2.1.

Skin-Simulating Phantom

We constructed the skin-simulating phantom using a silicone block containing appropriate concentrations of ${\mathrm{TiO}}_2$ to mimic the reduced scattering coefficient ($1{\mathrm{mm}}^{-1}$) of biological tissue at visible and near-infrared wavelengths (Fig. 1). We embedded a glass capillary tube, with an inner diameter of $550\mu \mathrm{m}$, at the surface of the block. We placed a second thin silicone skin-simulating phantom of varying thicknesses (190 to $1000\mu \mathrm{m}$) on top of the block to mimic the overlying tissue. We fabricated the thin phantoms using ${\mathrm{TiO}}_2$ powder and coffee to simulate the optical scattering and absorption coefficients, respectively, of the epidermis.¹⁹ By using different thicknesses of the overlying layer, we effectively modulated $\rho$.

For laser speckle imaging (LSI) with epi-illumination, we used an 808-nm laser (Ondax, Monrovia, California) as the excitation source, with a variable attenuator to adjust the intensity of illumination and ground-glass diffuser to expand and homogenize the incident laser light (spot illumination: 5-mm diameter). A Retiga EXi FAST cooled CCD camera (QImaging, Surrey, BC, Canada) collected the raw speckle images at 20 fps. The camera was equipped with a macrolens (Nikon, Melville, New York), with an aperture setting of $f/4$. We acquired images using Q-Capture Pro v5.1 software and selected the exposure time using the autoexpose function. We collected images of the phantom at exposure times ranging between $66\mu \mathrm{s}$ and 43 ms by using the variable attenuator to change the irradiance of the excitation light. We collected data from the phantom with the following configurations: no top layer present (i.e., microchannel at surface of phantom) and with overlying top-layer thicknesses (TLTs) of 190 m, 310, 510, and $1000\mu \mathrm{m}$. We used a syringe pump (Harvard Apparatus, Holliston, Massachusetts) to infuse 5% Intralipid solution as a blood surrogate (Baxter Healthcare, Deerfield, Illinois) into the channel at speeds of 0 to $18\mathrm{mm}/\mathrm{s}$.

2.2.

Tooth-Simulating Phantom

We also simulated transillumination LSI conditions, recently proposed by Stoianovici et al.,²⁰ for the study of pulpal blood flow in teeth (Fig. 2). Teeth are well suited for transillumination LSI because of the highly forward scattering feature of interior dentine tubules.²¹ We used an excised human adult molar as a phantom. We drilled a small hole from the middle of the occlusal surface of the tooth to the bottom of the tooth between the roots. We inserted a Tygon tube with an inner diameter of $250\mu \mathrm{m}$ into the hole and connected it to a syringe pump.

Our experimental setup consisted of a configuration currently under investigation for study of pulpal blood flow. We illuminated the tooth on one side with a fiber-coupled 632.8-nm HeNe laser (JDSU, Milpitas, California). On the opposite side of the tooth, we positioned a leached fiber bundle (Schott, Southbridge, Massachusetts)²² with a drum lens to focus the image on to a CCD camera (Flea3, Point Gray, Richmond, BC, Canada). We acquired images with FlyCap software (Point Gray) at a fixed exposure time of 10 ms and a gain of 24 dB. For this experiment, we calculated spatial and temporal contrasts in two regions of interest, one on the left side of the tooth and the other on the right. The tooth was approximately $300\text{-}\mu \mathrm{m}$ thicker on the right side than the left, effectively resulting in different $\rho$ at the two interrogated regions.

With both experimental setups, we collected a sequence of 30 images per experimental condition and processed with both spatial and temporal speckle imaging algorithms. With the spatial algorithm, we used a sliding $7\times 7$ pixel structuring element to calculate maps of speckle contrast from each acquired raw speckle image and obtained a final contrast image by averaging the 30 contrast images.¹⁵ We calculated temporal contrast on a pixel-by-pixel basis, across all 30 images in the sequence.¹⁶ All values shown in the data figures (Figs. 3Fig. 4Fig. 5–6) represent the average contrast in a region of interest ($20\times 100\text{pixels}$) positioned over the center of the tube.

Fig. 3

(a) Spatial speckle contrast increased with increasing top-layer thickness (TLT) at a given exposure time ($T$). The symbols represent the experimental data and the continuous lines data fits using Eq. (1). (b) At $T=1\mathrm{ms}$, for a given actual flow speed value, spatial speckle contrast increased with increasing TLT.

Fig. 4

Spatial speckle contrast depends strongly on the fraction of nonmoving optical scatterers (e.g., $1\text{-}\rho$) and hence on the TLT. (a) $\rho$ decreases in exponential fashion with TLT, and $K_m$ increases in linear fashion with TLT. Solid points represent the experimental data, and lines represent the fits to the data. (b) The sensitivity of $K$ to exposure time $T$ depends strongly on TLT, for short $T$ ($<1\mathrm{ms}$), the sensitivity decreases for thicker TL and for $T>1\mathrm{ms}$, the expected value of the contrast is constant [see Fig. 3(a)] and therefore the sensitivity approaches to zero.

Fig. 5

Temporal contrast versus $T$ (a) and versus actual flow speed (b) with different TLTs. The temporal processing scheme gives a more consistent measurement of contrast regardless of the presence of a static scattering layer.

Fig. 6

Spatial versus temporal contrast in different regions of interest on a tooth (different thicknesses) as a function of flow speed.

3.1.

Skin-Simulating Phantom

Similar to previously published data,⁸ for a given TLT, we observed that the spatial speckle contrast decreased with an increase in $T$ [Fig. 3(a)]. For a given $T$, with an increase in TLT, the contrast increased because of a decrease in $\rho$. For a given flow speed, the contrast increased with an increase in TLT [Fig. 3(b)]. Collectively, these data demonstrate that, for flow in a subsurface tube, the spatial speckle contrast analysis is incapable of enabling unambiguous assessment of flow speed within the tube.

For a given TLT [Fig. (3a)], the spatial speckle contrast was maximum ($K_M$) at the shortest $T$, and then asymptotically decayed to a minimum ($K_m$). For a given $T$, the dynamic range of spatial speckle contrast (i.e., $\mathrm{\Delta }K=K_M-K_m$) decreased with increasing TLT, because of a corresponding decrease in $\rho$. We fit Eq. (1) to the experimental data in Fig. 3(a) to estimate ${\tau }_C$, $\rho$, and $K_m$. From the fitting results, the mean value of ${\tau }_C$ was $61.0\pm 5.9\mu \mathrm{s}$, which is similar to the values reported by Parthasarathy et al.⁸ for similar flow speed. $\rho$ and $K_m$ are plotted versus TLT in Fig. 4. For a given actual flow speed, we observe an exponential decay of $\rho$ with an increase in TLT [Fig. 4(a)], which we postulate is associated with the exponential behavior of light attenuation described by Beer’s law. Because of the asymptotic behavior of $K_m$ with increasing $T$ (and hence increasing $x$), we determine $K_m$ as

Previous reports^8,12,18 present data that strongly suggest that the temporal speckle contrast is altered primarily by temporal variations in light remitted from the sample and considerably less sensitive to static optical scatterers. We set out to determine the degree to which temporal contrast depends on specific independent variables. We find that the temporal contrast decreases with increasing $T$ [Fig. 5(a)] and increasing flow speed [Fig. 5(b)], but we also observed that the contrast is relatively independent of TLT for a wide range of values (0 to $1000\mu \mathrm{m}$; Fig. 5).

3.2.

Tooth-Simulating Phantom

We also studied this relationship using a transillumination LSI configuration, a setup previously proposed for study of teeth²⁰ and joints,²³ and used routinely by our group to assess the blood flow in the rodent dorsal window chamber model.²⁴ We used a tooth model in which the thickness of the right side of the tooth was approximately $300\text{-}\mu \mathrm{m}$ thicker than the left side, resulting in a higher proportion of static scatterers (i.e., lower $\rho$). Similar to the data collected with the epi-illumination setup, we observed that the spatial contrast depends on TLT [Fig. 6(a)], and temporal contrast is independent of TLT [Fig. 6(b)].

In this work, we studied the impact of overlying optical scatterers on measurements of speckle contrast. We used two different imaging setups and both spatial and temporal contrast analyses. With spatial analysis and epi-illumination, we determined that the speckle contrast offset $K_m$ increases in a linear fashion with TLT [Fig. 4(a)] and the sensitivity of speckle contrast decreased with an increase in TLT [Fig. 4(b)]. With temporal speckle contrast analysis (Fig. 5), speckle contrast measurements were remarkably independent of TLT, presumably due to the relative immunity of temporal contrast to contributions from static optical scatterers.^16–18 Our data demonstrate that the temporal contrast analysis can characterize accurately speckle contrast because of subsurface moving scatterers for TLT as thick as 1 mm, and for a wide range of $T$ and flow speeds. We observed similar results with a transillumination geometry. Collectively, these results strongly suggest the potential of temporal LSI at a single-exposure time to assess the changes in blood flow even in the presence of substantial static optical scattering, which can ultimately be combined with methods to improve the localization of speckle contrast such as spatial frequency domain^25,26 or magnetomotive techniques.²⁷