Differential Pathlength Factor Research Articles

Investigating the effect of limited spectral information on NIRS-derived changes in hemoglobin and cytochrome-c-oxidase concentration with a diffusion-based model.

This paper investigates the theoretical capability of near-infrared spectroscopy (NIRS) systems to accurately measure changes in the oxidation state of cerebral cytochrome-c-oxidase (CCO) alongside the hemoglobins, for a deeper understanding of NIRS limitations. Concentration changes of oxy and deoxyhemoglobin (HbO and HbR) indicate the oxygen status of blood vessels and correlate with several other physiological parameters across different pathologies. The oxidation state of CCO indicates cellular energy usage efficiency through oxidative metabolism, potentially serving as a biomarker for brain and other tissue disorders. This study employs an analytical model based on the diffusion equation and statistical analyses to explore the dependency of estimated concentration changes on various systematic parameters, such as choice of wavelengths, spectral bandwidth, and uncertainties in extinction coefficient (ε) and differential pathlength factor (DPF). When there is a 10% uncertainty in DPF and ε, errors were found to be highly dependent on the number of discrete wavelengths, but not on their bandwidth if appropriate considerations are taken to account for it.

Estimation of differential pathlength factor from NIRS measurement in skeletal muscle

The utilization of continuous wave (CW) near-infrared spectroscopy (NIRS) device to measure non-invasively muscle oxygenation in healthy and disease states is limited by the uncertainties related to the differential path length factor (DPF). DPF value is required to quantify oxygenated and deoxygenated heme groups’ concentration changes from measurement of optical densities by NIRS. An integrated approach that combines animal and computational models of oxygen transport and utilization was used to estimate the DPF value in situ. The canine model of muscle oxidative metabolism allowed measurement of both venous oxygen content and tissue oxygenation by CW NIRS under different oxygen delivery conditions. The experimental data obtained from the animal model were integrated in a computational model of O2 transport and utilization and combined with Beer-Lambert law to estimate DPF value in contracting skeletal muscle. A 2.1 value was found for DPF by fitting the mathematical model to the experimental data obtained in contracting muscle (T3) (Med.Sci.Sports.Exerc.48(10):2013–2020,2016). With the estimated value of DPF, model simulations well predicted the optical density measured by NIRS on the same animal model but with different blood flow, arterial oxygen contents and contraction rate (J.Appl.Physiol.108:1169–1176, 2010 and 112:9–19,2013) and demonstrated the robustness of the approach proposed in estimating DPF value. The approach used can overcome the semi-quantitative nature of the NIRS and estimate non-invasively DPF to obtain an accurate concentration change of oxygenated and deoxygenated hemo groups by CW NIRS measurements in contracting skeletal muscle under different oxygen delivery and contraction rate.

Non-invasive estimation of in vivo optical properties and hemodynamic parameters of domestic animals: a preliminary study on horses, dogs, and sheep.

Biosensors applied in veterinary medicine serve as a noninvasive method to determine the health status of animals and, indirectly, their level of welfare. Near infrared spectroscopy (NIRS) has been suggested as a technology with this application. This study presents preliminary in vivo time domain NIRS measurements of optical properties (absorption coefficient, reduced scattering coefficient, and differential pathlength factor) and hemodynamic parameters (concentration of oxygenated hemoglobin, deoxygenated hemoglobin, total hemoglobin, and tissue oxygen saturation) of tissue domestic animals, specifically of skeletal muscle (4 dogs and 6 horses) and head (4 dogs and 19 sheep). The results suggest that TD NIRS in vivo measurements on domestic animals are feasible, and reveal significant variations in the optical and hemodynamic properties among tissue types and species. In horses the different optical and hemodynamic properties of the measured muscles can be attributed to the presence of a thicker adipose layer over the muscle in the Longissimus Dorsi and in the Gluteus Superficialis as compared to the Triceps Brachii. In dogs the absorption coefficient is higher in the head (temporalis musculature) than in skeletal muscles. The smaller absorption coefficient for the head of the sheep as compared to the head of dogs may suggest that in sheep we are indeed reaching the brain cortex while in dog light penetration can be hindered by the strongly absorbing muscle covering the cranium.

Estimation of the Differential Pathlength Factor for Human Skin Using Monte Carlo Simulations.

Near-infrared technology is an emerging non-invasive technique utilized for various medical applications. Recently, there have been many attempts to utilize NIR technology for the continues monitoring of blood glucose levels through the skin. Different approaches and designs have been proposed for non-invasive blood glucose measurements. Light photons penetrating the skin can undergo multiple scattering events, and the actual optical pathlength becomes larger than the source-to-detector separation (optode spacing) in the reflection-mode configuration. Thus, the differential pathlength factor (DPF) must be incorporated into the modified Beer-Lambert law. The accurate estimation of the DPF values will lead to an accurate quantification of the physiological variations within the tissue. In this work, the aim was to systematically estimate the DPF for human skin for a range of source-to-detector separations and wavelengths. The Monte Carlo (MC) method was utilized to mimic the different layers of human skin with different optical properties and blood and water volume fractions. This work could help improve the accuracy of the near-infrared technique in the measurement of physiological variations within skin tissue.

Quantitative Methods of Brain Tissue Differential Pathlength Factor Based on GS-SVM

Quantitative Methods of Brain Tissue Differential Pathlength Factor Based on GS-SVM

Influence of Detector Size and Positioning on Near-Infrared Measurements and Iso-pathlength Point of Turbid Materials

Measuring physical phenomena in an experimental system is commonly limited by the detector. When dealing with spatially defined behaviors, the critical parameter is the detector size. In this work, we examine near-infrared (NIR) measurements of turbid media using different size detectors at different positions. We examine cylindrical and semi-infinite scattering samples and measure their intensity distribution. An apparent crossing point between samples with different scatterings was previously discovered and named the iso-pathlength point (IPL). Monte Carlo simulations show the expected changes due to an increase in detector size or similarly as the detector’s location is distanced from the turbid element. First, the simulations show that the intensity profile changes, as well as the apparent IPL. Next, we show the average optical pathlength, and as a result, the differential pathlength factor, are mostly influenced by the detector size in the range close to the source. Experimental measurements using different size detectors at different locations validate the influence of these parameters on the intensity profiles and apparent IPL point. These findings must be considered when assessing optical parameters based on multiple scattering models. In cases such as NIR assessment of tissue oxygenation, size and location may cause false results for absorption or optical path.

Multi-Channel-Based Differential Pathlength Factor Estimation for Continuous-Wave fNIRS

Functional near-infrared spectroscopy (fNIRS) in brain imaging needs to be robust to subject-wise variability. The use of a fixed differential pathlength factor (DPF) per wavelength for the entire brain will degrade the accuracy of hemodynamic responses. Since the tissue composition varies within the brain, correct DPF values should be used for various emitter-detector distances and brain regions. In this article, a DPF estimation method combining a state-space model of the modified Beer-Lambert law (mBLL), a parameter model for estimating the reduced scattering coefficients, and dual square-root cubature Kalman filters (SCKFs) is proposed. To validate the proposed method, known light intensities (six channels, two wavelengths) and reference DPFs are generated using NIRFAST (a Matlab toolbox) using a presumed paradigm, known tissue properties, a Balloon model, and a finite element head model consisting of 58,818 mesh elements. Then, the DPF values are estimated using a Jacobian matrix from the head model and the mBLL. The results show that the estimated concentration changes correlate well with the reference data. Also, the estimated DPFs showed relative errors less than 1.33% maximum and 0.75% on average. A one-tailed $t$ -test revealed that the estimated DPFs matched the reference DPFs with more than 99.9% confidence. The developed method can efficiently access the actual DPFs even if emitter-detector distances vary significantly and the tissue properties are not uniform. With the developed state-space models for dual SCKFs, real-time estimation of the DPFs from one experiment to another has become plausible.

Effect of adipose tissue thickness and tissue optical properties on the differential pathlength factor estimation for NIRS studies on human skeletal muscle.

We propose a quantitative and systematic investigation of the differential pathlength factor (DPF) behavior for skeletal muscles and its dependence on different factors, such as the subcutaneous adipose tissue thickness (ATT), the variations of the tissue absorption (µa ) and reduced scattering (µ's ) coefficients, and the source-detector distance. A time domain (TD) NIRS simulation study is performed in a two-layer geometry mimicking a human skeletal muscle with an overlying adipose tissue layer. The DPF decreases when µa increases, while it increases when µ's increases. Moreover, a positive correlation between DPF and ATT is found. These results are supported by an in-vivo TD NIRS study on vastus lateralis and biceps brachii muscles of eleven subjects at rest, showing a high inter-subject and inter-muscle variability.

Performance Improvement for Detecting Brain Function Using fNIRS: A Multi-Distance Probe Configuration With PPL Method.

To improve the spatial resolution of imaging and get more effective brain function information, a multi-distance probe configuration with three distances (28.2, 40, and 44.7 mm) and 52 channels is designed. At the same time, a data conversion method of modified Beer–Lambert law (MBLL) with partial pathlength (PPL) is proposed. In the experiment, three kinds of tasks, grip of left hand, grip of right hand, and rest, are performed with eight healthy subjects. First, with a typical single-distance probe configuration (30 mm, 24 channels), the feasibility of the proposed MBLL with PPL is preliminarily validated. Further, the characteristic of the proposed method is evaluated with the multi-distance probe configuration. Compared with MBLL with differential pathlength factor (DPF), the proposed MBLL with PPL is able to acquire more obvious concentration change and can achieve higher classification accuracy of the three tasks. Then, with the proposed method, the performance of the multi-distance probe configuration is discussed. Results show that, compared with a single distance, the combination of the three distances has better spatial resolution and could explore more accurate brain activation information. Besides, the classification accuracy of the three tasks obtained with the combination of three distances is higher than that of any combination of two distances. Also, with the combination of the three distances, the two-class classification between different tasks is carried out. Both theory and experimental results demonstrate that, using multi-distance probe configuration and the MBLL with PPL method, the performance of brain function detected by NIRS can be improved.

Effects of Processing Methods on fNIRS Signals Assessed During Active Walking Tasks in Older Adults.

Functional near infrared spectroscopy (fNIRS) is a noninvasive optics-based neuroimaging modality successfully applied to real-life settings. The technology uses light in the near infrared range (650-950nm) to track changes in oxygenated (HbO2) and deoxygenated hemoglobin (Hb) obtained from measured light intensity using light-tissue interaction principles. fNIRS data processing involves artifact removal and hemodynamic signal conversion using modified Beer-Lambert law (MBLL) to obtain Hb and HbO2, reliably. fNIRS signals can get contaminated by various noise sources of physiological and non-physiological origins. Various algorithms have been proposed for the elimination of artifacts from frequency selective filters to blind source separation methods. Hemodynamic signal extraction using raw intensity measurements at multiple wavelengths based on MBLL usually involves apriori knowledge of certain conversion parameters such as molar extinction coefficients ( ε ) and differential path length factor (DPF). Different sets of conversion parameters dependent upon wavelength, chromophores, and age have been reported. Variation in processing algorithms and parameters can cause differences in Hb and HbO2 extraction which can in turn change study outcomes. Using fNIRS, we have previously shown significant increases in oxygenation in the prefrontal cortex from Single-Task-Walking (STW) to Dual-task-Walking (DTW) conditions in older adults due to greater cognitive demands inherent in the latter condition. In the current study, we re-analyzed our data and determined that although using different conversion parameters i.e. ε and age dependent DPF and filter cut-off frequencies at 0.14 and 0.08Hz including those designed to remove confounding effects of Mayer waves had caused some linear increases or decreases on the extracted Hb and HbO2 signals, those effects were minimal in task related comparisons and hence, the overall study outcomes.

Differential pathlength factor in continuous wave functional near-infrared spectroscopy: reducing hemoglobin's cross talk in high-density recordings.

Functional near-infrared spectroscopy (fNIRS) estimates the functional oscillations of oxyhemoglobin and deoxyhemoglobin in the cortex through scalp-located multiwavelength recordings. Hemoglobin oscillations are inferred through temporal changes in continuous-wave (CW) light attenuation. However, because of the diffusive multilayered head tissue structures, the photon path is longer than the source-detector separation, complicating hemoglobin evaluation. This aspect is incorporated in the modified Beer-Lambert law where the source-detector distance is multiplied by the differential pathlength factor (DPF). Since DPF estimation requires photons' time-of-flight information, DPF is assumed a priori in CW-fNIRS. Importantly, errors in the DPF spectrum induce hemoglobin cross talk, which is detrimental for fNIRS. We propose to estimate subject-specific DPF spectral dependence relying on multidistance high-density measurements. The procedure estimates the effective attenuation coefficient (EAC), which is proportional to the geometric mean of absorption and reduced scattering. Since DPF depends on the scattering-to-absorption ratio, EAC limits the spectral dependence assumption to scattering. This approach was compared to a standard frequency-domain multidistance procedure. A good association between the two methods ( ) was obtained. This approach could estimate low-resolution maps of the DPF spectral dependence through large field of view, high-density systems, reducing hemoglobin cross talk, and increasing fNIRS sensitivity and specificity to brain activity without instrumentation modification.

Estimating the Dependence of Differential Pathlength Factor on Blood Volume and Oxygen Saturation using Monte Carlo method.

Differential Pathlength Factor (DPF) is a vital parameter for the Beer-Lambert law based calculations in estimating tissue perfusion using non-invasive optical techniques. A significant error in the measured concentration of oxyhemoglobin and deoxyhemoglobin has been reported due to the usage of wrong DPF values. The dependence of DPF on blood oxygen saturation and blood volume has never been studied earlier. In this work, a Monte Carlo model of perfused skin tissue was developed and executed at 660 nm and 940 nm optical wavelengths at a reflectance geometry. DPFs were simulated through 1-10 mm source detector separations at different blood volumes and oxygen saturations. Results showed higher DPFs at lower wavelengths and considerable variation with blood volume and oxygen saturation.

Measurement of the Absolute Value of Cerebral Blood Volume and Optical Properties in Term Neonates Immediately after Birth Using Near-Infrared Time-Resolved Spectroscopy: A Preliminary Observation Study

The aim of this study was to use near-infrared time-resolved spectroscopy (TRS) to determine the absolute values of cerebral blood volume (CBV) and cerebral hemoglobin oxygen saturation (ScO2) during the immediate transition period in term neonates and the changes in optical properties such as the differential pathlength factor (DPF) and reduced scattering coefficient (μs’). CBV and ScO2 were measured using TRS during the first 15 min after birth by vaginal delivery in term neonates who did not need resuscitation. Within 2–3 min after birth, CBV showed various changes such as increases or decreases, followed by a gradual decrease until 15 min and then stability (mean (SD) mL/100 g brain: 2 min, 3.09 (0.74); 3 min, 3.01 (0.77); 5 min, 2.69 (0.77); 10 min, 2.40 (0.61), 15 min, 2.08 (0.47)). ScO2 showed a gradual increase, then kept increasing or became a stable reading. The DPF and μs’ values (mean (SD) at 762, 800, and 836 nm) were stable during the first 15 min after birth (DPF: 4.47 (0.38), 4.41 (0.32), and 4.06 (0.28)/cm; μs’: 6.54 (0.67), 5.82 (0.84), and 5.43 (0.95)/cm). Accordingly, we proved that TRS can stably measure cerebral hemodynamics, despite the dramatic physiological changes occurring at this time in the labor room.

Xây dựng ảnh não ba chiều sử dụng phương pháp quang cận hồng ngoại

Functional near-infrared spectroscopy (fNIRS) is a non-invasive technique utilized to measure hemoglobin concentration of human brain signal. Temporal resolution of this method is high (aproximately 1 ms). However, its spatial resolution is limited (approximately 10 mm) compared with other non-invasive techniques. Therefore, in the present study, fNIRS based 32-optodes are utilized to measure human brain hemodynamic response of 5 male participants with arithmetic tasks. Coordinates of 256 voxels are computed based on the optode geometry. Coefficient of differential path-length factor in Beer-Lambert equation is estimated as a distance function to compute absorption coefficients. The mean concentration of Oxy- and deOxy-hemoglobin obtained from absorption coefficients is utilized to reconstruct 3-dimension brain imaging. The experimental results showed that the proposed method can detect the brain activity with higher spatial resolution than that using conventional approach.

Initial-Dip Existence and Estimation in Relation to DPF and Data Drift.

Early de-oxygenation (initial dip) is an indicator of the primal cortical activity source in functional neuro-imaging. In this study, initial dip's existence and its estimation in relation to the differential pathlength factor (DPF) and data drift were investigated in detail. An efficient algorithm for estimation of drift in fNIRS data is proposed. The results favor the shifting of the fNIRS signal to a transformed coordinate system to infer correct information. Additionally, in this study, the effect of the DPF on initial dip was comprehensively analyzed. Four different cases of initial dip existence were treated, and the resultant characteristics of the hemodynamic response function (HRF) for DPF variation corresponding to particular near-infrared (NIR) wavelengths were summarized. A unique neuro-activation model and its iterative optimization solution that can estimate drift in fNIRS data and determine the best possible fit of HRF with free parameters were developed and herein proposed. The results were verified on simulated data sets. The algorithm is applied to free available datasets in addition to six healthy subjects those were experimented using fNIRS and observations and analysis regarding shape of HRF were summarized as well. A comparison with standard GLM is also discussed and effects of activity strength parameters have also been analyzed.

Investigating optical path and differential pathlength factor in reflectance photoplethysmography for the assessment of perfusion.

Photoplethysmography (PPG) is an optical noninvasive technique with the potential for assessing tissue perfusion. The relative time-change in the concentration of oxyhemoglobin and deoxyhemoglobin in the blood can be derived from DC part of the PPG signal. However, the absolute concentration cannot be determined due to the inadequate data on PPG optical paths. The optical path and differential pathlength factor (DPF) for PPG at red (660nm) and infrared (880nm) wavelengths were investigated using a heterogeneous Monte Carlo model of the human forearm. Using the simulated DPFs, the absolute time-change in concentrations were determined from PPG signals recorded from the same tissue site. Results were compared with three conditions of approximated DPFs. Results showed the variation of the optical-path and DPF with different wavelengths and source-detector separations. Approximations resulted in significant errors, for example, using NIRS DPF in PPG led to "cross talk" of -0.4297 and 0.060 and an error of 15.16% to 25.18%. Results confirmed the feasibility of using the PPG (DC) for the assessment of tissue perfusion. The study also identified the inappropriateness of the assumption that DPF is independent of wavelength or source-detector separations and set the platform for further studies on investigating optical pathlengths and DPF in PPG.

Differential Path-Length Factor's Effect on the Characterization of Brain's Hemodynamic Response Function: A Functional Near-Infrared Study.

Functional near-infrared spectroscopy (fNIRS) has evolved as a neuro-imaging modality over the course of the past two decades. The removal of superfluous information accompanying the optical signal, however, remains a challenge. A comprehensive analysis of each step is necessary to ensure the extraction of actual information from measured fNIRS waveforms. A slight change in shape could alter the features required for fNIRS-BCI applications. In the present study, the effect of the differential path-length factor (DPF) values on the characteristics of the hemodynamic response function (HRF) was investigated. Results were compiled for both simulated data sets and healthy human subjects over a range of DPF values from three to eight. Different sets of activation durations and stimuli were used to generate the simulated signals for further analysis. These signals were split into optical densities under a constrained environment utilizing known values of DPF. Later, different values of DPF were used to analyze the variations of actual HRF. The results, as summarized into four categories, suggest that the DPF can change the main and post-stimuli responses in addition to other interferences. Six healthy subjects participated in this study. Their observed optical brain time-series were fed into an iterative optimization problem in order to estimate the best possible fit of HRF and physiological noises present in the measured signals with free parameters. A series of solutions was derived for different values of DPF in order to analyze the variations of HRF. It was observed that DPF change is responsible for HRF creep from actual values as well as changes in HRF characteristics.

Changes in Scattering, Absorption, and Resulting Differential Pathlength Factor During Arterial Occlusion and Reperfusion

Continuous wave near-infrared spectroscopy (CW-NIRS) has been used to assess microvascular function and the balance between muscle oxygen delivery and oxygen consumption via post-occlusion reactive hyperemia (PORH) tests. However, CW-NIRS relies on the assumption that the scattering and absorption characteristics of the investigated tissue remain unchanged via a constant differential pathlength factor (DPF). PURPOSE: We tested the hypothesis that the DFP of forearm tissue would be significantly different among the phases of a PORH test (i.e. baseline, arterial occlusion, and arterial reperfusion). METHODS: 5 subjects (22.6 ± 1.8 yrs, 170 ± 5 cm, 66.0 ± 10.8 kg) completed three PORH tests consisting of 1 min of baseline, 5 min of brachial arterial cuff occlusion, and 3 min of recovery following arterial reperfusion. Reduced scattering (μs’) and absorption (μa) coefficients were continuously measured, and later used to calculate a DPF, at wavelengths of 692 and 834 nm (DPF692 and DPF834, respectively) via frequency domain near-infrared spectroscopy (FD-NIRS) during the entire duration of the PORH tests. The minute averaged DPF response was averaged among the three PORH tests. RESULTS: DPF692 was significantly greater that DPF834 during each minute of the PORH tests (p < 0.05). DPF834 did not significantly change during any phase of the PORH test from baseline (3.83 ± 0.79; p > 0.05). DPF692 was significantly less during the final minute of arterial occlusion (4.07 ± 0.69) when compared to baseline (4.67 ± 0.78; p < 0.001). Further, following arterial reperfusion, DPF692 was significantly greater (4.91 ± 0.78) when compared to the final minute of arterial occlusion (p < 0.001), but not different when compared to baseline. CONCLUSION: These data demonstrate that the DPF692 of forearm tissue does not remain constant across the phases of a PORH test. The assumption of a constant DPF may alter interpretations of data related to microvascular function and the balance between muscle oxygen delivery and oxygen consumption obtained via PORH tests.

Absolute Values of Optical Properties (μa, μ΄s, μeff and DPF) of Human Head Tissue: Dependence on Head Region and Individual.

Absolute optical properties (i.e., the absorption coefficient, μa, and the reduced scattering coefficient, [Formula: see text]) of head tissue can be measured with frequency-domain near-infrared spectroscopy (FD-NIRS). We investigated how the absolute optical properties depend on the individual subject and the head region. The data set used for the analysis comprised 31 single FD-NIRS measurements of 14 healthy subjects (9 men, 5 women, aged 33.4 ± 10.5years). From an 8-min measurement (resting-state; FD-NIRS device: Imagent, ISS Inc.; bilateral over the prefrontal cortex, PFC, and visual cortex, VC) median values were calculated for μa and [Formula: see text] as well as the effective attenuation coefficient (μeff) and the differential pathlength factor (DPF). The measurement was done for each subject one to three times with at least 24h between the measurements. (i) A Bayesian ANOVA analysis revealed that head region and subject were the most significant main effects on μa, [Formula: see text] and μeff, as well as DPF, respectively. (ii) At the VC, μa, [Formula: see text] and μeff had higher values compared to the PFC. (iii) The differences in the optical properties between PFC and VC were age-dependent. (iv) All optical properties also were age-dependent. This was strongest for the properties of the PFC compared to the VC. Our analysis demonstrates that all optical head tissue properties (μa, [Formula: see text], μeff and DPF) were dependent on the head region, individual subject and age. The optical properties of the head are like a 'fingerprint' for the individual subject. Assuming constant optical properties for the whole head should be carefully reconsidered.

Long-Term Changes in Optical Properties (μa, μ's, μeff and DPF) of Human Head Tissue During Functional Neuroimaging Experiments.

Frequency-domain near-infrared spectroscopy (FD-NIRS) enables to measure absolute optical properties (i.e. the absorption coefficient, μa, and the reduced scattering coefficient, [Formula: see text]) of the brain tissue. The aim of this study was to investigate how the optical properties changed during the course of a functional NIRS experiment. The analyzed dataset comprised of FD-NIRS measurements of 14 healthy subjects (9 males, 5 females, aged: 33.4 ± 10.5years, range: 24-57years old). Each measurement lasted 33min, i.e. 8 min baseline in darkness, 10 min intermittent light stimulation, and 15 min recovery in darkness. Optical tissue properties were obtained bilaterally over the prefrontal cortex (PFC) and visual cortex (VC) with FD-NIRS (Imagent, ISS Inc., USA). Changes in μa and [Formula: see text] were directly measured and two parameters were calculated, i.e. the differential pathlength factor (DPF) and the effective attenuation coefficient (μeff). Differences in the behavior of the optical changes were observed when comparing group-averaged data versus single datasets: no clear overall trend was presented in the group data, whereas a clear long-term trend was visible in almost all of the single measurements. Interestingly, the changes in [Formula: see text] statistically significantly correlated with μa, positively in the PFC and negatively in the VC. Our analysis demonstrates that all optical brain tissue properties (μa, [Formula: see text], μeff and DPF) change during these functional neuroimaging experiments. The change in [Formula: see text] is not random but follows a trend, which depends on the single experiment and measurement location. The change in the scattering properties of the brain tissue during a functional experiment is not negligible. The assumption [Formula: see text] ≈ const during an experiment is valid for group-averaged data but not for data from single experiments.