Time-Resolved NIRS

An alternative approach to handling the challenges associated with scalp signal contamination is to improve the depth sensitivity of the NIRS measurements. This reduces the impact of scalp signal fluctuations, thereby improving both the sensitivity and quality of fNIRS in terms of detecting activation-related cerebral hemodynamic changes. One approach for improving depth sensitivity is by time-resolved (TR) detection. Although TR-NIRS was initially proposed as a method for measuring the optical properties of tissue, it can also enhance depth sensitivity. The basic principle of TR-NIRS involves injecting extremely short pulses of light – no more than a few hundred picoseconds in width – into tissue and recording the arrival times of each detected photon. Since the arrival time of a photon reflects the distance it has travelled, late- arriving photons have a higher probability of reaching the brain compared to early- arriving photons that primarily interrogate superficial tissue.

TR-NIRS involves recording the arrival times of millions of photons in order to build up a DTOF. An example of a DTOF obtained on the surface of the head for a source- detector distance of 3 cm is shown in Figure 1.4. The right skewness of the DTOF is typical for scattering media such as tissue, and it reflects the basic principle that there are far more early photons detected than late photons. The most direct approach of exploiting the temporal information of a DTOF to enhance depth sensitivity is by time binning (Contini et al., 2006). Time-binning involves measuring signal changes in a selected range of arrival times, such as during the tail of the DTOF to focus on late-arriving photons. The width can range from picoseconds to nanoseconds depending on the SNR of the recorded DTOFs.

Figure 1.4: An example of a DTOF of photons. This DTOF was obtained on the surface of the head for a source-detector distance of 3 cm and a pulse repetition rate

of 80 MHz. The DTOF is plotted on a log scale.

Although conceptually straightforward, a practical limitation of time-binning is the temporal dispersion of recorded DTOFs due to the instrumentation itself. That is, the finite width of the light pulses, the effects of fiber optics used to couple reflected light to a detector, and the response time of detectors will all smear the true, or theoretical, DTOF. Consequently, arrival-time information from early and late photons will be mixed, reducing the expected depth benefit of a selected late bin (Diop and St Lawrence, 2013). Removing the effects of the instrumentation requires deconvolving the instrument response function from the measured DTOF to obtain the true DTOF from tissue (Diop and St Lawrence, 2013).

An alternative approach for extracting depth information from a DTOF is by calculating its statistical moments (Liebert et al., 2004). Due to the right skewness of the DTOF, higher moments are weighted towards the tail of the distribution and thus have higher sensitivity to late-arriving photons (Liebert et al., 2004). The equation used to calculate the kth statistical moment is:

𝑚_𝑘 = ∫∞ 𝑡𝑘

−∞ 𝐷𝑇𝑂𝐹(𝑡)𝑑𝑡, (1.9)

Generally, changes in the first three statistical moments are used since higher moments (skewness, kurtosis etc.) tend to have lower SNR. The zero-moment is referred to as the number of photons (N) and is analogous to CW intensity measurements. The first moment is the mean time-of-flight of photons <t>, which is the mean time taken by

photons to travel between a source and a detector and can be used to calculate the mean pathlength of photons. Lastly, the variance is related to the first and second moment and is calculated as V = m2 - (m1)2 (Kacprzak et al., 2007).

Similar to the modified Beer-Lambert law, the change in a statistical moment can be directly related to the change in μa (Δμa) by using the appropriate sensitivity factor (Milej

et al., 2016; Gerega et al., 2018). These factors describe the sensitivity of each moment to a change in absorption at a specific depth in tissue (see Figure 1.5) and are calculated using either the DA or Monte Carlo simulations to model light propagation through the head.

Figure 1.5: Illustration of a layered model of the head with j representing the different layers and d the thickness of each layer. The pink banana illustrates the photon profile between the source (red arrow) and detector (green arrow) placed at

a source-detector distance of ‘r’.

Sensitivity factors are generated by altering μa in a specific layer (typically by 1% from

the initial μa value) and calculating the corresponding change in the moments (Liebert et

al., 2004; Milej et al., 2014a, 2015): 𝑀𝑃𝑃_𝑗 = ∆𝑁 ∆𝜇𝑎,𝑗 , 𝑀𝑇𝑆𝐹𝑗 = ∆<𝑡> ∆𝜇𝑎,𝑗, 𝑉𝑆𝐹𝑗 = ∆𝑉 ∆𝜇𝑎,𝑗 (1.10)

where, Δμa,j is the change in the absorption coefficient in layer j, MPPj is the mean partial

pathlength, MTSFj is the sensitivity factor for <t>, and VSFj is the variance sensitivity

factor. ∆N is the change in the number of photons, ∆<t> is the change in mean-time-of- flight and ∆V is the change in variance. The sensitivity of each moment to the brain is then calculated as the sum of the sensitivity factors for layers below a certain depth.

A drawback with TR-NIRS is that the systems are complex compared to CW system (Torricelli et al., 2014). Time-resolved measurements require pulsed lasers operating at extremely high repetition rates (e.g. 80 MHz) and require specialized laser drivers. In addition, single-photon counting, which is necessary to generate a DTOF, requires fast, very sensitive photodetectors such as photomultiplier tubes (PMTs) coupled to photon counting board. These components not only increase the cost of TR systems, but also the overall size of the instruments, making the units less portable than CW systems. Due to their complexity, TR-NIRS systems typically have limited number of sources and detectors, and in fact there are no commercially available TR-fNIRS units. However, a number of research labs have developed their own systems for investigating the potential advantage of enhanced depth sensitivity for fNIRS applications. These have included studies of motor execution (Kacprzak et al., 2007; Re et al., 2013; Milej et al., 2014b; Lachert et al., 2017) and working memory (Kirilina et al., 2012). Motor execution, such as finger tapping, has been the most investigated functional task with TR-fNIRS studies since it produces robust brain activity in a well-defined cortical region. The study by Kirilina et al. elegantly demonstrated the potential benefit of TR detection by monitoring oxygenation changes from probes placed on the forehead during a working memory task. They showed that the extracerebral contribution to the ∆N signal, which is analogous to CW-NIRS, was twice as large as for the ∆V signal. As a consequence, the oxygenation signal derived from ∆N was heavily contaminated by hemodynamic oscillations in the scalp, while the corresponding ∆V signal exhibited the expected task-related change (Kirilina et al., 2012).