Bootstrap resampling method to estimate confidence intervals of activation-induced CBF changes using laser Doppler imaging

Journal of Neuroscience Methods 146 (2005) 61–68

Bootstrap resampling method to estimate confidence intervals of activation-induced CBF changes using laser Doppler imaging Sridhar S. Kannurpatti, Bharat B. Biswal ∗ Department of Radiology, UMDNJ-New Jersey Medical School, ADMC Bldg 5, Suite 575, Bergen Street, Newark, NJ 07103, USA Received 10 September 2004; received in revised form 14 January 2005; accepted 19 January 2005

Abstract Laser Doppler imaging (LDI) signal and noise characteristics can vary significantly depending upon the underlying vascular caliber. Further, noise characteristics are not constant over time (non-stationary) and can vary during resting and activated conditions in a typical experiment. Since only a limited number of images can be acquired in a single run, concatenation of data from similar experimental trials becomes necessary which can induce further variation in temporal noise due to instrumental response. In conventional statistical analysis methods such as cross-correlation, a fixed significance threshold is generally used (for the entire image) to detect activation assuming constant noise over time and a normal distribution. As a consequence, statistical significance can become strong or weak due to temporal differences in baseline LD noise, which can possibly deviate from a normal distribution. The main emphasis of this study was the application of bootstrap resampling in conjunction with cross-correlation to estimate the confidence intervals on a pixel-by-pixel basis to avoid distributional specifications on the additive measurement error leading to reliable whisker activation-induced CBF changes. At a 95% confidence level, bootstrap resampling followed by confidence intervals for the correlation coefficient distribution increased the number of active pixels by almost 45% when compared to conventional cross-correlation. These pixels were mostly confined to areas with intermediate and large baseline LD flux with considerable deviation from normality. It is suggested that confidence intervals of the bootstrap estimates can lead to unbiased detection of CBF change in the cerebral cortex, particularly in regions with large temporal variation in noise and low CNR. © 2005 Published by Elsevier B.V. Keywords: CBF; LDI; LDF; Rat; Barrel cortex; Bootstrap; Resampling

1. Introduction Laser Doppler flow (LDF) technique has been used extensively to characterize hemodynamic response to functional activation in animal models. Though well established, LDF measurements are limited by its spatial resolution to one or two probes that have a sampling volume of 1–2 mm3 (Haberl et al., 1989). These single probe measurements cannot account for spatial variations within or between different brain regions caused by stimulus-induced changes (Braverman et al., 1990). Laser Doppler imaging (LDI) systems with mechanically driven optics enable the measurement of blood flow change by scanning in a two-dimensional raster pattern ∗

Corresponding author. Tel.: +1 973 972 7498; fax: +1 973 972 7363. E-mail address: [email protected] (B.B. Biswal).

0165-0270/$ – see front matter © 2005 Published by Elsevier B.V. doi:10.1016/j.jneumeth.2005.01.021

(line-by-line) (Wardell et al., 1993, 1994). A significant improvement in LDI over LDF is that LDI measures blood flow from every point in the image to generate a planar surface map of laser Doppler flux representing cerebral blood flow. The LDI technique has been used on a number of physiological systems including skin, skeletal muscle and brain to study blood flow (Bray et al., 2003; Lauritzen and Fabricius, 1995; Linden et al., 1995; Sommer et al., 2003; Troilius et al., 1992). In currently available commercial LDI scanners, a temporal resolution in the range of a few seconds can be achieved. However, a limitation of this system is its ability to collect a limited number of sequential images in a single ‘run’ and a temporal resolution in the range of tens of seconds, which is not very optimal in functional imaging terms. Since perfusion images with substantial spatial resolution and reproducibility can be obtained, the LDI technique

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has been useful in micro imaging studies in small animal models (Ances et al., 1999). Recently we have applied the LDI technique to study negative CBF responses adjoining positively activated areas in response to whisker stimulation in the rat model (Kannurpatti and Biswal, 2004). Traditionally activation maps (location of stimulationinduced neuronal functional responses) are statistically determined by a t-test, F-test or cross-correlation. Subsequently a significance threshold for the t-value, F-value or the correlation coefficient is used to represent activation. The most commonly used statistics is the cross-correlation analysis where an idealized reference waveform representing the “ON/OFF” cycle of the stimulus is cross-correlated with every time-course of the image signal on a pixel-by-pixel basis. Subsequently a fixed significance threshold of the correlation coefficient is applied to the correlation map. Pixels that have a signal time-course similar to the reference waveform have a high correlation value and all pixels with high correlation coefficient or above a significant threshold are considered active. However, in the above methods it is assumed that variance in each pixel is constant over time which need not necessarily be true. Further, in case of LDI studies, data from several similar experimental runs would be necessary to obtain sufficient number of sampling points. Variation in instrumental response can also induce variation in the temporal noise. Thus, departure from the above assumptions would lead to sub-optimal detection of activation. To improve statistical reliability, the bootstrap technique, a commonly used resampling procedure was used to estimate the confidence interval of LDI parameters. In bootstrap resampling, parts of the original data set are randomly selected to empirically generate pseudo sample data sets that can reproduce the population distribution exactly as the number of resamples grow. The specific parameter of interest for the pseudo-set can then be determined. This procedure is repeated a large number of times with a different sample being analyzed each time. As a consequence, pixel-wise statistical characteristics or parameters of interest can be determined. The resulting advantage of bootstrap over other parametric statistical methods is that activation maps can be generated with all pixels having the same confidence interval such that the statistical power in pixels with equivalent increase in LD flux due to task would not be decreased due to violations in distributional assumptions.

2. Methods 2.1. Surgical preparation Sprague–Dawley rats (250–300 g, n = 5) from Taconic Labs, Germantown, NY were anesthetized with urethane (1.2 g/kg i.p.). Additional bolus of anesthesia (20% of initial dose) was injected at later times if blood pressure increased to a tail pinch during the protocol. A rectal probe was used to monitor the body temperature while the animal was maintained at 37.0 ± 0.5 using a homeothermic

feedback heating system (Baxter K-MOD100, Gaymar Industries). The femoral arteries were cannulated with PE50 tubing for monitoring mean arterial blood pressure (MAP) and blood gas sampling. The rats were endotracheally intubated and administered with a single dose of gallamine triethiodide (250 mg/kg i.p.), a muscle paralysis agent, prior to mechanical ventilation. Arterial blood pressure, end-tidal CO2 and inspired oxygen concentration were continuously monitored (8100 Poet Plus Vital Signs Monitor, Criticare Systems Inc., Wisconsin). The physiological parameters under the ventilator settings used with room air were: Pa O2 = 93.8 ± 7.1 mmHg, Pa CO2 = 35 ± 3 mmHg, pH = 7.4 ± 0.06 and MAP = 92.2 ± 7.1 mmHg. The study protocol followed institutional guidelines and was approved by the Animal Research Center of our institution. The head was secured to an adjustable stereotaxic frame and the scalp was retracted from the fronto-parietal cortex region of the intact cranium by a midline incision. The temporalis muscle was disconnected from the skull and an area of 5 mm × 5 mm (2 mm posterior and 5 mm lateral to the bregma) enclosing the whisker barrel on either hemisphere was thinned to translucency (Kannurpatti and Biswal, 2004). The underlying vasculature was visible when washed with saline. The stereotaxic frame was tilted by 30◦ on the midline axis to align the whisker barrel cortex normal to the laser beam. 2.2. Laser Doppler imaging Laser Doppler imaging was carried out using the Moor LDI device (Moor Instruments, Sussex, UK). The method uses the principle of monochromatic light incident on tissue being scattered by moving red blood cells and as a consequence is frequency broadened. The frequency-broadened light together with laser light scattered from static tissue is photo-detected and the resulting photocurrent is processed to provide a blood flow measurement. Blood flow measured by the laser Doppler technique usually termed LDI flux is a quantity proportional to the product of the average speed of the blood cells and their number concentration. A plane mirror in the device was used to direct the beam from a low power (2 mW ± 20%, 632.8 nm) He–Ne laser onto the tissue surface and also collect the scattered Doppler shifted beam from the tissue, which was focused onto a photodetector. The mirror controlled by a motor enabled the laser beam to scan in a raster pattern across the surface of the tissue and the signal proportional to the tissue perfusion at each measurement point was calculated and stored. When the scanning procedure was completed, the Doppler shift was processed to build up a color-coded flux image of blood flow. The Moor LDI image can be generated in a matrix of upto 256 × 256 pixels covering an area of 5 cm × 5 cm with a maximum distance of 1 m between the head of the scanner and the tissue surface imaged. Shortening the distance between the imaged tissue and the scanner head to about 20–30 cm results in the reduction of the cross-sectional area of the laser beam

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with improved spatial resolution suitable for micro-imaging studies (Ances et al., 1999) and sensitive to a tissue depth of 0.5 mm (Jakobsson and Nilsson, 1993). Images were initially obtained with a larger field of view but lower temporal resolution. Both hemispheres over the somatosensory cortex were covered to establish activation in the contralateral cortex in response to whisker stimulation. The location of bregma in LDI pixel coordinates was also recorded. Subsequently to improve temporal resolution, images were obtained only over the contralateral cortex with the image field of view completely covering the thinned skull window and centered to the square window. Since the image field of view did not include the bregma in the contralateral images, the thinning of the skull was always performed with a square geometry with its center 5 mm lateral and 2 mm posterior to the bregma. Images were obtained with a matrix of 45 × 45 pixels covering a field of view of 0.5 cm × 0.5 cm of the cortex. At a scan speed of 4 ms/pixel with additional delays to vertically increment in the raster pattern of scanning, each image was obtained at a rate of 18 s/image. Additional dead time of 4 s between images led to a temporal resolution of 22 s. The distance between the laser and the imaged surface was 20 cm. Twenty five sequential images were obtained in each experimental run consisting of rest for the first four images (88 s); whisker stimulation for the next two images (44 s); rest for the next four images (88 s); whisker stimulation for the next two images (44 s); rest for the next four images (88 s); whisker stimulation for the next two images (44 s); rest for the next seven images (154 s) to complete the acquisition. The total time length of a single experiment was 550 s. 2.3. Experimental stimulation The left vibrissae were cut to a length of approximately 3 cm from the face and fitted through a mesh screen fixed to a solenoid-driven actuator arm while the right vibrissae was completely trimmed. The screen was positioned approximately 1 cm from the rat’s face to ensure facial hair is not stimulated during whisker activation. A timing circuit controlled the solenoid driven actuator arm with an electrical TTL pulse output that was used to mark the stimulation period extent during data collection. Whiskers were mechanically stimulated at a frequency of 8 Hz. 2.4. Image processing and statistical analysis The Moor LDI software package was used to acquire the LDI images during experiments. The flow related signal derived from the Doppler spectrum was processed via an analog to digital (A/D) converter in the imaging system. The analog processing circuit in the Moor LDI sends two output signals to the computer’s A/D converter. One is a light intensity signal derived from the summation of outputs from the four photodiodes, while the other is a flow related signal obtained from the Doppler spectrum. The light intensity and the

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blood flux signals from the A/D converter and the mirror position information signals are processed. Before image reconstruction, the signal was compensated for noise effects and color-coded in arbitrary flux units (Essex and Byrne, 1991). Further statistical analysis was performed on the image data using custom made programs developed in our laboratory (MATLAB, Natik, MA). Due to a limited number of images (25 images) that could be acquired in a single experimental run in the Moor LDI device, five identical experimental trials were concatenated (125 time points) prior to any statistical analysis. Correlation data obtained using bootstrap resampling and confidence interval determination was compared with crosscorrelation analysis, a commonly used statistical technique to determine activation. 2.4.1. Cross-correlation analysis An idealized box-car function representing the ‘ON/OFF’ cycle of whisker stimulation was used as the reference waveform and cross-correlated with every pixel time-course in the image. Cross-correlation is a standard method of estimating the degree to which two series are correlated. If we represent the ideal reference waveform as ri whose mean value is µr and the time-course of the LDI signal as ti whose mean value is µt where i = 1, 2, 3, . . ., N are the number of data points, then the correlation coefficient (cc) between the reference waveform ri and the LDI signal time-course ti is given by the relationship (Bandettini et al., 1993):
N (ti − µt )(ri − µr ) cc = 
i=1 N 2
N 2 i=1 (ti − µt ) i=1 (ri − µr ) The distribution of the cross-correlation coefficient throughout the image when no stimulus was presented was used to determine the threshold (cc) value. The null distribution of cross-correlation coefficients after cross-correlating with the reference waveform when no stimulus was present was obtained which was close to a normal distribution. A threshold of 1.96 times the standard deviation for the null distribution corresponding to an error probability of P < 0.05 was used for determining the threshold. A high threshold implies that only pixels with a time-course very similar to the idealized waveform will be considered active. This reduces the probability of type I error (allows truly inactive pixels to be highlighted as active i.e., false positives), however, it may leave out pixels that really do represent activity but have a slightly lower value due to noise. The omission of these truly active pixels is called a type II error. The optimal correlation threshold of P < 0.05 was chosen using a simple data driven approach depending on the visual activation pattern to detect most active pixels while minimizing the number of false positives (Baudewig et al., 2003). 2.4.2. Bootstrap resampling technique Consider an empirical distribution Fn associated with the original sample. The non-parametric bootstrap procedure

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generates a large number of “new” pseudo datasets that are created from the original data with the same statistical distribution as the original data sets on a pixel-wide basis. These simulated data sets have the same size as the original data set and are also generated from the original data sets. As a consequence, samples (time-points) of the new “pseudo” data sets generated from the original data set may be repeated more than once while some may be absent (Efron and Tibshirani, 1993). The data can be assumed to be a vector, yobs of n independent observations. In order to estimate the confidence interval for θ(yobs ) (correlation coefficient in the present case), the observations were sampled randomly with replacement from yobs to obtain a bootstrap dataset Y* . The boot samples of the time series and the corresponding reference waveform were generated. Cross-correlation analysis was then performed between the pseudo data sets and the corresponding reference waveform on a pixel-wide basis to obtain the resulting correlation coefficient. The above procedure was repeated 10,000 times to obtain an estimate of the bootstrap distribution. This leads to the bootstrap version of the statistic of interest θ * = θ(Y* ). Activation maps were obtained using a 95% confidence interval for the correlation coefficient distribution i.e., 0.05 × 10,000th = 500th largest bootstrapped correlation value as the lower limit (or threshold) on the one sided unadjusted confidence interval. No prior assumptions regarding the nature of the data set needs to be made for the bootstrap analysis except that the observed LDI values are independent. The primary difference between the activation images obtained using bootstrap resampling is that because the inherent variability of the time-course has been included all active pixels have the same confidence levels, which is typically not the case with fixed significance threshold activation maps. Overlapping regions between activation maps obtained by using a fixed threshold on cross-correlation maps and bootstrapped confidence interval maps were obtained by converting the two activation images into binary masks. Overlapped regions were detected on a pixel-by-pixel basis using a logical AND operation on the two binary masks. The percent overlap was calculated as the number of active pixels in the resulting mask after an AND operation divided by the number of active pixels in the resulting binary mask after an OR operation. 2.4.3. LDI simulations Simulation studies were done to compare crosscorrelation and bootstrap methods on reliable detection of activation-induced signal changes. Resting state LDI data was used on which activation was simulated in two known regions of interest (6 × 6 pixels each) in the image to evaluate the two methods. The two region of interest designated to contain activation were chosen from a low baseline LD flux region and high baseline LD flux region, respectively. Simulated activations were constructed containing a reference function in pixels in each region of interest similar to the block design in the whisker stimulation experiments. One hundred

and twenty five sequential images (with 45 × 45 matrix size) were generated. Activation was simulated for various signal amplitudes.

3. Results Laser Doppler flux images with a rectangular field of view were obtained covering the thinned skull window on either hemisphere. Fig. 1a shows an averaged color-coded laser Doppler flux image obtained from a typical anesthetized rat during rest. The average baseline laser Doppler flux image was obtained after averaging all images at rest from a single experiment i.e., four resting images from each of the three periods and the seven images in the last resting period. Pixels lying over large blood vessels had higher baseline LDI flux values when compared to pixels over small vessels and capillaries. Large surface vessels with high flux values could be easily distinguished. To detect activation, an ideal boxcar waveform representing the ‘ON/OFF’ cycle of whisker stimulation was used as a reference and cross-correlated with every pixel time-course of the LDI signal. Fig. 1b shows the correlation coefficient image in response to whisker stimulation from a typical experiment. Contralateral cortex activation in response to stimulation manifested as large clusters of pixels with high correlation coefficients (arrow). Following measurements over the thinned skull area that included both hemispheres, the contralateral whisker barrel cortex was imaged with the image field centered on the thinned skull window. Selective imaging of the contralateral cortex not only enabled the imaging of the whisker barrel cortex area being normal to the scanning laser beam but also improved temporal resolution. Substantial variation in baseline LDI signal intensity as well as noise levels were observed

Fig. 1. Typical laser Doppler images obtained from an anesthetized rat covering the whisker barrel cortex on either hemisphere. Images are color-coded in relative perfusion units. (a) Typical baseline image during rest, (b) correlation coefficient image after cross-correlation with a box-car reference waveform. The pixels within the thinned skull window show higher average flux values when compared to pixels lying over the normal skull. Clusters of pixels showing high correlation coefficient values are observed in the contralateral cortex (arrow).

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Fig. 2. (a) Baseline LDI signal time series from two representative pixels with a low baseline flux (400 rpu) high baseline flux (1500 rpu) from a typical rat. (b) Correlation of baseline LDI flux intensity with the standard deviation in each pixel from a typical rat. (c, d) Distributions of LD signal noise from a typical rat during resting and whisker stimulated conditions, respectively.

across various regions. Usually large caliber vessels had higher LDI flux and noise levels. Baseline LDI flux values spatially varied between 80 and 2000 rpu (relative perfusion units) and the standard deviation between 5 and 350 rpu over all animals. The noise level in the signal time series was distinguishably larger in pixels with higher baseline flux values when compared to pixels with low baseline flux values (Fig. 2a). A significant correlation was observed between the baseline LDI flux intensity and its standard deviation in each pixel (Fig. 2b). Since the noise level correlated linearly with LD intensity, we investigated the noise characteristics during rest and continuous whisker stimulation. Fig. 2c and d shows the distribution of LD noise in a typical image during rest and whisker stimulated conditions, respectively. A significant difference was observed between the two distributions (Kolmogorov–Smirnov test, P < 0.05). Fig. 3a shows a typical baseline LDI flux image and Fig. 3c and d shows the respective spatial pattern of LD noise characteristics during resting and whisker stimulated conditions from the same region of interest. The noise in a pixel did not seem to remain constant over time (resting versus stimulated conditions). Significant increase in noise occurred during whisker stimulation in regions with intermediate and high baseline LD flux. To test for the homogeneity of errors, a linear regression model was fit using least squares to the time series data on a pixel-wise basis. The experimental data was then tested for normality using a Kolmogorov–Smirnov test using a significance threshold of P < 0.05. Fig. 3b shows the map of D-values values above the critical value of 0.12 obtained using the Kolmogorov–Smirnov test on a pixel-wise

basis. Data points in majority of pixels deviated from normality. From the D-value map, pixels with intermediate and large baseline LD flux can be distinguished to deviate much more from normality than those with low baseline LD flux.

Fig. 3. (a) Baseline LD flux image from the contralateral somatosensory cortex in a typical rat. (b) Map of D-values above the critical threshold after a pixel-wise statistical test for normality using the Kolmogorov–Smirnov test in the same region of interest (at 95% confidence, critical D√ value = 1.36/ 125 = 0.12). (c, d) LD signal noise during resting and whisker stimulated conditions respectively from the same region of interest.

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Fig. 4. (a) Typical activation map obtained using a 95% (0.05 × 10,000th = 500th highest bootstrapped cc value) confidence interval of the correlation coefficient after bootstrap resampling of the time series on a pixel-wise basis. (b) Activation map obtained using a fixed threshold (cc ≥ 0.18; P < 0.05) to the correlation coefficient image after conventional cross-correlation analysis. (c) Baseline flux image of the whisker barrel cortex in the absence of any whisker activation from the same region of interest. (d) Map of Dvalues above the critical threshold using the Kolmogorov–Smirnov test for normality on the bootsample distributions (at 95% confidence, critical D√ value = 1.36/ 10,000 = 0.0136).

Using the bootstrap technique, the image time series and the reference waveform were resampled 10,000 times on a pixel-wise basis. Activation maps were obtained using the 95th percentile of the correlation coefficient distribution i.e., 0.05 × 10,000th = 500th largest bootstrapped correlation value as the lower limit (or threshold) on the one sided unadjusted confidence interval. Fig. 4a shows a typical activation map in response to whisker stimulation ob-

tained using the confidence interval of the correlation coefficients at 95th percentile after bootstrap resampling. Fig. 4b shows the activation map obtained using a fixed threshold of cc ≥ 0.18 (P < 0.05) using conventional cross-correlation analysis. Fig. 4c shows the average baseline LD flux image obtained over the same region of the cortex during rest. An increase in active pixels using the confidence interval after bootstrapping occurred over regions with intermediate and high baseline flux values (>500–1000 rpu). These active pixels went undetected in the conventional cross-correlation analysis (compare Fig. 4a–c). To ascertain that the increase in the number of active pixels in the 95% confidence interval map after bootstrapping was perhaps due to deviation from normality, a pixel-wise test for normality was performed using the Kolmogorov–Smirnov test on the bootstrapped correlation coefficient distribution. As shown in Fig. 4d, majority of pixels had bootsample distributions that deviated from normality. The deviation from normality was larger for regions with high baseline LD flux values (large vessels). A significant increase in the number of activated pixels was observed in the confidence interval maps when compared to those obtained by a fixed threshold for the mean correlation coefficients after conventional cross-correlation. The spatial overlap between the conventional cross-correlation maps and confidence interval maps after bootstrapping was 60 ± 16% over all animals (explained in Section 2). The number of active pixels increased by 45 ± 8% in the 95% confidence interval maps after bootstrapping when compared to the conventional cross-correlation map. Fig. 5 shows the activation maps using the confidence interval after bootstrap resampling and conventional cross-correlation followed by a fixed threshold over all animals. Though the activation pattern varied with spatial overlap of about 60% on a pixel-wise basis between the two methods, the visual spatial extent of activation was not drastically different. Simulated activations were constructed containing a reference function in pixels in two regions of interest similar to the block design in the whisker stimulation experiments. The two

Fig. 5. Activation maps in response to whisker activation using a 99th percentile confidence interval after bootstrap resampling (first row) and conventional cross-correlation followed by a fixed threshold of P < 0.01 for the correlation coefficient (second row) over all animals. The confidence interval maps after bootstrap resampling show more activated pixels than conventional cross-correlation using a fixed threshold.

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Fig. 6. Detection of truly active pixels as a function of contrast to noise ratio using the conventional cross-correlation and bootstrap methods. Simulated activations were constructed in two 6 × 6 pixel regions of interest: (a) from a low baseline LD flux region (mean LD flux = 225 and standard deviation = 47 rpu) and (b) from a high baseline LD flux region (mean LD flux = 1560 and standard deviation = 223 rpu).

region of interest designated to contain activation were chosen from a low baseline LD flux region and high baseline LD flux region, respectively. Data sets were simulated for various activation signal intensities. Fig. 6a and b shows the ratio of truly active to false positive pixels (Tp /Fp ) versus the contrast to noise ratio (CNR) for the two regions of interest. It can be observed that for both the scenarios, bootstrap performs better than cross-correlation analysis especially for lower CNR. However, for higher CNR, the performance between the two methods was similar (accurate).

4. Discussion Spatial resolution in the present study was sufficiently high to differentiate between macroscopic and intermediate blood vessels. Hence, pixel signal intensity from low flux regions represents flow with very minimal contamination from macroscopic blood vessels. Whisker stimulation-induced responses that led to a large change in LD flux values originated primarily from regions with intermediate to low baseline flux and to a much lesser extent from macroscopic blood vessels with high baseline flow values. The spatial location of the activation observed in the present study was 2.2 mm posterior and 6 mm lateral to the bregma. This is in agreement with previous electrophysiological studies and somatosensory cortex maps using stereotaxic coordinates (Chapin and Lin, 1984; Dowling et al., 1996; Hall and Lindholm, 1974; Rousche et al., 1999). In a typical LDI experiment, only a limited number of images can be obtained sequentially. For example, in the Moor LDI instrument, a maximum number of 25 images could be acquired in a single run, which limited the number of data points in the time-series. In order to improve statistical power, concatenation of data from several similar experiments was necessary. While instrumental response in different experimental runs can induce variation in temporal noise, our results also demonstrate that the LD noise levels were not similar during resting and stimulated conditions. Different variance in the LD flux values during rest-

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ing and stimulated conditions violate one of the assumptions of the parametric method of conventional cross-correlation. The bootstrap estimates (Efron and Tibshirani, 1993; Shao and Tu, 1995) may be considered more reliable as it does not assume the nature of the noise distribution. Using bootstrap resampling technique a pixels-wise distribution of almost any statistical parameter of interest (correlation coefficient in this case) could be obtained. The activation maps generated by using the confidence interval after bootstrap resampling was distinct from the maps obtained after conventional cross-correlation (60% overlap). An increase in the spatial pattern of activation after bootstrap resampling may imply better detection of truly active pixels since the confidence interval threshold may reduce the chance of pixels registering as false negatives, in this case it seems to be likely that activation from regions with higher baseline noise were detected in a robust manner using bootstrap resampling since prior assumptions about the nature of the distribution is not needed. As demonstrated by our results, the deviation from normality was far greater in pixels with intermediate and large baseline LDI flux than those with low baseline LD flux (Fig. 3d). Hence statistical power using conventional cross-correlation analysis would diminish over large vessels depending on the extent of deviation from normality. For small deviations from normality, usually from regions with small baseline LD intensities, the conventional cross-correlation analysis performed equally well as the bootstrap analysis (Fig. 6a). However, for large deviations from normality, the bootstrap resampling method performed better than the cross-correlation analysis, particularly for low CNR values (Fig. 6b). Thus, regardless of whether the underlying data is non-normal or has low-CNR, bootstrap resampling leads to a reliable detection of activation when compared to the cross-correlation method. No assumptions were necessary for the bootstrap analysis regarding the distribution of the time series data sets except that the observed LDI values are independent. This is most likely true in our study, due to the low temporal resolution used. Nonetheless, if images were acquired at a faster rate leading to time dependent data sets, the bootstrap method can easily be modified to take the time dependency into account. Bootstrap generates “pseudo” data sets that have the same distribution as the original data set. In this study, a simple “ON/OFF” stimulus paradigm (whisker activation) was used primarily to identify the spatial pattern of activation in the whisker barrel cortex. The bootstrap resampling technique can be extended to more complex parametric tasks (e.g. signal response as the frequency of stimulation) to analyze the differences in signal responses as a function of the stimulation frequency. Here the bootstrap method can generate confidence interval not only between two levels (ON versus OFF) but also between multiple parameters (varying stimulus frequency). Although, cross-correlation was used in this study, bootstrap technique can be modified for virtually any statistical test including ttest, F-test, etc.

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The advantage of bootstrap over other resampling methods such as “Jackknife” is that the number of sampling points need not be discarded during resampling and can be applied when limited number of sampling points are available (Biswal et al., 2001). This is particularly important in case of LDI measurements when the number of time points are limited. Although bootstrap is computationally expensive in a sense that instead of one cross-correlation one has to perform a large number of cross-correlations (10,000 in our case), an IBM compatible Pentium PC takes less than 30 min to perform the entire bootstrap statistical procedure. Even if the data was collected in an ideal environment and all underlying statistical assumptions were true, bootstrap technique would not be compromised in any way and would still give the correct statistics. Though the bootstrap method implemented in this study did not consider spatial correlation, which would influence the correlation threshold, it can be modified to a method similar to permutation resampling to account for spatial correlation (Logan and Rowe, 2004). 5. Conclusion The bootstrap resampling technique was robust and was able to detect activation from high flux regions with large baseline noise in the LD images where conventional method such as cross-correlation analysis was unsuccessful. Since errors are not homogeneous in the LDI images of the rat brain, representation of confidence interval maps after bootstrap resampling can be considered more reliable since it does not make any assumptions regarding the nature of the additive measurement error distribution. It may be the case that the parametric models such as conventional cross-correlation are robust to mild departures from the distributional assumptions as demonstrated by the overall spatial pattern of activation almost being similar between the two methods. Bootstrap resampling followed by the confidence interval to represent activity would be reliable in regions that deviate from normality particularly signals from regions with large vessels with low CNR. Acknowledgement This study was supported by NIH grant NS-39044 (BB). References Ances BM, Greenberg JH, Detre JA. Laser Doppler imaging of activation-flow coupling in the rat somatosensory cortex. Neuroimage 1999;10:716–23.

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