Analytical models for time-domain diffuse correlation spectroscopy for multi-layer and heterogeneous turbid media

Quantification of blood flow index in diffuse correlation spectroscopy using a robust deep learning method

Significance

Diffuse correlation spectroscopy (DCS) is a powerful, noninvasive optical technique for measuring blood flow. Traditionally the blood flow index (BFi) is derived through nonlinear least-square fitting the measured intensity autocorrelation function (ACF). However, the fitting process is computationally intensive, susceptible to measurement noise, and easily influenced by optical properties (absorption coefficient μ a and reduced scattering coefficient μ s ' ) and scalp and skull thicknesses.

Aim

We aim to develop a data-driven method that enables rapid and robust analysis of multiple-scattered light's temporal ACFs. Moreover, the proposed method can be applied to a range of source-detector distances instead of being limited to a specific source-detector distance.

Approach

We present a deep learning architecture with one-dimensional convolution neural networks, called DCS neural network (DCS-NET), for BFi and coherent factor (β ) estimation. This DCS-NET was performed using simulated DCS data based on a three-layer brain model. We quantified the impact from physiologically relevant optical property variations, layer thicknesses, realistic noise levels, and multiple source-detector distances (5, 10, 15, 20, 25, and 30 mm) on BFi and β estimations among DCS-NET, semi-infinite, and three-layer fitting models.

Results

DCS-NET shows a much faster analysis speed, around 17,000-fold and 32-fold faster than the traditional three-layer and semi-infinite models, respectively. It offers higher intrinsic sensitivity to deep tissues compared with fitting methods. DCS-NET shows excellent anti-noise features and is less sensitive to variations of μ a and μ s ' at a source-detector separation of 30 mm. Also, we have demonstrated that relative BFi (rBFi) can be extracted by DCS-NET with a much lower error of 8.35%. By contrast, the semi-infinite and three-layer fitting models result in significant errors in rBFi of 43.76% and 19.66%, respectively.

Conclusions

DCS-NET can robustly quantify blood flow measurements at considerable source-detector distances, corresponding to much deeper biological tissues. It has excellent potential for hardware implementation, promising continuous real-time blood flow measurements.

Numerical approach to quantify depth-dependent blood flow changes in real-time using the diffusion equation with continuous-wave and time-domain diffuse correlation spectroscopy

Diffuse correlation spectroscopy (DCS) is a non-invasive optical technique that can measure brain perfusion by quantifying temporal intensity fluctuations of multiply scattered light. A primary limitation for accurate quantitation of cerebral blood flow (CBF) is the fact that experimental measurements contain information about both extracerebral scalp blood flow (SBF) as well as CBF. Separating CBF from SBF is typically achieved using multiple source-detector channels when using continuous-wave (CW) light sources, or more recently with use of time-domain (TD) techniques. Analysis methods that account for these partial volume effects are often employed to increase CBF contrast. However, a robust, real-time analysis procedure that can separate and quantify SBF and CBF with both traditional CW and TD-DCS measurements is still needed. Here, we validate a data analysis procedure based on the diffusion equation in layered media capable of quantifying both extra- and cerebral blood flow in the CW and TD. We find that the model can quantify SBF and CBF coefficients with less than 5% error compared to Monte Carlo simulations using a 3-layered brain model in both the CW and TD. The model can accurately fit data at a rate of <10 ms for CW data and <250 ms for TD data when using a least-squares optimizer.

High-density diffuse correlation tomography with enhanced depth localization and minimal surface artefacts

A spatially weighted filter applied to both the measurement and the Jacobian is proposed for high-density diffuse correlation tomography (DCT) to remove unwanted extracerebral interferences and artefacts along with better depth localization in the reconstructed blood flow images. High-density DCT is implemented by appropriate modification of recently introduced Multi-speckle Diffuse Correlation Spectroscopy (M-DCS) system. Additionally, we have used autocorrelation measurements at multiple delay-times in an iterative manner to improve the reconstruction results. The proposed scheme has been validated by simulations, phantom experiments and in-vivo human experiments.

Two-layer analytical model for estimation of layer thickness and flow using Diffuse Correlation Spectroscopy

Diffuse correlation spectroscopy (DCS) has been widely explored for its ability to measure cerebral blood flow (CBF), however, mostly under the assumption that the human head is homogenous. In addition to CBF, knowledge of extracerebral layers, such as skull thickness, can be informative and crucial for patient with brain complications such as traumatic brain injuries. To bridge the gap, this study explored the feasibility of simultaneously extracting skull thickness and flow in the cortex layer using DCS. We validated a two-layer analytical model that assumed the skull as top layer with a finite thickness and the brain cortex as bottom layer with semi-infinite geometry. The model fitted for thickness of the top layer and flow of the bottom layer, while assumed other parameters as constant. The accuracy of the two-layer model was tested against the conventional single-layer model using measurements from custom made two-layer phantoms mimicking skull and brain. We found that the fitted top layer thickness at each source detector (SD) distance is correlated with the expected thickness. For the fitted bottom layer flow, the two-layer model fits relatively consistent flow across all top layer thicknesses. In comparison, the conventional one-layer model increasingly underestimates the bottom layer flow as top layer thickness increases. The overall accuracy of estimating first layer thickness and flow depends on the SD distance in relationship to first layer thickness. Lastly, we quantified the influence of uncertainties in the optical properties of each layer. We found that uncertainties in the optical properties only mildly influence the fitted thickness and flow. In this work we demonstrate the feasibility of simultaneously extracting of layer thickness and flow using a two-layer DCS model. Findings from this work may introduce a robust and cost-effective approach towards simultaneous bedside assessment of skull thickness and cerebral blood flow.

First-in-clinical application of a time-gated diffuse correlation spectroscopy system at 1064 nm using superconducting nanowire single photon detectors in a neuro intensive care unit

Recently proposed time-gated diffuse correlation spectroscopy (TG-DCS) has significant advantages compared to conventional continuous wave (CW)-DCS, but it is still in an early stage and clinical capability has yet to be established. The main challenge for TG-DCS is the lower signal-to-noise ratio (SNR) when gating for the deeper traveling late photons. Longer wavelengths, such as 1064 nm have a smaller effective attenuation coefficient and a higher power threshold in humans, which significantly increases the SNR. Here, we demonstrate the clinical utility of TG-DCS at 1064 nm in a case study on a patient with severe traumatic brain injury admitted to the neuro-intensive care unit (neuroICU). We showed a significant correlation between TG-DCS early (ρ = 0.67) and late (ρ = 0.76) gated against invasive thermal diffusion flowmetry. We also analyzed TG-DCS at high temporal resolution (50 Hz) to elucidate pulsatile flow data. Overall, this study demonstrates the first clinical translation capability of the TG-DCS system at 1064 nm using a superconducting nanowire single-photon detector.

Performance assessment of laser sources for time-domain diffuse correlation spectroscopy

Time-domain diffuse correlation spectroscopy (TD-DCS) is an emerging optical technique that enables noninvasive measurement of microvascular blood flow with photon path-length resolution. In TD-DCS, a picosecond pulsed laser with a long coherence length, adequate illumination power, and narrow instrument response function (IRF) is required, and satisfying all these features is challenging. To this purpose, in this study we characterized the performance of three different laser sources for TD-DCS. First, the sources were evaluated based on their emission spectrum and IRF. Then, we compared the signal-to-noise ratio and the sensitivity to velocity changes of scattering particles in a series of phantom measurements. We also compared the results for in vivo measurements, performing an arterial occlusion protocol on the forearm of three adult subjects. Overall, each laser has the potential to be successfully used both for laboratory and clinical applications. However, we found that the effects caused by the IRF are more significant than the effect of a limited temporal coherence.

Optimization of time domain diffuse correlation spectroscopy parameters for measuring brain blood flow

Significance: Time domain diffuse correlation spectroscopy (TD-DCS) can offer increased sensitivity to cerebral hemodynamics and reduced contamination from extracerebral layers by differentiating photons based on their travel time in tissue. We have developed rigorous simulation and evaluation procedures to determine the optimal time gate parameters for monitoring cerebral perfusion considering instrumentation characteristics and realistic measurement noise. Aim: We simulate TD-DCS cerebral perfusion monitoring performance for different instrument response functions (IRFs) in the presence of realistic experimental noise and evaluate metrics of sensitivity to brain blood flow, signal-to-noise ratio (SNR), and ability to reject the influence of extracerebral blood flow across a variety of time gates to determine optimal operating parameters. Approach: Light propagation was modeled on an MRI-derived human head geometry using Monte Carlo simulations for 765- and 1064-nm excitation wavelengths. We use a virtual probe with a source-detector separation of 1 cm placed in the pre-frontal region. Performance metrics described above were evaluated to determine optimal time gate(s) for different IRFs. Validation of simulation noise estimates was done with experiments conducted on an intralipid-based liquid phantom. Results: We find that TD-DCS performance strongly depends on the system IRF. Among Gaussian pulse shapes, ∼ 300    ps pulse length appears to offer the best performance, at wide gates (500 ps and larger) with start times 400 and 600 ps after the peak of the TPSF at 765 and 1064 nm, respectively, for a 1-s integration time at photon detection rates seen experimentally (600 kcps at 765 nm and 4 Mcps at 1064 nm). Conclusions: Our work shows that optimal time gates satisfy competing requirements for sufficient sensitivity and sufficient SNR. The achievable performance is further impacted by system IRF with ∼ 300    ps quasi-Gaussian pulse obtained using electro-optic laser shaping providing the best results.

Time-domain diffuse correlation spectroscopy (TD-DCS) for noninvasive, depth-dependent blood flow quantification in human tissue in vivo

Monitoring of human tissue hemodynamics is invaluable in clinics as the proper blood flow regulates cellular-level metabolism. Time-domain diffuse correlation spectroscopy (TD-DCS) enables noninvasive blood flow measurements by analyzing temporal intensity fluctuations of the scattered light. With time-of-flight (TOF) resolution, TD-DCS should decompose the blood flow at different sample depths. For example, in the human head, it allows us to distinguish blood flows in the scalp, skull, or cortex. However, the tissues are typically polydisperse. So photons with a similar TOF can be scattered from structures that move at different speeds. Here, we introduce a novel approach that takes this problem into account and allows us to quantify the TOF-resolved blood flow of human tissue accurately. We apply this approach to monitor the blood flow index in the human forearm in vivo during the cuff occlusion challenge. We detect depth-dependent reactive hyperemia. Finally, we applied a controllable pressure to the human forehead in vivo to demonstrate that our approach can separate superficial from the deep blood flow. Our results can be beneficial for neuroimaging sensing applications that require short interoptode separation.

In vivo time-domain diffuse correlation spectroscopy above the water absorption peak

Time-domain diffuse correlation spectroscopy (TD-DCS) is a newly emerging optical technique that exploits pulsed, yet coherent light to non-invasively resolve the blood flow in depth. In this work, we have explored TD-DCS at longer wavelengths compared to those previously used in literature (i.e., 750-850 nm). The measurements were performed using a custom-made titanium-sapphire mode-locked laser, operating at 1000 nm, and an InGaAs photomultiplier as a detector. Tissue-mimicking phantoms and in vivo measurements during arterial arm cuff occlusion in n=4 adult volunteers were performed to demonstrate the proof of concept. We obtained a good signal-to-noise ratio, following the hemodynamics continuously with a relatively fast (1 Hz) sampling rate. In all the experiments, the auto-correlation functions show a decay rate approximately five-fold slower compared to shorter wavelengths. This work demonstrates the feasibility of in vivo TD-DCS in this spectral region and its potentiality for biomedical applications.

Beyond diffuse correlations: deciphering random flow in time-of-flight resolved light dynamics

Diffusing wave spectroscopy (DWS) and diffuse correlation spectroscopy (DCS) can assess blood flow index (BFI) of biological tissue with multiply scattered light. Though the main biological function of red blood cells (RBCs) is advection, in DWS/DCS, RBCs are assumed to undergo Brownian motion. To explain this discrepancy, we critically examine the cumulant approximation, a major assumption in DWS/DCS. We present a precise criterion for validity of the cumulant approximation, and in realistic tissue models, identify conditions that invalidate it. We show that, in physiologically relevant scenarios, the first cumulant term for random flow and second cumulant term for Brownian motion alone can cancel each other. In such circumstances, assuming pure Brownian motion of RBCs and the first cumulant approximation, a routine practice in DWS/DCS of BFI, can yield good agreement with data, but only because errors due to two incorrect assumptions cancel out. We conclude that correctly assessing random flow from scattered light dynamics requires going beyond the cumulant approximation and propose a more accurate model to do so.

Effects of the instrument response function and the gate width in time-domain diffuse correlation spectroscopy: model and validations

Time-domain diffuse correlation spectroscopy (TD-DCS) is an emerging noninvasive optical technique with the potential to resolve blood flow (BF) and optical coefficients (reduced scattering and absorption) in depth. Here, we study the effects of finite temporal resolution and gate width in a realistic TD-DCS experiment. We provide a model for retrieving the BF from gated intensity autocorrelations based on the instrument response function, which allows for the use of broad time gates. This, in turn, enables a higher signal-to-noise ratio that is critical for in vivo applications. In numerical simulations, the use of the proposed model reduces the error in the estimated late gate BF from 34% to 3%. Simulations are also performed for a wide set of optical properties and source–detector separations. In a homogeneous phantom experiment, the discrepancy between later gates BF index and ungated BF index is reduced from 37% to 2%. This work not only provides a tool for data analysis but also physical insights, which can be useful for studying and optimizing the system performance.

Using a simulation approach to optimize time-domain diffuse correlation spectroscopy measurement on human head

Time-domain diffuse correlation spectroscopy (TD-DCS) has been recently proposed to improve detection of deep blood flow dynamics in a biological tissue, such as human brain. To obtain a high sensitive measurement, several experimental parameters such as the source-detector (SD) distance, gate opening time, and width need to be considered and optimized. We use a simulation approach to optimize these parameters based on Monte Carlo computations using a realistic human head model. Two cortical regions are investigated including the frontal and temporal lobes. SD distance ranging from 0 to 45 mm, gate opening time from 400 to 1000 ps, and gate width from 50 to 3000 ps are considered. The goal is to find out the optimal combinations of these parameters by which the higher contrast measurement on the cortical dynamics can be achieved. The simulations show that with an acceptable input power of light, the combinations of SD distance ranging from 0 to 15 mm, gate opening time at 700 to 800 ps, and gate width of 800 ps are optimal for achieving higher contrast measurement on the cortical dynamics. The simulation approach and results are helpful for the optimization of TD-DCS experimental design focused on brain functional detection.