The diffuse light correlation techniques are built upon dynamic light-scattering concepts. The original ‘dynamic light scattering’ or ‘quasi-elastic light scattering’ techniques [5–8] recorded temporal fluctuations of light intensity scattered from a sample in order to learn about the motions of sample constituents, e.g. the Brownian dynamics of suspended colloidal particles or macromolecules. In typical single-scattering measurements, illuminated particles re-radiate incident light into many directions and the re-radiated light travelling along one direction is detected; when particles move, the relative phases of the collected re-radiated signals will vary and the detected light intensity fluctuates. Typically, when particles move through distances of the order of the wavelength of light, the collected signals are observed to fluctuate significantly. Information about these particle motions is derived from the scattered light electric field temporal autocorrelation function (or its Fourier transform).

The simple dynamic light-scattering method does not work when samples become turbid and incident light fields are multiply scattered. In practice, one can carry out the same temporal autocorrelation function measurements described above; however, inversion of correlation function data to recover quantitative information about scatterer motion is non-trivial in the multiple-scattering limit. Thus, direct application of the method to biological tissue is challenging.

Of course, similar challenges were faced by researchers aiming to carry out absorption spectroscopy of tissue, and these challenges were surmounted by modelling light transport through tissue as a diffusion problem. The diffusion approximation enabled experimenters to quantitatively understand the trajectory of light through tissue and then to ‘effectively reset’ the pathlengths employed in the traditional absorption spectroscopy measurement to new, tissue-scattering-dependent values. In a similar spirit, one can envision the electric field temporal autocorrelation function propagating through tissue, scattering from small volume elements within the sample and then propagating ballistically, then scattering again, etc., all in a random manner as the photons travel from one side of the tissue sample to a tissue surface (figure 1a). A key steady-state mathematical equation governing the transport of electric field temporal autocorrelation through tissue is given below, i.e. the correlation diffusion equation [9,10] Here, G₁(r,t)=E*(r,t)E(r,t+τ) is the unnormalized temporal electric field (E(r, t)) autocorrelation function in the medium at position r and time t; τ is the autocorrelation function time delay, and the brackets represent time and/or ensemble averages. D1/(3μ′_s) is the light diffusion coefficient in the medium; μ_a is the absorption coefficient; μ′_s is the reduced scattering coefficient (i.e. the inverse of the photon random walk step-length); v is the speed of light in the medium, and S(r, t) represents the light source.

The primary new features of the correlation diffusion equation compared with the conventional steady-state light diffusion equation (obtained from equation (1.1) by letting the autocorrelation time, τ, approach zero) are associated with particle motion: α represents the fraction of photon-scattering events that occur from moving particles in the medium (e.g. red blood cells; RBCs); Δr²(τ) is the mean-square particle displacement in time τ (i.e. in tissue, the mean-square displacement factor could characterize the motions of RBCs in the tissue vasculature); k₀=2π/λ is the wavenumber of the light diffusing through the medium. Diffuse correlation spectroscopy (DCS) refers to the measurement of the diffusing temporal field autocorrelation function to obtain information about tissue dynamics. Equation (1.1) is essentially a differential equation formulation of diffusing wave spectroscopy (DWS) [11–13], a technique developed earlier in the soft condensed matter community for studies of a variety of highly scattering complex fluids. DCS, as formulated above, is better suited than DWS (which essentially dealt with homogeneous turbid media) for handling point sources, heterogeneous media and as a starting formulation for correlation tomography in tissue.

As is the case for traditional dynamic light scattering, the intensity autocorrelation function is usually measured by the experimenter, rather than the field correlation function. The Siegert relation [14] links these two correlation functions. It can be used to relate measurements of the intensity autocorrelation function to the theory for the electric field autocorrelation function, without direct measurement of phase information, Here, g₁(τ) and g₂(τ) are the normalized autocorrelation functions for the electric field and intensity, respectively; β is a coherence factor, which is mainly determined by the optical detection system, and it should be close to unity for an ideal experimental set-up and is often one-half in our measurements. Typically, best fits to either g₁(τ) or g₂(τ) are employed to derive a best estimate for the dynamical tissue factor, αΔr²(τ).

The precise physiological origin of the factor, αΔr²(τ), is not well understood. Much of the experimental evidence suggests that DCS, like near-infrared spectroscopy (NIRS, also called diffuse optical spectroscopy; DOS), is most sensitive to the physiology in the microvasculature (i.e. capillaries, arterioles and venules). In fact, DCS shares many of the light penetration and modelling advantages of NIRS, but it provides a qualitatively different physiological signal. In NIRS, the signal is related to the haemoglobin concentration changes via optical absorption [1,15–17]. By contrast, the DCS signal is due to the motion of scatterers in the tissue (i.e. RBCs); therefore, DCS provides a rather direct measure of blood flow. Although no significant cross-talk between NIRS and DCS has been observed, large changes in the blood volume (proportional to the sum of oxy- and deoxyhaemoglobin concentrations) will change the fraction of photon-scattering events, α, therefore affecting the product, αΔr²(τ). Such effects will be small and can be accounted for by independent NIRS/DOS measurements. For the mean-square particle displacement, in practice, the Brownian model, Δr²(τ)=6D_Bτ, fits the observed correlation decay curves fairly well over a wide range of tissue types and source–detector separations, including rat brain [18–22]; mouse tumours [23–26]; piglet brain [27]; and human skeletal muscle [28–32], human tumours [33–39] and human brain [40–48] (figure 1c). Here, D_B is an effective diffusion coefficient that is a few orders of magnitude larger than the traditional thermal Brownian diffusion coefficient of cells in blood given by the Einstein–Smoluchowski relation [49]. Use of the Brownian model is hardly satisfying. In fact, RBCs in the microvasculature do not move purely ballistically or diffusively; they experience position-dependent shear stresses and hydrodynamic interactions, and they roll, tumble and translate through the vasculature. The Brownian model provides a convenient approximation for data fitting and for defining a blood flow index (BFIαD_b) from the DCS measurement. The BFI is not a measure of absolute blood flow in the strict sense (e.g. it has the wrong units), but the relative change in BFI (i.e. rBFI) has been repeatedly shown (table 1) to be a quantitative measure of relative changes in blood flow (rBF) [1,3,22,27,29,46].

The complete details of a typical DCS experimental set-up can be found elsewhere [2–4]. Briefly, a narrowband continuous wave (CW) diode laser in the NIR range with long coherence length (i.e. greater than 20m) is used as the light source. The light beam is delivered to the tissue through an optical fibre, with an output power of approximately 10–25mW. The light-intensity fluctuations within a single speckle area are detected using a single-mode fibre and a fast single photon-counting device (e.g. an avalanche photo-diode). Finally, an autocorrelator takes the detector output and uses photon arrival times to compute the light-intensity temporal autocorrelation function. The integration time for generating a reliable curve depends on source–detector separation, etc., but typically varies from 1 to 3s. Since single-mode fibres are employed for detection, the detection area is small and achieving a high signal-to-noise ratio (SNR) is challenging at the largest source–detector separations. Besides the laser power and the integration time, the SNR also depends on the source–detector distance, ρ. For small animals such as mice and rats, in which 0.3≤ρ≤1.2cm, the SNR can be as high as 100, with a photon counting superior to 500kHz. For brain human experiments, on the other hand, large source–detector distances are desirable to separate cortical responses from scalp and skull responses. Since the mean photon depth sensitivity is approximately one-third to one-half of the distance between a source and a detector [55], separations of 2.5cm or more on the surface of the human head are needed to probe the cerebral cortex. These large separations limit the SNR for a single detection fibre to vary from 2 to 10 in most cases (i.e. corresponding to photon counting rates of 10–100kHz). In these cases, by averaging over many trials and/or a population sample, or by averaging over many detection fibres, it is possible to further improve measurement SNR and derive meaningful results in the human brain.

Validation of DCS in the clinic has begun relatively recently [32–38, 52–54, 58]. Figure 3 exhibits one example. In this case, DCS measurements of cerebral blood flow (CBF) are compared with flow measurements obtained by xenon-CT in brain-injured patients in the neuro-intensive care unit [54]. Although it is a current clinical ‘standard of care’ flow measurement, xenon-CT is an invasive technique and is not suitable for continuous bedside monitoring. In this study, we used xenon-CT images of the same tissue volumes covered by our DCS probes, and we compared rBF changes during various regular interventions in the neuro-intensive care unit, such as increased dose of vasopressor drugs (i.e. agents that cause constriction of blood vessels, leading to an increase in blood pressure). The blood flow changes obtained from both techniques were quite strongly correlated, i.e. a correlation coefficient of r=0.73 was obtained for eight subjects (figure 3).

A second DCS validation example was performed with very low birth-weight preterm infants [53]. The skull anatomy of this patient population permits us to probe a significant fraction of the cortex. Briefly, in this study, we compared microvascular CBF, measured with DCS, with macrovascular blood velocity in the middle cerebral artery, measured with transcranial Doppler ultrasound (TCD), a technique routinely used in the clinic. The absolute BFI obtained by DCS was quite well correlated with peak systolic velocity measured by TCD (r=0.76). Although not fully understood, the evidence points towards a relationship between microvasculature perfusion in brain tissue and flow velocity in the middle cerebral artery.

While tissue function is often manifested in haemodynamic signatures that can be measured with DOS/NIRS and DCS, the interpretation of these haemodynamic-dependent techniques can be complicated because of competing effects during brain activation, and because of lack of information about the relationships between evoked neuronal, metabolic and vascular responses. The interplay between vascular supply, tissue oxygen consumption and regulatory effects, although greatly debated, remains poorly understood. Clearly, more comprehensive sets of haemodynamic data containing independent information about haemoglobin concentration, blood oxygenation and blood flow are desirable.

The measurement of changes in all three of these haemodynamic parameters permits experimenters to compute changes in another fundamental tissue property: oxygen metabolism. The cerebral metabolic rate of oxygen (CMRO₂) is related to CBF, to arterial oxygen concentration ([O₂]_a) and to the oxygen extraction fraction (OEF) by Fick’s law [19,59,60] OEF is defined as the fractional conversion of oxygen concentration from arterioles to venules. By assuming a compartment model in which the optical signal originates from a mixture of arterial, capillary and venous blood, it is possible to write the OEF in terms of both the arterial and tissue oxygen saturations [19], Typically, S_aO₂ is either assumed constant or obtained from blood gas measurements, and γ indicates the percentage of blood volume contained in the venous compartment of the vascular system, while S_tO₂ is obtained from DOS/NIRS. For relative changes, and under the assumption of constant compartmentalization, the factor γ divides out. Then, assuming that [O₂]_a remains constant, the calculation of relative changes of CMRO₂ (rCMRO₂) gives As DOS/NIRS can be used measure S_tO₂, and, therefore, to provide a measure OEF through equation (3.2), and as DCS measures CBF, tissue oxygen metabolism (especially relative changes in oxygen metabolism) can be derived from information available to all the optical methods.

The use of combined DCS and DOS/NIRS to monitor changes in CMRO₂ was demonstrated in both animal and humans by our group [18,19,40,52]. The first demonstration of combined DCS and DOS/NIRS to monitor concurrent flow and oxygenation changes in brain was carried out in a pre-clinical rat model during hypercapnia [18]. The first in vivo all-optical demonstrations of the measurement of CMRO₂ (again, employing concurrent DCS and DOS/NIRS) was subsequently carried out in both animals [19] and humans [40]. The utility of the technique for measurement of relative changes in CMRO₂ (i.e. rCMRO₂) is shown in figure 5. In this work, variation of haemodynamic parameters was monitored during temporary focal cerebral ischaemia in rats. By occluding the middle cerebral artery over 60min, average blood flow in the ischaemic region across five rats dropped by 58 (±4)%, while OEF increased by approximately 39 (±6)%. This interplay combined to induce a decrease in CMRO₂ of 59 (±7)% from its baseline in the most strongly affected tissue. Haemodynamic and metabolic changes in the contralateral side of the occlusion showed slight (but not significant) decreases compared with baseline.

One such example is in the care of acute ischaemic stroke (AIS) patients. In this case, optimization of CBF is a major sub-goal for salvaging as much of the ischaemic penumbra as possible. Cerebrovascular autoregulatory mechanisms become impaired in this population; hence CBF becomes dependent on cerebral perfusion pressure. Clinically, a real-time bedside monitor of CBF is not available.

Current guidelines recommend an empirical technique, whereby the head-of-bed (HOB) angle is altered; a flat HOB angle is employed in order to maximize CBF following AIS. In a recent study, we monitored cerebral haemodynamics at the bedside when changes were induced in HOB positioning [47,58]. In healthy populations, CBF responses to posture change were shown to be small owing to autoregulation [47]. Figure 7a shows CBF measured on the forehead of a healthy subject at different HOB positions of 30^°, 15^°, 0^°, −5^° and 0^°, and normalized to their values at 30^°. Figure 7b shows changes in CBF for a stroke patient. Ischaemic stroke disrupts cerebral autoregulation, and the impaired relationship between CBF and perfusion pressure leads to larger changes in CBF in the infarcted hemisphere by comparison with the healthy contralesional hemisphere. A clear differentiation can be observed between the two hemispheres. This difference was statistically significant over the whole population. On the other hand, approximately 20 per cent of the patients exhibited a paradoxical response, wherein CBF in the ipsilesional hemisphere decreased with increasing HOB angle (figure 7c). This behaviour was also previously observed in traumatic brain injury patients and was probably a result of a substantial increase in intracranial pressure—a parameter that is not routinely monitored in ischaemic stroke patients. Thus, this example illustrates the potential of DCS as a bedside CBF monitor of critically ill patients, which may also allow changes in CBF and metabolism to be detected prior to the onset of clinical symptoms.

Another clinical example concerns haemodynamic monitoring of tumour responses to treatment, especially during the early stages of therapy. The feasibility of DCS/NIRS for this type of application in humans has been demonstrated for breast [33,36,38], head and neck tumours [34,37] and for basal cell carcinomas [39]. The early flow changes that were found may be significant in affecting drug-delivery efficacy and/or tumour oxygenation during chemoradiation therapy.

In a different vein, motion artefacts, generated by the relative movement of ‘static’ scatterers with respect to optical fibres, are common and can generate signals that can mislead physiological interpretation. This problem is especially important for exercise experiments. While some progress has been made towards decreasing the magnitude of this problem by time-gating the measurements [31], a detailed analysis is needed to learn better how motion artefacts affect the signal and/or how assumptions in analysis schemes may be violated, when motion artefacts are present [32]. The influence of optical probe pressure is another important parameter that has yet to be fully considered. In brain experiments, for example, the pressure between the probe and the scalp can alter blood flow indices; in muscle experiments, increased pressure may squeeze blood out of the region probed.

On the instrumentation side, the low SNR levels in human brain experiments, mainly owing to higher absorption in the brain and the use of small diameter single-mode fibres, are also challenging. Methods to overcome this problem include placement of many detection fibres around the same region for parallel detection (i.e. effectively increased detection area). Another difficulty faced by many probes on the brain is the presence of hair (especially dark hair) on the scalp that reduces collection efficiency, among other things.