Time-of-flight resolved light field fluctuations reveal deep human tissue physiology

The study addresses limitations of classical diffuse optical flowmetry methods (e.g., DWS/DCS) that infer blood flow from coherent light intensity fluctuations without resolving time-of-flight and often relying on empirical models. These approaches struggle to connect measured autocorrelations to underlying light-scattering physics, particularly in layered tissues, and commonly fit Brownian-motion-like decays despite expectations of random flow. The research introduces interferometric near-infrared spectroscopy (iNIRS) to add optical phase and high-resolution TOF dimensions, aiming to directly probe RBC dynamics, discriminate between Brownian versus advective motion models, and clarify how absorption, anisotropic RBC scattering, and tissue layering affect conventional DOF interpretations.

Background encompasses incoherent NIRS modalities (continuous wave, frequency domain, spatial frequency domain, time-domain) and coherent methods (DWS/DCS, laser Doppler, speckle) used to assess deep tissue hemodynamics. Prior theory links scatterer motion to light fluctuations, but classical DWS/DCS lacks TOF resolution and often yields autocorrelations resembling Brownian motion, creating ambiguity between Brownian diffusion and random flow. At intermediate source–detector separations, single-scattering with Brownian motion and diffuse multiple scattering with random flows can yield similar TOF-integrated autocorrelations. Numerical simulations of correlation transport in vascular beds have suggested Brownian-like behavior even in laminar flow, but existing TOF-integrated in vivo measurements are too coarse to adjudicate competing models. Emerging TOF-discriminating DCS approaches exist, but with limited resolution. This work builds on and unifies concepts from DLS/DWS theory, diffusion approximation in TD-NIRS, and prior hybrid motion models to provide a TOF-resolved, field-based framework.

The authors advanced interferometric NIRS (iNIRS) for human in vivo use. iNIRS measures the interference spectrum between light traversing tissue and a reference arm using an 855 nm DFB laser rapidly tuned at 100 kHz, yielding a lag-time resolution of 10 µs and an instrument response function with 21.9 ps TOF resolution. The complex mutual coherence function time series is Fourier transformed to produce TOF-resolved field autocorrelations G_INIRS(τ_t, τ_d). A key innovation is non-contact measurements at short source–detector separations to exploit a large intrinsically static backscattered reference that enables estimation and correction of bulk motion phase drift (Doppler-induced linear phase rotation). Phase drift is estimated over short windows (2 ms) at the TPSF peak TOF and via TOF-integrated signals, then unwrapped and removed, yielding real-valued intrinsic field autocorrelations. Motion correction was validated by co-registered OCT (1320 nm) Doppler velocity, demonstrating high correlation (R^2=0.95) between modalities. Experimental datasets include: Intralipid phantom (µ_s'≈10 cm^-1, µ_a≈0.045 cm^-1), human forearm, nude mouse head/brain, and human forehead. TPSFs were obtained and fitted (after convolution with the measured IRF) using diffusion theory to extract µ_a and µ_s'. TOF-resolved field autocorrelations were modeled using: (i) a 3-parameter exponential model (static + dynamic single exponential; Eq. 7) derived from DLS/DWS for Brownian motion, (ii) an empirical 5-parameter bi-exponential model (static + slow + fast components; Eq. 8) to capture systematic deviations at early/intermediate TOFs, and (iii) simplified 2-parameter and normalized 1-parameter exponential fits in the DWS regime (Eqs. 9–10). Brownian DWS predicts a linear increase of decay rate with TOF with near-zero intercept (Eq. 11). TOF-dependent averaging (20% TOF window) was used to improve SNR at long TOFs, followed by 2-parameter fits for decay rates. Physiological perturbations tested included: intravenous Intralipid-20% in mice (increasing dynamic scattering and momentum transfer), 5% hypercapnia in mice (increasing CBF), and human prefrontal activation via covert reading. Monte Carlo simulations with layered tissue models and varying dynamic scattering anisotropy, phase functions, and hybrid motion (advection + diffusion) were performed to interpret slow versus fast components and long autocorrelation tails. The team deconstructed DWS/DCS by TOF-integrating either full iNIRS autocorrelations or isolated fast/early-lag components to compare with DCS theory, assessing the impact of absorption assumptions and fit regions on recovered BFI.

- Motion correction: Phase drift due to bulk axial motion produces apparent rapid decorrelation; correction using short-TOF static backscatter yields stable intrinsic autocorrelations and restores the modified Siegert relationship. iNIRS-derived bulk motion matched OCT Doppler measurements with R^2=0.95. - Optical properties: iNIRS TPSFs fitted with diffusion theory accurately recovered µ_s' and µ_a across media; in phantoms, µ_s' was recovered within 0.5% of ground truth. - TOF-resolved dynamics: After correction, field autocorrelations show a prominent static component at early TOFs in tissue (extravascular scattering) and dynamic components with decay rates increasing with TOF. Intercepts of decay rate versus TOF moved closer to t=0 post-correction, consistent with DWS Brownian theory. - Bi-exponential behavior: In vivo data up to 200–400 ps TOF require a bi-exponential fit (static + slow + fast). The slow component is absent in Intralipid (g≈0.6) but present in tissues, suggesting association with high RBC forward-scattering anisotropy (g≈0.975). The fast component dominates at long TOFs; decay rate increases with TOF. Adjusted R^2 analyses confirm the need for the 5-parameter model at early/intermediate TOFs; at late TOFs, single exponentials suffice. - Physiological manipulations: In mice, Intralipid injection increased decay rate slope vs TOF and BFI (baseline to post-injection: 8.3×10^-8 to 1.4×10^-7 cm^2 s^-1). Hypercapnia increased BFI from 4.7×10^-8 to 8×10^-8 cm^2 s^-1. In humans, prefrontal activation increased early-phase BFI from 3.8×10^-9 to 6.7×10^-9 cm^2 s^-1 and raised the late-phase slope by 140%. - Layered tissue signatures: Human head showed two decay stages with lower slope at early TOFs (superficial scalp/skull) and higher slope at later TOFs (cerebral blood flow), directly evidencing different superficial vs deep dynamics. - Mechanism of slow tails: Simulations indicate long decay tails arise from small-angle intravascular dynamic forward scattering (“dynamical snake paths”) and depend on anisotropy and scattering phase function; hybrid advection+diffusion alters decay rates and TOF-attenuation of the slow component but preserves bi-exponential character. - Deconstructing DWS/DCS: Classical DCS BFI depends strongly on fit region and absorption assumptions. TOF-integrating only iNIRS fast or early-lag single-exponential components yields DCS-like autocorrelations that agree with DCS theory across lags and produce fit-region-invariant BFIs. Even with best practices (early-lag fits and accounting for absorption), conventional DCS shows only modest agreement with iNIRS; agreement markedly improves when slow tails are excluded. - Brownian model support: Exponential decays at early lags and late TOFs with 22 ps TOF resolution provide strong experimental support for Brownian displacement of RBCs in coherent scattering, undermining a pure advection model.

The findings directly address the ambiguity in coherent diffuse optical flowmetry by adding phase and TOF resolution to the measurements. iNIRS disentangles static, slow, and fast dynamic components along TOF, revealing that observed exponential decays at appropriate regimes predominantly reflect Brownian motion of RBCs. The approach clarifies how anisotropic RBC scattering and layered tissues produce long autocorrelation tails and bi-exponential decays that can confound TOF-integrated DWS/DCS, especially at short source–detector separations. By isolating fast components or early-lag exponential behavior, iNIRS reconciles discrepancies and yields BFI estimates consistent with DWS/DCS theory without requiring prior absorption knowledge. The two-stage decay behavior in human head measurements provides direct, TOF-resolved evidence of distinct extracerebral and cerebral blood flow dynamics, challenging homogenous semi-infinite assumptions and opening avenues for more brain-specific monitoring. Overall, iNIRS elevates DOF toward a physics-grounded interpretation, improving accuracy and interpretability in vivo.

This work demonstrates that interferometric NIRS, with high-resolution TOF and phase information and robust motion correction, can quantify TOF-resolved field dynamics in humans and animals, directly supporting a Brownian displacement model for RBC motion. The method separates static, slow, and fast components, explains long autocorrelation tails via dynamical snake paths, and deconstructs how these features bias classical DWS/DCS. It enables recovery of blood flow index without explicit absorption knowledge and reveals layered tissue dynamics, enhancing specificity to cerebral versus extracerebral flow. Future work should develop rigorous theory for the long-tail behavior beyond the cumulant approximation, better characterize RBC scattering phase functions and anisotropy effects, increase sampling to probe very early collision times, and translate TOF-resolved flow measurements to clinical brain monitoring and brain–computer interface applications with improved depth specificity.

- The sampling rate was insufficient to conclusively identify very early collision time scales, leaving early-lag deviations from theory unresolved in some media. - The bi-exponential fit used at early/intermediate TOFs is empirical; a rigorous theoretical framework for the slow tails is not yet established. - Interpretation depends on RBC scattering anisotropy and phase function, which carry uncertainties and can affect tail amplitudes and decay. - Layered tissue complexity may violate simplifying assumptions (e.g., cumulant approximation, homogenous media) used in conventional models; extracerebral contamination remains an issue at some separations. - While motion correction was validated, residual motion or instrument limitations could introduce errors, especially at early TOFs. - DWS/DCS comparisons indicate improved agreement when excluding slow tails, but generalization across all geometries and separations requires further validation.