A comprehensive overview of diffuse correlation spectroscopy: theoretical framework, recent advances in hardware, analysis, and applications

Diffuse correlation spectroscopy (DCS) is a powerful tool for assessing microvascular hemodynamic in deep tissues. Recent advances in sensors, lasers, and deep learning have further boosted the development of new DCS methods. However, newcomers might feel overwhelmed, not only by the already complex DCS theoretical framework but also by the broad range of component options and system architectures. To facilitate new entry into this exciting field, we present a comprehensive review of DCS hardware architectures (continuous-wave, frequency-domain, and time-domain) and summarize corresponding theoretical models. Further, we discuss new applications of highly integrated silicon single-photon avalanche diode (SPAD) sensors in DCS, compare SPADs with existing sensors, and review other components (lasers, fibers, and correlators), as well as new data analysis tools, including deep learning. Potential applications in medical diagnosis are discussed, and an outlook for the future directions is provided, to offer effective guidance to embark on DCS research.

Effective real-time BF monitoring can aid in the diagnosis and management of broad range of medical conditions such as stroke, traumatic or hypoxic-ischemic encephalopathy (HIE) (Weigl et al., 2016;Durduran et al., 2004), neurological disorders, cardio-cerebral diseases, cancer treatment strategies, tissue perfusion in peripheral vascular diseases (Ma et al., 2019), brain health/functions (Duncan et al., 1996), wound healing, sepsis and shock (Becker et al., 2004), skeletal muscle (Gurley et al., 2012) injuries or tissue viability during surgeries.
Available real-time BF measurement tools are predominantly Doppler ultrasound based.However, Doppler ultrasonography requires a highly-skilled operator at the bedside and is operator-dependent (Tupprasoot and Blaise, 2023).Cerebral perfusion can be mapped using medical imaging scanners, including positron emission tomography (PET) (Vaquero and Kinahan, 2015), single photon emission computed tomography (SPECT) (Ljungberg and Pretorius, 2018), xenon-enhanced computed tomography (XeCT) (Yonas et al., 1996), dynamic susceptibility contrast magnetic resonance imaging (DSC-MRI) (Kwong et al., 1992), and arterial spin labelling MRI (ASL-MRI) (Barbier et al., 2001;Durduran et al., 2010;Yu et al., 2007).However, these techniques only provide 'snapshot' observations, are inappropriate for continuous monitoring, and typically require moving patients to imaging suites, which is unpractical for many patients.Additionally, a supine scan is necessary for MRI, PET and CT techniques.Further, PET, SPECT, and CT present additional risks of radiation exposure.Laser Doppler flowmetry (LDF) (Shepherd and Öberg, 2013) is another perfusion technique, but it can only measure superficial tissue blood flow; thus, tissue samples must be thin to permit adequate sampling.Thus, there is a critical need to develop bedside techniques that are free from the limitations mentioned above and can noninvasively monitor microvascular BF in deep tissue at the bedside with a high sampling rate and at a low cost.For a thorough comparison of the modalities mentioned above, readers can refer to previous reviews (Durduran and Yodh, 2014;Fantini et al., 2016;Wintermark et al., 2005).
Diffuse light correlation techniques, on the other hand, are rooted in the fundamental principles of dynamic light scattering (DLS).These methods, sometimes called 'quasi-elastic light (QELS) scattering' techniques (Berne and Pecora, 1990;Chu, 1991;Clark et al., 1970;Van de Hulst, 1981), measure light intensity fluctuations scattered from samples to observe motions of sample constituents, e.g., Brownian motions of particles or macromolecules.Conventionally, DLS can provide detailed information about the dynamics of scattering media by using photon correlation techniques to analyze scattered light fluctuations (Berne and Pecora, 2000).However, QELS belongs to the single-scattering regime (Clark et al., 1970;Fuller et al., 1980) and is unsuitable for turbid media in which the incident light is scattered multiple times.In 1987, Maret and Wolf (Maret and Wolf, 1987) reported experimental measurements of the intensity autocorrelation function in the multiple-scattering regime and suggested a simple method for analyzing the measurements.One year later, Stephen derived a theoretical framework that extends QELS to the multiple-scattering regime (Stephen, 1988).
A diagram of the history of DCS development is shown in Fig. 1(a).Fig. 1(b) displays the number of DCS publications over the past 20 years, with more than 400 publications to date (we only counted articles containing "DCS").Fig. 1(c) presents DCS measurements from human brain tissue, organizing current studies by ρ (x-axis) and the blood flow sampling rate (y-axis).It highlights the trend of using parallel or multispeckle and interferometric DCS for higher sampling rates at a larger ρ and indicates the required penetration depth.
Fig. 2 illustrates the principle of DCS.Briefly, a long-coherence laser emits NIR light through an optical fiber to the tissue, Fig. 2(a), and the recorded light intensity exhibits temporal fluctuations, Fig. 2(b).These fluctuations are attributed to the motion of moving scatterers, such as red blood cells (RBC).To quantify the motion of RBC, a hardware or software correlator calculates the normalized intensity autocorrelation, g 2 (τ) as shown in Fig. 2(c).Typically, DCS systems are implemented in a reflection geometry, where a source and a detector are placed at a finite distance, ρ.Photons travelling from the source to the detector follow a "banana-shaped", stochastic scattering profile, as shown in Fig. 2(d), where the penetration depth of these DCS instruments is roughly between ρ/3 ∼ ρ/2) (Buckley et al., 2014).Fig. 2(c) and (e) show that the g 2 (τ) curves decay faster with increased flow or ρ.The slope or the decay rate provides information about the optical properties and the motion of the scatters.The largest ρ in the current state-of-the-art is 4 cm, corresponding to a depth of about 2 cm (Kreiss et al., 2024;Mattioli della Rocca et al., 2024).
Although there have been around 15 review DCS papers (Durduran and Yodh, 2014;Fantini et al., 2016;Buckley et al., 2014;Mesquita et al., 2011;Yu, 2012;Yu, 2012;Zhou et al., 2022;Ayaz et al., 2022;Li et al., 2022;Carp et al., 2023;James and Munro, 2023;Durduran et al., 2010;Lee, 2020;Shang et al., 2017;Bi et al., 2015) in the last two decades, new approaches have emerged, including theoretical layered models, artificial intelligence (AI) methods for DCS analysis, and the use of novel sensors like highly integrated complementary metal-oxide-semiconductor (CMOS) single-photon avalanche diodes (SPAD) cameras.These aspects were not covered in previous reviews, which is why this review summarizes and systematically compares various analytical layered models, including continuous-wave (CW)-, time-domain (TD)-DCS, AI-enhanced DCS analysis methods, as well as the use of SPAD cameras in DCS.Furthermore, we also derived analytical models for the frequency domain (FD)-DCS, which was newly introduced in 2022 (Moka et al., 2022).The main contributions of this review include: • We thoroughly derive and compare different layered analytical models used in CW-, TD-, and FD-DCS, highlighting their strengths and applications (Section 2).• Section 3.3 examines new applications of CMOS SPAD cameras and compares them with existing sensors used in DCS.. • Section 3.5 compares TD-DCS and CW-DCS systems and emphasizes the benefits of TD-DCS and its potential for future development.
• We discuss novel AI-enhanced DCS analysis strategies, addressing their effectiveness and potential (Section 4).• Discussion and outlooks are provided in Section 6.
This review aims to serve as a practical information resource for researchers and newcomers venturing into the field, offering a clearer understanding of the evolving DCS landscape and equipping them with the necessary knowledge to navigate it effectively.Q. Wang et al. NeuroImage 298 (2024) 120793

Theory background
The propagation of light in highly scattering media such as biological tissues can be characterized by an absorption coefficient μ a and a reduced scattering coefficient μ ʹ s using the radiative transfer equation (RTE) (Durduran et al., 2010).Similarly, to study the photon propagation under dynamic scatterers, the correlation transport equation (CTE) (Durduran and Yodh, 2014;Mesquita et al., 2011) is adopted to obtain the field (electrical) autocorrelation function G 1 (τ) under general conditions of photon migration.The primary difference between the CTE and RTE lies in the fact that CTE describes the time-dependent specific intensity, reflecting an angular spectrum of the mutual coherence function.In the NIR spectral window, the unnormalized G 1 (τ) can be expressed as, G T 1 (r, Ω,τ) = 〈E(r, Ω,t)⋅E * (r, Ω,t + τ)〉, where 〈⋅⋅⋅〉 denotes a time average.E(r, Ω, t) is the electric field at the position r and time t propagating in the Ω direction, inside the tissue that can be described by CTE (Ackerson et al., 1992;Dougherty et al., 1994;Boas and Yodh, 1997) applicable for CW systems analogous to RTE: where μ t = μ s + μ a is the transport coefficient.S(r, Ω) is the source distribution; g s 1 ( Ω, Ωʹ , τ) is the normalized field correlation function for single scattering; and f( Ω, Ωʹ ) is the normalized differential cross-section.
For a time dependent source, Eq. ( 1) becomes: where v is the light speed in the medium.DCS BF measurements can be analyzed using the correlation diffusion equation (CDE) (Durduran and Yodh, 2014;Boas et al., 1995), derived from CTE using the standard diffusion approximation.The derivation procedure is summarized in Fig. 3.
Furthermore, DCS instruments can be divided into three categories according to the light illumination strategy.The most straightforward approach is employing a CW laser, as the instrumentation is relatively simple.The frequency-domain approach utilizes an amplitudemodulated laser, with the modulation frequency set to a radiofrequency (RF) ranging (from tens to a thousand MHz).In contrast, the time-domain (TD) approach uses a short pulse laser and measures the delayed and temporally broadened output pulse.Time domain measurements have the most information content; however, they are more complex and expensive than the other two methods.
The depth sensitivity of the DCS measurements can be improved using advanced techniques, such as TD-and FD-DCS.However, it may not be sufficient to minimize the superficial layer contamination.For this aim, different analytical models have been introduced to account for the contribution of the individual layers.These models typically include parameters of the optical system (e.g., the wavelength) and presumptions of optical tissue properties (e.g., μ a , μ ʹ s , n) to fit mathematical models to the measurements.A summary of the analytical models commonly used in DCS analysis is shown in Fig. 4.

CW Semi-infinite homogenous (one layer) model
In traditional DCS systems, the tissue is commonly considered a homogenous semi-infinite medium, as shown in Fig. 4(a).Under the standard diffusion approximation (Boas, 1996), we reduce Eq.(1) to CDE as: where ) is the photon diffusion coefficient, v is the speed of light in the medium, and μ ʹ s = μ s (1 − g) is the reduced scattering coefficient, where g ≡ 〈cosθ〉 (ranging from -1 to 1) is the scattering anisotropy factor.k 0 is the wavenumber in the medium, α represents the probability that a light scattering event is with a moving scatterer (e.g., a flowing red blood cell (RBC)), and 〈 Δr 2 (τ) 〉 represents the mean square displacement of moving scatterers, and is commonly described using two different models, including the Brownian motion and random ballistic models in biological tissues.For the Brownian motion, 〈 Δr 2 (τ) 〉 = 6D B τ (Maret and Wolf, 1987), where D B is an 'effective' diffusion coefficient for moving particles.For random ballistic flow, , where V 2 is the mean square velocity of the scatterer in the vasculature.The relationships between the RBC movements and the flow models (random ballistic flow and Brownian motion) have already been investigated (Boas et al., 2016;Zhu et al., 2020;Sie et al., 2020).
In particular, for a semi-infinite, homogenous system with a point source S(r) = S 0 δ(r), G 1 (r, τ) is the solution of Eq. (3), obtained using an image source approach following Kienle and Patterson (Kienle and Patterson, 1997) as, where , r 1 and r 2 are the distances between the detector and the source/image source, respectively.

CW two-layer model
We have stated above that the DCS theory is based on the correlation transport (Boas et al., 1995;Ackerson et al., 1992; Dougherty et al., Q. Wang et al. NeuroImage 298 (2024) 120793 1994), approximated by CDE (Boas andYodh, 1997, Boas, 1996).By assuming that light propagates in a homogenous medium, the simple solution of Eq. ( 3) has been widely used in the DCS community (Durduran, 2004).However, biological tissues (Kienle et al., 1998) are usually layered encompassing unique physiological and optical properties (Gagnon et al., 2008b, Lesage et al., 2008).For example, the simple two-layer model is useful in cerebral blood flow monitoring in newborns, especially preterm infants, because their skull and scalp are relatively thin, allowing clear differentiation between the superficial scalp layer and the deeper brain tissue layer.We assume that an infinitely thin beam shines the turbid two-layered medium.The first layer of the two-layer medium has a thickness Δ 1 , and the second layer is semi-infinite.The beam is scattered isotropically in the upper layer at a depth of z = z 0 , where z 0 = 1/ ( . We also assume that the Brownian movement is independent in each layer, meaning that the particles can not move from one layer to another in the medium.The incident light is perpendicular to the surface of the turbid medium (on the x-y plane).Then Eq. (3) becomes: ( where Although Kienle et al.'s derivations (Kienle et al., 1998;Kienle and Glanzmann, 1999;Kienle et al., 1998) are initially for diffuse reflectance spectroscopy (DRS), we re-derive them for DCS following the same procedure and obtain the solution of Eqs. ( 5) and ( 6) at z = 0 (Layer 1) in the Fourier domain by where ) /D j , j =1 and 2, q is the radial spatial frequency and And G 1 1 (ρ, z = 0, τ) at r = {ρ, z = 0} on the medium surface is then obtained from the inverse spatial Fourier transform as, where J 0 stands for the zeroth order Bessel function of the first kind computed by the MATLAB function besselj.
The field autocorrelation at the tissue surface, G 1 (r, z = 0, τ), can be obtained by solving Eq. ( 10) in the Fourier domain with respect to ρ as: where q is the radial spatial frequency.Thus, in the Fourier domain Eq. ( 10) can be rewritten: where κ 2 We divided the top layer into two sublayers: Sub-layer 0 (0 < z < z ʹ ) identified by p = 0, and Sub-layer 1 (z ʹ < z < L 1 ), identified by p hereafter.The solution of Eq. ( 12) at Layer p (p = 1, 2, 3) can be written as: where A p and B p are constant factors for Layer p determined by the boundary conditions: where s are the extrapolation lengths taking into account internal reflections at external (z = 0 and z = L 4 ) boundaries.
By performing the inverse Fourier transform of Eq. ( 15) with respect to q, Ĝ0 (q, z, τ) can be obtained as: where J 0 denotes the first-kind zero-order Bessel function.This three-layered solution has been tested with Monte Carlo simulations and used to analyze in vivo measurements (Verdecchia et al., 2016;Zhao et al., 2021;Zhao et al., 2023).The three-layer model can be used in monitoring cerebral blood flow in adults, particularly in clinical settings such as during surgery or in intensive care units because it is necessary to account for scalp, skull, and brain tissues, which can significantly affect light propagation and DCS signals.
Fig. 5(a), (b), and (c) show g 1 curves for semi-infinite, two-, and three-layer analytical models, respectively.Typically, in DCS data analysis, the measured g 2 is fitted with one of the models shown in Fig. 4, using the Siegert relation g 2 (τ) = 1 + βg 2 1 (τ).Usually, the homogenous semi-infinite analytical model is used in data analysis, assuming free diffusion for speckle decorrelation, giving rather poor agreement with experimental scenarios.This is because homogeneous fitting is more sensitive to the dynamic properties of the superficial layers.Compared with the semi-infinite model, two-and three-layered models can separate the signal between the superficial and brain layers.The layered models can mitigate the discrepancies between the one-layer model and realistic tissues.The accuracy of the three-layer analytical model has been investigated in previous studies (Mesquita et al., 2011;Li et al., 2005;Zhao et al., 2021).Although multi-layered models provide a superior fit to measured data and are more accurate, they are susceptible to measurement noise, and much longer BFi estimation time is needed (Wang et al., 2024).
(21) However, it is not easy to measure the pathlength of a photon in tissues.Therefore, the total scattered electric-field autocorrelation function g 1 (τ, s) is obtained by incoherently summing the contributions over all s (Maret and Wolf, 1987;Yodh et al., 1990).Thus g 1 (τ, s) is a weighted average over all possible pathlengths as: where P(s) represents the probability that an incident photon travels a distance s before emerging from the medium; it can be calculated as (Kienle and Patterson, 1997): where the variables are the same as in Eq. ( 4) and s = vt, with t being the photon time-of-flight (ToF) and v the speed of light in the medium.By employing a sufficiently narrow time gate, Eq. ( 22) can be simplified, and the normalized time-gated g 1 (τ) is modelled by a single exponential term: Then g 2 (τ) can be linked to g 1 (τ)through the Siegert relation:

TD two-layer model
For the second layer model, Eq. ( 19) can be rewritten: Similarly, we can derive the Fourier transform of G(r, τ, t) for the real space (ρ,z), as well as time t, and then solve Eq. ( 26) in the Fourier space (q, z, w).
Ĝ(q, z, w, τ) The solution of Eq. ( 28) can be written as: where , γ p and φ p are constant for Layer p (p = 1, 2), determined by the boundary conditions: Thus, we can obtain the solution of Eq. ( 28): The inverse Fourier transform for G(ρ, z, t, τ) at z = 0 is:
(35) Fig. 6 displays the numerical simulation g 1 for time-domain DCS from the semi-infinite, two-, and three-layer analytical models.Fig. 6(a) is g 1 (τ) for the early gate and late gate;

Frequency domain semi-infinite model
We also obtain G 1 (ρ, ω, τ) when modulated illumination is used, G 1 (ρ, ω, τ) follows a slightly different CDE as: where ω is the source modulation frequency and s 0 e − iωt is the modulated source term.For a semi-infinite homogeneous tissue, the solution of Eq. ( 36) is given by where is the frequencydependent wave vector.The other parameters are the same as before.Fig. 7 shows g 1 (τ) for the FD semi-infinite model.By fitting the measurement data from FD-DCS systems to Fig. 7, we can extract optical properties (μ a and μ ʹ s ) and blood flow simultaneously by multi-frequency measurements.In contrast, the traditional CW-DCS system is only used for blood flow measurements.Another merit is that the laser source for FD-DCS is much cheaper than CW-DCS and TD-DCS systems.There are two reasons: 1) FD-DCS removes the necessity for collocating the source and phase-sensitive detectors; 2) FD-DCS can be executed by simply substituting the source of a traditional DCS system with an intensitymodulated coherent laser.
Although the two-and three-layer theoretical DCS models shown in Fig. 4 have improved the SNR, those with regular tissue boundaries (including the simi-infinite model) may lead to BFi estimation errors in small-volume tissues with large curvatures.To address this, Shang et al. developed an Nth-order linear model that can accurately extract BFi without tissue volume and geometry restrictions.They demonstrated the algorithm's accuracy with computational simulations and in vivo experiments.Interested readers can consult the referenced studies (Shang et al., 2014;Shang and Yu, 2014;Zilpelwar et al., 2022) for more details.38), assuming an 8.05 kcps at 785 nm (Carp et al., 2010), at different noise levels with T int = 1 s (green line) and T int = 10 s (blue line).

Noise model
In most simulation reports (Dong et al., 2013;Carp et al., 2020;Mazumder et al., 2021;Irwin et al., 2011), a proper estimate of measurement noise is needed to reflect practical scenarios.A noise model suitable for photon correlation measurements was previously developed for a single scattering limit (Schätzel, 1983;Koppel, 1974).Later on, the noise model developed by Koppel (Koppel, 1974) for fluorescence correlation spectroscopy (FCS) in the single scattering limit was introduced into DCS in 2006 (Zhou et al., 2006).In DCS, the noise comes from photon counting statistics (Schätzel, 1983), and it has been derived (Zhou et al., 2006) with the standard deviation of (g 2 (τ) − 1), σ(τ) estimated as: where T is the frame exposure time (equal to the correlator bin time interval).T int is the integration time (measurement duration) or the measurement time window.τ c is the speckle correlation time.〈M〉 (〈M〉 = IT, where I is the detected photon count rate) is the average number of photons within bin time T, m is the bin index.To obtain τ c , g 2 (τ) usually approximated with a single exponential function as g 2 (τ) ≈ 1 + βexp(− τ/τ c ) under the Brownian motion model (Zhou et al., 2006).Once τ c is obtained, we can obtain σ(τ).This noise model was then adopted by (Sie et al., 2020;Cheng et al., 2021;Helton et al., 2023;Zhang et al., 2018).nm was assumed to be 8.05 kcps (Carp et al., 2020) at ρ of 30 mm.In Fig. 8, the DCS measurement noise decreases as τ increases.

Instrumentation
A DCS system consists of a laser source, source/detection fibers and sensors.Fig. 9 shows a schematic of the representative systems for CW-, TD-, FD-, and Hybrid DCS systems.Fig. 9(a) and (b) are for CW-and TD-DCS systems, respectively.The primary difference lies in the pulsed laser (Ti:Sa laser) in the TD system.Fig. 9(c) showcases the schematic of FD-DCS system, representing the latest DCS technology in the frequency domain.Lastly, Fig. 9(d) presents a typical hybrid DCS system.To date, very few companies have initiated commercialization of DCS systems, including HemoPhotonics S.L. (http://www.hemophotonics.com),and ISS Inc. (https://iss.com/biomedical/metaox).

Lasers
There are three types of laser used in DCS: CW, modulated, and pulsed lasers corresponding to CW-, FD- Moka et al., 2022), and TD-DCS systems.As was mentioned above, the estimated BFi is derived from intensity fluctuations of the speckle pattern of back scattered light from the tissue surface, and the bright and dark patterns arise because photons emerging from the sample have travelled along different paths that interfere constructively and destructively at different detector positions (Durduran and Yodh, 2014;Durduran et al., 2010;Maret and Wolf, 1987).Consequently, one of the main challenges is to select a laser with Q. Wang et al. NeuroImage 298 (2024) 120793 a long coherence length (Maret and Wolf, 1987), l c , designated by Eq. ( 39) assuming that the measured power spectral density has a Gaussian profile (Bigio and Fantini, 2016), where λ is the central wavelength and Δλ is the optical bandwidth.The diffusion theory and Monte Carlo simulations of light transport show that the minimum coherence length must be longer than the width of the photon path-length distribution (Bellini et al., 1991), typically around 5ρ ∼ 10ρ (e.g., 100 mm for ρ = 10mm) (Biswas et al., 2021).For homodyne measurements, the coherence length needs to be substantially longer than the spread of pathlengths in tissue (which is within an order of ρ), and in heterodyne, care needs to be taken that the difference in length of the reference vs. sample arms, when summed with the expected pathlength variation, should also be substantially lower than the laser coherence length.Therefore, generally, the minimum coherence length is recommended as l c, min ≫10ρ ∼ 15ρ, and since most practical DCS systems utilize ρ ∼ 3 cm (Durduran and Yodh, 2014;Carp et al., 2020;Kim et al., 2010), the coherence length should be 35∼ 50 cm, accounting for the variations of differential pathlength distances (Delpy et al., 1988).
For clinical applications, the laser power should comply with the American National Standard for Safe Use of Lasers (ANSI) (Institute, 2007) limit for safe skin exposure with an proper irradiance.Spacers or prisms (Biswas et al., 2021;Zavriyev et al., 2021;Wu et al., 2023;Lee et al., 2019) are often between source fiber and sample to illuminate a larger area, which allows a higher laser power (more photons) while maintaining the same maximal permissible exposure (MPE) limit for intensity.Typically, lasers with wavelengths of 670 nm (Liu et al., 2021), 760nm (Samaei et al., 2021), 785 nm (Biswas et al., 2021;Huang et al., 2016), 850 nm (James and Munro, 2023;Zauner et al., 2002;Maret and Wolf, 1987;Carp et al., 2017), or 1064 nm (Carp et al., 2020) are employed.Although NIR wavelengths provide a higher number of photons for the same output power (P = E/t = h c / λ, E is photon energy), a higher MPE (more photons) and a deeper penetration depth, the photon detection efficiency (PDE) of most detectors is typically reduced for longer wavelengths.As a result, 785 nm and, more recently, 850 nm lasers are the most prevalent choice for most DCS techniques.This trade-off between the laser and the detector PDE is discussed in detail below.
Regarding TD-DCS, we can pinpoint the photons (either through gating or time-correlated single-photon counting (Wahl and GmbH, 2009)) that exhibit a similar path length in the tissue to provide depth-resolved information.This allows relaxing the requirement for a high coherence length compared with the scenario in which all the photon paths are considered.Moreover, the laser pulse width limits the maximum coherence length for a pulsed laser.Usually, a narrow laser pulse is preferable for precise depth-resolved measurements, however, a narrow pulse means a lower l c , meaning a g 2 curve is closer to the noise floor.Therefore, there is a trade-off between l c and the pulse width (Tamborini et al., 2019).In fact, g 2 ʹ s maximum amplitude depends on l c , with β ranging from 0 for incoherence light to 1 for linearly polarized light (Ferreira et al., 2020) (0.5 for unpolarized light) with l c longer than the longest photon path.Therefore, the main limitation of the broad use of TD-DCS is the availability of an ideal pulsed laser considering power settings, pulse width, coherence, stability, and robustness.To obtain a more in-depth investigation, readers can check Refs.Samaei et al. (2021), Tamborini et al. (2019), Ozana et al. (2022).In Table 1, we extend the conclusions made by Samaei et al. (2021), Ozana et al. (2022) and Tamborini et al. (2019) to show the relevant parameters of pulse lasers.

Source and detection fibers
In DCS experiments, a pair of source and detection fibers are strategically placed on the tissue surface, with a separation of ρ (ranging from millimeters to centimeters).The laser emits long-coherence light through the source fiber into tissues, and the fiber collects the scattered light to a sensor.This distance ρ then defines the extent of the scattering paths of all detected photons, and thereby, the maximal measurement depth of DCS, as illustrated above in Fig. 2(d).The diagrams in Fig. 10 (a)-(c) illustrate three fibers with distinct modes, namely single-mode, few-mode, and multi-mode.Usually, a multi-mode fiber (core diameter D = 62.5, 200, 400, 600, 1000 μm) (Dong et al., 2012;Ozana et al., 2022;Shang et al., 2011;Lin et al., 2012) is used for the source side.
Here, it should be noted that a larger diameter fiber translates to a larger illumination area allowing a higher laser power (more photons) at the same MPE limit for intensity (see Section 3.1).For the detection, previously published DCS systems used single-mode (e.g., 5 μm) (Gurley et al., 2012;Zhou et al., 2007;Dong et al., 2012;Shang et al., 2011;Cheng et al., 2012;Han et al., 2015;Stapels et al., 2016;Farzam et al., 2017;Sathialingam et al., 2018;Poon et al., 2020, Cortese et al., 2021;Cowdrick et al., 2023;Nakabayashi et al., 2023), few-mode (Li et al., 2005), or multi-mode fibers (Sie et al., 2020;Liu et al., 2021;Wayne et al., 2023;Samaei et al., 2022).Single-mode fibers are usually directly coupled to the respective detector.For parallelized DCS with SPAD arrays, multi-mode fibers are used for detection.In that case, the fiber is placed at a distance z to the detector, to match the speckle diameter (d) to the diameter of the detector's active area, according to Ref. Freund (2007) where D is the core diameter of the detection fiber.Thus, adjusting the distance between fiber and detector (z) allows controlling the speckle size on the detector and therefore the number of measured speckles per pixel.Using single-mode fibers limits the measured light intensity because only the fundamental mode of light can be transported, limiting ρ's dynamic range.Unlike conventional fibers, few-mode fibers allow not only the fundamental mode but also a few higher-order modes of light.Expanding the fiber diameter and numerical aperture (NA) in fewmode fibers to encompass multiple speckles enhances the detected signal intensity, consequently enhancing the signal-to-noise ratio (SNR).However, the multiple speckles detected by the few-mode fibers exhibit uncorrelated behaviour, and the decrease in β effectively counteracts the SNR enhancement.Finally, this flattens the autocorrelation function curve, potentially diminishing the sensitivity of DCS flow measurements  (Zhou et al., 2006, Zhou, 2007).To further increase the detected light intensity, multi-mode fibers with a larger core diameter have been used to accommodate larger sensor arrays (e.g., 5 × 5, 32 × 32, 192 × 128, 500 × 500, 512 × 512 SPAD arrays).Usually, these SPAD arrays are set up in a way (Eq.( 40)) that each pixel measures a single speckle on average.However, these detectors only have fill factors of 1-15% so there can be mismatches in the position.
Additionally, the PDE of SPAD arrays is often lower than single detectors, reducing SNR (Sie et al., 2020;Liu et al., 2021;Wayne et al., 2023;Johansson et al., 2019;Mattioli della Rocca et al., 2023).For more details on large SPAD arrays, see Section 3.3.He et al. (He et al., 2013) compared single-mode, few-mode, and multi-mode fibers on the detection side, and concluded that few-mode and multi-mode detection fibers can improve SNR compared with single-mode fibers, but it reduces β.

Sensors
Detectors are pivotal in DCS systems for accurate BF measurements, with the advances being intricately connected to the adoption of new high-efficiency massively parallel detectors.
In early DCS systems, photomultipliers (PMTs) were commonly employed for detecting single photons (Boas and Yodh, 1997;Boas et al., 1995).However, PMTs are bulky, so early systems only contain a few channels.Additionally, driving these PMTs requires a high bias voltage, at least hundreds of volts, to start the electron multiplication process.These requirements pose challenges for developing compact and portable devices.
In the last two decades, avalanche photon diodes (e.g., APDs, such as the SPCM series, Excelitas, Canada) (Irwin et al., 2011;Han et al., 2015;He et al., 2013) were used nearly exclusively in DCS systems, replacing PMTs.APDs, known for their high sensitivity, leverage an internal avalanche multiplication effect for capturing single photons.These detectors offer several benefits compared with PMTs, including lower cost, simpler operations, and a smaller size.Although APDs offer high quantum efficiency, they are prone to higher dark current and noise in low-light conditions (Lawrence et al., 2008).Additionally, these detectors are typically single-channel devices.In DCS, each speckle grain carries independent information about the dynamic scattering process.By averaging the autocorrelation signals from multiple speckles, we can enhance the SNR.However, advances in CMOS manufacturing technologies have enabled the integration of large SPAD arrays on a single chip, offering highly parallel single-photon detection.
Using SPAD arrays in a multispeckle approach directly enhances SNR, with an enhancement of the square root of the number of independent speckle measurements.Using such new sensors in DCS experiments is straightforward without increasing the setup complexity.Besides SNR and PDE, the exposure time of SPAD arrays is another critical consideration, as it defines the interval between two adjacent time lags Δτ of the autocorrelation curves.Especially for fast decay rates (e.g., at large source-detector separations or for high flow rates), the relatively slow frame rate of large SPAD arrays (3 μs for 32 × 32(Liu  Notes: iDCS stands for interferometric diffuse correlation spectroscopy; iDWS is interferometric diffusing wave spectroscopy; fiDWS presents functional interferometric diffusing wave spectroscopy; πNIRS is abbreviation of parallel interferometric near-infrared spectroscopy, ρ is source-detection separation; SNSPD stands for superconducting nanowire single-photon detectors; PDE is photon detection efficiency.et al., 2021;Sie et al., 2020;Xu et al., 2022) or 10 μs for 500 × 500 (Wayne et al., 2023)) can be a limiting factor in in vivo experiments.Another limitation of the SPAD arrays, though, is the difficulty in light coupling and the thinner active areasthus an element of the SPAD array has a sensitivity lower than a dedicated SPAD.Nevertheless, the large number of elements allows one to exceed the performance of individual SPADs.Fig. 12 shows the primary processing of a Parallelized DCS (PDCS) system (Liu et al., 2021).
Commercial CMOS cameras are also used in DCS due to their larger array sizes, higher fill factors, and lower cost.However, they do not have single-photon sensitivity.To address this, Zhou et al. (2018) employed a heterodyne detection method to enhance the signal; they also used MMFs to capture multiple speckle patterns, thereby increasing the throughput.They successfully conducted pulsatile blood flow measurements.Meanwhile, Liu et al. ( 2024) integrated a CMOS detector into a wearable, fiber-free probe, enabling the testing of CBF in neonatal pigs.Of note, the heterodyne detection approach can also be applied in SPAD-based DCS systems, where it offers at least a doubling of SNR and reduced sensitivity to dark counts and environmental light (Robinson et al., 2020).
Very recently, superconducting nanowire single-photon detectors (SNSPDs), a relatively new class of photo-detectors, have been used in TD-DCS systems (Parfentyeva et al., 2023).SNSPD has many advantages, including a high PDE of >80% at longer wavelengths (e.g., 1064 nm), and a better timing resolution (< 20 ps) (Schuck et al., 2013;Esmaeil Zadeh et al., 2021).Nevertheless, SNSPD detectors come with a high cost, necessitating cryostats to maintain an operational temperature of 2 -3.1 K (Esmaeil Zadeh et al., 2021).Moreover, their cooling time spans several hours, and they are noisy and emit a significant amount of heat, constraining their practical applicability in clinical settings.Table 2 summarizes the existing DCS systems with SPAD and representative non-SPAD sensors.
Table 2 shows the existing SPAD-DCS systems.Some SPAD are equipped with a TCSPC module, and TD-DCS systems can timetag detected photons to obtain their ToF, allowing distinguishing early and late arriving photons from fewer or more scattering events respectively, thereby enabling depth-resolved evaluation of BFi within tissues.

Correlators (incl. on-FPGA correlators)
To date, most DCS instruments employ commercial hardware correlators (Durduran et al., 2009;Munk et al., 2012;Cheung et al., 2001;Durduran et al., 2004;Sunar et al., 2007;Shang et al., 2009) to process detected signals and record the arrival of a Transistor-Transistor Logic (TTL) digital pulse for every photon from a photon counting detector.A commercial correlator (Diop et al., 2011), for example, uses the distribution of arrival times to quantify the temporal fluctuation of detected intensity.Traditionally, correlators embed a multi-τ processor (Schätzel et al., 1988;Schatzel, 1990;Schätzel, 1987) to compute the autocorrelation functions over a long delay period; this design was derived from early experiments in DLS (Cipelletti and Weitz, 1999) and diffusing wave spectroscopy (DSW) (Dietsche et al., 2007), primarily conducted on non-biological samples.
There are two kinds of hardware digital correlators, linear and multiτ correlators, as shown in Fig. 13.Usually, the multi-τ framework is based on a logarithmic spacing spanning a massive lag-time range with a small number of channels without substantial sampling errors.Additionally, the multi-τ scheme significantly reduces the computational load compared with linear correlators.Although hardware correlators can operate at a faster sampling speed and offer real-time computing with a wide lag time dynamic range, they are relatively costly and not  flexible since the fixed number of bits per channel results in a fixed lag time scale.Meanwhile, software correlators (Magatti and Ferri, 2001;Magatti and Ferri, 2003) have also been developed.For example, Dong et al. (2012) proposed a fast Fourier transform (FFT)-based software correlator in 2012, reaching a sampling rate of ~400 kHz.In 2016, Wang et al. (2016) designed another software correlator using the shift-and-add method, and the temporal resolution can be 50 ~100 Hz.
Compared with Dong's FFT correlator, Wang's correlator is less memory intensive.Although they show comparable performances to commercial hardware correlators and have notable flexibility, cost-effectiveness and adaptability advantages, they require high-performance processors for real-time data analysis.As a result, field programmable gate array (FPGA) based correlators (Mattioli della Rocca et al., 2023;Moore and Lin, 2022;Moore et al., 2024) are becoming popular, as they significantly increase computational power, making low-cost real-time applications possible.For most DCS applications with SPAD arrays, the autocorrelations are usually post-processed (Wayne et al., 2023;Johansson et al., 2019;Sie et al., 2020;Liu et al., 2021) and on-FPGA solutions (Mattioli della Rocca et al., 2023) are trendy.Table 3 shows the existing commercial correlators.

Comparison between CW-, TD-and FD-DCS
Conventionally, enhancing depth sensitivity in CW-DCS measurements involves using a larger ρ.This allows detecting photons with longer pathlengths.An inherent drawback of this approach is the reduced detection of photons at a large ρ, reducing the SNR of g 2 .
Although Yodh et al. (1990) have demonstrated pathlength-resolved DCS, their method required nonlinear optical gating and high laser powers, which are unsuitable for in vivo applications.Sutin et al. (2016) first reported a novel time-domain (or pathlength-resolved) DCS on phantoms and a rat brain, showing the potential for clinical applications.
Compared with CW-DCS, there are many advantages in TD-DCS: Firstly, TD-DCS can measure the time point spread function (TPSF) of the tissue.Consequently, we can apply photon diffusion theories developed for time-domain near-infrared spectroscopy (TD-NIRS) to estimate tissue optical properties using the TPSF.Thus, we reduce errors in estimating dynamical properties, as we do not need to assume optical property values as traditional CW-DCS systems do (Sutin et al., 2016).
Secondly, TD-DCS adds one further variable time, which can be exploited to select photons to increase the depth sensitivity (Martelli et al., 2016).Typically, the photons with a longer pathlength travelled deeper into the medium before reaching the detector.In contrast, those taking a shorter pathlength from source to detector reach only superficial tissue layers.Time-of-flight (ToF) measurements can achieve a higher depth resolution, as the ToF is proportional to the pathlength through the medium.Consequently, when computing the autocorrelation only with photons showing a ToF below a specific threshold, we can estimate the dynamic properties of the superficial layers, whereas a longer ToF allows for assessing deeper layers.
Thirdly, the pulsed laser utilized in the TD-DCS system can be integrated into the TD-NIRS setup (Samaei et al., 2021).This integration enables simultaneous measurements of NIRS and DCS, providing a comprehensive understanding of blood flow and hemodynamics variations.A temporal resolution of approximately one second and a favourable SNR in dynamic in vivo measurements was validated (Pagliazzi et al., 2017).
However, the primary obstacle preventing the broad adoption of TD-DCS is the need for an optimal pulsed laser (in power, pulse width, coherence, stability, and cost, around 6-fold more expensive than CW lasers).The effect of each of these factors has been evaluated in different studies, and various data processing strategies have been introduced to overcome the destructive influence of the instrument response function (IRF) (Colombo et al., 2019) and the limited coherence length of the emitter.Moreover, Colombo et al. (2020) demonstrated the contamination of non-moving scatters on the TPSF using a coherent pulsed laser utilized in the TD-DCS technique.Samaei et al. (2021) have conducted the systematic discussion.Another drawback is that using narrow time gates to calculate the autocorrelation limits the SNR due to the scarcity of photons.Consequently, its applicability to in vivo experiments on human tissue is also restricted (Pagliazzi et al., 2017).Although Ozana et al. (2022) have designed a functional TD-DCS system that combines an optimized pulsed laser (a custom 1064 nm pulse-shaped, quasi transform-limited, amplified laser source), it is still costly, primarily due Note: SPAD stands for Single-Photon Avalanche Diode, and SNSPD stands for Superconducting Nanowire Single-Photon Detectors Q. Wang et al. NeuroImage 298 (2024) 120793 to the SNSPD.Unlike CW-DCS, both TD-and FD-DCS can retrieve dynamic optical properties (e.g., BFi) and static optical properties (e.g., μ a and μ ʹ s ), which are typically assumed in the conventional CW-DCS measurements.FD-DCS eliminates the requirement for collocated sources and phasesensitive detectors, promising a portable and cost-effective system.
Through data acquisition at a single ρ, FD-DCS effectively minimizes partial volume effects.This technology eliminates the need for extensive calibration in data analysis by acquiring flow and absorption from intensity-normalized data.FD-DCS shows high-speed acquisition, as flow and oxygenation information are inherently present in the dataset.Moreover, the implementation of FD-DCS is simplified by replacing a traditional DCS system's source with an intensity-modulated coherent laser.The detection mechanism remains unchanged, leading to reduced development time and cost.
Typically, to separate deep from superficial blood flow signals for CW-DCS, adding more detectors at different ρ to obtain multipledistance measurements is needed, which, however, increases the cost.General linear models (GLM) have been applied to CW-DCS data from multiple source-detector separations (ρ) to regress out the effect of superficial flow.Therefore, large-ρ DCS data is expressed as a linear combination of superficial blood flow (measured at a small ρ) and the desired deep blood flow (Cowdrick et al., 2023), a method derived from fNIRS (Von Lühmann et al., 2020).Table 4 summarizes representative existing TD-DCS systems, which use time-gating and TCSPC electronics to distinguish between photons travelling superficial layers and those propagating deeper into the tissue.In contrast to fNIRS, which measures flow volume, DCS directly measures the BFi, which is related to flow speed.Since the flow speed differs significantly over different vessel diameters and tissue layers, the relation between superficial BFi and deep BFi is not linear.Therefore, new analysis tools that integrate additional data on vasculature structure are required to derive more accurate deep flow estimation from such multiple-distance DCS measurements.

Data processing
The accuracy and performance of multilayered analytical models have been extensively evaluated in prior literatures (Gagnon et al., 2008a;Verdecchia et al., 2016;Zhao et al., 2021;Zhao et al., 2023;Samaei et al., 2021;Milej et al., 2020;Wu et al., 2022;Forti et al., 2023).In addition to the analytical models described in Section 2, other data processing methods have been introduced to distinguish cerebral and extracerebral information.Baker et al. (2015) introduced a pressure measurement paradigm combined with the modified Beer-Lambert law (Baker et al., 2014) and multi-distance measurement to reduce the extracerebral contamination from the signal associated with the deep layers.Furthermore, Samaei et al. (2021) extended the bi-exponential model utilized in interferometric near-infrared spectroscopy (iNIRS) (Kholiqov et al., 2020) to describe the TD-DCS signals influenced by scatterers moving at different speeds.They also conducted experimental validation using layered phantoms and in vivo experiments.
Traditionally, to extract BFi and β, we fit measured g 2 with Eqs. ( 4), ( 9), ( 18), ( 24), ( 25), ( 31), ( 32) and ( 35) in Section 2 by minimizing the . Nonlinear least square fitting routines, e.g., Levenberg-Marquardt (Li et al., 2005, Mazumder et al., 2021), fminsearchbnd (Verdecchia et al., 2016) are usually used to quantify BFi.These approaches, however, are iterative, and sensitive to data noise.To address these constraints, the N th -order (NL) algorithm (Shang et al., 2014;Shang and Yu, 2014), least-absolute minimization (L1 norm), and support vector regression (SVR) were introduced (Zhang et al., 2018).Yet, with the NL framework, the extraction of BFi is determined by the chosen linear regression approach (Zhang et al., 2018).Although L1 norm and SVR are novel for processing DCS data, they are sensitive to signal deviations (Vapnik, 1999).For example, the computation time for BFi is 28.07 and 52.93 s (Zhang et al., 2018) (using the Lenovo ThinkCentre M8600t desktop with a 3.4 GHz CPU and 16GB memory) when employing L1 norm and SVR, respectively, still too slow for real-time applications.In 1986, Dechter introduced "deep learning" (DL) to the machine learning community (Dechter, 1986).With rapid advances in computing technologies, DL has become a game-changer in many fields, including photonics (Ma et al., 2021), chemistry (Mater and Coote, 2019), biology (Ching et al., 2018), and medical diagnosis (such as electroencephalogram (EEG) and electrocardiogram (ECG) (Zhang et al., 2020;Liu et al., 2021)), but is not yet broadly used in DCS.Recently, Zhang et al. (Zhang et al., 2019) proposed the first recurrent neural network (RNN) regression model to DCS, followed by 2D convolution neural networks (2DCNN) (Poon et al., 2020), long short-term memory (LSTM) (Li et al., 2021) and ConvGRU (Feng et al., 2023).LSTM, as a typical RNN structure, has proven stable and robust for quantifying relative blood flow in phantom and in vivo experiments (Li et al., 2021).2DCNN, on the other hand, tends to require massive training datasets for complex structures, demanding memory resources.ConvGRU, the newest deep learning method introduced to DCS, has also exhibited excellent performances in BFi extraction.Although the training of DL takes a long time, once it is done, DL is much faster than traditional fitting methods and more promising for real-time analysis and display.Fig. 14 and Table 5 summarize existing DL methods applied to DCS.It shows that DCS-NET's training is much faster than two-dimensional CNN, approximately 140~fold faster.Although the remaining models, RNN, LSTM and ConvGRU have fewer total layers, they are limited to a specific ρ (Wang et al., 2024).Xu et al. (2022) introduced a different DL approach and trained a deep neural network on DCS data of temporal speckle fluctuations from 12 fibers at different surface locations to reconstruct videos of flow dynamics 8 mm beneath a decorrelating tissue phantom.The reconstructed images had a millimetre-scale spatial resolution and a temporal resolution of 0.1-0.4s.
This section includes an overview of DCS applications in animals, followed by applications in neonates, focusing on perinatal care, cardio-  cerebral diseases, and children's brain health.Finally, it explores DCS applications in adults, divided into neurovascular assessment, cardiocerebrovascular diseases, skeletal muscle health, and tumor diagnosis and therapy.

Animals
DCS has been applied to animals since the late 1990s, such as estimating burn depth in pigs (Boas and Yodh, 1997) (Fig. 15(b)) and probing rat vascular hemodynamics (Cheung et al., 2001) with a hybrid DCS-NIRS instrument in 2001.Carp et al. used DCS to examine CBF during hypercapnia-induced cerebrovascular perturbation, with MRI-ASL as the standard measuring reference (Carp et al., 2010).In addition, Menon et al. were the first to use DCS for tumor monitoring (Menon et al., 2003) by assessing tumor oxygenation in mice with human melanoma xenografts achieved by vascular endothelial growth factor (VEGF) transfection.They combined DCS with Doppler ultrasound (DUS) to investigate microvessel density (MVD), BF, blood volume (BV), blood oxygen saturation, tissue oxygen partial pressure (pO 2 ), and oxygen consumption rate.
Moreover, DCS is pivotal in monitoring tumor blood flow changes in animal studies related to photodynamic therapy (PDT).Marrero et al. (2011), Yu et al. (2005), and Busch et al. (2009) have employed DCS to monitor BF in tumors before, during, and after PDT.Sunar et al. (2007) also used DCS to assess anti-vascular and ionizing radiation therapies.Farzam et al. (2017) observed a dropped BFi in the high oxygen saturation tumor region using DCS and DOS after anti-vascular chemotherapy.These preclinical investigations have paved the way for human cancer research and clinical applications.
Ischemia monitoring assesses potential damage to the brain or the secondary brain injury and paraparesis.Experiments have been conducted to study the perturbation of hemodynamics and cerebral blood metabolism induced by ischemia brain injury in rats (Culver et al., 2003), piglets (Diop et al., 2011) and sheep (Mesquita et al., 2013), see Fig. 15.Notably, Diop et al. developed a method integrating (TR-NIR) and DCS to quantify the absolute cerebral metabolic rate of oxygen (CMRO 2 ) (Diop et al., 2011;Verdecchia et al., 2013).
To further investigate vessel hemodynamics, diffuse correlation tomography (DCT) has been developed to provide 3D blood flow contrast imaging by measuring blood flow perturbations caused by optical heterogeneities, providing blood flow contrast imaging of the region of interest (Zhou et al., 2006;Han et al., 2016;Huang et al., 2021).DCT is a safe and cost-effective imaging technique offering real-time monitoring and functional information on hemodynamics, complementing other imaging modalities like MRI, CT, or PET scans.

Neonates
The cortex of newborns is more easily detectable as the scalp and skull are much thinner in newborns and more light reaches the cerebral tissue than in adults.Thus, neonates are an attractive population for bedside DCS measurements.Generally, DCS is often combined with NIRS, which can measure human blood metabolism (Villringer and Chance, 1997;Danen et al., 1998) or transcranial Doppler ultrasound (TCD), enabling comprehensive measurements of microvascular blood flow and oxygen metabolism in neonatal human subjects (Buckley et al., 2014).

Perinatal care
Babies born before 37 weeks of pregnancy are premature, and preterm birth is the leading cause of neonatal mortality (Ohuma et al., 2023).According to the World Health Organization (WHO) 2023 report, there are around 13.4 million premature babies worldwide (Preterm birth, 2023).Premature babies are more likely to suffer from brain injuries such as HIE, stroke, and periventricular leukomalacia, related to neurological deficits (Kiechl-Kohlendorfer et al., 2009).Roche-Labarbe et al. developed a hybrid instrument combining DCS for measuring CBF and quantitative FD-NIRS for assessing cerebral tissue oxygenation (StO 2 ) and CBV in premature neonates.The results indicate that the CBF-CBV correlation is unstable in premature neonates (Roche-Labarbe et al., 2010).In addition, Germinal matrix-intraventricular hemorrhage (GM-IVH) in premature neonates can be monitored by measuring CBF and CMRO 2 to identify the vulnerability of potential brain damage in newborns (Lin et al., 2016).Buckley et al. used DCS for continually monitoring CBF in the middle cerebral arteries of low birthweight premature infants during a postural manipulation, discovering a significant correlation between TCD and DCS measurements (Buckley et al., 2009).CBF monitoring during the first three days after birth was conducted to assess the risk of brain injury due to CBF instabilities in preterm infants (Rajaram et al., 2022).DCS holds a promising potential for preterm human infants' brain health care.

Neonatal cardio-cerebral diseases
DCS is also a promising tool for the monitoring of congenital heart defects in newborns.Durduran et al. used a hybrid NIRS-DCS instrument to study the changes in oxyhemoglobin, deoxyhemoglobin, total hemoglobin concentrations, CMRO 2 , and CBF during hypercapnia.The validation of CBF and CMRO 2 was conducted using MRI-ASL, and the results showed a good agreement with DCS measurements (R = 0.7, p = 0.01) (Durduran et al., 2010).Buckley et al. (2013) and Shaw et al. (2023) measured changes in cerebral hemodynamics and oxygen metabolism during cardiac surgeries using DCS and DOS to evaluate the risk of surgery duration and surgical procedures, respectively.In addition, therapeutic hypothermia (TH) for neonatal HIE has also been studied using hybrid FD-NIRS and DCS (Dehaes et al., 2014;Sutin et al., 2023).Sutin et al. (2023) revealed the effects presented by therapeutic hypothermia (TH) on cerebral hemodynamics and blood oxygen metabolism by measuring CBF and CMRO 2 , indicating that CMRO 2 is a good indicator of TH evaluation and can be measured repeatedly at the point of care.Busch et al. (2016) observed CBF attenuation in the brains of children (aged 6-16 years) diagnosed with obstructive sleep apnoea syndrome (OSAS) and hypercapnia using DCS.Besides, Nourhashemi et al. (2023) combined EEG, NIRS, and DCS to simultaneously capture changes in electrical and optical dynamics in children (aged 6-10 years) affected by absence epilepsy.The outcomes revealed a consistent correlation among EEG, NIRS, and DCS, suggesting that DCS holds promise in detecting hemodynamic changes of pediatric brain disorders.Moreover, DCS has been employed for real-time CBF measurements during chronic transfusion therapy for children with autism spectrum disorder (Lin et al., 2023) and sickle cell diseases (Lee et al., 2019;Cowdrick et al., 2023;Lee et al., 2022).Fig. 16 shows representative applications of DCS in neonates.

Adults
In this section, we focus on DCS applications in human adults and divide them into four sections: neuroscience study, cardiocerebrovascular diseases, skeletal muscle and exercise physiology study, and tumor diagnosis and therapy evaluation.Fig. 17 shows the use of DCS in adults.

Neurovascular assessment
Measuring CBF facilitates investigating neurovascular coupling, brain injuries, stroke, and neurological disorders.Neurovascular coupling denotes the connection between regional neural activity and subsequent alterations in CBF.The extent and spatial positioning of blood flow fluctuations are intricately connected to shifts in neural activity through a sophisticated sequence of coordinated processes involving neurons, glial cells, and vascular elements (Pasley and Freeman, 2008).DCS can quantify changes in human cerebral blood flow in response to various stimuli, including sensorimotor cortex activation (Durduran et al., 2004), visual cortex activation (Jaillon et al., 2007;Li et al., 2008), Broca's area activation (Tellis et al., 2018), transcranial magnetic stimulation (TMS) (Mesquita et al., 2013), and vasoactive stimuli (Cowdrick et al., 2023).These studies presented noninvasive and straightforward means of monitoring cognitive neuronal activity in human brains.Older adults with mild cognitive impairment exhibit significantly higher CBF increments during motor and dual-task activities, whereas their counterparts display normal cognitive functions (Udina et al., 2022).Another investigation highlighted the consistency of CBF with the posture changes within a healthy population (aged 20 to 78 years).Zavriyev et al. examined the role of DCS during hypothermic circulatory arrests (HCA) therapy among older people (mean age 61.8 ± 19.4 years) (Zavriyev et al., 2021).These findings offer good references for future research on age-related alterations in CBF (Edlow et al., 2010).In addition, DCS has been effectively applied for assessing cerebral hemodynamics under hypotension (Shoemaker et al., 2023), obstructive sleep apnea (Busch et al., 2016), and adult comatose (Johnson et al., 2022).However, most state-of-the-art DCS setups are relatively limited for measuring blood flow in deeper cerebral tissue since the most common source-detector separations only enable measurements at ~1-1.5cm depth, which barely penetrates the non-cerebral tissues of the scalp and skull.

Cardio-cerebrovascular diseases
Several studies have assessed human artery diseases and treatments.For example, Carotid endarterectomy (CEA) can lead to hypoperfusion syndrome and potential cerebral ischemia, making cerebral hemodynamics monitoring crucial during and after the procedure.Shang et al. found that DCS measured CBF more responsively to internal carotid artery clamping compared to EEG (Shang et al., 2011).Furthermore, Kaya et al. (2022) integrated DCS with NIRS to demonstrate the feasibility of real-time cerebral hemodynamics and oxygen metabolism monitoring during CEA procedures.Mesquita et al. (2013) also established a physiological connection between CBF and oxygenation in patients with peripheral artery disease.CBF during the cardiac cycle has been acquired using DCS before and during ventricular arrhythmia in adults (Lafontant et al., 2022).DCS has also been used for monitoring CBF (Durduran et al., 2009;Favilla et al., 2014) and critical closing pressure (CrCP) (Wu et al., 2021) of ischemic stroke patients, intrathecal nicardipine treatment after subarachnoid hemorrhage (Sathialingam et al., 2023), and thrombolysis therapy evaluation in ischemic stroke (Zirak et al., 2014).In neurocritical care, DCS combined with NIRS serves as an effective bedside tool for managing CBF and head-of-bed treatment for critical brain injuries (Kim et al., 2010;Kim et al., 2014).

Skeletal muscle health
DCS is valuable for investigating human skeletal muscle physiology and assessing tissue vascular diseases.Yu et al. compared muscle blood flow and oxygenation between healthy individuals and those with peripheral arterial disease during cuff occlusion and plantar flexion exercise (Yu et al., 2005), integrating MRI-ASL with DCS for monitoring BFi (Yu et al., 2007).Shang et al. studied muscle blood flow, oxygenation, and metabolism in women with fibromyalgia during exercise (Shang et al., 2012).Matsuda et al. (2022) evaluated local skeletal muscle blood flow during manipulative therapy, which enhanced blood flow with minimal effects on systemic circulatory function (Matsuda et al., 2022).Nevertheless, conventional technologies like DUS, electromyography (EMG), and MRI face challenges with motion artifacts, leading to inaccurate blood flow measurements.DCS offers more reliable measurement (Bangalore-Yogananda et al., 2018), though muscle fiber motion artifacts may still result in overestimating BFi changes.Methods such as dynamometer co-registration (Shang et al., 2010), hardware-integrated gating (Gurley et al., 2012;Henry et al., 2015), and a random walk correction model with FD-NIRS (Quaresima et al., 2019) have been proposed to address this.

Tumor diagnosis and therapy evaluation
DCS has been employed in the diagnosis of human breast cancer, prostate, and neck tumors.Durduran et al. (2005) conducted an initial comparative analysis of blood flow disparities between tumor and normal tissues in the human breast.The investigation revealed a noteworthy increase in blood flow within tumor tissues, paving the way for noninvasive tumor diagnosis.Choe et al. (2014) confirmed these findings, and non-contacted DCT has enabled 3D visualization of blood flow in human breast tumors.Yu et al. (2006) combined DCS with NIRS to measure BF and oxygenation in human prostate cancer and head/neck tumors (Sunar et al., 2006), assessing treatment efficacy.Also, DCS has been used to evaluate photosensitizer 2-1[hexyloxyethyl]-2-devinylpyropheophorbide-a (HPPH)-mediated PDT (HPPH-PDT), showing significant drug photobleaching and reductions in blood flow and oxygenation (Sunar et al., 2010).Additionally, DCS can evaluate chemotherapy (Zhou et al., 2007;Chung et al., 2015) or radiation delivery (Dong et al., 2012) in human tumors.However, more extensive patient studies are needed for accurate clinical applications, as most studies involved only 7 to 11 patients (Choe and Durduran, 2012) with varying response definitions.Longitudinal studies with larger populations and refined DCS models are necessary for precise clinical use (Yu, 2012;Shang et al., 2017).
In addition to the applications listed above , DCS has also been used for critical care (Poon et al., 2022), anesthesiology (Tagliabue et al., 2023), and thyroid blood flow measurements (Lindner et al., 2016).

Discussion and outlook
Non-invasive DCS techniques have great potential for early diagnosis, prognosis, and a broad range of clinical conditions.Although DCS is simple and cost-effective, human applications still face challenges.Increasing DCS's SNR is crucial for effective probing through thick nearsurface tissue layers, especially at larger source-detector separations.A solution for increasing SNR is simply increasing the amount of light delivered to tissues under the maximum permissible exposure (MPE) limited by safety standards (ANSI safety limit (ANS Institute, 2007)) or using high photon detection efficiency sensors that collect more scattered photons.Additionally, with new CMOS manufacturing techniques, the improvement in SNR has been shown in multi-speckle DCS systems using SPAD arrays with 5 × 5 (Johansson et al., 2019), 32 × 32 (Sie et al., 2020;Xu et al., 2022;Liu et al., 2021), 192 × 128 (Mattioli della Rocca et al., 2023), 500 × 500 (Wayne et al., 2023), or 512 × 512 (Mattioli della Rocca et al., 2024) pixels.The latest parallelized DCS system with a SPAD array of 500 × 500 pixels has already been demonstrated to boost the SNR by 500, compared to a single SPAD pixel of the same device.In 2020, a SPAD camera with 1024 × 1000 pixels was demonstrated (Morimoto et al., 2020), although its relatively low frame rate of 24 kfps still prevented a practical use in DCS.We believe this ongoing development of larger and faster SPAD technologies (Morimoto et al., 2020;Bruschini et al., 2019) will continue to boost the SNR of DCS, thereby allowing feasible measurements at longer source-detection separation and effectively enabling the measurement of deeper blood flow.
Another method that has a similar goal is the interferometric approach based on a Mach-Zehnder interferometer.Over the past five years, the interferometric detection for diffusely scattered light in biological tissues has been investigated (Zhou et al., 2021;Zhou et al., 2022;Zhou et al., 2018;Robinson et al., 2020;Kholiqov et al., 2020;James and Powell, 2020;Xu et al., 2020;Zhou et al., 2021;Borycki et al., 2017;Kholiqov et al., 2022).There are many advantages, including: 1) offering comparable or superior functionality to photon counting but at a significantly lower cost per pixel (Zhou et al., 2021;Zhou et al., 2018;Robinson et al., 2020;Zhou et al., 2021); 2) altering the temporal coherence of light proves to be an effective and adaptable method for attaining Time-of-flight (ToF) resolution or discrimination within an interferometric arrangement, eliminating uncertainties for precise signal interpretation (Zhou et al., 2018;Kholiqov et al., 2020;Borycki et al., 2017;Kholiqov et al., 2022); 3) holding significant promise for analyzing blood flow fluctuations, whereas conventional DCS is hindered by its expensive nature and limited throughput (Zhou et al., 2021;Dietsche et al., 2007); 4) insensitive to ambient light, which is a considerable benefit for practical use cases.Recently, Robinson et al. (2023) proposed long wavelength (1064 nm), interferometric DCS (LW-iDCS), which outperforms the long wavelength DCS (LW-DCS) based on SNSPD (Ozana et al., 2021) in terms of SNR and implementation cost.Safi et al. (2021) presented a novel coherence-gated DCS instrument designed for pathlength-resolved measurement of flow and tissue optical properties, utilizing a CW low-coherence source with an interferometric approach, in which specialized pulsed/modulated laser sources with high temporal coherence and speed improvements to traditional DCS detectors are not required.Similarly, Robinson et al. (2024) proposed an enhanced DCS method called pathlength-selective, interferometric DCS (PaLS-iDCS), which improves upon both the sensitivity of the measurement to deep tissue hemodynamics and the SNR of the measurement using pathlength-specific coherent gain.Moreover, PaLS-iDCS does not require expensive time-tagging electronic and low-jitter detectors because of the interferometric detection.However, the drawback of the interferometric approach is its relatively complex setup with a reference arm and higher stability requirements for the platform accommodating the setup.
One substantial advantage of TD-DCS techniques, as described in Section 3.5, is their capability to reduce the superficial layer contamination by selecting photons propagated into the deep tissues.Although TD-DCS measurements are typically conducted at a short ρ, due to the limited coherence length of the currently available emitters, this feature overcomes the influence of short ρ measurements and provides a higher depth sensitivity than CW-DCS methods.Therefore, TD-DCS requires a pulsed lasers and a TCSPC (or time-gating) module, which increases cost.To reduce the cost, Moka et al. (2022) proposed FD-DCS.A faster acquisition speed can be achieved using FD-DCS as BF and oxygenation information is implicit in the collected data.This can be a good solution for some traditional DOS and DCS systems.Moreover, implementing FD-DCS is simplified using an intensity-modulated coherence laser, which can be cost-effective.
Indeed, large arrays comprising thousands of SPADs equipped either with in-pixel Time-to-Digital Converters (TDCs) (Villa et al., 2014;Villa et al., 2012;Gersbach et al., 2012) or with a set of TDCs shared across various pixels (Jahromi et al., 2015;Charbon, 2014) are being developed in cost-effective CMOS process.Despite recent advances in SPAD technologies, state-of-the-art TD-DCS has not yet been implemented using TCSPC techniques based on TDC techniques (Wang et al., 2024;Wang et al., 2023).There is no doubt that large SPAD arrays with embedded TCSPC can be a parallelizable solution for next-generation TD-DCS, with a potential breakthrough in the SNR of the measurements and the depth-encoding.We expect this kind of TD-DCS system to be released in the coming years.
Combining DCS and DRS (Munk et al., 2012;Shang et al., 2009;Cheung et al., 2001) for concurrent BF and oxygenation measurements is also a trend.Quantifying blood oxygenation, metabolism, and tissue BF is essential for the diagnosis and therapeutic assessments of vascular/cellular diseases (Barth et al., 2010;Caprara and Grimm, 2012;Edul et al., 2011;Schober and Schwarte, 2012;White et al., 2012;Wolf et al., 2003).However, most relevant instruments assess tissue hemodynamics and metabolism by employing optical probes in direct contact with tissue surfaces.Contact measurements pose notable challenges, such as an elevated risk of infection in ulcerous tissues and potential deformation of delicate tissues (e.g., breasts and muscles) due to probe-tissue contact.This deformation can lead to distortions in the measured tissue properties.Thus, noncontact probes have been designed for deep tissues (Lin et al., 2012;Cheung et al., 2001;Yu et al., 2005).
Over the past 25 years, we have witnessed the emergence of DCS to quantify BF dynamics of deep tissues more accurately with a higher SNR.We expect low-cost, user-friendly DCS technologies will be introduced and applied soon.Combining NIRS with DCS will provide a better solution for critical bottlenecks in neuroscience and clinical applications.Although the speckle contrast optical spectroscopy (SCOS) setup, particularly the fiber-based configuration, is similar to that of DCS, SCOS can achieve a much higher SNR at a reduced cost (using inexpensive detectors).Recent studies (Zilpelwar et al., 2022;Robinson et al., 2024;Kim et al., 2023;Cheng et al., 2024) from Boas's research group have used SCOS for measuring human brain functions at a larger ρ, demonstrating greater sensitivity to CBF, suggesting that SCOS could provide an alternative approach to functional neuroimaging for cognitive neuroscience applications.2021).(c) Schematic of the off-axis heterodyne parallel speckle detection (the Fourier-domain approach); the figure adopted from Ref. James and Powell (2020).(d) The schematic of the fiber-based SCOS set-up and the corresponding data analysis pipeline (Kim et al., 2023).

Fig. 1 .
Fig. 1.(a) The roadmap of DCS historical development; (b) the number of published DCS papers based on PUBMED (*value for 2024 extrapolated as of the date of writing); (c) blood flow sampling rate vs measurement depths.PDCS: parallelized DCS, iDCS: interferometric DCS.

Fig. 2 .
Fig. 2. The DCS principle for blood flow measurements.(a) The schematic of DCS measurements in the semi-infinite geometry.Highly coherent laser light is used to illuminate the sample via optical fibers.The source and detector fibers are placed on the tissue surface within a distance ρ; (b) the scattered light intensity fluctuates due to moving scatterers (e.g., red blood cells); (c) two intensity autocorrelation curves (g 2 (τ)) showing different flow rates.(d) Photons scattered from moving particles travel along "banana-shaped" paths between source and detection fibers; (e) Autocorrelation functions for different ρ.
Gagnon et al. (2008a) first proposed a two-layer analytical model, based on Kienle et al.'s model for reflectance spectroscopy with the two-layered geometry in Fig. 4(b).

Fig. 4 .
Fig. 4. Analytical models including the source and the detector for DCS (a) homogenous semi-infinite model, (b) two-layer analytical model, (c) three-layer analytical model.Here, μ a(n) and μ ʹ s(n) are the absorption and reduced scattering coefficients in the n-th layer, respectively.Δ i is the thickness of Layer i.
Fig. 8 shows noise (orange line) and noiseless (blue line) g 2 (τ).The noise model predicted standard deviations for g 2 (τ) at each τ was applied by randomly sampling a normal distribution, where the T int = 1s and 10 s and the delay time 1 × 10 − 6 s ≤ τ ≤ 1 × 10 − 1 s (128 data points) was used.Considering realistic photon budgets, the photon count rate at 785

Fig. 12 .
Fig. 12.A schematic layout of the SPAD array with representative raw data of temporal light intensity fluctuations from single pixels and the corresponding intensity autocorrelation curves.The blue and red lines in the rightmost figure represent the autocorrelation curves of a single pixel and the whole SPAD array (1024 pixels), respectively.Data and plots are adopted from Liu et al. (2021).

Fig. 13 .
Fig. 13.Diagrams for linear-and multi-tau correlators provided by the CCO of LS Instruments, Dr Ian Block.

Fig. 15 .
Fig. 15.(a) Detailed schematics of measurements on sheep, featuring the instrument and its thin fiber optic probe, images adopted from Ref. Mesquita et al. (2013); (b) The setup for pig experiments.The shaded areas on the pig indicate burns of various depths.Figures were reproduced from Ref (Boas and Yodh, 1997); (c) The non-contact scanning system set-up for mice.(black lines: outline of the bones; red lines: outline of the graft).Figures were reproduced from Ref. Han et al. (2016); (d) Experiment setup with the placement of optical fibers and pressure sensor as well as the catheter on the exposed skull of monkey.The traces at the right show an example of changes in cerebral blood flow (ΔCBF) and ICP.Figures were reproduced from Ref. Ruesch et al. (2020).

Fig. 16 .
Fig. 16.(a) DCS sensor was attached to the infant's head for blood flow monitoring, figures adopted from Ref. Sunwoo et al. (2022) (b) The high-density EEG cap and optical probe (NIRS-DCS) and schematic representation of the location of the EEG and optical probes on a child's head.The figure was reproduced from Nourhashemi et al. (2023).(c) The hybrid DCS system for neonatal blood flow monitoring, figures reproduced from Ref. Rajaram et al. (2020).

Fig. 17 .
Fig. 17.(a) Hybrid DCS system applied to the human forehead, image reprinted from Ref. Durduran and Yodh (2014); (b) Experimental configuration with a contactless probe, figures adopted from Ref. Li et al. (2013); (c) Schematic of hybrid instrument, hybrid Imagent/DCS instrument for simultaneous measurement of tumor oxygenation and blood flow during chemoradiation therapy, images adopted from Ref. Dong et al. (2016); (d) Drawing of a subject cycling on a stationary bicycle with a multi-distance FDNIRS-DCS probe attached to the right superficial rectus femoris.The figure was adopted from Ref. Zavriyev et al. (2021); (e) Hybrid DCS/NIRS device for muscle measurement.Figures were adopted from Ref. Henry et al. (2015); (f) Diagram of DCS working on a breast, figures adopted from Ref. Choe et al. (2014).

Fig. 19 .
Fig. 19.(a) Schematic diagram of functional TD-DCS at 1064 nm; the figure adopted from Ref. Ozana et al. (2022).(b) Schematic of functional interferometric DWS; the figure adopted from Ref. Zhou et al. (2021).(c) Schematic of the off-axis heterodyne parallel speckle detection (the Fourier-domain approach); the figure adopted from Ref.James and Powell (2020).(d) The schematic of the fiber-based SCOS set-up and the corresponding data analysis pipeline(Kim et al., 2023). ;

Table 2
Existing DCS systems using SPAD array and other representative sensors.

Table 3
Existing commercial correlator.

Table 4
Representative existing time-domain DCS systems.

Table 5
Comparison of existing AI methods for BFi estimation.