Chromophore detection by fluorescence spectroscopy in tissue-like phantoms

In the near-infrared spectral region (700 - 900 nm) light penetrates a few centimeters into tissues and hemoglobin dominates the absorption. Consequently, in vivo near-infrared tissue absorption spectroscopy becomes difficult for endogenous compounds of biological interest other than hemoglobin. Exogenous chromophore detection by fluorescence spectroscopy has the potential to provide enhanced sensitivity and specificity for in vivo optical tissue spectroscopy, facilitating the study of many important metabolites in tissues other than hemoglobin. We have performed measurements of the dc fluorescence intensity generated by a fluorophore (rhodamine B) homogeneously dissolved inside a highly scattering tissue-simulating phantom (aqueous suspension of titanium-dioxide particles). The phantom was prepared with optical coefficients (absorption and reduced scattering) similar to those of tissue in the near-infrared; these coefficients were measured with a frequency-domain spectrometer. Measurable dc fluorescence intensity signals from 1 nM rhodamine concentrations inside the phantom are reported. Furthermore, we were able to resolve changes in rhodamine concentration on the order of 1% using the dc fluorescence intensity. This dc fluorescence sensitivity is characterized experimentally at two concentrations (55 and 360 nM) and over a range of source-detector separations. Other aspects of the sensitivity are discussed over a large range of concentrations using a fluorescence photon migration model.

important substances in tissues, such as glucose and Ca, do not stand out from the rest of the tissue as detectable absorbers of near-JR light. Thus, many important endogenous substances in tissues are quite difficult to monitor with absorption spectroscopy in the near-JR region.

FLUORESCENCE SPECTROSCOPY OFFERS THE POTENTIAL OF ENHANCED SENSITIVITY
Favorable signal-to-noise ratios are a general strength of fluorescence spectroscopy. Exogenous fluorescent markers, known for their specificity, may be used to selectively selective bind to specific substances of critical biological importance. Highly specific binding fluorescent dyes have been used for many years in microscopy and in the study of biological macromolecules. Although the autofluorescence of tissues has been used for diagnosing tissue slices,4 exogenous fluorophores can provide sensitive markers for specific physiological metabolites. The ability to monitor in vivo substances in tissues would be of great usefulness to the medical/physiological community. Various aspects of fluorescence spectroscopy, such as fluorescence spectra5 and lifetime sensing,6 have been considered for in vivo tissue diagnostics.
However, the application of fluorescence spectroscopy to tissues revolves around an understanding of how fluorescence originates and propagates inside the tissue. Several groups have adopted diffusion theory to describe the creation and propagation of fluorescence light inside highly scattering media such as tissues in steady-state,7 time-resolved,8 and 91 cases. Although this approach has been experimentally verified both qualitatively and quantitatively, its experimental limits remain an open question.

GOAL AND SCOPE OF THIS WORK
Although fluorescence spectroscopy offers greater sensitivity than absorption spectroscopy in standard lowconcentration non-scattering solutions, we would like to know if this is still true in the multiple-scattering regime.
We sought to establish if nM concentrations of uniformly distributed fluorophores are realistically detectable inside multiple-scattering media. The quantification of the fluorescence sensitivity remains unanswered. For example, how well can we resolve between two similar, but not equal, fluorophore concentrations? Within what concentration ranges does fluorescence spectroscopy have its greatest sensitivity? The problem of sensitivity applied to inhomogeneities inside multiple scattering media has been addressed in terms of contrast for both fluorescence intensity and fluorescence lifetime.10 Our paper investigates the sensitivity of fluorescence spectroscopy applied to multiple-scattering media with a uniformly distributed fluorophore. Both emission and excitation photons traveling inside of a highly-scattering medium undergo frequent collisions that give rise to diffusive transport. Diffusion theory, which is a special case of the general formulation of transport theory, has become the standard model used to describe this process.'2'13 The experimental quantity of interest is the photon density, U(r,t) (photonsxm3) where r represents the distance between the source and the point in space, and t denotes the time. We shall employ diffusion theory to model the propagation of both excitation and emission light signals; throughout this work the subscripts x and m will denote the excitation and the emission, respectively.
The medium we shall consider may be characterized for our purposes by the optical coefficients (excitation background absorption coefficient), Itam (emission background absorption coefficient), j.t' (excitation reduced scattering coefficient), and tsm' (emission reduced scattering coefficient), all given in cm'. In addition, we shall uniformly distribute a fluorophore throughout the medium. This fluorophore contributes the additional absorptions ifr fld J.1a for the excitation (2') and the emission (7m) wavelengths, respectively.
In the framework of diffusion theory in the frequency-domain, the excitation photon density satisfies the familiar equation: where c) is the angular modulation frequency of the source (not the color of the light), v is the speed of light in water, vD is the excitation diffusion coefficient (cm2xs1) defined as v(3.t')', and q(r, o,t) is the excitation source term.
Equation (1) may also be expressed for the emission photon density, provided that we use emissiondependent parameters (i.e., Dm, q(r,o,t) etc.). The main difference between solving the diffusion equation for the excitation and for the emission photon densities lies in the source terms for these photons. We shall now consider the mathematical expressions for these two very different source terms in the frequency-domain approach.

ExcITATIoN SOURCE TERM: AN ISOTROPIC POINT SOURCE
In the case of the excitation, the photons are injected into the medium by a light source via an optical fiber or pencil beam. The spatial distribution of the excitation source is assumed to be an isotropic point source. In the frequencydomain approach, such an excitation source has the 14 q (r,c, ,t) = (r)P(o)exp[-iot] , (2) where 6(r) is the Dirac delta function, and P(o) is the source strength in photons per second.

EMISSIoN SOURCE TERM: A DISTRIBUTION OF POINT SOURCES
However, in the case of the emission, there are many point sources distributed throughout the medium, since any fluorophore may become an emission point source after absorbing an excitation photon. The strength of a given emission source depends upon four physical factors. First of all, q(r,co,t) depends upon the excitation photon density at that location (i.e., U(r,o,t)), since a greater density of excitation photons will result in a greater probability of absorption by the fluorophore. Secondly, q(r,w,t) must scale with the probability of excitation absorption per unit time by the fluorophore, Vaft. Additionally, we must consider that the emission source radiates into a range of wavelengths. The probability that the fluorophore radiates into a wavelength range dX about X is given by Aq(X)dX, where A is the fluorescence quantum yield and pj)) is the normalized (over all ?) emission 142 spectrum of the fluorophore without any scattering. In other words, pQ) 5 the relative emission probability per unit wavelength at 7. Finally, the emission source must reflect the fact that the fluorophore radiates at different times. If we assume a single decay rate, then the fluorophore emits on the average after a time -c (the fluorescence lifetime). After temporal convolution, the emission source term for a single fluorophore becomes: dqrn(r,o) = AVaft Ux(r,(D)(,,,(2n,)dXm. (3)

1+ (cot)
This expression further assumes negligible photobleaching, and a minimal contribution from fluorescence light that is re-absorbed and eventually re-emitted (i.e., secondary fluorescence). In other words, once an emission photon is absorbed we assume it cannot resurface again.

THE EMISSION PHOTON DENSITY
The solution to the diffusion equation for the excitation photon density, using the source of Eq. (2) takes the well known form13'5 of U(r,co)exp(-icot), where: In this expression, k(co) is a complex wave-vector (cm1) for the photon density wave with the form: This excitation photon density wave travels through the medium, exciting fluorophores in its path, and produces many fluorescence point sources along the way. Each emitting fluorophore creates its own emission photon density of the form of Eq. (4), so that numerous emission photon densities from the individual fluorophores will contribute to the total emission photon density. This fact may be expressed mathematically as a three-dimensional convolution of the emission source (Eq. (3)) with the Green's function for the diffusion equation (i.e., the form of Eq. (4) but with emission parameters). The final result takes the form: rn\' -47cvDD11, The factor J?m is a factor that contains the experimental detection system's relative spectral response, as well as the fluorophore emission efficiency pm(Xm). m may be determined experimentally. The concentration of the fluorophore (i.e., aft) is contained within the k. Only in the limit <<t is Umfr,CO) linear with  The tissue-like sample phantom consisted of an aqueous suspension of titanium-dioxide particles from white paint, mixed with black-india ink. Continuous mixing ensured that the particles remained suspended in the water. This part ofthe phantom will be referred to as the 'background', since it does not fluoresce within our wavelength region of interest. The frequency-domain spectrometer was needed to measure the phantom's background optical coefficients. For this measurement, we employed a multiple-distance, single-modulation frequency protocol.'8 The measured optical coefficients are recorded below in Table I. These particular values were chosen to reflect the optical properties of tissue exposed to near-JR light. In order to measure the phantom's background properties at 580 nm, a 580 nm beam from a Nd:YAG pumped rhodamine-6G dye laser (Coherent) excited the sample, and the signal was detected after passing through the 580 nm interference filter.  Table I -Opticaiproperties ofthe phantom at the excitation (532 nm) and the emission (580 nm) wavelengths. The background absorption and reduced scattering were measured using the frequency-domain spectrometer as described above. Note that of these four coefficients are not related to the fluorescence properties ofthe rhodamine. The extinction coefficients were measured using a commercial spectrophotometer along with a published value of the extinction coefficient at the absorption spectrum peak (554 nm). The extinction coefficients are presented in base 10. The symbol for each coefficient is provided in parentheses for convenience.
The fluorophore in the phantom was laser-grade rhodamine B (Eastman Kodak, Rochester, NY).
Rhodamine B in water has a lifetime of 1.5 ns and a quantum yield of 0.3 1 . Given that rhodamine B undergoes single exponential decay and does not photobleach easily, it is compatible with our assumptions for Eq. (6).' The rhodamine does not interact appreciably with the titanium-dioxide particles. The non-scattering absorption spectrum of this fluorophore was obtained from a commercial spectrophotometer, which provided the extinction coefficient ratios. We were able to determine the extinction coefficient at each wavelength of interest by using a published vale for the extinction coefficient at the absorption maximum, namely 6554 = 10.3x104 M 19 Concentrations in the spectrophotometer were kept below 1 .tM, ensuring that no rhodamine dimers formed.

EXPERIMENTAL PROTOCOL
Once the background optical properties of the phantom had been determined with the frequency-domain spectrometer, we then added the fluorophore. The excitation wavelength was always Xx 532 fill. The experiment followed two basic steps. First, we added rhodamine B from our aqueous stock solution (179 .tM) to the phantom with a pipette. After thoroughly mixing the solution, we then measured the DC fluorescence intensity (also referred to as emission) over a range of source-detector separations (also referred to as r), namely 1 .0 to 3 .4 cm, in 4 mm steps, using the 580 nm interference filter. The DC reference channel was also recorded. This multiple-distance scan was repeated three times, resulting in three measurements for each source-detector separation at each measured rhodamine concentration in the phantom. We also performed a measurement on the background phantom (i.e., no fluorophore) excited at 532 nm using the emission filter to measure the amount of excitation light leaking through the 580 nm interference filter. This excitation background was subtracted from the measured DC fluorescence intensity.

4.
EXPERIMENTAL RESULTS Table II Table II, as we mentioned previously. Thus, we are assured that these intensity data represent purely emission signals.
2) Each signal has been scaled to the first measurement via the DC reference channel. This sample channel scaling accounts for drifts in the laser.
3) The listed uncertainties are the standard deviations from the three independent multiple-distance scans.
• All of the uncertainties reflect the standard deviations of both the sample and reference channels, taking care to properly combine them since these errors are not independent. The errors in measuring the background subtraction have also been incorporated.
Since the counts listed are only proportional to the photon density, they are arbitrary. Nevertheless, these count values for our purposes may be used with absolute meaning. As has been previously demonstrated, we may measure the spectral response of the detector, which enables us to fmd the absolute quantum yield of the  Table II -DC fluorescence intensity in the phantom with a fluorophore measured at 580 nm. The first column reports the amount of stock rhodamine solution added to the phantom in terms ofvolume (ML). The next column converts the volume into a concentration (nM) in the phantom. The next three columns report the measured DC fluorescence intensity detected through the 580 nm interference filter at source-detector separations of 1 .8, 2.6, and 3.0 cm. These data were scaled with the DC reference channel to filter out drifts in the excitation laser intensity. Each value represents the average ofthree measurements. The uncertainties are the standard deviations, taking into account the dependent nature ofthe errors in both sample and reference channels. Since some excitation light still passed through the 580 nm interference filter, a small excitation background subtraction was taken from these data. is even more striking when we consider that for rhodamine B in water, a concentration of 1 nM creates a iafr of only 0.0001 cm* Detecting the change in the excitation light emerging from such a small change in absorption via differential absorption spectroscopy is impossible with our instrument, since the change falls within the error of the measurement. Also, changes in the excitation intensity were concealed by the noise of the measurement. Therefore, we have evidence that in the diffusion regime, nM fluorophore concentrations are measurable, even if concealed behind a substantial background absorption.

How FLUORESCENCE INTENSITY CHANGES WITH REDUCED SCATTERING
The detection of such large fluorescence signals from such small fluorophore concentrations is plausible if we consider that the multiple-scattering medium increases the path length of the excitation light. In a standard cuvette for a commercial spectrophotometer (where minimal scattering is present), the path length is typically 1 cm. In our example (at 0.894 nM) the excitation path length is on the order of 10 cm even though the source-detector separation is only 1 cm. As the reduced scattering increases, more and more fluorophores will be able to contribute to the resulting emission signal because the excitation photons travel along longer path lengths in the phantom. However, at some level the scattering will become so great that the excitation and emission photon densities will be severely attenuated. The rhodamine concentration in the phantom was I 34 nM, and the source-detector separation was 1 .8 cm.
All other values, such as the absorption and extinction coefficients, were taken from Table I. The absorption due to the fluorophore (calculated using the extinction coefficients in Table I) is given in the figure. Although the peak of the emission signal varies for different fluorophore concentrations, the emission maximum stays relatively close to iS1 10 cm1. This value of the reduced scattering is of the same order as those found in tissues.

SMALL CONCENTRATION CHANGES EXPERIMENTALLY RESOLVABLE WITH FLUORESCENCE INTENSITY
How reliably may we use the DC fluorescence intensity to resolve two similar, yet different, concentrations? By the term 'resolve' we imply that the two signals, including errors, do not overlap; they are experimentally distinguishable. In our measurements, we could consistently experimentally resolve between changes in the DC fluorescence intensity with concentration changes of about 5% (56.4 to 59. 1 nM). Smaller concentration changes from 56.4 to 58.2 nM (3 .2 %) were also resolvable for all source-detector separation of 1 .8 cm or greater. We were not able to consistently resolve between signals with changes of 1 .5 % in rhodamine concentration, but the failures were again at the closest distances. This concentration change is on the order of 1 nM at 54nM. Note that even a 10 nM change would be difficult to resolve if we used only the excitation intensity, yet here a 10 nM change is easily resolvable if we use the fluorescence intensity.
The same general pattern exists in the 357 nM range. Changes of 1 % (357 to 361 nM) in rhodamine concentration were resolvable for the larger source-detector separations, whereas changes in the neighborhood of 5 % were always resolvable (i.e., 357 to 375 nM). A change of 5% at this concentration results in a 18 nM change, which translates into a of 0.00 19 cm1. This value is still within the noise region for the determination of  Table I, using source-detector separations of 1.0, 2.6, and 3.4 cm. The absorption coefficients due to the fluorophore (iafr d La) were calculated using the extinction coefficients presented in Table I. For the sake of comparison, all three curves have been independently normalized. The maxima of these curves, using the same scale as in Fig. 2 linear, and our best sensitivity results. In the Eq. (6) was used to calculate the fluorescence intensity as a function of rhodamine region of 360 nM, we see that the concentration for three different source-detector separations. Data for the plot was fluorescence begins to level off and hence taken from Table I. Note that the concentration where the emission maximum occurs decreases significantly with increasing source-detector separation. some sensitivity is lost. Eventually the fluorescence reaches a maximum, the slope approaches zero, and the sensitivity vanishes. An important observation is that the fluorophore concentration at this maximum decreases sharply with an increase in source-detector separation. Continuing onward with increasing fluorophore concentration, we see that the DC fluorescence intensity actually begins to decrease, an effect which has been noted previously.9 If we go to higher fluorophore concentrations, the sensitivity begins to improve since the magnitude of the slope begins to increase. The location of the fluorophore concentration where the slope vanishes is a balance between the conversion rate of excitation to emission photons and the absorption rate of the emission photons. When relatively few fluorophores are present, an increase in the number of fluorophores will increase the excitation absorption rate, and hence increase the rate of emission photon generation. However, changing the fluorophore concentration will also change the absorption ofthe emission intensity (see Table I).
It is clear from the above measurements that the sensitivity of fluorescence spectroscopy greatly exceeds that of normal absorption spectroscopy in the limit of small chromophore concentrations. However, this advantage is not enjoyed over all chromophore concentrations. This may be seen with a calculation comparing the signal-tonoise ratios for changes in the detected signal for both emission and excitation photon densities. For the data presented here, small fractional changes in the concentration will be easier to detect with changes in the emission intensity as compared to changes in the excitation intensity for concentrations below approximately 600 nM and 1 80 nM for source detector separations of 1 .0 and 3 .4 cm, respectively."

CoNcLusioNs
From within the diffusion regime, we were able to detect measurable DC fluorescence intensities from 1 nM concentrations of rhodamine uniformly distributed inside of a realistic absorbing and scattering tissue-like phantom. The increased path length of the excitation photons provided by the multiple scattering phantom permits these relatively low concentrations of fluorophores to build up into a detectable emission photon density. Changes in concentration as small as approximately 1% were resolved using the DC fluorescence intensity, although this level of resolvability was found only for the longer source-detector separations. We could resolve at least 5% changes in fluorophore concentration for every source-detector separation (1 .0 to 3.4 cm) examined. A more stable excitation source should permit better resolution. Using a frequency-domain fluorescence photon migration model, we were able to see that the fluorescence sensitivity experiences pronounced changes as functions of fluorophore concentration and source-detector separation. The concentration where the fluorescence peaks, and subsequently where the sensitivity is the poorest, decreases with increasing source-detector separation. This variation in sourcedetector separation may allow for precise concentration determination with a multiple-distance protocol. We also used the fluorescence photon migration model to demonstrate that the emission signal peaks at reduced scattering values in the range of those encountered in tissues. 7.