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Laser speckle spatial contrast analysis (LSSCA) is superior to laser speckle temporal contrast analysis (LSTCA) in monitoring the fast change in blood flow due to its advantage of high temporal resolution. However, the application of LSSCA which is based on spatial statistics may be limited when there is nonuniform intensity distribution such as fiber-transmitting laser speckle imaging. In this study, we present a normalized laser speckle spatial contrast analysis (nLSSCA) to correct the detrimental effects of nonuniform intensity distribution on the spatial statistics. Through numerical simulation and phantom experiments, it is found that just ten frames of dynamic laser speckle images are sufficient for nLSSCA to achieve effective correction. Furthermore, nLSSCA has higher temporal resolution than LSTCA to respond the change in velocity. LSSCA, LSTCA and nLSSCA are all applied in the fiber-transmitting laser speckle imaging system to analyze the change of cortical blood flow (CBF) during cortical spreading depression (CSD) in rat cortex respectively, and the results suggest that nLSSCA can examine the change of CBF more accurately. For these advantages, nLSSCA could be a potential tool for fiber-transmitting/endoscopic laser speckle imaging.
©2011 Optical Society of America
1. Introduction
Over recent decades, laser speckle imaging (LSI) has become a powerful tool to investigate the spatio-temporal changes of blood flow under physiological and pathological conditions in retina [1,2], skin [3,4], cortex [5–8] and so on [9–14]. When the target is illuminated by the expanded laser source and imaged with a camera, a laser speckle pattern is generated. Due to the advantages of full field and higher spatio-temporal resolution than some other blood flow measurement techniques, such as conventional laser-Doppler flowmetry [13], LSI has shown significant potential to be a clinical tool to monitor blood flow in real time. Specially, fiber-transmitting/endoscopic laser speckle imaging which can realize blood flow measurements in human cavity becomes an important developing trend [15–18]. But for this case, the laser speckle image recorded through an imaging fiber bundle shows significant spatial discontinuous intensity distribution resulting from remarkable energy losses in fiber cladding and fiber interstitial space [19]. Because spatial contrast is defined as the ratio of the standard deviation of the intensity to the mean intensity over a 5 × 5 or 7 × 7 window sliding in one image, LSSCA would be influenced by the nonuniform intensity distribution, which results in the contrast to be risen around the border between different intensity regions. In fact, the ‘fake rise’ of the speckle contrast may result from the increase of the standard deviation of the intensity rather than the decrease of the velocity. Song et al has proposed a image processing method based on Butterworth filter to remove the fixed pattern of the fiber bundle from the fiber-transmitting laser speckle image, but the image information of the high frequency may be lost due to the low-pass filtering [20].
Since LSTCA is based on temporal statistics, it is little affected by nonuniform intensity distribution. So up to now, LSTCA is popularly adopted in previous studies [15–18] involving the fiber-transmitting/endoscopic laser speckle imaging. Although LSTCA could resist the detrimental effects of nonuniform intensity distribution, the temporal ‘smoothing’ [1] will hinder investigating the fast changes in blood flow. Moreover, a longer acquiring time needed to obtain one blood flow image will increase the incidence of motion artifact in practical applications. Forrester et al has suggested to discard the laser speckle images when the motion artifact occurred, but this is at the further expense of temporal resolution [15]. Therefore, to monitor the fast change of blood flow in time when suffering nonuniform intensity distribution, it is necessary to develop a new method to correct the negative effects of nonuniform intensity distribution on spatial contrast analysis.
In this paper, we present a nLSSCA method to correct the detrimental effects of nonuniform intensity distribution on laser speckle spatial statistics. Numerical simulation, phantom experiments and animal experiments were performed to validate and investigate the performance of this method.
2. Framework of nLSSCA
For nLSSCA, the normalized operation is firstly adopted as:
where x and y denote the coordinate of a pixel, I (x, y, i) represents the ith acquired raw laser speckle image and In(x, y, i) is the corresponding normalized laser speckle image. Iave (x, y, i) is the average of previous N frames of acquired laser speckle images.Then the local spatial contrast values of In can be calculated within a 7 × 7 sliding window which is the compromise between the loss of spatial resolution and the reliability of the contrast [21].
3. Methods and materials
3.1 Numerical simulation
By using copula tool [22,23], numerical simulation of a sequence of statistically independent dynamic laser speckle images was performed on MATLAB platform. Firstly, two statistically independent, uniformly distributed random variables X1 and X2 were produced by a random number generator. The size of the random variable determines the size of the simulated image. Secondly, by using a Gaussian copula [22], which is consist of the Box-Muller transformation and the scaling and rotation, a sequence of Z(k) following Gaussian distribution could be obtained through Eq. (2)
where n is the length of the sequence. In this paper n was set to be 50. k ranged from 1 to n. Then, through Eq. (3) the percentile transformation was performedwhere Fz is normal cumulative distribution function. After these operations, a statistically correlated sequence of T(k) following uniform distribution could be obtained. Consequently, 50 frames of correlated static laser speckle images were produced by performing Fast Fourier Transformation to scatter fields which could be expressed aswhere a is the amplitude and 2πT(k) is the phase of the scatter field A(k). m is a multiplicative factor to modulate the correlation degree of the sequence to simulate varied velocity; the bigger the m is, the faster the velocity is. In this paper for a fixed value of m, one frame of blurred dynamic laser speckle image could be obtained through averaging consecutive 30 frames of the static laser speckle images to simulate the integration process of the camera.Repeating the aforementioned simulating process with different random variables X1 and X2, a sequence of statistically independent dynamic laser speckle images could be got. In all the simulation, the minimum speckle size was set twice the size of the detector pixel to satisfy Nyquist criterion [24].
3.2 Fiber-transmitting laser speckle imaging system
The schematic setup of the fiber-transmitting laser speckle imaging system is shown in Fig. 1 . A He-Ne laser beam (Melles Griot, 632.8 nm, 15 mW, America) was expanded and collimated to illuminate an object at an incidence angle of about 30 degree. The light backscattered from the object was imaged by a lens system (two plano-convex lens, f = 25.4 mm) and the dynamic laser speckle image of the object was transmitted by an imaging fiber bundle (IG-154, SCHOTT, America) from distal-end to proximal-end. Then the image was acquired by a 12-bit charge coupled device (CCD camera, PixelFly, PCO Computer, Germany) attached to a stereo microscope (Z16 APO, Leica, Germany). The exposure time of the camera was 25 ms. The aperture diaphragm of the microscope was adjusted to make sure that the speckle size is larger than two CCD pixels [24]. The whole imaging system was placed on a vibration-isolator table (VH3036W, Newport, America).
3.3 Phantom experiments
0.5% intralipid fluid was pushed into a glass capillary tube with inner-diameter of 500 μm by a syringe-based infusion pump (Stereotaxic Syringe Pump, Stoelting CO., America). The velocity of the intralipid fluid was changed from 0.41 to 7 mm/s at the interval of 0.51 mm/s. For each velocity, 30 frames of laser speckle images of the intralipid were acquired using the fiber-transmitting laser speckle imaging system.
For the validation experiments in section 4.1, the imaging fiber bundle and the lens system were removed temporarily and the intralipid was directly imaged by the stereo microscope to the CCD camera. So the laser speckle images with uniform intensity distribution could be acquired to check whether the contrast calculated by nLSSCA is in agreement with that calculated by LSSCA.
3.4 Animal experiments
An adult male Wistar rat, weighing about 200 g, was anesthetized and fixed in a stereotactic frame. A craniotomy (about 4 mm × 3 mm) was made on the skull overlying one side of parietal cortex with a high speed dental drill under constant cooling. Cortical spreading depression (CSD) [25] is an important physiological process relating to neurological disease [26], and it is companied with a significant hyperemia phenomenon [27]. In this study, it would be induced by dropping KCl (1 M) in a burr hole located in the ipsilateral frontal bone. Also the fiber-transmitting laser speckle imaging system was used to probe the hyperemia phenomenon during CSD. After recording twenty frames of the laser speckle images of the cortex as baseline, CSD was induced and the imaging process was continued until the hyperemia phenomenon finished. The whole record process lasted for about 4 min and the interval between two adjacent frames was 1 second.
3.5 Data processing
For LSSCA, a 7 × 7 sliding window was used to calculate the local spatial contrast. The algorithm for nLSSCA was carried out as described in section 2. The same N frames of laser speckle images were used to calculate the temporal contrast for comparison with nLSSCA.
In animal experiments, to directly examine the hyperemia phenomenon during CSD, the contrast image was converted into the image of T/τc values [28,29]. Here T is the exposure time of the CCD camera, τc is decorrelation time. The relative change of T/τc was used to reflect the relative change of blood flow.
4. Results and discussion
4.1 Validation of nLSSCA
In this section, nLSSCA was validated through numerical simulation and phantom experiments. For numerical simulation, the size of the image was set to be 100 × 100, a in Eq. (4) was set to be one for whole image to produce uniform intensity distribution. One resultant simulated dynamic laser speckle image is shown in Fig. 2(a) . m was changed from 1 to 31 at the interval of 3 to produce variable contrast. For each m, 30 frames of dynamic laser speckle images were simulated in accordance with the frame number in the phantom experiments acquired for each velocity, so here the value of N for nLSSCA was 30. The mean contrast value over the whole contrast image obtained by nLSSCA (denoted as KnLSSCA) for each m is plotted as a function of that by LSSCA (denoted as KLSSCA) in Fig. 2(b). Figure 2(d) is a dynamic laser speckle image of the intralipid fluid. The mean contrast value KnLSSCA calculated from randomly selected 30 points for each velocity is plotted as a function of KLSSCA in Fig. 2(e). For numerical simulation the derived T/τc is plotted as a function of m in Fig. 2(c) and the derived 1/τc (divide T/τc by T = 25 ms) for phantom experiments is plotted as a function of the velocity in Fig. 2(f).
Fig. 2 (a) A simulated dynamic laser speckle image. (b) KnLSSCA for each m as a function of KLSSCA. (c) The derived T/τc as a function of m for numerical simulation. (d) A dynamic laser speckle image of the intralipid. (e) KnLSSCA for each velocity as a function of KLSSCA. (f) The derived 1/τc as a function of the velocity for phantom experiments.
It shows that KnLSSCA is highly correlated with KLSSCA in both numerical simulation (Fig. 2(b)) and phantom experiments (Fig. 2(e)), suggesting the validation of nLSSCA. In Fig. 2(c), the derived T/τc of our numerical simulation when m ranged from 1 to 31 is similar as 1/τc of the phantom experiments (Fig. 2(f)) when the velocity of the intralipid fluid imaged with 25 ms exposure time was changed from 0.41 to 7 mm/s.
4.2 Correcting for nonuniform intensity distribution by nLSSCA
4.2.1 Comparing nLSSCA with LSSCA
In this section the comparison between nLSSCA and LSSCA was realized through numerical simulation. The image size was set to be 200 × 200, and a in Eq. (4) was defined as shown in Fig. 3(a) to produce nonuniform intensity distribution. Different regions (denoted as background and R1 to R4) in the image were assigned different m values to indicate discrepant velocity. One resultant simulated dynamic laser speckle image is show in Fig. 3(b). Figures 3(c) and 3(d) are the contrast image of Fig. 3(b) using LSSCA and nLSSCA respectively. Here the value of N for nLSSCA was also set to be 30. In Fig. 3(e), the longitudinal changes of the contrast K in Figs. 3(c) and 3(d) are plotted.
Fig. 3 (a) The defined value of a: abackground = 1; aR1 = 0.6, aR2 = 0.3, aR3 = 0.3, aR4 = 0.6. The number of rows for R1 to R4 is 30, 5, 10, and 10 respectively. (b) The resultant simulated dynamic laser speckle image: mbackground = 2, mR1 = 5, mR2 = 15, mR3 = 15, mR4 = 15. (c) Contrast image of (b) using LSSCA. (d) Contrast image of (b) using nLSSCA. (e) The longitudinal changes of the contrast in (c) and (d).
By comparing Fig. 3(c) with Fig. 3(d), it shows that there is an obvious improvement for nLSSCA when encountering the problem of nonuniform intensity distribution. The longitudinal changes of the contrast values of the two methods are shown in Fig. 3(e). For LSSCA method, the contrast values around the border between different regions are always risen, indicated as ‘fake rise’. The rise cannot correctly reflect the change of velocity. And by comparing the ‘fake rise’ of R3 and R4, it indicates that the larger the intensity discontinuity scales is, the more significant the LSSCA contrast rise is. Even worse, for R2, which has a distinct intensity difference with background and the fewer rows than the size of the sliding window, the contrast values present completely inverse. Therefore, it can be inferred that, for practical applications of LSSCA, nonuniform intensity distribution will introduce errors in estimating diameter of the vessels and the change in blood flow, even result in the small vessels disappearing from the blood flow image [30]. However, these problems have been greatly corrected by nLSSCA in this study. In Fig. 3(e), for nLSSCA, the ‘fake rise’ does not appear anymore and the contrast of R2 is lower than that of background as expected. Besides, the contrast value in each region using nLSSCA is consistent well with that using LSSCA.
For nLSSCA, speckle size influences the mean contrast value and the statistical accuracy as it does for LSSCA [23,24]. But LSSCA contrast rise due to nonuniform intensity distribution is little influenced by speckle size.
4.2.2 Comparing nLSSCA with LSTCA
50 frames of independent dynamic laser speckle images were simulated to compare nLSSCA with LSTCA and find a proper value of N for nLSSCA. The image size was set to be 100 × 100, and a in Eq. (4) was set to be 0.9 for the left half of the image and 0.1 for the right half. So the resultant speckle image as shown in Fig. 4(a) has a significant intensity difference in the center. The whole image was assigned the same value of m so the contrast values should be similar. Two equal-size regions were chosen, one of which, marked as R1, crossed the different intensity regions and the other, marked as R2, was in the left half of the image. The mean contrast KRI and KR2 were calculated by nLSSCA and LSTCA respectively. The frame number used to calculate Iave for nLSSCA and the temporal contrast for LSTCA was equal. The ratio of KR1 to KR2 is plotted as a function of the frame number in Fig. 4(b). When the frame number equals one, nLSSCA is actually LSSCA.
Fig. 4 (a) The simulated dynamic laser speckle image with nonuniform intensity distribution. (b) The ratio of KR1 to KR2 as a function of the frame number. (c) The noise level expressed as σk /μk as a function of the frame number.
As shown in Fig. 4(b), the ratio of KR1 to KR2 using LSTCA almost maintains unity, suggesting that nonuniform intensity distribution has little influence on temporal statistics. So LSTCA can be regarded as a criterion to assess the correction ability of nLSSCA in the subsequent sections. The ratio of KR1 to KR2 using nLSSCA can also approach unity which means this method can effectively correct the detrimental effects of nonuniform intensity distribution on spatial statistics; when the frame number reaches ten, the ratio is already greater than 0.9 and then steadily asymptotic to unity. Furthermore, the noise level of the contrast, which is expressed as the ratio of the standard deviation of the contrast σk to the mean contrast μk [23], within R1 was investigated. As shown in Fig. 4(c), even when the frame number is just ten, the noise level of nLSSCA has already been kept at about 12%, which is obviously less than 25% of LSTCA. Cheng et al has pointed out that for modified LSI method at least 15 frames of laser speckle images should be used to make sure that the temporal contrast values are well correlated with the true velocity [31] and here it indicates that more than 30 frames should be required for LSTCA to decrease the noise level. Combining the ratio of KR1 to KR2 and the noise level together, it is demonstrated that ten frames of dynamic laser speckle images are sufficient for nLSSCA to achieve effective correction.
Since nLSSCA uses the current laser speckle image to analyze the contrast values and the normalization is just to correct for nonuniform intensity distribution, this method has a higher temporal resolution than LSTCA which calculates the contrast values from a sequence of images. As shown in Fig. 5 , when the velocity of the intralipid imaged by the fiber-transmitting laser speckle imaging system was abruptly changed from Brownian motion to 7mm/s at the moment of t0, nLSSCA using ten frames could not only correct the LSSCA contrast rise of the fiber-transmitting laser speckle images, but also respond immediately the change in velocity. However, LSTCA using ten frames shows an obvious delay on responding the velocity change. What’s worse, there is a significant delay for LSTCA using thirty frames to decrease the noise level. The delay phenomenon would influence monitoring the fast change in blood flow. In clinical applications, the high temporal resolution of nLSSCA could reduce the incidence of motion artifact.
Fig. 5 The response for the abrupt change in velocity of the intralipid obtained by LSSCA, nLSSCA and LSTCA respectively.
4.2.3 Phantom experiments
Here the ability of nLSSCA for correcting the detrimental effects of nonuniform intensity distribution was verified by the phantom experiments. As shown in Fig. 6(a) , the laser speckle image of the intralipid fluid is disturbed by the fiber bundle arrangement pattern (the grid structure) and the LSSCA contrast rise is serious in Fig. 6(b). It could be observed in Fig. 6(c) that once encountering the obvious intensity drop due to the fiber geometry structure, the LSSCA contrast rise would happen and be significant. However, the contrast image calculated by nLSSCA in Fig. 6(d) is uniform as expected. The mean contrast K and the derived T/τc calculated from randomly selected 30 points using LSSCA, LSTCA and nLSSCA respectively are plotted as a function of the velocity of the intralipid in Figs. 6(e) and 6(f). The frame number N for LSTCA and nLSSCA were both ten.
Fig. 6 (a) A dynamic laser speckle image of the intralipid acquired by the fiber-transmitting laser speckle imaging system. (b) The contrast image of (a) calculated by LSSCA. (c) The contrast value in the 40th column of (b) and the intensity in the 40th column of (a). (d) The contrast image of (a) calculated by nLSSCA. (e) The mean contrast K using LSSCA, LSTCA and nLSSCA as a function of the velocity of the intralipid. (f) The derived T/τc as a function of the velocity of the intralipid.
The geometry factors and intensity discontinuity scales in the fiber-transmitting laser speckle image contribute to significant LSSCA contrast rise (Fig. 6(b) and Fig. 6(e)) and the derived T/τc does not keep a linear relationship with the true velocity. However, the contrast using nLSSCA is well consistent with that using LSTCA, and both the derived T/τc of nLSSCA and LSTCA have a linear relationship with the velocity. The results also suggest that the contrast has been largely corrected by nLSSCA when the value of N is set to be ten.
4.2.4 In vivo blood flow imaging
In order to confirm the correction ability of nLSSCA in practical applications, LSSCA, LSTCA and nLSSCA were used to investigate the change of blood flow during CSD when the laser speckle images were acquired by the fiber-transmitting laser speckle imaging system.
In the CBF image (the image of T/τc) calculated by LSSCA as shown by Fig. 7(a) , the distribution of vessels cannot be distinguished, replaced by the fiber bundle arrangement pattern, and the ΔCBF (the average relative change of CBF of all the pixels within the red rectangle of Fig. 7(b)) during CSD is just about 20%, which is significantly lower than that of LSTCA and nLSSCA as shown in Fig. 7(c). For the CBF image calculated by nLSSCA, the vessels can be easily distinguished in Fig. 7(b) and the ΔCBF during CSD is greater than 100%, which is consistent with that of LSTCA using the same frame number. Therefore, nLSSCA can be considered as an alternative to LSTCA for fiber-transmitting/endoscopic LSI.
Fig. 7 (a) The CBF image calculated by LSSCA. (b) The CBF image calculated by nLSSCA using 10 frames. For improving the quality of the CBF image, there is temporal average for (b). (c) The ΔCBF during CSD as a function of time obtained by LSSCA, LSTCA using 10 frames, LSTCA using 50 frames and nLSSCA using ten frames. (d) The comparison of the time course of ΔCBF obtained by nLSSCA using 10 frames with that using 50 frames.
Furthermore, by comparing the moment when peaks or troughs of ΔCBF occurred during CSD obtained by nLSSCA and LSTCA both using ten frames, it is found that there is a little delay for LSTCA. Due to the change in blood flow during CSD is not very fast, the delay might be not significant enough. But it is worsen when more frames are used for LSTCA to get a low noise level as shown by the green line in Fig. 7(c) calculated from 50 frames. Moreover, the amplitude of ΔCBF is underestimated and the duration of the change is overestimated due to the temporal smooth of LSTCA. However, as shown by Fig. 7(d) there is still no response delay or inaccurate estimation even if the normalization of nLSSCA also uses 50 frames. Therefore, nLSSCA may be a better choice to analyze the change of CBF when the images are acquired by the fiber-transmitting laser speckle imaging system. Here the curve of LSTCA seems more smooth than other methods due to the adequate spatial average [23,30].
4.3 Noise level of nLSSCA
In section 4.2, the noise levels of nLSSCA and LSTCA are compared through numerical simulation. Here they are further compared through the practical applications. In Fig. 8(a) , the values of σk /μk calculated from the selected points in the phantom experiments are plotted as a function of the velocity of the inpralipid, and in Fig. 8(b) the values of σk /μk in the three blue regions of interest (ROI1-ROI3) located in Fig. 7(b) are analyzed for animal experiments. The size of the ROIs were small to make sure the blood flow inside could be considered as uniform.
Fig. 8 (a) The values of σk /μk as a function of the velocity of the intralipid. (b) The values of σk /μk in the three ROIs located in Fig. 7(b).
From Fig. 8, it can be observed that the noise level of nLSSCA is lower than that of LSTCA when using ten frames, not only for phantom experiments but also for animal experiments. Therefore, nLSSCA has a higher statistical accuracy than LSTCA. Due to the statistical accuracy is mainly determined by the statistical samples, the intensity difference has little influence on the noise level of nLSSCA. Because nLSSCA uses time averaging to realize normalization, the contrast error will increase in case of spatial sample dynamics occur.
5. Conclusion
By comparing nLSSCA with LSSCA and LSTCA through numerical simulation, phantom experiments and animal experiments, it is demonstrated that nLSSCA can effectively correct the detrimental effects of nonuniform intensity distribution on laser speckle spatial statistic by involving just ten frames of dynamic laser speckle images. The small number of processing frames needed for nLSSCA will be helpful to reduce the incidence of motion artifact in clinical applications. Therefore, nLSSCA may be a valuable tool to investigate the fast change in blood flow when suffering nonuniform intensity distribution in the laser speckle image, such as in fiber-transmitting/endoscopic laser speckle imaging application.
Acknowledgments
This work is supported by Science Fund for Creative Research Group of China (Grant No.61121004), the Program for New Century Excellent Talents in University (Grant No. NCET-08-0213), the National Natural Science Foundation of China (Grant Nos. 30970964, 30800339, 30801482, 30800313) and the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20090142110054).
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