Short Source-detector Separations Research Articles

Development of a Monte Carlo-wave model to simulate time domain diffuse correlation spectroscopy measurements from first principles.

.Significance: Diffuse correlation spectroscopy (DCS) is an optical technique that measures blood flow non-invasively and continuously. The time-domain (TD) variant of DCS, namely, TD-DCS has demonstrated a potential to improve brain depth sensitivity and to distinguish superficial from deeper blood flow by utilizing pulsed laser sources and a gating strategy to select photons with different pathlengths within the scattering tissue using a single source–detector separation. A quantitative tool to predict the performance of TD-DCS that can be compared with traditional continuous wave DCS (CW-DCS) currently does not exist but is crucial to provide guidance for the continued development and application of these DCS systems.Aims: We aim to establish a model to simulate TD-DCS measurements from first principles, which enables analysis of the impact of measurement noise that can be utilized to quantify the performance for any particular TD-DCS system and measurement geometry.Approach: We have integrated the Monte Carlo simulation describing photon scattering in biological tissue with the wave model that calculates the speckle intensity fluctuations due to tissue dynamics to simulate TD-DCS measurements from first principles.Results: Our model is capable of simulating photon counts received at the detector as a function of time for both CW-DCS and TD-DCS measurements. The effects of the laser coherence, instrument response function, detector gate delay, gate width, intrinsic noise arising from speckle statistics, and shot noise are incorporated in the model. We have demonstrated the ability of our model to simulate TD-DCS measurements under different conditions, and the use of our model to compare the performance of TD-DCS and CW-DCS under a few typical measurement conditions.Conclusion: We have established a Monte Carlo-Wave model that is capable of simulating CW-DCS and TD-DCS measurements from first principles. In our exploration of the parameter space, we could not find realistic measurement conditions under which TD-DCS outperformed CW-DCS. However, the parameter space for the optimization of the contrast to noise ratio of TD-DCS is large and complex, so our results do not imply that TD-DCS cannot indeed outperform CW-DCS under different conditions. We made our code available publicly for others in the field to find use cases favorable to TD-DCS. TD-DCS also provides a promising way to measure deep brain tissue dynamics using a short source–detector separation, which will benefit the development of technologies including high density DCS systems and image reconstruction using a limited number of source–detector pairs.

Evaluation of fNIRS signal components elicited by cognitive and hypercapnic stimuli

Functional near infrared spectroscopy (fNIRS) measurements are confounded by signal components originating from multiple physiological causes, whose activities may vary temporally and spatially (across tissue layers, and regions of the cortex). Furthermore, the stimuli can induce evoked effects, which may lead to over or underestimation of the actual effect of interest. Here, we conducted a temporal, spectral, and spatial analysis of fNIRS signals collected during cognitive and hypercapnic stimuli to characterize effects of functional versus systemic responses. We utilized wavelet analysis to discriminate physiological causes and employed long and short source-detector separation (SDS) channels to differentiate tissue layers. Multi-channel measures were analyzed further to distinguish hemispheric differences. The results highlight cardiac, respiratory, myogenic, and very low frequency (VLF) activities within fNIRS signals. Regardless of stimuli, activity within the VLF band had the largest contribution to the overall signal. The systemic activities dominated the measurements from the short SDS channels during cognitive stimulus, but not hypercapnic stimulus. Importantly, results indicate that characteristics of fNIRS signals vary with type of the stimuli administered as cognitive stimulus elicited variable responses between hemispheres in VLF band and task-evoked temporal effect in VLF, myogenic and respiratory bands, while hypercapnic stimulus induced a global response across both hemispheres.

Optical property recovery with spatially-resolved diffuse reflectance at short source-detector separations using a compact fiber-optic probe.

We describe a compact fiber-optic probe (2 mm outside diameter) that utilizes spatially-resolved diffuse reflectance for tissue optical property recovery. Validation was performed in phantoms containing Intralipid 20% as scatterer, and methylene blue (MB), MnTPPS, and/or India ink as absorbers. Over a range of conditions, the reduced scattering coefficient was recovered with a root mean square error (RMSE) of 0.86-2.7 cm-1 (average error = 3.8%). MB concentration was recovered with RMSE = 0.26-0.52 µM (average error = 15.0%), which did not vary with inclusion of MnTPPS (p=0.65). This system will be utilized to determine optical properties in human abscesses, in order to generate treatment plans for photodynamic therapy.

Microvascular blood flow changes of the abductor pollicis brevis muscle during sustained static exercise.

A practical assessment of the general health and microvascular function of the palm muscle, abductor pollicis brevis (APB), is important for the diagnosis of different conditions. In this study, we have developed a protocol and a probe to study microvascular blood flow using near-infrared diffuse correlation spectroscopy (DCS) in APB during and after thumb abduction at 55% of maximum voluntary contraction (MVC). Near-infrared time resolved spectroscopy (TRS) was also used to characterize the baseline optical and hemodynamic properties. Thirteen (n=13) subjects were enrolled and subdivided in low MVC (N=6, MVC<2.3 kg) and high MVC (N=7, MVC≥2.3 kg) groups. After ruling out significant changes in the systemic physiology that influence the muscle hemodynamics, we have observed that the high MVC group showed a 56% and 36% decrease in the blood flow during exercise, with respect to baseline, in the long and short source-detector (SD) separations (p=0.031 for both). No statistical differences were shown for the low MVC group (p=1 for short and p=0.15 for long SD). These results suggest that the mechanical occlusion, due to increased intramuscular pressure, exceeded the vasodilation elicited by the higher metabolic demand. Also, blood flow changes during thumb contraction negatively correlated (R=-0.7, p<0.01) with the absolute force applied by each subject. Furthermore, after the exercise, muscular blood flow increased significantly immediately after thumb contractions in both high and low MVC groups, with respect to the recorded values during the exercise (p=0.031). An increase of 251% (200%) was found for the long (short) SD in the low MVC group. The high MVC groups showed a significant 90% increase in blood flow only after 80 s from the start of the protocol. For both low and high MVC groups, blood flow recovered to baseline values within 160 s from starting the exercise. In conclusion, DCS allows the study of the response of a small muscle to static exercise and can be potentially used in multiple clinical conditions scenarios for assessing microvascular health.

Short-channel regression in functional near-infrared spectroscopy is more effective when considering heterogeneous scalp hemodynamics.

.Significance: The reliability of functional near-infrared spectroscopy (fNIRS) measurements is reduced by systemic physiology. Short-channel regression algorithms aim at removing systemic “noise” by subtracting the signal measured at a short source–detector separation (mainly scalp hemodynamics) from the one of a long separation (brain and scalp hemodynamics). In literature, incongruent approaches on the selection of the optimal regressor signal are reported based on different assumptions on scalp hemodynamics properties.Aim: We investigated the spatial and temporal distribution of scalp hemodynamics over the sensorimotor cortex and evaluated its influence on the effectiveness of short-channel regressions.Approach: We performed hand-grasping and resting-state experiments with five subjects, measuring with 16 optodes over sensorimotor areas, including eight 8-mm channels. We performed detailed correlation analyses of scalp hemodynamics and evaluated 180 hand-grasping and 270 simulated (overlaid on resting-state measurements) trials. Five short-channel regressor combinations were implemented with general linear models. Three were chosen according to literature, and two were proposed based on additional physiological assumptions [considering multiple short channels and their Mayer wave (MW) oscillations].Results: We found heterogeneous hemodynamics in the scalp, coming on top of a global close-to-homogeneous behavior (correlation 0.69 to 0.92). The results further demonstrate that short-channel regression always improves brain activity estimates but that better results are obtained when heterogeneity is assumed. In particular, we highlight that short-channel regression is more effective when combining multiple scalp regressors and when MWs are additionally included.Conclusion: We shed light on the selection of optimal regressor signals for improving the removal of systemic physiological artifacts in fNIRS. We conclude that short-channel regression is most effective when assuming heterogeneous hemodynamics, in particular when combining spatial- and frequency-specific information. A better understanding of scalp hemodynamics and more effective short-channel regression will promote more accurate assessments of functional brain activity in clinical and research settings.

Contribution of speckle noise in near-infrared spectroscopy measurements.

.Near-infrared spectroscopy (NIRS) is widely used in biomedical optics with applications ranging from basic science, such as in functional neuroimaging, to clinical, as in pulse oximetry. Despite the relatively low absorption of tissue in the near-infrared, there is still a significant amount of optical attenuation produced by the highly scattering nature of tissue. Because of this, designers of NIRS systems have to balance source optical power and source–detector separation to maximize the signal-to-noise ratio (SNR). However, theoretical estimations of SNR neglect the effects of speckle. Speckle manifests as fluctuations of the optical power received at the detector. These fluctuations are caused by interference of the multiple random paths taken by photons in tissue. We present a model for the NIRS SNR that includes the effects of speckle. We performed experimental validations with a NIRS system to show that it agrees with our model. Additionally, we performed computer simulations based on the model to estimate the contribution of speckle noise for different collection areas and source–detector separations. We show that at short source–detector separation, speckle contributes most of the noise when using long coherence length sources. Considering this additional noise is especially important for hybrid applications that use NIRS and speckle contrast simultaneously, such as in diffuse correlation spectroscopy.

Diffuse Correlation Spectroscopy at Short Source-Detector Separations: Simulations, Experiments and Theoretical Modeling

Diffuse correlation spectroscopy (DCS) has widely been used as a non-invasive optical technique to measure tissue perfusion in vivo. DCS measurements are quantified to yield information about moving scatterers using photon diffusion theory and are therefore obtained at long source-detector separations (SDS). However, short SDS DCS could be used for measuring perfusion in small animal models or endoscopically in clinical studies. Here, we investigate the errors in analytically retrieved flow coefficients from simulated and experimental data acquired at short SDS. Monte Carlo (MC) simulations of photon correlation transport was programmed to simulate DCS measurements and used to (a) examine the accuracy and validity of theoretical analyses, and (b) model experimental measurements made on phantoms at short SDS. Experiments consisted of measurements from a series of optical phantoms containing an embedded flow channel. Both the fluid flow rate and depth of the flow channel from the liquid surface were varied. Inputs to MC simulations required to model experiments were obtained from corrected theoretical analyses. Results show that the widely used theoretical DCS model is robust for quantifying relative changes in flow. We also show that retrieved flow coefficients at short SDS can be scaled to retrieve absolute values via MC simulations.

Efficient estimation of subdiffusive optical parameters in real time from spatially resolved reflectance by artificial neural networks.

Subdiffusive reflectance captured at short source-detector separations provides increased sensitivity to the scattering phase function and hence allows superficial probing of the tissue ultrastructure. Consequently, estimation of subdiffusive optical parameters has been the subject of many recent studies focusing on lookup-table-based (LUT) inverse models. Since an adequate description of the subdiffusive reflectance requires additional scattering phase function related optical parameters, the LUT inverse models, which grow exponentially with the number of estimated parameters, become excessively large and computationally inefficient. Herein, we propose, to the best of our knowledge, the first artificial-neural-network-based inverse Monte Carlo model that overcomes the limitations of the LUT inverse models and thus allows efficient real-time estimation of optical parameters from subdiffusive spatially resolved reflectance. The proposed inverse model retains the accuracy, is about four orders of magnitude faster than the LUT inverse models, grows only linearly with the number of estimated optical parameters, and can be easily extended to estimate additional optical parameters.

Modeling subdiffusive light scattering by incorporating the tissue phase function and detector numerical aperture

To detect small-scale changes in tissue with optical techniques, small sampling volumes and, therefore, short source–detector separations are required. In this case, reflectance measurements are not adequately described by the diffusion approximation. Previous studies related subdiffusive reflectance to ? or ? , which parameterize the phase function. Recently, it was demonstrated that ? predicts subdiffusive reflectance better than ? , and that ? becomes less predictive for lower numerical apertures (NAs). We derive and evaluate the parameter R p NA , which incorporates the NA of the detector and the integral of the phase function over the NA in the backward and forward directions. Monte Carlo simulations are performed for overlapping source/detector geometries for a range of phase functions, reduced scattering coefficients, NAs, and source/detector diameters. R p NA improves prediction of the measured reflectance compared to ? and ? . It is, therefore, expected that R p NA will improve derivation of optical properties from subdiffusive measurements.

Adopting higher-order similarity relations for improved estimation of optical properties from subdiffusive reflectance.

Estimation of optical properties from subdiffusive reflectance acquired at short source-detector separations is challenging due to the sensitivity to the underlying scattering phase function. In recent studies, a second-order similarity parameter γ has been increasingly used alongside the absorption and reduced scattering coefficients to account for some of the phase function variability. By using Monte Carlo simulations, we show that the influence of the scattering phase function on the subdiffusive reflectance for the biologically relevant variations can be captured sufficiently well by considering γ and a third-order similarity parameter δ. Utilizing this knowledge, we construct an inverse model that estimates the absorption and reduced scattering coefficients, γ and δ, from spatially resolved reflectance. Nearly an order of magnitude smaller errors of the estimated optical properties are obtained in comparison to the inverse model that only composes γ.

Artificial neural networks for retrieving absorption and reduced scattering spectra from frequency-domain diffuse reflectance spectroscopy at short source-detector separation.

Diffuse reflectance spectroscopy (DRS) based on the frequency-domain (FD) technique has been employed to investigate the optical properties of deep tissues such as breast and brain using source to detector separation up to 40 mm. Due to the modeling and system limitations, efficient and precise determination of turbid sample optical properties from the FD diffuse reflectance acquired at a source-detector separation (SDS) of around 1 mm has not been demonstrated. In this study, we revealed that at SDS of 1 mm, acquiring FD diffuse reflectance at multiple frequencies is necessary for alleviating the influence of inevitable measurement uncertainty on the optical property recovery accuracy. Furthermore, we developed artificial neural networks (ANNs) trained by Monte Carlo simulation generated databases that were capable of efficiently determining FD reflectance at multiple frequencies. The ANNs could work in conjunction with a least-square optimization algorithm to rapidly (within 1 second), accurately (within 10%) quantify the sample optical properties from FD reflectance measured at SDS of 1 mm. In addition, we demonstrated that incorporating the steady-state apparatus into the FD DRS system with 1 mm SDS would enable obtaining broadband absorption and reduced scattering spectra of turbid samples in the wavelength range from 650 to 1000 nm.

Quantifying phase function influence in subdiffusively backscattered light.

Light backscattering at short source-detector separations is considerably influenced by the scattering phase function of a turbid medium. We seek to more precisely relate a medium's subdiffusive backscattering to the angular scattering characteristics of its microstructure. First, we demonstrate the inability of the scattering asymmetry g1 = < cos θ > to predict phase function influence on backscattering and reveal ambiguities related to the established phase function parameter γ. Through the use of high-order similarity relations, we introduce a new parameter that more accurately relates a scattering phase function to its subdiffusive backscattering intensity. Using extensive analytical forward calculations based on solutions to the radiative transfer equation in the spatial domain and spatial frequency domain, we demonstrate the superiority of our empirically derived quantifier σ over the established parameter γ.

On the geometry dependence of differential pathlength factor for near-infrared spectroscopy. I. Steady-state with homogeneous medium.

This work analytically examines some dependences of the differential pathlength factor (DPF) for steady-state photon diffusion in a homogeneous medium on the shape, dimension, and absorption and reduced scattering coefficients of the medium. The medium geometries considered include a semi-infinite geometry, an infinite-length cylinder evaluated along the azimuthal direction, and a sphere. Steady-state photon fluence rate in the cylinder and sphere geometries is represented by a form involving the physical source, its image with respect to the associated extrapolated half-plane, and a radius-dependent term, leading to simplified formula for estimating the DPFs. With the source-detector distance and medium optical properties held fixed across all three geometries, and equal radii for the cylinder and sphere, the DPF is the greatest in the semi-infinite and the smallest in the sphere geometry. When compared to the results from finite-element method, the DPFs analytically estimated for 10 to 25 mm source–detector separations on a sphere of 50 mm radius with μa=0.01 mm(−1) and μ′s=1.0 mm(−1) are on average less than 5% different. The approximation for sphere, generally valid for a diameter≥20 times of the effective attenuation pathlength, may be useful for rapid estimation of DPFs in near-infrared spectroscopy of an infant head and for short source–detector separation.

Pressure modulation algorithm to separate cerebral hemodynamic signals from extracerebral artifacts.

We introduce and validate a pressure measurement paradigm that reduces extracerebral contamination from superficial tissues in optical monitoring of cerebral blood flow with diffuse correlation spectroscopy (DCS). The scheme determines subject-specific contributions of extracerebral and cerebral tissues to the DCS signal by utilizing probe pressure modulation to induce variations in extracerebral blood flow. For analysis, the head is modeled as a two-layer medium and is probed with long and short source-detector separations. Then a combination of pressure modulation and a modified Beer-Lambert law for flow enables experimenters to linearly relate differential DCS signals to cerebral and extracerebral blood flow variation without a priori anatomical information. We demonstrate the algorithm's ability to isolate cerebral blood flow during a finger-tapping task and during graded scalp ischemia in healthy adults. Finally, we adapt the pressure modulation algorithm to ameliorate extracerebral contamination in monitoring of cerebral blood oxygenation and blood volume by near-infrared spectroscopy.

Multiregional functional near-infrared spectroscopy reveals globally symmetrical and frequency-specific patterns of superficial interference.

Linear regression with short source-detector separation channels (S-channels) as references is an efficient way to overcome significant physiological interference from the superficial layer for functional near-infrared spectroscopy (fNIRS). However, the co-located configuration of S-channels and long source-detector separation channels (L-channels) is difficult to achieve in practice. In this study, we recorded superficial interference with S-channels in multiple scalp regions. We found that superficial interference has overall frequency-specific and globally symmetrical patterns. The performance of linear regression is also dependent on these patterns, indicating the possibility of simplifying the S-channel configurations for multiregional fNIRS imaging.

Efficient construction of robust artificial neural networks for accurate determination of superficial sample optical properties

In general, diffuse reflectance spectroscopy (DRS) systems work with photon diffusion models to determine the absorption coefficient μa and reduced scattering coefficient μs' of turbid samples. However, in some DRS measurement scenarios, such as using short source-detector separations to investigate superficial tissues with comparable μa and μs', photon diffusion models might be invalid or might not have analytical solutions. In this study, a systematic workflow of constructing a rapid, accurate photon transport model that is valid at short source-detector separations (SDSs) and at a wide range of sample albedo is revealed. To create such a model, we first employed a GPU (Graphic Processing Unit) based Monte Carlo model to calculate the reflectance at various sample optical property combinations and established a database at high speed. The database was then utilized to train an artificial neural network (ANN) for determining the sample absorption and reduced scattering coefficients from the reflectance measured at several SDSs without applying spectral constraints. The robustness of the produced ANN model was rigorously validated. We evaluated the performance of a successfully trained ANN using tissue simulating phantoms. We also determined the 500-1000 nm absorption and reduced scattering spectra of in-vivo skin using our ANN model and found that the values agree well with those reported in several independent studies.

Virtual-source diffusion approximation for enhanced near-field modeling of photon-migration in low-albedo medium.

Most analytical methods for describing light propagation in turbid medium exhibit low effectiveness in the near-field of a collimated source. Motivated by the Charge Simulation Method in electromagnetic theory as well as the established discrete source based modeling, we herein report on an improved explicit model for a semi-infinite geometry, referred to as "Virtual Source" (VS) diffuse approximation (DA), to fit for low-albedo medium and short source-detector separation. In this model, the collimated light in the standard DA is analogously approximated as multiple isotropic point sources (VS) distributed along the incident direction. For performance enhancement, a fitting procedure between the calculated and realistic reflectances is adopted in the near-field to optimize the VS parameters (intensities and locations). To be practically applicable, an explicit 2VS-DA model is established based on close-form derivations of the VS parameters for the typical ranges of the optical parameters. This parameterized scheme is proved to inherit the mathematical simplicity of the DA approximation while considerably extending its validity in modeling the near-field photon migration in low-albedo medium. The superiority of the proposed VS-DA method to the established ones is demonstrated in comparison with Monte-Carlo simulations over wide ranges of the source-detector separation and the medium optical properties.

Effects of time-gated detection in diffuse optical imaging at short source-detector separation

The adoption of a short source-detector distance, combined with a time-resolved acquisition, can be advantageous in diffuse optical imaging due to the stricter spatial localization of the probing photons, provided that the strong burst of early photons is suppressed using a time-gated detection scheme. We propose a model for predicting the effect of the time-gated measurement system using a time-variant operator built on the system response acquired at different gate delays. The discrete representation of the system operator, termed Spread Matrix, can be analyzed to identify the bottlenecks of the detection system with respect to the physical problem under study. Measurements performed on tissue phantoms, using a time-gated single-photon avalanche diode and an interfiber distance of 2 mm, demonstrate that inhomogeneities down to 3 cm can be detected only if the decay constant of the detector is lower than 100 ps, while the transient opening of the gate has a less critical impact.

Spatial resolution in depth for time-resolved diffuse optical tomography using short source-detector separations.

Diffuse optical tomography for medical applications can require probes with small dimensions involving short source-detector separations. Even though this configuration is seen at first as a constraint due to the challenge of depth sensitivity, we show here that it can potentially be an asset for spatial resolution in depth. By comparing two fiber optic probes on a test object, we first show with simulations that short source-detector separations improve the spatial resolution down to a limit depth. We then confirm these results in an experimental study with a state-of-the-art setup involving a fast-gated single-photon avalanche diode allowing maximum depth sensitivity. We conclude that short source-detector separations are an option to consider for the design of probes so as to improve image quality for diffuse optical tomography in reflectance.

RLS adaptive filtering for physiological interference reduction in NIRS brain activity measurement: a Monte Carlo study

The non-invasive measurement of cerebral functional haemodynamics using near-infrared spectroscopy (NIRS) instruments is often affected by physiological interference. The suppression of this interference is crucial for reliable recovery of brain activity measurements because it can significantly affect the signal quality. In this study, we present a recursive least-squares (RLS) algorithm for adaptive filtering to reduce the magnitude of the physiological interference component. To evaluate it, we implemented Monte Carlo simulations based on a five-layer slab model of a human adult head with a multidistance source–detector arrangement, of a short pair and a long pair, for NIRS measurement. We derived measurements by adopting different interoptode distances, which is relevant to the process of optimizing the NIRS probe configuration. Both RLS and least mean squares (LMS) algorithms were used to attempt the removal of physiological interference. The results suggest that the RLS algorithm is more capable of minimizing the effect of physiological interference due to its advantages of faster convergence and smaller mean squared error (MSE). The influence of superficial layer thickness on the performance of the RLS algorithm was also investigated. We found that the near-detector position is an important variable in minimizing the MSE and a short source–detector separation less than 9 mm is robust to superficial layer thickness variation.