## Abstract

Seven fluorescent microsphere colors can be used in a single experiment to estimate regional blood flow without correcting for spillover of emitted fluorescence. To extend the method to 13 colors, we compared the accuracy of three methods for spillover correction. Fixed wavelength intensities were corrected by matrix inversion, and synchronous scan spectra were corrected by least squares fit of an overdetermined system of linear equations and by least squares fit of a sum of Gaussian and Lorentzian functions. Correction methods were validated in pigs and sheep by simultaneous injections of radioactive microspheres and fluorescent microspheres of 7, 10, and 13 different colors. We induced extreme changes in flow to create regions with low fluorescent signals bound on either side by high fluorescent signals. Blood flow was determined by radioactivity and by fluorescence using both fixed excitation and emission wavelength pairs and synchronous scanning and then corrected for spillover. Correlation between fluorescent intensity and radioactivity were excellent for all three correction methods [*R*
^{2} = 0.98 ± 0.02 (mean ± SD)]. Low-flow regions requiring large spillover correction had systematic errors for some color combinations in all methods. We conclude that for 13 fluorescent colors spillover error can be minimized so that all three correction methods provide accurate estimates of regional blood flow.

- perfusion
- fluorescence
- spillover correction
- synchronous scanning

since introductionin 1967, use of radioactive-labeled microspheres has become a common investigative tool to determine regional organ blood flow (12). Quantification of radioactive microspheres in tissue, considered the gold standard method, is accurate and requires minimal sample preparation (6, 14). However, there are significant disadvantages to using radioactive labels, including licensing restrictions, disposal costs, short shelf life, and potential health risks associated with exposure. To overcome these limitations, nonradioactive labeling methods were recently introduced including color absorption, fluorescence, and X-ray fluorescence (4, 9,11).

In particular, fluorescent microspheres have been used as an alternative to radioactivity to measure regional blood flow in many tissue types, including heart, lung, kidney, muscle, skin, and brain (3, 4, 17). Fluorescent dyes are designed to have narrow and well-separated spectral emission bands that minimize spillover between adjacent color spectra. This property of fluorescent dyes provides a unique advantage over radioactivity and other methods. Currently, seven fluorescent colors can be used in one experiment without significant spillover (4). Thirteen colors are available that have emission bands spaced such that spillover is low (generally <10% of peak maxima) and occurs primarily between adjacent fluorescent colors. In contrast, both radioactive and colored microspheres have complex overlapping emission/absorption spectra requiring mathematical correction when using more than one blood flow marker. Several correction methods have been applied to radioactive counts, depending on type and number of isotopes. The most common methods are stripping, which can be used for up to six simultaneous isotopes (6) and matrix inversion, which has been used for up to nine simultaneous isotopes (14). Additionally, least squares fit of an overdetermined set of linear equations has been used for up to nine simultaneous isotopes (1, 18) and also has been applied to colored microspheres (9).

Spillover becomes problematic for some color combinations and introduces error when more than seven fluorescent colors are used, resulting in overestimates of regional blood flow. Matrix inversion, commonly applied to radioactivity, is one possible method for correcting for spillover contribution to neighboring fluorescent intensities. Alternatively, with the use of a spectrofluorometer equipped with variable monochrometers, fluorescent color intensities can be determined by synchronous scanning over a wavelength range so that multiple fluorescent emission bands are acquired within a single spectral curve. As with fixed wavelength intensities, up to seven colors can be acquired in a single spectrum without correcting for spillover because there is no overlap in the region of peak maxima. However, for more than seven colors there may be significant spectral overlap. It should be possible to quantify individual color intensities using curve-fitting methods developed for other more complex applications such as infrared and UV/visible spectroscopy.

The purpose of this investigation is to compare the accuracy of three methods for spillover correction when using up to 13 fluorescent colors: *1*) matrix inversion of fixed wavelength intensities,*2*) least squares fit of an overdetermined system of linear equations for synchronous scan spectra, and *3*) least squares fit of combined Gaussian and Lorentzian function for synchronous scan spectra. Combinations of 7, 10, and 13 different fluorescent microsphere colors are used in individual experiments to quantify pulmonary blood flow in anesthetized sheep and pigs. To create a challenging test of accuracy for spillover correction, extreme changes in flow were induced to produce alternating high and low fluorescent intensities along the wavelength spectrum. Fluorescent measurements were validated against simultaneous measurements using radioactive microspheres.

## METHODS

#### Matrix inversion method for fixed wavelength intensities.

Each fluorescent dye used for the microsphere method is designed to be excited and to emit light over narrow wavelength ranges (∼50 to 70 nm) with peak excitation and emission at a unique wavelength pair. In dilute solutions with no significant spillover, intensity is linear with concentration. The number of fluorescent microspheres for each color in a sample is quantified by releasing the dye label into solution and measuring emitted intensities for each color at or near peak excitation and emission wavelengths. Spillover occurs when fluorescence is emitted by more than one dye label for a given wavelength pair (Fig. 1
*A*). Therefore, the observed intensity for a given wavelength pair is the sum of the intensities for the primary fluorescent color and the spillover from adjacent colors. If spillover is linear with respect to dye concentration, true intensities can be determined by simultaneous solution of a set of linear equations using matrix inversion as described by Schosser et al. (14). The linear range for spillover with increasing numbers of fluorescent colors in solution was determined for up to 10 simultaneous colors. Methods and results from in vitro experiments are presented in appendix
.

For a set number (*N*) of fluorescent colors, maximum intensity and spillover for each color is determined by measuring intensities for a pure color solution at *N* wavelength pairs. Spillover for a specific wavelength pair is computed as the fraction of emitted intensity relative to the maximum intensity (see Fig.1
*B*). With the use of matrix algebra, fractional spillover intensities become coefficients for an *N*×*N*matrix, where *N* equals the number of colors and the matrix represents a system of *N* linear equations. With the use of matrix inversion, these equations are solved simultaneously to determine a unique solution for each unknown, i.e., true pure color intensity at each wavelength pair (see Fig. 1
*C*).

As with maximum emission, spillover intensity depends on both excitation and emission wavelengths and can be minimized by careful wavelength selection. For 13 colors, mean spillover between adjacent colors was 10.4%, ranging from 0% to 46.7% (see Table1).

The intensity acquisition and correction procedure for the matrix inversion method (MATRIX) is a three-step process: *1*) acquire intensities for each set of fixed wavelength pairs for blank solvent, pure color reference solutions of known number of microspheres, and multicolor samples; *2*) for pure color intensities subtract blank solvent intensities and compute spillover matrix; and *3*) for multicolor samples subtract blank solvent intensities, solve for individual intensities by matrix inversion, and convert intensity to number of microspheres.

#### Curve-fitting methods for synchronous scan spectra.

With the use of a standard research grade spectrofluorometer equipped with variable monochrometers, fluorescent intensity can be measured by simultaneous scanning of the excitation and emission monochrometers through a wavelength range so that multiple fluorescent emission bands are acquired in a single spectral curve. The monochrometers are scanned at a fixed separation interval, the scan interval, close to the average stokes shift of the fluorophors of interest. Peak shape, width, and position depend on the scan interval. For select scan intervals, each synchronous scan spectrum for a pure fluorescent color, contains a single symmetrical peak with a typical half-width of 20 to 25 nm and a measurable intensity range of 50 to 70 nm (Fig. 2).

Thirteen colors were selected with peak maxima occurring at well-separated intervals along the working range of a standard spectrofluorometer (300 to 700 nm) by using a scan interval of 15 nm. Peak widths and positions were sufficiently narrow and well separated so that accurate separation could be expected on the basis of infrared applications (16).

Curve fitting requires a mathematical model to describe the shape of the component bands determined from pure reference spectra. There are two basic approaches to modeling pure spectra: *1*) as an overdetermined set of linear equations and *2*) as an empirical function arising from the probability characteristics of the measurement method and energy emission process to be measured (10). Once pure component spectra have been defined as a set of mathematical functions multicomponent spectra can be separated into individual components by using a least squares fitting method.

#### Overdetermined system.

Each pure color spectrum is represented by a set of linear equations that define relative intensities at specified wavelengths similar to matrix inversion except that each unknown is described by more than one equation (7). For each pure color, a set of five wavelengths were selected to be spaced equally between the wavelength values corresponding to half of the peak intensity (Fig.3
*A*). Matrix coefficients that define relative intensities were determined for all selected wavelengths for each color so that each pure color was described by five equations. Spectra containing three colors, as shown in Fig.3
*B*, would have 15 linear equations to describe three unknowns. Hence the system is overdetermined and simultaneous solution of these equations may not have a unique solution. The best fit was determined by least squares optimization of the overdetermined system (ODLSQ) by using a program written in MATLAB (MathWorks; Natick, MA).

Synchronous scan acquisition and curve fitting using the ODLSQ method is a three-step process: *1*) acquire spectra for blank solvent, pure color reference solutions of known number of microspheres, and ulticolor samples; *2*) for individual pure color spectra subtract blank solvent spectra, select five wavelengths bound by each pure color FWHM, and compute the overdetermined matrix for all wavelength positions; and *3*) for multicolor samples subtract blank solvent spectra, perform least squares optimization of overdetermined matrix, and convert intensity to number of microspheres.

#### Gaussian and Lorentzian sum.

In spectroscopy, combinations of Gaussian and Lorentzian probability functions are commonly used to describe spectral band shape. The Gaussian shape arises from instrumental line broadening due to optical factors, electrical effects, and counting statistics. In the absence of Gaussian effects, the Lorentzian distribution function is the natural spectral band shape arising from probability factors associated with quantum emission processes (8). The Lorentzian peak function is narrow and has broader tails with respect to the Gaussian shape. We determined that a linear combination of Gaussian and Lorentzian functions best described the shape of each fluorescent dye spectra according to *Eq. 1
*
Equation 1Spectral shape, for each pure color, is defined by a unique set of values for peak center (*C*), width (*W*), and shape factor (*S*) that are fixed for a given instrument and configuration (Fig. 4). Then for a given experimental configuration intensity (*y*) is a function of wavelength (*x*) and amplitude (*A*) because amplitude is directly proportional to the concentration of fluorescent dye or number of microspheres. The shape factor accounts for the relative contribution of Gaussian or Lorentzian functions with a shape factor of 1 being pure Gaussian. Multicolor spectra can be represented by the sum of the pure component functions.

With the use of pure color spectra of a known concentration, the center, width, and shape factor values for each color are determined and fixed for subsequent fitting routines. Amplitudes are determined for specified concentrations. Table 2presents the fitted parameters for 13 colors. For unknown spectra, individual fluorescent intensities are determined by a least squares method (GAUSS) performed by using MATLAB (MathWorks) where only amplitudes are varied to determine the optimal fit of component spectra.

Synchronous scan acquisition and curve fitting using the GAUSS method is a three-step process: *1*) Acquire spectra for blank solvent, pure color reference solutions of known number of microspheres, and multicolor samples. *2*) For individual pure color spectra, subtract blank solvent spectra; fix center, width, and shape for each pure color; and determine amplitude for the specified number of microspheres. *3*) For multicolor samples, subtract blank solvent spectra, perform least squares optimization by varying amplitudes, and convert intensity to the number of microspheres.

#### In vivo perfusion studies.

These studies were approved by the animal care committee at the University of Washington and performed in accordance with regulations of the Association for Assessment and Accreditation of use of Laboratory Animals.

One sheep (25 kg) and three pigs (12–22 kg) were studied in the supine position. Anesthesia was induced with xylazine and maintained with intravenous ketamine-phenobarbital. The animals were intubated and mechanically ventilated on room air with the use of a minute ventilation sufficient to maintain arterial Pco
_{2} below 40 Torr. Catheters were placed in a femoral artery and vein and two Swan-Ganz catheters were placed, one in each pulmonary artery via the jugular vein.

Simultaneous injections of fluorescent microspheres (Molecular Probes; Eugene, OR, and Bangs Laboratories; Carmel, IN) and radioactive microspheres (DuPont-NEN Research Products; Boston, MA) were used for intermethod comparisons. Just before injection, radioactive microspheres (15 μm diameter, 1.5–20 × 10^{6} per isotope) and fluorescent microspheres (15 μm diameter, 1.0–1.5 × 10^{6} spheres per color) suspended in distilled water and 0.02% Tween were sonicated, vortexed, and mixed in one syringe. Once the animals achieved a stable hemodynamic condition, one set of fluorescent microspheres consisting of either four, five, or seven different colors and either ^{113}Sn or ^{95}Nb were injected into a femoral vein. Then a second injection of fluorescent microspheres consisting of three, five, or six different colors and ^{46}Sc was performed. During the second injection, the balloon of one pulmonary artery catheter was partially inflated to reduce flow to one lung, thereby causing a large decrease in flow to some regions. Fluorescent microspheres were selected so that adjacent colors alternated between high and low intensities along the spectrum (see Fig. 5). Injections were performed over 15–30 s. Scandium was used for the second injection so that radioactive spillover into the low-flow pieces was minimized.

Animals received papaverine (3 mg/kg) and heparin (10,000 units) to facilitate flushing of the lungs. They were deeply anesthetized, exsanguinated, and euthanized by intravenous injection of pentobarbital sodium (150 mg/kg). The lungs were excised, flushed with saline until clear, and dried at total lung capacity at a continuous airway pressure of 25 cmH_{2}O. The dry lungs were precoated with a cold setting foam (KWIK FOAM, DAP; Dayton, OH), suspended vertically in a plastic-lined box, and embedded in rapid-setting urethan foam (Polyol and Isocyanate, International Sales; Seattle, WA). Each foam block was sliced and cubed into ∼1.9 cm^{3} pieces (*n*
_{sheep} = 1,529 pieces,*n*
_{pigs} = 431, 529, and 586 pieces).

Radioactive count rates were determined for each lung piece with the use of a 3 × 3.5-in. sodium well crystal gamma counter (Minaxi Auto Gamma 5300, Packard; Downers Grove, IL). Energy windows were selected to optimize count rate and to minimize spillover for isotopes used ^{113}Sn and ^{46}Sc or ^{95}Nb and^{46}Sc. Count rates were measured to <1% counting error or for a maximum time of 10 min. Values were corrected for decay, background, and spillover by using matrix inversion (14).

Fluorescent dyes were extracted from each lung piece. Each sample was soaked in 2-ethoxyethyl acetate (3 ml each) for 4 days, stored below 22°C, and protected from light. Fluorescent intensities were determined at fixed wavelengths and by synchronous scanning using a Perkin-Elmer LS-50B spectrofluorometer equipped with an automated sampler and WINFAC software (13). The LS-50B has variable excitation and emission monochrometers (200–800 nm and 200–900 nm, respectively), bandpass widths of 2.0–20 nm, a pulsed xenon light source, two red sensitive photomultiplier tubes (R928, 200–900 nm), and a 0.4-ml high-sensitivity flow cell, in line with a DS-6 diluter and AS-91 robotic sample probe. During each analysis run, a multicolor reference solution and blank solvent were measured every 50 samples to monitor measurement reproducibility.

Fixed wavelength pairs were selected to maximize intensity and minimize spillover between adjacent colors, by using pure color reference solutions. Bandpass widths were selected to optimize signal to noise and give a broad range of intensities for a given color (4–8 nm). Count times were 1.0 s per color. Synchronous scan intensity data were acquired at 0.5-nm intervals by using a 15-nm separation between the excitation and emission monochrometers and a scan rate of 240 nm/min. Bandpass widths were 4 or 5 nm to provide optimal resolution of overlapping peaks and sufficient intensity over the entire spectra. The 50 most concentrated samples were diluted 1:1 and, if necessary, fluorescence was remeasured using the same instrument conditions to correct for quenching.

At the beginning of each sample set, blank solvent and pure color reference solutions of known numbers of microspheres (250 or 500 microspheres/ml) were measured to determine the spillover matrix or curve-fitting parameters and to convert fluorescent intensities to numbers of microspheres. Blank solvent intensity was subtracted from pure reference and sample intensity before spillover correction by using MATRIX, ODLSQ, and GAUSS methods.

Relative regional blood flow (Q) was determined for fluorescent and radioactive intensities (I) by dividing the measured fluorescence or radioactivity for each piece (I_{i}) by the mean fluorescence or radioactivity for all pieces (I_{mean}). Relative blood flow results for pairs of simultaneously injected fluorescent microspheres (Q_{FM}) and radioactive microspheres (Q_{RM}) were compared using least squares linear regression. The coefficient of determination (*R*
^{2}) was computed for each pair. Slopes and intercepts were compared with unity and zero, respectively, for a two-sided 95% confidence interval. The method of Bland-Altman (2) was used to evaluate absolute measurement error between Q_{FM} and Q_{RM} to elucidate systematic errors underestimated by linear regression. The difference between flow values for a given piece i (Q_{i,FM}and Q_{i,RM}) is plotted against Q_{i,RM}, the gold standard flow for that piece, in the Bland-Altman comparison. The coefficient of variation (CV) for repeat analyses is reported as a measure of sample fluorescence reproducibility, where CV = 100% · (SD/mean). The SD for a CV is computed from multiple measures (multiple colors) for each repeat analysis.

## RESULTS

#### In vivo perfusion studies.

The intermethod correlations for estimates of lung perfusion determined by fluorescent microspheres using MATRIX, ODLSQ, and GAUSS correction methods and radioactive microspheres are presented in Table3, for 7, 10, and 13 colors, respectively. The combined *R*
^{2} for all colors for all experiments was comparable for all three methods,*R*
^{2} = 0.98 ± 0.02, 0.98 ± 0.02, and 0.99 ± 0.02, for MATRIX, ODLSQ, and GAUSS, respectively.

As shown in Table 3, for each method, some correlations had slopes >1.0. Only the color violet, determined by the MATRIX method, had a slope significantly <1.0 (slope = 0.96) and an intercept >0 (int = 0.045). Most intercepts did not differ significantly from zero or the difference was small, ranging from 0.0 to −0.053. This occurred for some cases where the slope was >1.0.

The linear relationship and the Bland-Altman comparison for a single paired injection (carmine and ^{95}Niobium) from the 13-color experiment using the MATRIX method are presented in Fig.6, *A* and *B*, respectively. Carmine, a baseline blood flow marker, has the largest relative spillover from adjacent colors for fixed wavelength intensities and synchronous scanning (shown in Tables 1 and 2).

We also made intermethod comparisons for a subset of pieces where flow decreased to ∼20% of baseline after inflation of the pulmonary artery balloon. These low-flow pieces were expected to have the greatest spillover error. The intermethod correlations for estimates of low-flow pieces, determined by fluorescent microspheres using MATRIX, ODLSQ, and GAUSS correction methods and radioactive microspheres are presented in Table 4, for 7, 10, and 13 colors, respectively. The combined low-flow *R*
^{2}for all colors in all experiments was comparable for all methods (low-flow *R*
^{2} = 0.97 ± 0.02, 0.97 ± 0.03, and 0.97 ± 0.02, for MATRIX, ODLSQ, and GAUSS, respectively). When using 10 or 13 different colors, most colors had slope estimates significantly >1.0, ranging from 1.0 to 1.12 for all three methods. In these cases, intercepts either did not differ significantly from zero or the difference was small, ranging from 0.0 to −0.061. This occurred for some cases where the slope was >1.0. Corrected intensities for blue were underestimated by both ODLSQ and GAUSS curve-fitting methods.

The linear relationship and the Bland-Altman comparison, for a single-paired injection of crimson and ^{46}Sc for the low-flow subset from the 13-color experiment corrected using the ODLSQ method, are presented in Fig. 7,*A* and *B*, respectively. Flows determined by crimson, for these low-flow pieces, were systematically overestimated by about 10% relative to radioactivity, as evidenced by the biased distribution of scatter above zero for the Bland-Altman comparison.

Except for the color blue, no significant quenching was observed for the 50 highest flow samples, which were checked by 1:1 dilution. Observed intensities for blue were underestimated by up to 5% for some diluted samples. However, when compared with radioactivity, there was no significant difference in slopes and intercepts for flow values determined by blue with and without dilution correction.

To determine whether spillover correction methods were also valid for multiple colors with similar fluorescent intensities, we looked at a subset of lung pieces in which perfusion remained the same or increased from the first to the second injection. We found that the slopes and intercepts were not significantly different from those presented in Table 3.

## DISCUSSION

The important findings of this study are that *1*) the fluorescent microsphere method can be extended to 13 measures of regional perfusion in a single experiment and *2*) three correction methods for spillover (MATRIX method for fixed wavelength intensities, and ODLSQ and GAUSS methods for synchronous scan spectra) work equally well for most conditions.

Seven different fluorescent microsphere colors can be used in a single experiment to estimate regional blood flow, without correcting for spillover. To extend the method to 13 colors, we compared the accuracy for three methods for spillover correction including: *1*) matrix inversion of fixed wavelength intensities, *2*) least squares fit of an overdetermined system of linear equations for synchronous scan spectra, and 3) least squares fit of a sum of Gaussian and Lorentzian functions for synchronous scan spectra. Simultaneous injection of multiple colored fluorescent and radioactive microspheres is the traditional approach to validation of nonradioactive methods. However, systematic error between different colors cannot be elicited using simultaneous injections. When all labels are injected under the same conditions, true spectral intensity and contribution due to spillover from adjacent colors will vary identically in proportion to flow. Correlations and slope estimates between fluorescence and radioactivity will be the same, with and without spillover correction of fluorescence, for relative or absolute flows. Ideally, to rigorously quantify method error using multiple colors, each color should be injected with a separate radioactive label at different flow conditions. However, except for ^{46}Sc, increasing the number of radioactive labels present increases the error in estimates of radioactivity (1, 18). Because spillover only occurs in between adjacent colors, only two flow conditions are necessary to quantify spillover error for 13 fluorescent colors. We created a scenario to minimize error in the radioactive microsphere measurements and to induce the largest possible systematic spillover errors for all 13 fluorescent colors. Two sets of alternating colors of fluorescent microspheres with a single radioactive label for each set were injected at dramatically different flow conditions. We compared correlations and slope estimates between simultaneous fluorescent colors and radioactivity for all flow states and for a subset of low-flow pieces expected to have the greatest spillover error.

We found that over a broad range of flows, all three methods for spillover correction provide accurate estimates of blood flow. Systematic errors occur in all methods for some “high-flow/low-flow” color combinations. In pieces with the most extreme differences between adjacent colors, flow was overestimated up to 10% in low-flow pieces. Correction error for a given color depends on the relative intensity of adjacent colors and can, therefore, be minimized by careful color selection related to the specific experiment design.

Synchronous scanning is an accurate alternative to fixed wavelength intensities for quantification of fluorescent microspheres. Up to seven colors can be used without significant spillover between spectral bands for a single synchronous scan. To correct for spillover when using more than seven colors in a single experiment, curve-fitting methods can be successfully applied to synchronous scan spectra.

#### In vivo perfusion studies.

The linear correlation between regional lung perfusion estimates (relative to the mean) determined by simultaneous injections of fluorescent and radioactive microspheres was excellent for all correction methods for 7, 10, and 13 colors. The*R*
^{2} for all colors in all experiments was 0.98 or better (see Table 3). The three correction methods gave comparable results for a wide range of flows. There was a tendency to overestimate flow values for colors that emit at longer wavelengths, including crimson, carmine, dark red, scarlet, and violet, particularly for the curve-fitting methods, GAUSS and ODLSQ. This tendency was accentuated for low-flow pieces and with increasing numbers of colors. The primary limitation of all these correction models is the assumption that fluorophors act independently in solution, regardless of concentration or other species present. Increasing the number of colors available within the analytical range of a standard spectrofluorometer requires use of fluorescent dyes that emit in the excitation range of neighboring colors. If absorption of emitted intensity by a neighbor dye occurs, then spectral band shape or spillover is changed and is, therefore, no longer independent of other fluorescent species present in solution. Dyes that excite at longer wavelengths tend to have broad excitation and emission ranges compared with those that excite in the yellow to orange spectrum. Changes in spectral band shape is a likely cause of overestimation at longer wavelengths with an increased number of colors. This may have more effect on the synchronous scan method, which acquires intensity data for a given color over a range of wavelengths rather than for one wavelength pair. Further study is necessary to determine whether nonlinear effects are significant and can be readily accounted for within these models.

For a fivefold reduction in flow, correction methods tended to systematically overestimate flow except for blue. Most correlations were excellent. The *R*
^{2} for all colors in all experiments was 0.97 or better, except for blue and scarlet (see Table4). This overestimation occurs only in a piece where there is a large difference in flow values obtained from adjacent colors. This systematic error is likely due to limitations of the model fit at the peak extremes that tend to coincide with neighboring peak maxima. Minor underestimation of the spillover for a large peak results in overestimation of small underlying neighbor peaks. Refinement of all models for peak shape at the extremes of detection will improve the accuracy of low-flow estimates when bound by high-intensity neighbors.

In pieces with very low blue and high blue-green signals, the blue fluorescence was underestimated by all methods. Curve-fitting methods that use synchronous scan data underestimated blue by 31% and 45%, respectively, and had the poorest correlations. For synchronous scan data acquisition there is overlap of the blue spectra with minor secondary peaks for scarlet and violet. This is a significant factor for underestimation of flow and was consistent with in vitro studies using low concentrations of blue and high concentrations of scarlet or violet. Additionally, during the extraction of fluorescent dye from microspheres in lung tissue, two or more tissue compounds are released that fluoresce in the blue region with intensities equivalent to that observed with 10 to 100 blue microspheres per piece. For the 10-color experiments, blue was a low-flow marker and averaged 240 microspheres per piece, whereas tissue fluorescence was estimated to be comparable to 40 blue microspheres per piece. It is likely that tissue fluorescence was the most significant factor contributing to low correlations for all methods. Blue is the least desirable marker for low signal intensities and is modeled best using the MATRIX method.

Correlations for scarlet were also lower than for other colors, ranging from 0.93 to 0.95. Greater scatter for scarlet with a high bias relative to radioactivity has been noted in previous experiments both for in vivo studies and in vitro perfusion studies. Measurement error was eliminated as the cause of increased error for one perfusion study (13). In vitro experiments suggest either higher variability in manufacturing tolerances for dye loading of microspheres or clustering of microspheres after sonication.

To minimize spillover error, low-flow estimates should be quantified by using the most intense fluorescent colors from the yellow-green to orange-red range of the spectrum and by utilizing a minimum of 100 microspheres/piece. High-flow estimates can be accurately determined by the least intense fluorescent colors at either end of the spectrum. Increasing solvent volume for increasing numbers of fluorophors will minimize nonlinear interactions between neighboring dyes.

#### Synchronous scanning.

Synchronous scanning is a reliable alternative to the fixed wavelength method for acquisition of intensity data. As with fixed wavelength intensity, spectral amplitude for a given color is linear with concentration for dilute solutions, and up to seven colors can be used without correcting for spectral overlap. The advantages of synchronous scanning are speed and simplicity for setup and acquisition of data. Because fluorescent intensities for all colors in a given sample are acquired in a single spectral curve little preliminary work or information is necessary for a complete and accurate analysis. Acquisition time for a 10-color analysis is about 1 min for both fixed wavelength intensities using a 1-s count per color and synchronous scanning using a scan rate of 480 nm/min. The CV was computed for 50 repeat analyses for each of 10 colors in a multicolor reference solution corrected for spillover using MATRIX, ODLSQ, and GAUSS methods. All CV values were >1%. The mean CV values for 10 colors were comparable for each method (0.44 ± 0.08%, 0.74 ± 0.27%, and 0.63 ± 0.21%, respectively). When using synchronous scanning the signal-to-noise ratios are less good for colors in the blue to green range of the spectrum that tend to have longer stokes shifts and are better suited for the yellow-green to red range. Other disadvantages of synchronous scanning include *1*) less optimal signal-to-noise ratio for low-intensity colors because only a single band width is used during intensity acquisition and*2*) less optimal resolution for some color combinations when spillover is significant. The advantage of ODLSQ over the GAUSS method is speed of off-line data processing and the ability to vary the scan interval to maximize intensity and minimize spillover because ODLSQ does not depend on peak shape. The GAUSS method limits use of scan intervals to conditions where the peak shapes are symmetrical.

We have shown that up to 13 colors can be used reliably to determine regional organ blood flow using any of the three methods presented. We believe that the three methods used to correct for spillover work equally well because of the narrow excitation and emission spectra of the fluorescent dyes. Because correction for spillover by any method is not perfect, error can be minimized by careful selection of fluorescent colors relative to experiment protocol and analysis methods that minimize spillover. In addition, synchronous scanning is a reliable alternative to the fixed wavelength method for acquisition of fluorescent intensities and has the advantage of simplicity because all information is determined for a single scan.

From a practical standpoint, blue and violet colors should be avoided if possible. If dramatic changes in flow are to be expected, the low-flow measurements should use colors in the midrange of the spectrum. Larger volumes of solvent should also be used to decrease the interactive effects between adjacent fluorophors.

Software for MATRIX and ODLSQ fitting methods can be downloaded free of charge at http://fmrc.pulmcc.washington.edu. Practical information regarding color selection, spillover, and other aspects of the fluorescent microsphere method are also available on this site.

## Acknowledgments

We thank Dowan An and Shen-Sheng Wang for expertise and technical assistance.

## LINEARITY

Fluorphors in solution can lose absorbed energy by a number of pathways other than the emission of light including rotation, vibration, and interaction with other fluorphors such as collisions (5). These nonlinear interactions, collectively known as quenching, become significant at high concentrations causing a loss of emitted intensity. Previous studies have determined that intensity is linear with concentration for pure color fluorescent micropheres for ranges of 0 to 10,000 microspheres/ml solvent or higher (4,15). However, it is not known whether increasing the number of different fluorescent microphere colors in a single solution causes quenching to occur for lower concentrations per color. Additionally, it is not known how concentration affects spillover intensity.

### Methods

To determine the effect of increasing the number of microsphere colors on quenching, we measured fluorescent intensity for serial dilutions of fluorescent microspheres (Molecular Probes) dissolved in 2-ethoxyethyl acetate, for concentration ranges of 0 to 10,000 microspheres/ml per color, at 1,000 microspheres/ml increments, for *1*) single-color solutions of blue, blue-green, yellow-green, orange, red, crimson, and scarlet;*2*) four-color solutions of blue-green, yellow-green, orange, and red; and *3*) seven-color solutions of blue, blue-green, yellow-green, orange, red, crimson, and scarlet. To determine whether spillover is linear with concentration, we measured fluorescent intensity at peak and adjacent fixed wavelength pairs for serial dilutions for 13 different colors of fluorescent microspheres dissolved in 2-ethoxyethyl acetate for concentration ranges of 0 to 10,000 microspheres/ml. Fluorescent intensity was measured at fixed wavelengths and by synchronous scanning using a scan interval of 15 nm with bandpass widths of 4 nm. Intensities were corrected for solvent background.

### Results

We found that as the number of different colors in solution increased, quenching was detected at lower concentrations (microspheres/ml) of microspheres per color (Fig.8). Except for blue, quenching occurred between 3,000 and 4,000 microspheres/ml per color for both four- and seven-color solutions. Nominal quenching occurred at these concentrations for most pure color solutions, as well. For a seven-color solution, blue quenched at ∼800 microspheres/ml, significantly lower than other colors. Results were reproducible on two different spectrofluorometers and for two different excitation and emission bandpass widths of 2.5 nm each and 4 nm each.

Spillover was determined to be constant within the linear range of a given fluorescent microsphere color. For very low concentrations (<50 microspheres/ml), spillover increased slightly.

### Discussion

Accurate quantification of blood flow using fluorescent microspheres assumes that emitted intensities are linear with concentration. We determined that the effective linear concentration range for a given color is significantly reduced by increasing the number of different fluorescent microphere colors present in solution. In practice, linearity can be readily achieved by dilution of concentrated samples so that no quenching is observed. For the perfusion experiment that used 13 different colors, the average number of microspheres per piece was 2,000 per color, with a maximum of 5,000 to 9,000 ms per color for some high-flow pieces. The solvent volume used was 3 ml so that sample concentrations after dilution ranged as high as 1,700 to 3,000 microspheres/ml per color for each of the 13 colors. Except for blue no significant quenching was observed for the 50 highest flow samples, which were checked by 1:1 dilution. Observed intensities for blue were underestimated by up to 5% for some diluted samples. However, when compared with radioactivity, there was no significant difference in slopes and intercepts for flow values determined by blue with and without dilution correction.

## Footnotes

This study was supported by National Heart, Lung, and Blood Institute PO1-HL-24163.

Address for reprint requests and other correspondence: R. Glenny, Univ. of Washington, Division of Pulmonary and Critical Care Medicine, Box 356522, Seattle, WA 98195 (E-mail:glenny{at}u.washington.edu).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “

*advertisement*” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

- Copyright © 2001 the American Physiological Society