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docs/intro.md

@@ -4,26 +4,23 @@ We are currently evaluating the [Flow2](https://www.kernel.com/products) by Kern
 This website will share information with members of our community about how to acquire and analyze the data. We recommend reading the Kernel preprint on the [validation](https://www.biorxiv.org/content/10.1101/2024.04.30.591765v1.abstract) and [reliability](https://www.nature.com/articles/s41598-024-68555-9) of the Flow2 system.
 
 ## Time Domain Functional Near Infrared Spectroscopy (TD-fNIRS)
-Time-Domain Near-Infrared Spectroscopy (TD-NIRS) is an advanced non-invasive technique used to measure the optical properties of biological tissues, primarily for medical and physiological studies. Near-infrared light can penetrate several centimeters into biological tissues, making TD-NIRS suitable for monitoring deep tissue and brain activities. TD-fNIRS systems use short pulses of light and detectors capable of measuring single photons to capture a distribution of times of flight (DTOF) of photons. This fine-grained measurement capability allows TD-fNIRS systems to measure absolute optical properties of the underlying tissue including the absorption (μa) and reduced scattering (μs′) coefficients, instead of only measuring relative changes in light intensity like continuous wave (CW) systems. The increased information from TD-fNIRS systems also allows for advanced signal processing methods to more heavily weight photons that arrive late in the DTOF in order to emphasize data from deeper in the head (i.e., from the brain). TD-fNRIS  allows for the quantification of absolute concentrations of chromophores, such as oxyhemoglobin and deoxyhemoglobin. This provides precise measurements of tissue oxygenation and hemodynamics.
 
-### Principle of Operation:
-
-TD-fNIRS systems use short pulses of light and detectors capable of measuring single photons to capture a distribution of times of flight (DTOF) of photons. This fine-grained measurement capability allows TD-fNIRS systems to measure absolute optical properties of the underlying tissue including the absorption (μa) and reduced scattering (μs′) coefficients, instead of only measuring relative changes in light intensity like continuous wave (CW) systems. The increased information from TD-fNIRS systems also allows for advanced signal processing methods to more heavily weight photons that arrive late in the DTOF in order to emphasize data from deeper in the head (i.e., from the brain).
+Time-Domain Near-Infrared Spectroscopy (TD-NIRS) is an advanced non-invasive technique used to measure the optical properties of biological tissues, primarily for medical and physiological studies. Near-infrared light can penetrate several centimeters into biological tissues, making TD-NIRS suitable for monitoring deep tissue and brain activities. Unlike more traditional continuous wave (CW) systems that only measure relative changes in light intensity, TD-fNIRS systems use short pulses of light and detectors capable of measuring single photons to capture a distribution of times of flight (DTOF) of photons. This allows TD-fNIRS to measure signals deeper in the brain to quantify absolute concentrations of chromophores such as oxyhemoglobin (HbO) and deoxyhemoglobin (HbR).
 
 ### Quantitative Information:
 
-TD fNIRS uses time gating to discriminate the photons arriving to the detector as a function of their time of flight. As photons traveling longer distances are more likely to have reached deeper layers of the tissue, TD-fNIRS has increased sensitivity to the brain hemodynamics when longer-traveling photons are selected. However, this advantage over CW fNIRS is limited in real instrumentation by the instrument response function (IRF), which causes a broadening of the distribution of times of flight (DTOF), complicating the inter- pretation of the time gates. Moment analysis of the DTOF, which is relatively immune to the IRF, has been proposed as an alternative to time gates analysis in TD-fNIRS. Higher statistical moments of the DTOF present increased sensitivity to deeper tissue layers compared to signal intensity changes as the kernel for the moment calculation grows as a function of the time of flight.
-
-A common way to summarize information from time-of-flight histograms is to compute the first three moments of the histogram corresponding to the total counts (sum), mean time-of-flight (first moment), and variance of the times of flight (second central moment). Moments have a convenient property: the moments of the DTOF can be obtained from calculating the moments of the TPSF and of the IRF straightforwardly. Accordingly, with Flow2, system drift in the DTOF moments can be corrected for, using the internal IRF detector. However, the instrument response function (IRF) can complicate data interpretation in TD-fNIRS. To address this, moment analysis of the distribution of times of flight (DTOF) has been proposed as an alternative to time gates analysis. Higher statistical moments of the DTOF show increased sensitivity to deeper tissue layers.
+TD-fNIRS uses time gating to discriminate the photons arriving to the detector as a function of their time of flight. As photons traveling longer distances are more likely to have reached deeper layers of the tissue, TD-fNIRS has increased sensitivity to the brain hemodynamics when longer-traveling photons are selected. However, this advantage over CW fNIRS is limited in real instrumentation by the instrument response function (IRF), which causes a broadening of the DTOF, complicating the interpretation of the time gates. Moment analysis of the DTOF, which is relatively immune to the IRF, has been proposed as an alternative to time gates analysis in TD-fNIRS. Higher statistical moments of the DTOF present increased sensitivity to deeper tissue layers compared to signal intensity changes as the kernel for the moment calculation grows as a function of the time of flight. A common way to summarize information from time-of-flight histograms is to compute the first three moments of the histogram corresponding to the total counts (sum), mean time-of-flight (first moment), and variance of the times of flight (second central moment). 
 
 ![flow2](images/DTOF.png)
 
 
 ## Flow 2
 The Kernel Flow2 is an advanced time-domain functional near-infrared spectroscopy (TD-fNIRS) system designed for brain imaging. It uses time gating to discriminate photons based on their time of flight, potentially increasing sensitivity to brain hemodynamics compared to continuous-wave fNIRS, especially when selecting longer-traveling photons.
 
-The system consists of 40 modules arranged in a headset covering frontal, parietal, temporal, and occipital cortices. Each module contains 3 dual-wavelength sources and 6 detectors, plus a central detector for continuous instrument response function (IRF) monitoring. The modules provide multiple source-detector distances (8.5mm, 17.9mm, and 26.5mm), allowing for measurements at different depths. In total, the system offers 2,565 possible channels with source-detector separations ≤ 50mm.
+The system consists of 40 modules arranged in a headset covering frontal, parietal, temporal, and occipital cortices. Each module contains 3 dual-wavelength sources and 6 detectors, plus a central detector for continuous instrument response function (IRF) monitoring. Channels represent one source-detector pairing, which measure signal at different distances. Within a single module, channel distances are 8.5mm (6 source-detector pairs), 17.9mm (6 source-detector pairs), and 26.5mm (6 source-detector pairs), for a total of 18 dual-wavelength channels within a module. It is possible to increase the density of channels by also considering between module source-detector channels. For example, the density of channels can be increaed to 2,565 possible channels with a source-detector separation of ≤ 50 mm, or up to 3,583 when considering distances ≤ 60mm. 
+
 The module optics are carefully designed to conduct laser light into the scalp and couple returning light to detectors. They use spring-loaded light pipes to conform to head curvature and reduce interference from hair. Each light pipe is optically isolated to prevent crosstalk. The source optics use a two-lens system with integrated micro-prisms to direct and homogenize light. Similarly, the detector optics use a two-lens system to maintain constant received optical intensity regardless of spring compression.
+
 A critical feature is the continuous IRF monitoring. Each module has a dedicated IRF detector that captures light directly from the lasers without passing through tissue. This provides reliable estimates of IRF contributions from both detectors and lasers, helping to account for variations due to temperature and voltage changes.
 
 The system uses temporal multiplexing of lasers to avoid optical crosstalk. It operates in a 38-state pattern, completing a full cycle of data collection for all modules and wavelengths every 76 histograms. This results in a system sampling frequency of 3.76 Hz, with each source operating at 7.52 Hz in the full headset configuration. The integration time for constructing histograms is set at 3.5ms, allowing for a histogram sampling rate of 285.7 Hz per wavelength.

docs/signal.md

@@ -2,17 +2,17 @@
 # Measurement
 Here are details about the signals that are being measured and how they are currently being preprocessed by Kernel.
 
-- Moments provides the time courses for each channel:
+- **Moments** provide the time courses for each channel:
     - 0th moment: integral (# photons, from 0 to ~1e7),
     - 1st moment: mean time of flight (mean time of flight, in picoseconds is on the order of 1000)
     - 2nd moment: variance of time-of-flight (variance of time of flight, in picoseconds^2 is on the order of 100000)
-- Hb/Moments includes an analysis indicating concentration of HbO (oxyhemoglobin) and HbR (deoxyhemoglobin). 
-- Gating - Time Gating
-- Reconstruction - HD-DOT
+- **Hb/Moments** includes an analysis indicating concentration of HbO (oxyhemoglobin) and HbR (deoxyhemoglobin) using the modified Beer–Lambert law. 
+- **Gating** - Time Gating
+- **Reconstruction** - High Density - Diffustion Optical Tomography (HD-DOT)
 
 
 ## Relative changes in HbO and HbR concentrations (moments method)
-The data preprocessing procedures have been extensively detailed in our previous studies (15). Initially, we applied a channel selection method based on histogram shape criteria (14). Subsequently, histograms derived from the chosen channels were utilized to calculate the moments of the DTOFs, specifically focusing on the sum, mean, and variance moments. The alterations in preprocessed DTOF moments were then translated into changes in absorption coefficients for each wavelength, employing the sensitivities of the various moments to absorption coefficient changes, as outlined in (13). To determine these sensitivities, a 2-layer medium with a superficial layer of 12 mm thickness was employed. Utilizing a finite element modeling (FEM) forward model from NIRFAST (58, 59), the Jacobians (sensitivity maps) for each moment were integrated within each layer to assess sensitivities. The changes in absorption coefficients at each wavelength were further converted into alterations in oxyhemoglobin and deoxyhemoglobin concentrations (HbO and HbR, respectively), employing the extinction coefficients for the respective wavelengths and the modified Beer–Lambert law (mBLL (60)). The HbO/HbR concentrations underwent additional preprocessing through a motion correction algorithm known as Temporal Derivative Distribution Repair (TDDR (61)). To address spiking artifacts arising from baseline shifts during TDDR, they were identified and rectified using cubic spline interpolation (62). Lastly, data detrending was performed using a moving average with a 100-second kernel, and short channel regression was employed to eliminate superficial physiological signals from brain activity (63), utilizing short within-module channels with a source-detector separation (SDS) of 8.5 mm.
+The data preprocessing procedures details are available in [Castillo et al., 2023](https://www.nature.com/articles/s41598-023-38258-8). Initially, we applied a channel selection method based on histogram shape criteria (14). Subsequently, histograms derived from the chosen channels were utilized to calculate the moments of the DTOFs, specifically focusing on the sum, mean, and variance moments. The alterations in preprocessed DTOF moments were then translated into changes in absorption coefficients for each wavelength, employing the sensitivities of the various moments to absorption coefficient changes, as outlined in (13). To determine these sensitivities, a 2-layer medium with a superficial layer of 12 mm thickness was employed. Utilizing a finite element modeling (FEM) forward model from NIRFAST (58, 59), the Jacobians (sensitivity maps) for each moment were integrated within each layer to assess sensitivities. The changes in absorption coefficients at each wavelength were further converted into alterations in oxyhemoglobin and deoxyhemoglobin concentrations (HbO and HbR, respectively), employing the extinction coefficients for the respective wavelengths and the modified Beer–Lambert law (mBLL (60)). The HbO/HbR concentrations underwent additional preprocessing through a motion correction algorithm known as Temporal Derivative Distribution Repair (TDDR (61)). To address spiking artifacts arising from baseline shifts during TDDR, they were identified and rectified using cubic spline interpolation (62). Lastly, data detrending was performed using a moving average with a 100-second kernel, and short channel regression was employed to eliminate superficial physiological signals from brain activity (63), utilizing short within-module channels with a source-detector separation (SDS) of 8.5 mm.
 
 ## Absolute concentrations of HbO and HbR (curve fitting method)
 The DTOF results from convolving the time-resolved TPSF with the IRF. Utilizing Flow2’s online IRF measurements, we employed a curve fitting technique to extract the absolute optical properties of the tissue beneath. Generating candidate TPSFs through an analytical solution of the diffusion equation for a homogeneous semi-infinite medium, we convolved these with the known IRF and compared them with the recorded DTOF. The search for optical properties was carried out using the Levenberg-Marquardt algorithm, focusing on fitting within the range spanning from 80% of the peak on the rising edge to 0.1% of the peak on the falling edge, with a refractive index set to 1.4. These absorption coefficient estimates were then converted to HbO and HbR concentrations. A single value for HbO and HbR was obtained by computing the median value across well-coupled long, within-module channels (SDS=26.5mm) of two prefrontal modules.