Dynamic light scattering and laser speckle contrast imaging of the brain: theory of the spatial and temporal...

Dynamic light scattering (DLS) and laser speckle contrast imaging (LSCI) are closely related techniques that exploit the statistics of speckle patterns, which can be utilized to measure cerebral blood flow (CBF). Conventionally, the temporal speckle intensity auto-correlation function $$ is calculated in DLS, while the spatial speckle contrast K is calculated in LSCI measurements. Due to the rapid development of CMOS detection technology with increased camera frame rates while still maintaining a large number of pixels, the ensemble or spatial average of $$ as well as the temporal contrast K can be easily calculated and utilized to quantify CBF. Although many models have been established, a proper summary is still lacking to fully characterize DLS and LSCI measurements for spatial and temporal statistics, laser coherence properties, various motion types, etc. As a result, there are many instances where theoretical models are misused. For instance, mathematical formulas derived in the diffusive regime or for ergodic systems are sometimes applied to small animal brain measurements, e.g., mice brains, where the assumptions are not valid. Therefore, we aim to provide a review of the speckle theory for both DLS and LSCI measurements with detailed derivations from first principles, taking into account non-ergodicity, spatial and temporal statistics of speckles, scatterer motion types, and laser coherence properties. From these calculations, we elaborate on the differences between spatial and temporal averaging for DLS and LSCI measurements that are typically ignored but can result in inaccurate measurements of blood flow, particularly the spatially varying nature of the static component in $$ and K. We also obtained $$ maps in in vivo mouse brain measurements using high frame rate CMOS cameras which have not been demonstrated before, and compared with $$ and K. This work provides a useful guide for choosing the correct model to analyze spatial and temporal speckle statistics in in-vivo DLS and LSCI measurements.