Assessing the reliability of diffuse correlation spectroscopy models on noise-free analytical Monte Carlo data

Interferometric near-infrared spectroscopy (iNIRS) reveals that blood flow index depends on wavelength

Blood flow index (BFI) is an optically accessible parameter, with unit distance-squared-over-time, that is widely used as a proxy for tissue perfusion. BFI is defined as the dynamic scattering probability (i.e. the ratio of dynamic to overall reduced scattering coefficients) times an effective Brownian diffusion coefficient that describes red blood cell (RBC) motion. Here, using a wavelength division multiplexed, time-of-flight- (TOF) - resolved iNIRS system, we obtain TOF-resolved field autocorrelations at 773 nm and 855 nm via the same source and collector. We measure the human forearm, comprising biological tissues with mixed static and dynamic scattering, as well as a purely dynamic scattering phantom. Our primary finding is that forearm BFI increases from 773 nm to 855 nm, though the magnitude of this increase varies across subjects (23% ± 19% for N = 3). However, BFI is wavelength-independent in the purely dynamic scattering phantom. From these data, we infer that the wavelength-dependence of BFI arises from the wavelength-dependence of the dynamic scattering probability. This inference is further supported by RBC scattering literature. Our secondary finding is that the higher-order cumulant terms of the mean squared displacement (MSD) of RBCs are significant, but decrease with wavelength. Thus, laser speckle and related modalities should exercise caution when interpreting field autocorrelations.

Lawrence K, Amendolia O, Quattrone F, Balu R, Kofke WA, Yodh AG. Noninvasive continuous optical monitoring of absolute cerebral blood flow in critically ill adults

We investigate a scheme for noninvasive continuous monitoring of absolute cerebral blood flow (CBF) in adult human patients based on a combination of time-resolved dynamic contrast-enhanced near-infrared spectroscopy (DCE-NIRS) and diffuse correlation spectroscopy (DCS) with semi-infinite head model of photon propogation. Continuous CBF is obtained via calibration of the DCS blood flow index (BFI) with absolute CBF obtained by intermittent intravenous injections of the optical contrast agent indocyanine green. A calibration coefficient ( γ ) for the CBF is thus determined, permitting conversion of DCS BFI to absolute blood flow units at all other times. A study of patients with acute brain injury ( N = 7 ) is carried out to ascertain the stability of γ . The patient-averaged DCS calibration coefficient across multiple monitoring days and multiple patients was determined, and good agreement between the two calibration coefficients measured at different times during single monitoring days was found. The patient-averaged calibration coefficient of 1.24 × 10 9    ( mL / 100    g / min ) / ( cm 2 / s ) was applied to previously measured DCS BFI from similar brain-injured patients; in this case, absolute CBF was underestimated compared with XeCT, an effect we show is primarily due to use of semi-infinite homogeneous models of the head.

Derivation of the correlation diffusion equation with static background and analytical solutions

A new correlation diffusion equation has been derived from a correlation transport equation allowing one to take into account the presence of moving scatterers and static background. Solutions for the reflectance from a semi-infinite medium have been obtained (point-like and ring detectors). The solutions have been tested by comparisons with "gold standard" Monte Carlo (MC) simulations. These formulas suitably describe the electric field autocorrelation function, for Brownian or random movement of the scatterers, even in the case where the probability for a photon to interact with a moving scatterer is very low. The proposed analytical models and the MC simulations show that the "classical" model, often used in diffuse correlation spectroscopy, underestimates the normalized field autocorrelation function for increasing correlation times.

Pressure injury prediction using diffusely scattered light

Pressure injuries (PIs) originate beneath the surface of the skin at the interface between bone and soft tissue. We used diffuse correlation spectroscopy (DCS) and diffuse near-infrared spectroscopy (DNIRS) to predict the development of PIs by measuring dermal and subcutaneous red cell motion and optical absorption and scattering properties in 11 spinal cord injury subjects with only nonbleachable redness in the sacrococcygeal area in a rehabilitation hospital and 20 healthy volunteers. A custom optical probe was developed to obtain continuous DCS and DNIRS data from sacrococcygeal tissue while the subjects were placed in supine and lateral positions to apply pressure from body weight and to release pressure, respectively. Rehabilitation patients were measured up to four times over a two-week period. Three rehabilitation patients developed open PIs (POs) within four weeks and eight patients did not (PNOs). Temporal correlation functions in the area of redness were significantly different ( p < 0.01 ) during both baseline and applied pressure stages for POs and PNOs. The results show that our optical method may be used for the early prediction of ulcer progression.

Analytical solution of the correlation transport equation with static background: beyond diffuse correlation spectroscopy

The correlation transport equation (CTE) is the natural generalization of the theory for diffusion correlation spectroscopy and represents a more precise model when dealing with measurements of particle movement in fluids or red blood cell flow in biological tissues. Unfortunately, the CTE is not methodically used due to the complexity of finding solutions. It is shown that actually a very simple modification of the theory/software for the solution of the radiative transport equation allows one to obtain exact solutions of the CTE. The presence of a static background is also taken into account and its influence on the CTE solutions is discussed. The proposed approach permits one to easily work beyond the diffusion regime and potentially for any optical and/or physiological value. The validity of the approach is demonstrated by using "gold standard" Monte Carlo simulations.

Optical methods for quantitative and label-free sensing in living human tissues: principles, techniques, and applications

We present an overview of quantitative and label-free optical methods used to characterize living biological tissues, with an emphasis on emerging applications in clinical tissue diagnostics. Specifically, this review focuses on diffuse optical spectroscopy, imaging, and tomography, optical coherence-based techniques, and non-linear optical methods for molecular imaging. The potential for non- or minimally-invasive assessment, quantitative diagnostics, and continuous monitoring enabled by these tissue-optics technologies provides significant promise for continued clinical translation.

Fast blood flow monitoring in deep tissues with real-time software correlators

We introduce, validate and demonstrate a new software correlator for high-speed measurement of blood flow in deep tissues based on diffuse correlation spectroscopy (DCS). The software correlator scheme employs standard PC-based data acquisition boards to measure temporal intensity autocorrelation functions continuously at 50 - 100 Hz, the fastest blood flow measurements reported with DCS to date. The data streams, obtained in vivo for typical source-detector separations of 2.5 cm, easily resolve pulsatile heart-beat fluctuations in blood flow which were previously considered to be noise. We employ the device to separate tissue blood flow from tissue absorption/scattering dynamics and thereby show that the origin of the pulsatile DCS signal is primarily flow, and we monitor cerebral autoregulation dynamics in healthy volunteers more accurately than with traditional instrumentation as a result of increased data acquisition rates. Finally, we characterize measurement signal-to-noise ratio and identify count rate and averaging parameters needed for optimal performance.

Probability density function of the electric field in diffuse correlation spectroscopy of human bone in vivo

Diffuse correlation spectroscopy (DCS) is the technique of choice for non-invasive assessments of human bone blood flow. However, DCS classical algorithms are based on the fundamental assumption that the electric field of the light reaching the DCS photodetector is a zero-mean complex Gaussian variable. The non-validity of this hypothesis might produce inaccurate blood flow estimations. It is shown that for the human tibia, the "Gaussian hypothesis" holds for interoptode distances ≥20  mm. This lower boundary seems to depend on the type of investigated tissue.

Lawrence K. Assessment of the best flow model to characterize diffuse correlation spectroscopy data acquired directly on the brain

Diffuse correlation spectroscopy (DCS) is a non-invasive optical technique capable of monitoring tissue perfusion. The normalized temporal intensity autocorrelation function generated by DCS is typically characterized by assuming that the movement of erythrocytes can be modeled as a Brownian diffusion-like process instead of by the expected random flow model. Recently, a hybrid model, referred to as the hydrodynamic diffusion model, was proposed, which combines the random and Brownian flow models. The purpose of this study was to investigate the best model to describe autocorrelation functions acquired directly on the brain in order to avoid confounding effects of extracerebral tissues. Data were acquired from 11 pigs during normocapnia and hypocapnia, and flow changes were verified by computed tomography perfusion (CTP). The hydrodynamic diffusion model was found to provide the best fit to the autocorrelation functions; however, no significant difference for relative flow changes measured by the Brownian and hydrodynamic diffusion models was observed.

Calibration of diffuse correlation spectroscopy blood flow index with venous-occlusion diffuse optical spectroscopy in skeletal muscle

We investigate and assess the utility of a simple scheme for continuous absolute blood flow monitoring based on diffuse correlation spectroscopy (DCS). The scheme calibrates DCS using venous-occlusion diffuse optical spectroscopy (VO-DOS) measurements of arm muscle tissue at a single time-point. A calibration coefficient (γ) for the arm is determined, permitting conversion of DCS blood flow indices to absolute blood flow units, and a study of healthy adults (N=10) is carried out to ascertain the variability of γ. The average DCS calibration coefficient for the right (i.e., dominant) arm was γ=(1.24±0.15)×10(8) (mL·100  mL(−1)·min(−1))/(cm(2)/s). However, variability can be significant and is apparent in our site-to-site and day-to-day repeated measurements. The peak hyperemic blood flow overshoot relative to baseline resting flow was also studied following arm-cuff ischemia; excellent agreement between VO-DOS and DCS was found (R(2)=0.95, slope=0.94±0.07, mean difference=−0.10±0.45). Finally, we show that incorporation of subject-specific absolute optical properties significantly improves blood flow calibration accuracy.