DLS-OCT has several advantages over conventional techniques. As for the application to blood flow imaging, laser Doppler flowmetry is used to measure blood flow at a fixed point [19
], and its imaging corollary provides the 2D map of blood flow [21
]. Doppler OCT enables 3D imaging of the axial flow velocity with microscopic resolution [22
]. Compared to these techniques, DLS-OCT can simultaneously and independently measure the axial and transverse components of the flow velocity. Further, DLS-OCT can distinguish diffusion from flow, leading to a separate 3D map of the diffusion coefficient. In addition, DLS-OCT may offer additional contrast mechanisms (e.g., those based on R2
). The R2
map quantitatively images the degree of how much the motion is close to translational or diffusive ones; and for example it clearly revealed characteristic dynamics of the vessel boundaries. The MF
map will quantify the fraction of moving particles in each voxel, which is similar to the mobile fraction suggested in non-ergodic DLS studies [10
Each term in the DLS-OCT model we derived is similar to those predicted in several DLS studies. The velocity-dependent decay term is similar to that predicted in the study of the effect of the finite sample volume on DLS analysis [7
], although the autocorrelation function in our theory was directly derived from the OCT signal whereas the finite size of the sample volume in the literature resulted from the illuminating and collecting optics. The linear decomposition of the static component and the flowing/diffusing component is similar to the decomposition shown in the study of DLS in non-ergodic media [10
]. The combined diffusion-oriented and flow-oriented decay terms were similarly introduced in the study of DLS where diffusion and flow are mixed [12
]. Therefore, our theory can be understood as a mathematical combination of the phase-resolved OCT signal, the finite sample volume DLS model, the non-ergodic DLS model, and the model for the mixture of diffusion and flow.
Our DLS-OCT theory assumed that the composition ratios of the static and diffusing/flowing particles (MS and MF) do not vary during the measurement time. The validity of this assumption will depend on the measurement time and the magnitude of dynamics within a sample. For example, the assumption was reasonable when imaging blood flow of the brain with the measurement time of ~2 ms, because the blood flow velocity is typically 1-5 mm/s and thus leads to 2-10 μm displacement during the measurement time, smaller than or approximately comparable to the resolution volume. When we used a longer measurement time (200 ms), the autocorrelation function deviated from our model. In contrast, the fitting result was not reliable if only very short correlation times were used. Therefore, the correlation and measurement times for DLS-OCT imaging should be chosen carefully, taking into account both the scale of target dynamics and the fitting performance.
This study used the DLS-OCT theory for distinguishing whether the motion is translational or diffusive, not for measuring the mixture of the two motions. Nevertheless, the model seems to be able to measure the mixture of translational and diffusive motions. It was reported, however, that the diffusion is estimated inaccurately when mixed with large flow [12
]. We also observed this tendency in a phantom experiment, where the diffusion coefficient was overestimated by ≈1.5 times when it was mixed with flow whose velocity is larger than >1 mm/s. In this study, the relative magnitudes of flow and diffusion can be estimated based on how much they contribute to the decay in the autocorrelation function. With the parameters used in this study, v
= 0.1 and 1 mm/s approximately correspond to D
= 0.004 and 0.4 μm2
/s, respectively. The coupling between diffusion and large flow will not be a critical problem in the studies investigating a sample where diffusion and flow are spatially separated. Meanwhile, considerable caution would be required if one wants to apply the present technique to the measurement of diffusion that is mixed with large flow within the resolution volume. On the other hand, the voxels with large blood flow in vessels often exhibited high diffusion, which can be either a real diffusive motion or decorrelation of the OCT signal that can be quantified by the exponential decay with the diffusion coefficient. This high diffusion in vessels might be attributed to the mixture of non-translational motion of red blood cells including rotation, turbulence in blood flow, and the variance in the velocity distribution within the resolution volume. Since this interpretation has not been yet validated, and since the present study used the DLS-OCT theory for determining whether the motion is translational or not, we overlaid the diffusion map with the velocity map as in and . This overlay means that our analysis gave priority to flow over diffusion so that diffusion is of interest only at the voxels with low flow. Therefore, the coupling between diffusion and large flow was not an important concern at those vessel boundaries.
OCT uses coherence gating to collect light only scattered from the resolution volume and is known to effectively exclude multiply scattered photons [23
]. However, strong multiple scattering can give rise to a distortion in the OCT signal, which often causes an undesired shadow of large vessels [13
]. This multiple scattering also affected DLS-OCT estimation of dynamics at the voxels located beneath the surface vessels. This effect can be seen clearly by comparing the merged images in , where presents the maximum projection over the whole depth while only presents a single plane at the depth of 120 μm. High velocity and diffusion appeared in the shadow of the large surface vessels as shown in the single-plane image. This multiple scattering effect also can be found in the cross-section image of the velocity map of , where the absolute velocity was estimated large in the vessel shadow but the axial velocity was not. Although this multiple scattering would not cause a serious problem as one may generally build an en face
image by including surface vessels as in , in the future it will be interesting to derive a DLS-OCT model that considers the effect of multiple scattering.
Future theoretical efforts should consider the possibility of measuring a mixture of translational and diffusive motions, and the effect of multiple scattering. Although there can be various modified versions of the DLS-OCT theory, the one described here will work well for 3D imaging of dynamics in a highly heterogeneous sample where static and moving particles can be mixed within the micrometer-scale resolution volume and the moving particles can exhibit either diffusion or flow, as long as it is used in the single-scattering regime.