Laser speckle imaging of flowing blood: A numerical study

Laser speckle imaging (LSI) can be used to study dynamic processes in turbid media, such as blood flow. However, it is presently still challenging to obtain meaningful quantitative information from speckle, mainly because speckle is the interferometric summation of multiply scattered light. Consequently, speckle represents a convolution of the local dynamics of the medium. In this paper, we present a computational model for simulating the LSI process, which we aim to use for improving our understanding of the underlying physics. Thereby reliable methods for extracting meaningful information from speckle can be developed. To validate our code, we apply it to a case study resembling blood flow: a cylindrical fluid flow geometry seeded with small spherical particles and modulated with a heartbeat signal. From the simulated speckle pattern, we successfully retrieve the main frequency modes of the original heartbeat signal. By comparing Poiseuille flow to plug flow, we show that speckle boiling causes a small amount of uniform spectral noise. Our results indicate that our computational model is capable of simulating LSI and will therefore be useful in future studies for further developing LSI as a quantitative imaging tool.

Figure 1

Sketch of laser speckle imaging applied to an artery: a plane wave of coherent light enters the medium, multiply scatters on the particles, and is finally gathered at a camera set at a ${90}^{\circ }$ angle w.r.t. the incoming light. The result is a noiselike interferometric pattern, known as a speckle pattern, from which we wish to obtain quantitative information.

Figure 2

We sample instantaneous data rapidly (interval $\mathrm{\Delta }{t}_{\mathrm{int}}$) to mimic a real camera and at distant intervals ($\mathrm{\Delta }t$ apart) to gather temporal data.

Figure 3

A few characteristic speckle figures: the influence of the camera integration time and resolved versus unresolved speckle. (b) The temporally blurred version of panel (a). Note that the color ranges differ: absolute values are meaningless, and the blurred image (b) has a factor 10 lower intensity range than panel (a), which would have caused panel (b) to appear mostly dark blue. The $16\times 16$ grid used for local speckle contrast analysis is also shown (c). Deviations from Table 1: the camera size in panels (a) and (b) is 1 $\mathrm{mm} \times$ 4 $\mathrm{mm}$, and all three figures use ${256}^2$ pixels.

Figure 4

The effect of the spatial (number of pixels, $M$) and temporal ($n_{\mathrm{s},\mathrm{int}}$) resolution and the effect of windowing on the computed speckle contrast ($C$). The notation “grid ${16}^2$” denotes subdividing the image in a $16\times 16$ grid of calculation windows [i.e., windows of $8^2$ pixels for ${128}^2$ ($2^7$) total pixels], as is illustrated in Fig. 3.

Figure 5

Simulation results for the sinusoidally modulated flow. Top: obtained speckle contrast time series, shown for five simulated periods. Bottom: its frequency spectrum obtained from 40 simulated periods. Insets on bottom: the frequency spectrum as obtained from merely two simulated periods.

Figure 6

Simulation results, like Fig. 5, but now for a heartbeat-modulated flow.