2.1.

Spatial Resolution

It is assumed that the speckle image sample statistics faithfully represent the true statistics of the speckle ensemble. This can be so only if the speckle pattern is spatially sampled at or above the spatial Nyquist rate, i.e., the speckle size is at least twice the size of a pixel. Because the normalized spatial autocorrelation function $g^2(\mathrm{\Delta }x)$ of the speckle image is the point spread function of the optical system, the full width at half maximum (FWHM) of $g^2(\mathrm{\Delta }x)$ is taken as the speckle size, also defined as the spatial resolution.^27–31

Experimentally, the normalized spatial autocorrelation function $g^2(\mathrm{\Delta }x)$ is measured using

2.2.

Choosing an LSCI Model

LSCI quantifies the SC and blood flow relationship through the intensity autocorrelation function $g^2(\tau )$. Briefly, the SC $K$ is given as

Here, $erf(x)$ is the error function and is defined as

2.3.

BFI Calculation

2.3.3.

Blood flow index

The procedure for deriving the BFI is shown in Fig. 1. First, the system parameter $\beta$ and the proportions of the dynamic scattering $\rho$ are derived. Second, we obtain a series of SC values $K$ of the speckle patterns scattered from different blood flow rates. Then, we calculate the BFI ($T/{\tau }_c$) from Eq. (3). Additionally, it is essential that the speckle patterns are recorded with a high frame rate.

Fig. 1

Calculation of BFI ($T/{\tau }_c$).

2.4.

Transit Time Flow Measurement

The TTFM (Transonic, TS 420)) is used as a reference method to measure the blood flow rate. The blood flow volume detected through TTFM is acquired and saved with a National Instrument (NI) data acquisition card together with the customized LabVIEW program. TTFM is based on the fact that the time required for ultrasound to pass through blood is slightly longer upstream ($t_u$) than downstream ($t_d$). The flow volume Q is

2.5.

Animal Sample Preparation

All experimental procedures were approved by the Experimental Animal Management Ordinance of Beijing, China, and carried out in accordance with the guidelines for the humane care of animals. After shaving and disinfecting the ventral surface of the neck with iodine, the rat was placed on a heating pad. The common carotid arteries were accessed via a midline prelaryngeal incision and cleanly dissected from the sympathetic and vagus nerves. The rat was anesthetized by inhalation of 2% to 3% isoflurane in oxygen through a nose cone. The hair on the thorax was shaved, and the animal was fixed on the experimental platform. A CPB model for a rabbit with cardioplegic arrest using aortic cross clamping and cold crystalloid cardioplegia was established to remove the noise from the dynamic speckle. The sternum was divided in midline, the thymus was retracted, the aorta was isolated, and a Prolene 6-0 purse-string suture was placed in the right atrium. After systemic anticoagulation with heparin ($300\mathrm{IU}/\mathrm{kg}$ given intravenously), the proximal aortic cannulated with an 18G trocar. A venous drainage tube (inner diameter 4 mm) was placed in the right atrium. The aortic and right atrial cannulas were connected to the perfusion circuit. The distal aorta was ligated with an aortic cross-clamp and cold (4°C) cardioplegic solution infused into the aortic root.

4.1.

Phantom Experiment

To demonstrate that our WDR-LSCI method has the capability to measure a wide range of velocities, we designed a phantom experiment. A stack of raw speckle images of the phantom was acquired with an exposure time of $49\mu \mathrm{s}$ and a frame rate of 20,000 Hz. A $7\times 7$ sliding window was used to calculate the spatial SC maps, and the temporal contrast $K_t$ images were calculated at each pixel over 1000 consecutive frames. The system parameter $\beta$ was estimated by calculating the spatial speckle variance $K_s$ for 100 speckle patterns that scatter from the diffuser within 4.9 ms. The $\beta$ ($=K_s^2$) of our setup was derived to be 0.48. Next, we set the blood flow in the microfluidic cavity to be zero, i.e., the red blood cells were allowed to undergo natural Brownian motion, and the speckle images were recorded. Using Eq. (6), $\rho$ was calculated to be 0.93. With $\beta$ and $\rho$ determined, the BFI value was extracted by interpolation using the contrast-to-blood flow relationship of Eq. (3).

Figure 3(a) is a theoretical simulation of the SC $K$ versus the BFI ($T/{\tau }_c$) on a logarithmic scale with 7% static scattering. The region enclosed by the blue dashed lines is enlarged in the inset, in which the experimental data (red dots), shown on a linear scale, are the averaged values of three groups of data as the step motor was driven at varying rates from 0.2 to $8\mathrm{mm}/\mathrm{s}$. The corresponding flow rate in the microfluidic cavity varied from 25.4 to $635\mathrm{mm}/\mathrm{s}$. The values of $K$ in the simulated $K$-BFI plot agree well with the experimental data. Figure 3(b) shows the linear relationship between the BFI ($T/{\tau }_c$) and the blood flow rate from 25.4 to $635\mathrm{mm}/\mathrm{s}$. The black squares correspond to the experimental data, and the red line is the fitted curve, plotted as $\mathrm{BFI}=1.38+0.031v$, where $v$ is the absolute blood flow (mm/s). The results indicate that $\beta$ and $\rho$ are critical parameters for deducing the BFI, and their accurate determination can greatly improve both the linearity and WDR.^13,19,25,26 Conventionally, when it comes to realizing a WDR for a flow rate with LSCI, the multi-exposure technique in which the camera exposure time range has been clearly given has been mentioned.^13,14 However, for obtaining the blood flow rate, compared with 15 exposure times from $50\mu \mathrm{s}$ to 80 ms with a standard multi-exposure speckle imaging (MESI) and 6 exposure times from 1 to 20 ms with a synthetic MESI implementation, in our LSCI setup, we only used 50 ms (for 1000 speckle images with $50\mu \mathrm{s}$ exposure time).

Fig. 3

Theoretical simulation of the SC $K$ versus the BFI ($T/{\tau }_c$) with 7% static scattering and (inset) experimental data (red dots); blue solid lines are the simulated curve. (b) The BFI versus driving blood flow rate. Square dots, experimental values; red solid line, fitted curve ($\mathrm{BFI}=1.38+0.031v$).

4.2.

Animal Experiment Validation

To support the phantom results, we compared blood flow changes during carotid artery ligation estimated with both LSCI (BFI: $T/{\tau }_c$) and TTFM. Before performing the animal experiment, the normalized spatial autocorrelation function ${\mathrm{g}}^2(\mathrm{\Delta }x)$ versus $\mathrm{\Delta }x$ was calculated using Eq. (1), in which the intensities at a fixed pixel point $(x,y)$ are convoluted with those of the other speckles at $(x+\mathrm{\Delta }x,y)$ for each speckle pattern. As shown in Fig. 4(a), a series of speckle images are recorded in the inset, and the $31\mu \mathrm{m}$ FWHM of ${\mathrm{g}}^2(\mathrm{\Delta }x)$ of the peak gives the resolution of the system.

Fig. 4

(a) Second-order autocorrelation $g^2(\mathrm{\Delta }X)$ as a function of distance with 2000 measurements. Inset: the speckle patterns recorded to calculate the spatial resolution. The FWHM corresponding to the spatial resolution or speckle size is $31\mu \mathrm{m}$. Blue dots, experimental data; solid curve, Gaussian fit. (b)–(g) During the process of the rat carotid artery being ligated and back to normal, its blood flow map, estimated by BFI ($T/{\tau }_c$), varies on the spatial and temporal scales at times 11, 12, 13, 14, 15, and 16 s. Color bar: red represents larger blood flow rate, and blue indicates lower flow rate.

Figure 2(c) illustrates the experimental setup that we constructed to perform a rat carotid artery ligation. The micrometer was rotated forward until the blood flow of the carotid artery was compressed to zero and then rotated backward, during which both the speckle data and the blood volume were simultaneously monitored by LSCI and TTFM. The ratio dynamic scattering from the carotid artery $\rho$ was measured to be 0.98. From Figs. 4(b)–4(g), we can see that the blood flow rate map of the rat carotid artery characterized by BFI decreases and then becomes normal again, corresponding to the BFI values in Fig. 5 at times 11, 12, 13, 14, 15, and 16 s. The color bar value, i.e., BFI value, is deduced to range from 0 to 30. Red represents a higher blood flow, and blue indicates a lower flow rate. In Fig. 5, the black/red dots and lines represent the results measured by LSCI and TTFM, respectively. The blood flow measured with both methods at first fluctuates around a constant, then slows down to an extremely low value, and then rises. Compared with TTFM, LSCI performs better in line with the vessel unbinding process and has a higher sensitivity. During the period from 12 to 15 s when the carotid artery was gradually loosened, the BFI was 4.22, 12.73, 16.38, and 17.71, and the results measured by TTFM sharply increased, resulting in some loss of detail.

Fig. 5

Blood flow changes during carotid artery ligation, estimated with LSCI (black dots and line) and TTFM (red dots and line).

To further deduce the blood flow rate from TTFM, the diameter of the rat carotid artery was measured. A segment of the artery sample was fixed by 4% paraformaldehyde, then trimmed, dehydrated, embedded, sliced, dyed, and sealed. Finally, qualified samples were chosen through microscopic inspection. First, the panoramic slice scanner (3DHISTECH, Hungary, PANNORAMIC) scans and images the tissue slice. Then, the scanning software (3DHISTECH, Hungary, CaseViewer2.4) and analysis software (Media Cybemetics, United States, Image-Pro Plus 6.0) are used to measure the diameter of the blood vessel. As shown in the inset of Fig. 6, the inner diameter of the rat carotid artery ($354.6\mu \mathrm{m}$) is the average diameter measured in the red area by the software (Media Cybemetics, United States, Image-Pro Plus 6.0). The blood flow rate (blood volume/inner area/s) during the ligation process is shown in Fig. 6, where the blood flow volume from 0 to $1.8472\mathrm{mL}/\min$ corresponds to the flow rate of 0 to $320\mathrm{mm}/\mathrm{s}$. Compared with TTFM, LSCI not only measures the blood flow rate over a WDR, but also has a higher sensitivity. Additionally, LSCI obtains a wide-field two-dimensional blood flow rate in a noncontact way, which can be applied in observing spatio-temporal changes of the blood flow rate in the ROI, especially in the spatio-temporal evolution of myocardial blood flow perfusion.

Fig. 6

Relation between blood flow rate and blood volume in rat carotid artery. Inset: rat carotid artery slice. The averaged inner diameter is 0.3546 mm, which is measured by the software in the red area.

4.3.

Preliminary Application of WDR-LSCI Method in Myocardial Blood Flow Imaging

If an LSCI device could monitor blood flow over a wide range, its function would be greatly expanded. Specifically, it could be applied to imaging myocardial blood flow distribution, which would benefit visualization of the spatio-temporal evolution of the myocardial perfusion and provide important information for studying the pathogenesis and surgery of coronary heart diseases. Here, we preliminarily apply our WDR-LSCI method to myocardial blood flow imaging. Irregular motion artifacts from the heart beating and ventilator do significantly affect the measurement accuracy of the myocardial blood flow rate in our LSCI method. Chizari et al.¹⁷ proposed a model based on the optical Doppler effect to predict SC drop as an indication of motion artifacts. However, the main focus of our paper is the WDR measurable by LSCI, with the possibility of its application to myocardial perfusion imaging in vivo. Thus, in our experiment, we utilized a CPB model for a rabbit with cardioplegic arrest and a high-speed camera to circumvent motion artifacts. The regions of interest include large and small veins, as well as veins surrounded by fat and myocardial arteriole, the diameter of which, marked by a black arrow, is 1178, 168, 140, and $104\mu \mathrm{m}$, as shown in Fig. 7. The vessels in the black box are the raw vessel images illuminated by white light and the corresponding BFI map as deduced by ${\mathrm{SO}}_{n = 2}$ LSCI together with coherent parameter $\beta$ (=0.48) and dynamic scattering fraction $\rho$. We should notice, however, that, unlike the simulation and phantom results, the $\rho$ in the vessel of the four regions needs to be calculated separately because the optical properties of turbid media across the four regions marked by black boxes are nonergodic. We chose $20\times 20\text{pixels}$ marked by the blue boxes to deduce $\rho$ to be 0.965, 0.992, 0.985, and 0.971. From Fig. 7, it is clear that WDR-LSCI can provide good images of the myocardial blood flow distribution. Indeed, Padmanaban et al.³² found that there is a consistent change in the $\rho$ factor as the channel diameter increases, i.e., increasing the tube diameter causes a higher drop in the SC for a certain volumetric flux. There are two reasons for the $\rho$ values not being consistent with the results of Padmanaban et al.³²: (1) The heart of a rabbit is small, and its surface is not flat. We have to translate or tilt the LSCI system to focus on the ROI, which leads to variation in the coherent parameter $\beta$. (ii) The optical properties of vessels in the four ROIs are all different; for example, because the scattering coefficient of the fat is larger than that of myocardial tissue, the exposure time has to be reduced when imaging the ROI in Fig. 7(c); the myocardial arteriole is located deeper, so the exposure time has to be longer. These changes would affect the value of $\beta$. In this work, we simply assume $\beta$ to be invariant when calculating $\rho$, so the $\rho$ values here do not increase or decrease with the vessel diameter.

Fig. 7

BFI ($T/{\tau }_c$) maps of different myocardial vessels corresponding to the region in the black box with individual dynamic scattering fractions $\rho$ that are calculated in the region enclosed by a blue square: (a) large veins with a diameter of about $1178\mu \mathrm{m}$ and $\rho =0.965$; (b) small veins with a diameter of about $168\mu \mathrm{m}$ and $\rho =0.992$; (c) veins surrounded by fat with a diameter of about $140\mu \mathrm{m}$ and $\rho =0.985$; and (d) myocardial arteriole with a diameter of about $104\mu \mathrm{m}$ and $\rho =0.971$.