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1. Derivation of Neutral Red Absorbance from the intensity of backscattered light.
Mathematically, the reduction in the amount of backscattered light (I) in the presence of Neutral Red can be treated in a way similar to the more familiar, absorptionmediated decrease in transmitted light (T). In a very thin slice of absorbing medium, the reduction in transmitted light dT is proportional to light intensity, slice thickness (dx), and the concentration (c) and specific extinction coefficient () of the absorbing agent, or
EMBED Equation.3 , or EMBED Equation.3 (formula 1)
Integrating this over total depth (x) of absorbing medium gives rise to:
EMBED Equation.3 , or EMBED Equation.3 (formulas 2,3)
or in reverse form to:
EMBED Equation.3 (formula 4)
Here, specific absorption (c*) is proportional to the natural logarithm of transmitted (Tx) to initial light intensity (T0). As transmitted light passes through many thin optical layers, a reverse process takes place, causing reflection of a fraction of transmitted light. Neglecting surface reflection and assuming a simple proportional factor (rp) between backscattered (I) and transmitted (T) light, TV camera recorded light backscattering becomes a function of T(x), integrated over medium depth of x:
EMBED Equation.3 (formula 5)
In the final form, this becomes:
EMBED Equation.3 (formula 6)
Assuming that almost all light is absorbed within the tissue by the time it reaches the deep end and does not bounce from the backend of the tissue back to the front (i.e. lim ec**x ! 0), the formula for backscattered light obtains the form of:
EMBED Equation.3 , or simply EMBED Equation.3 (formula 7)
with A representing the previous double absorption term c*. In this context, light reflected within the tissue is inversely proportional to tissue absorbance (AT). Assuming that the absorbance due to Neutral Red (ANR) is simply additive, i.e. does not interfere or synergise with tissue absorbance, backscattered light from tissue containing Neutral Red (RNR) would be defined by the formula:
EMBED Equation.3 (formula 8)
and reflected light (RT) from nave tissue not containing Neutral Red as:
EMBED Equation.3 (formula 9)
Under these conditions, the ratio of backscattered light from tissue not containing (IT) to tissue containing Neutral Red (INR) will simply represent the ratio of AT + ANR to AT:
EMBED Equation.3 or EMBED Equation.3 (formulas 10, 11)
and subtracting 1 on both sides, this resolves into:
EMBED Equation.3 (formula 12)
2. Colour Balance and Green & Blue Absorbance Calculations
Recorded images from tissues containing or without Neutral Red were used to determine the colour balance (GreenRed, BlueRed, BlueGreen), and then employed to calculate the absorbance in green, blue and green/blue ratio, needed for the pseudocolour pH maps.
Colour balances were calculated from images from nave mice without Neutral Red. The BlueRed (Bbr) balance for each individual pixel of the image was determined by subtracting the Optical Luminosity Values (OLV, 0255, 8bit) for Red (OLVred) from that for blue (OLVblue). Similar formulas were also used for the GreenRed and GreenBlue balance. In the case of GreenRed (Bgr), 30 points were added, as the 8bit Optimas calculations only support operations in the 0255 range and luminosity in green was lower than in red. For the GreenBlue balance, additional 20 points were added, for the same reason:
EMBED Equation.3 (formula 13)
EMBED Equation.3 (formula 14)
EMBED Equation.3 (formula 15)
For processing RGB images from Neutral Red injected mice for pH map data, redderived Blue (rdB) value was calculated by starting with OLVred/nr and adding the BlueRed balance, and, in case of redderived Green (rdG), the GreenRed balance
EMBED Equation.3 (formula 16)
EMBED Equation.3 (formula 17)
The relative absorption in the blue bandwidth (Abl) was calculated according to formula 7 by substracting OLVblue/nr from rdB and dividing it by OLVblue/nr; that for absorption in green (Agr) by substracting and dividing it with OLVgreen/nr. Relative absorption in green to blue (Agr/bl) was obtained by dividing the two:
EMBED Equation.3 (formula 18)
EMBED Equation.3 (formula 19)
EMBED Equation.3 (formula 20)
3. pHi Calibration
We used the pHmediated changes in the absorption spectrum of brainpermeable pH indicator Neutral Red (La Manna, 1984), via colour photometry of backscattered light (INR). The apparent pHi was deduced from Neutral Red absorption in the green and blue wavebands using 3CCD RGB video camera and Optimas 6.5 image processing software. This change in absorption was first calibrated using 10mm tall, fluid well columns containing 10% brain homogenate in 0.1M phosphate/boric acid buffer with defined pH values ranging from 5.0 to 8.0 (fig 1A) (La Manna 1984). Homogenates of fresh brain tissue in 0.9% saline were prepared by passing the tissue sequentially through 20, 23 and 26gauge needles. In a microtitre plate (Nunc) 200(l standard brain homogenate solutions were made containing 10% brain homogenate, in 0.1M phosphate/boric acid buffer corrected to known pH (5.08.0). To explore whether intravital binding of the indicator would change its pH or spectroscopic properties, in one set of experiments, brain homogenates were mixed with neutral red in vitro; in the second, brain homogenates were prepared from animals injected with Neutral Red 2 hours previously. Calibration curves were constructed using brain homogenates from mouse pups injected in vivo, 2h previously, with neutral red (as above), and with unstained brain homogenate to which 15(l of 0.1% Neutral Red was added. Phosphate/borate buffered brain homogenates without Neutral Red were used as controls for light backscattering (I0) in the absence of Neutral Red absorption. Absorption in blue and green (and red), were calculated from I0/INR for blue and green wavebands, respectively (see formulas 112, supplemental material 1), and the resulting Green/Blue ratio (G/B) fitted using a formula derived from the law of mass action:
EMBED Equation.3
with the relative absorptions c1 and d1 of acidic Neutral Red in the green and blue wavebands, and c2 and d2 for the basic Neutral Red, respectively.
EMBED Equation.3
with the c1/d1 building the upper (acidic) asymptote and c2/d2 ( = c2/d1 / d2/d1) the lower (basic) asymptote of the calibration curve shown in Supplemental fig.1B. Spectroscopic differences between intravital and invitro admixture of Neutral Red were minimal. Best fit minimum squares algorithm for intravital Neutral Red revealed an apparent pKnr of 6.35, c1/d1 of 3.84, c2/d1 of 1.05, and d2/d1 of 0.87. The calculated curve fitted the data points with an r2 value of 0.977. In the following part, the pH was calculated using the reverse formula:
EMBED Equation.3
4. Single image processing technique
Since both basic and acidic forms of Neutral Red absorb only weakly in the red part of the visible spectrum compared with their maxima in blue and green, respectively, we next explored the potential of using the red waveband recording from the same section as a surrogate marker for the wouldbe intensity of backscattered green and blue light in the absence of Neutral Red. This would then allow calculation of absorbance from the actual (with Neutral Red) and the wouldbe intensity (without Neutral Red) of backscattered light in the green and blue waveband, allowing pixel by pixel determination of pH from directly recorded RGB images of the cut brain surface.
As shown in fig.1, the colour balance analysis of backscattered light following unilateral carotid occlusion alone (fig.1C), showed very similar mean values for the green to red differential (i.e. difference in the optical luminosity values/OLV in between blue and red) averaged across the brain for the occluded (left) and nonoccluded (right side) in the absence of Neutral Red. Similar absence of significant ipsi to contralateral difference was also observed for the average blue to red, and blue to green balance. Further analysis also showed very similar levels of intraimage, pixel to pixel standard deviations on the occluded, as well as the nonoccluded side (fig.1D). Similar absence of ipsi to contralateral difference for mean and SD values was also observed after 90 min exposure to 8% oxygen (fig.1E,F).Moreover, the interpixel standard deviations were also relatively moderate, i.e. at most 4 OLV points or just 1020% of the absolute colour balance values.
To determine whether these balances stay the same or change before, during or after hypoxic/ischemic insult, we next examined the changes in the green to red, blue to red and green to blue colour balance in unoperated control animals, after carotid occlusion alone, after 3090 min exposure to 8% oxygen and at 224h of reoxygenation (fig.1GI). With the exception of the moderate ipsi to contralateral difference of 34 points in green to red, and blue to green balances at 30 and 60 minutes of 8% oxygen (p<0.05, paired ttest), all other time points did not reveal a significant difference between occluded and nonoccluded side. As shown in fig.1J, inclusion of the 3.5 poik{P
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In contrast to the green to red balance, that for blue to red increased, from approx 17.5 points for the right as well as the left side in control animals, peaking at approx 25 points after 90min of hypoxia (p<0.05 in one way ANOVA and posthoc Tukey, vs. the nave, 30min hypoxia, and 2&6h of reperfusion). It then decreased to 13 points at 6h of reoxygenation (p<0.05 vs. CROC, 60&90min hypoxia and 2&24h reperfusion) and returned to approx 23 points at 24hours. As expected, reverse changes were observed for the green to blue balance, with a peak in control animals and 6h reoxygenation, and a trough following 90 min of hypoxia. To avoid systemic errors and for reasons of consistency, all pH map calculations were therefore based on settings derived from nave mice not injected with Neutral Red but that experienced the same HI insult and reoxygenation conditions as the animals injected with Neutral Red.
Page PAGE 5 of NUMPAGES 5
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