values for measured baseline values of ${\mu }_a$ and ${{\mu }_s}^{\prime }$ (a scaling of all optical parameters for each layer was done in proportion with the individual measured homogeneous data values). The offset was smaller with 690 nm than with 830 nm. Averaging over all young and old adults showed that simulated DPF estimates increased slightly. TRS measures showed a larger increase with age but not in the range proposed by Duncan et al.¹⁸ signalling a potential plateau effect in older adults. Two sample $t$-tests were carried out on young versus old’ adults DPF. Results showed no significant difference confirming the variability previously observed in Duncan et al. but $p$ values were seen to decrease with increasing source detector separation.

Finally, to validate the hypothesis that the individual anatomy was the main driver of the observed variability in the DPF, we computed in each case the value of the DPF as a function of the thickness of the first two layers (skin and skull) which were shown in simulations to affect the DPF. Table 2 shows the sum of standard errors (SSE) resulting from a linear regression between the thickness of the first two layers and the DPF. Results showed that more than 90% of the variability could not be explained by thickness changes suggesting that optical parameter changes were more likely to drive DPF values. Using individual parameters in Monte-Carlo simulations confirmed this observation by increasing the residual variability while the simulation using literature optical properties²⁶ (which only accounts for anatomy changes) showed very high correlation between DPF and the first two layers thickness. While using individual optical parameters increased the variability, providing some indication that it is a cause of DPF changes, an ANOVA analysis did not confirm that the increased variance was better explained by the model with measured values of optical parameters. This may be due to the proportional redistribution of individual measured optical parameters $({\mu }_a,{\mu }_s^{\prime })$ to all layers in the absence of a clear procedure to set tissue optical properties from measurements.

Table 2

Sum of squares due to error of linear regression of the DPF with respect to thickness of both skin and skull for 30 mm pair.

	690 nm	830 nm
TRS	15.56	12.62
Monte-Carlo: measured optical properties	3.92	2.79
Monte-Carlo: literature optical properties26	1.04	0.78

4.

Discussion

This work measured DPFs in young and older adults using time-domain optical imaging and provided for the first time values of the DPF for a population over 51 years of age. Despite documented evidence on anatomical changes of the brain and modifications in physiology and tissue optical properties, our data did not show significant deviations from the empirical law derived by Duncan et al.¹⁸ We observed a lower increase in the DPF than what was expected from the empirical law but high variability in our data did not allow to disprove it. This work thus confirms that extrapolating the empirical law in older populations is possible and can be expected to yield correct results.

Simulations showed that the main geometrical determinants of the DPF were mainly the first two layers of tissue: skin and skull. Clear changes were observed in Monte-Carlo estimations of the DPF with the thickness of those layers in long source-detector pairs. In short source detector pairs, very small variations were observed. In experimental measures, short pairs did indeed show a small change with age suggesting a low dependence on layers thickness. However, in all pairs, experimental measures displayed a large intra-group variability (young versus old) which could not be explained by changes in anatomy. Indeed, when performing Monte-Carlo simulations with literature values of optical properties, the variability of the DPF across our anatomical scans was much lower than measured with TRS suggesting that anatomy alone is not sufficient to explain the large variability in the data. Potential errors could originate from inaccurate segmentations but this would be expected to increase, not decrease variability. We performed separate simulations to test whether using scaled individual optical parameters would explain the variance observed in the data. It was observed that part of the increased variance was explained by the optical parameters, however, a clear procedure to choose how to scale each optical parameter in each layer would be required to generate precise results. The results however still suggests that changes in optical properties were the main determinant of the variability observed in values of the DPF. As a result, vascularization, pigmentation, and other factors are potentially larger causes of DPF changes than the anatomy.

The high variability of the DPF and the fact that it is left unexplained by an accurate depiction of the anatomy raises questions about the accuracy of tomography techniques. Our Monte-Carlo simulations which are expected to be accurate did not explain the changes observed in the data and also systematically provided much lower values of DPF. A statistical test confirmed that result ($P<0.05$) except for young subjects measured at 690 nm on the two largest source-detector distances. Using Monte-Carlo based reconstructions and literature values of optical properties, even with a correct anatomy, it was shown here to lead to systematic bias in the estimation of a simple measure, the DPF. The systematically lower values may result from literature values being biased with respect to real tissue values. How this bias will translate in studies of brain activation remains to be evaluated. Combining MRI and optical imaging simultaneously may yield some answers to these systematic biases.

A limitation of this study is the fact that optical parameters were computed using a homogeneous model when estimated from TRS data. We previously used a two layer model to estimate parameters from the combined skin-skull-CSF first layer and a second brain layer.²⁷ Since our simulations showed that the first two layers (skin and skull) were the most important and that the two layer model would be unable to distinguish optical properties for these layers, we found the more stable homogeneous fits to be a better choice. It also allowed a direct comparison with the work of Duncan et al.¹⁸

5.

Conclusion

In this work we extended the range of a previously measured empirical law for the diffusion pathlength factor and studied the main determinants of the variability of DPF in a population of young and old subjects. The results underline the difficulty in explaining measured data in the absence of measures for each tissue layer’s optical properties, even with accurate light propagation models. It suggests a cautious approach to image reconstruction techniques associated with NIRS brain imaging.