Fluorescence lifetime spectroscopy in multiple-scattering environments: an application to biotechnology

Over the past few years, there has been significant research activity devoted to the application of fluorescence spectroscopy to strongly scattering media, where photons propagate diffusely. Much of this activity focused on fluorescence as a source of contrast enhancement in optical tomography. Our efforts have emphasized the quantitative recovery of fluorescence parameters for spectroscopy. Using a frequency-domain diffusion-based model, we have successfully recovered the lifetime, the absolute quantum yield, the fluorophore concentration, and the emission spectrum of the fluorophore, as well as the absorption and the reduced scattering coefficients at the emission wavelength of the medium in different measurements. In this contribution, we present a sensitive monitor of the binding between ethidium bromide and bovine cells in fresh milk. The spectroscopic contrast was the approximately tenfold increase in the ethidium bromide lifetime upon binding to DNA. The measurement clearly demonstrated that we could quantitatively measure the density of cells in the milk, which is an application vital to the tremendous economic burden of bovine subclinical mastitis detection. Furthermore, we may in principle use the spirit of this technique as a quantitative monitor of the binding of fluorescent drugs inside tissues. This is a first step towards lifetime spectroscopy in tissues.

as udder swelling and by systemic symptoms such as fever and appetite loss.Cows infected with clinical mastitis also produce abnormal milk.Subclinical mastitis, the precursor stage of clinical mastitis, is much more difficult to detect since there are no visible symptoms from the cow or from her milk to suggest infection.The only hints given by subclinical mastitis are decreases in milk production, compositional changes in the milk, and increased numbers of both bacteria and somatic (meaning 'ofthe body') cells in the milk.For every case ofclinical mastitis detected in a herd, there may be between 15 to 40 cases of subclinical mastitis [2].1.3.Counting Cells Is the Preferred Method to Gauge Subclinical Mastitis In terms ofthe ability of a method to predict the infection status on the day oftesting, the somatic cell count (SCC) has been one ofthe best [3].Upon infection, the cow secretes leukocytes (i.e., white blood cells) to combat the invading pathogens.The term somatic refers to all cells in the milk, including leukocytes and epithelial cells.In a strong infection, well over 90% ofthese somatic cells will be leukocytes (neutrophils, macrophages, and lymphocytes).
Many researchers have found that an increase in the SCC is indicative of udder infections, but it must be stressed that this is not always true in every single case [4].Although the correlation between the SCC and mastitis is not perfect, the relationship between the SCC and lost milk production follows a general logarithmic pattern.In a large-scale statistical study, Jones et al. found that cows with a SCC above iO cells per mL produced less milk and possessed higher infection rates than cows with lower a SCC [5].Because also they found that this relationship was even stronger for a SCC above 2x105 cells per mL, most diary personnel consider 2x105 cells per mL to be the maximwn SCC for an animal considered free of mastitis.1.4 Fluorescence Lifetime Specfroscopy as a Means for Determining a Somatic Cell Count In order to "count" cells with fluorescence we must have a fluorophore that will bind somewhere onto the cell itself.One common cellular target for this purpose is DNA.There is a variety of fluorescent DNA markers but one very common (and inexpensive) one is ethidium bromide.The binding of ethidium bromide to DNA has been the subject of a considerable number of articles [6].Ethidium bromide binds very tightly to the base pairs of double stranded DNA and RNA.In addition, the emission properties of ethidium bromide change considerably upon binding to these base pairs.For example, the fluorescence lifetime ofthe ethidium bromide-DNA complex is about 12.5 times longer than the fluorescence lifetime of free ethidium bromide in aqueous solution [7].Our goal is to use this stark lfetime contrast as a quantitative indicator of the presence ofcells inside a turbid medium, in the same way as one would do so in a non-scattering medium.

Multiple Scattering Affects Measurements of the Fluorescence Lifetime
The multiple scattering of the medium does, however, change the physics of the problem.Photons propagating inside a multiple-scattering medium undertake a path length that is on average many times longer than the geometrical separation between source and detector.This path length depends upon the optical properties of the medium, unlike the case of the fixed path length of a photon travelling inside a purely absorbing medium.The elongated photon path length complicates measurements ofthe fluorescence lifetime in both the time-and the frequency-domain approaches by augmenting the time or arrival of a single photon or by increasing the phase shift of the whole collection of detected photons.In cases of photon transport in tissues, photons require a few nanoseconds to traverse a centimeter of tissue, providing a transit time scale comparable with the nanosecond time scale of the fluorescence lifetime.One way to account for the changes in time (phase) from scattering and from fluorescence is the diffusion model of photon transport, which is the subject of the next section.This diffusion-based fluorescence model was first introduced in steady state by Wu et al. in 1993 [8].Patterson and Pogue [9] and Tromberg et al. [10] first tested the diffusion model within a frequency-domain approach in 1994.Our model is an extension ofthis frequency-domain model.

Why Investigate this Problem?
The first problem ofinterest entails the development of an inexpensive instrument for determining the SCC of a milk sample.Mastitis is widely regarded as the most costly disease in the U.S. dairy industry and in the entire U.S. animal agriculture a whole [ 1 1].It has been estimated that mastitis costs the U.S. dairy industry $2 billion annually, which amounts to roughly $200 per cow.The economic burden ofmastitis is felt the strongest in reduced milkproduction.Bacteria damage the inside of the mammary gland, and eventually lactating tissue is replaced by non-lactating scar tissue.The decrease in milk production costs the dairy industry an estimated $1 .3 billion a year, or 70% of the total estimated loss due to mastitis.Most ofthese mastitis losses ( 75%) have been associated with the subclinical as opposed to the clinical stage [12].
In addition, a cell-laced milk sample provides a realistic tissue phantom for the purpose ofinvestigating fluorescence spectroscopy in tissues.To date, there are few fluorophores that possess lifetime contrast mechanisms which have been approved for human testing by the Food and Drug Administration.

2.1.
Notation Conventions Our chromophores may be divided into two groups.The background chromophores, designated by the subscript b, form the first group.In this treatise, we employ the term 'background' to mean anything that is not fluorescent.The N independent fluorescent chromophores, designated by the subscriptf form the second group.Further, we shall use the subscript n as a species index for the fluorophores.Thus, the total absorption ofthe medium takes the form: We have also used the subscript conventions ofx and m to denote the excitation and the emission wavelengths, respectively.Thus, Lam represents the absorption of the medium as a whole at the emission wavelength (i.e., km), whereas , represents the absorption of only the fluorescent species n at Am.The medium also scatters with a strength denoted by the reducedscattering coefficients ' and m'• We assume that the fluorophores themselves contribute negligible scattering.The fluorescence properties of interest in our case comprise the fluorescence lifetime, -r, the fluorescence quantum yield, A, and the fluorophore concentration, which is proportional to and p.t,, through the molar-extinction coefficient, , at the appropriate wavelength.Note that t, A, and j,, are all species-dependent quantities.

2.2.
Model for Light Propagation: Diffusion Theory 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 [13], [14].In the frequency-domain approach to diffusion theory, the quantity of interest in the diffusion equation is the photon density, U(r,a,t) (photonsxm3) where r represents the distance between the source and the point in space, t denotes the time, and o represents the angular frequency of the intensitymodulated-light source (i.e., turned on and off at frequency o/(2ir)).Our usage of diffusion theory is contingent upon meeting the following approximations (at any wavelength): (1) We must be at least one transport-mean-free path (-S from sources and boundaries. (2) The media must be scattering dominant (i.e., ' >>). (3) The collision frequency must be much greater than the modulation frequency, orf<< v.t'/(2ir), where v is the speed oflight in water (cmxs').
We shall employ diffusion theory to model the propagation ofboth excitation and emission light signals.

Expression for the Excitation Photon Density
The excitation source term is assumed to be an isotropic point source.The solution to the diffusion equation with infinitemedium boundary conditions for an intensity-modulated point source yields the familiar solution of the form U(r,o)exp(-kot) (Ref.15).If we define P1(o) as the source strength (photonsxs'), 4(a) as the source phase (degrees), and vD v(3p')' as the excitation diffusion coefficient (cm2xs'), then U(r,co) has the form: where k(o) is the photon-density wave-vector (cm1): k)=11-. (3)

Emission Photon Density
In stark contrast with the excitation point source, the emission source is a distribution of point sources dispersed throughout the entire medium.Any fluorophore may become a point source after absorbing an excitation photon.If we add up the photon density waves from all N fluorescent species, and include the detector response, we obtain the total detected emission photon density Um(r,CO)exp(iCOt), where Um(r,o) is given by [9], [10], [16], [17]: rests upon a few additional assumptions: (a) there are no interactions between the fluorescent species, (b) photobleaching is negligible, and (c) once an emission photon is absorbed, it cannot be re-emitted (i.e., negligible secondaryfluorescence contribution.tm 5 defined as the probability that our detector will detect an emission photon from species ii (details may be found in [18]).1m depends upon the detector's spectral response, the detector's spectral bandpass, and also the emission probability of species n.The emission optical coefficients now reflect average values taken over the spectral bandpass ofthe detector. 2.4.

Binding Characteristics
Ifwe desire to use Eq. ( 4) to monitor any binding process, we need a binding model that quantifies the amount of bound and free molecules in the system.One of the simplest models of a reaction is one where the binding sites on the receptor molecule are independent of each other (i.e., not cooperative, as in the cooperative case of hemoglobin and oxygen).The mathematical description of such as reaction is: where R is the number of binding sites (i.e., the receptor molecule), G is the ligand (i.e., the free molecule), and C is the complex (i.e., the bound form of R and G).The association coefficient Ka describes the formation of the complex C: Starting with a given number of ligands G0, the amount of free ligands available will be G =G0 -C as the complex forms.Similarly, the number of binding sites remaining will be R =R0 -C.Inserting these relationships into Eq.( 6) and solving for C results in the following solution in terms of concentration: The significance of Eq. ( 7) lies in that for a given total ligand concentration [G0], [C]/[G0] provides the bound fraction of the fluorophore.

EXPERIMENT
3.1.Theme of the Measurement: Titration in Cell Density The principle behind our measurement was to monitor a cell titration in a milk sample using the emission phase as the indicator.We did not know the SCC at the start ofthe measurement; all we knew at the start ofthe measurement was that the cow in question was most likely plagued with subclinical mastitis.Given the possibly of an enormous SCC at the start of the measurement, we found it was easier to dilute the number of cells in the sample, while keeping everything else (i.e., the ethidium bromide concentration and the optical properties) constant.

Instrumentation
The basic components of our standard frequency-domain instrwnent are presented in Figure 1.The 514.5 nm line of an laser (Stabilite 2017; Spectra Physics, Mountain View, CA) provided the excitation.A Pockels cell provided the intensity modulation (ISS, Urbana, IL).This Pockels cell was biased at 100 V and driven by a radio-frequency sine wave of frequency fthat was amplified to an amplitude of about 20 V. The modulated light was collected by a lOX microscope objective and then focused down into a 2 mm core diameter fiber.We took some light away for an optical reference channel by attaching directly a smaller 1 mm core diameter fiber to the side ofthe larger fiber.
The large-core source fiber was placed inside a I L cylindrical beaker.A three-axis positioning device (not shown) moved the source fiber anywhere inside the sample.A 0.6 mm core diameter detector fiber was placed at a distance r away.This fiber was placed well inside the medium so that we simulated an infinite-medium geometry.We used an aspheric lens and a bi-concave lens to collimate the collected light.This collimation was necessary for the interference filters that follow since the throughput ofthese filters depends heavily upon the angle ofthe light striking the filter.
When studying the excitation signal, we used an interference bandpass filter centered at 514.5 nm with a 10 rim FWHM (03-Fil-004-5 14.5; Melles Griot, Irvine, CA).When studying the emission signal, we used a combination of two filters: an interference bandpass filter centered at 600 rim with a 10 rim FWHM (P10-600-F; Corion, Holliston, MA), plus one standard glass longpass filter.The total transmission of this filter combination was approximately 40% at 600 rim, and provided at least 6 OD rejection at 514.5 rim.
The collected light was then focused onto a photomultiplier tube (PMT).This sample channel PMT was driven by another amplified synthesizer signal, this time at a frequency off+0.00125MHz.A heterodyning effect was achieved, which produced a 1250 Hz signal that was digitized, Fourier transformed, and analyzed with a personal computer [19].A master synthesizer provided both a 2 MHz clock signal for the data-acquisition card, and a 10 MHz reference signal to phase lock the synthesizers with the data acquisition card.The software for the card perfonned the averaging and the fast Fourier transform ofthe data, which provided the average intensity (DC), the amplitude (AC), and the phase relative to the source.

The Sample
The major element of the sample was a 1 L volume of fresh bovine milk, which had been taken from a cow who had displayed signs of subclinical mastitis.A testing facility later reported that the milk contained 2.263x 106 cells per mL.We made certain to complete all measurements with the milk within 24 hours after milking.Throughout the measurement, we verified that the milk was at room temperature.Although we did not measure the pH of the milk, the pH of healthy and infected milk (pH 6.5) does not alter noticeably the binding characteristics of ethidium bromide.In order to label the cells, we added ethidium bromide to the milk to a final concentration of 19.4 M. Since ethidium bromide cannot traverse the cell membrane, we also added the detergent Triton-X to the sample (0.002 % of the total volume).The pertinent spectroscopic properties of ethidium bromide are listed in Table I [20], [21].
We diluted the milk in order to change the SCC.However, this dilution also lowered in linear fashion the scattering and the absorption optical coefficients ofthe milk.In order to keep everything of importance constant, we replaced the milk we removed from the sample with an equivalent amount of a Liposyn suspension (20% solids, Abbott Laboratories, Chicago, IL).The Liposyn suspension possessed optical coefficients within about 10 % ofthe optical coefficients ofthe milk at ?.In addition, both ethidium bromide and TritOn-X concentrations in the Liposyn suspension were the same as those in the milk sample.Thus, by replacing milk with this Liposyn suspension, we could keep essentially everything of importance constant, while decreasing the number ofcells per mL.
We could not help but notice the interesting colors of milk and Liposyn when laced with ethidium bromide.Without ethidium bromide, both are, of course, white.Upon the addition of ethidium bromide, the Liposyn suspension turned a light pinkish-red color (sort of the color of strawberry milk).This we expected, since the dye remains in solution in the Liposyn, and as such the emission is centered at about 620 nm.However, in the milk the same concentration of ethidium bromide produced an orange hue.This is possible only if DNA is present, since the peak emission for the bound form of ethidium bromide is closer to 600 rim, and hence more orange in color.
Figure 1 -ExperimentalApparatus.An laser beam, modulated by a Pockels Cell Modulator, provided a 514.5 rim beam that was focused into a bifljrcated optical fiber by an optical objective.One leg of this fiber directed light to a reference photomultiplier tube (PMT) to correct for laser drifts.The other leg of the bifurcated fiber (the source fiber) injected light into the sample medium.Another fiber (the sample fiber) collected light from inside the medium.Both source and sample fibers were placed inside the 1 L sample volume to form an infinite-medium geometry.Although not shown, the sample fiber was moved by a computer-controlled 3D positioning device.The sample fiber sent the collected light to a collection of lenses to collimate the light before passing through optical interference filters.The light was then focused onto a sample PMT.Both PMT's were driven by an amplified (AMP) synthesizer signal.The sample and reference signals were independently cross-correlated down to 1250 Hz, and sent to a data-acquisition card inside a 486 PC computer.The card converted the current to a voltage and then digitized it.Software recorded the sample and reference DC intensities, AC sample intensity, and the phase.All components of this instrument were phase locked, as indicated by the dotted lines in the figure.Also not shown is the magnetic mixing plate.

Experimental Protocol
At each cell concentration, we measured the excitation photon density (514.5 rim) at both 10 and 100 MHz, as well as the emission photon density (600 nm) at 10 MHz.We performed the measurement at 100 MHz in order to measure the optical properties ofthe medium using a multi-distance protocol as described by Fantmi et al. 22 The excitation measurement served as a reference for the phase in order to determine 4xo(a); in other words, instead ofusing a reference fluorophore to determine the instrumental phase, as is commonly done in frequency-domain lifetime spectroscopy, we referenced the phase against the scattering of the medium.Starting with the pure milk-dye sample, we diluted the sample in steps of 2 by removing half of the milk-dye sample, and replacing it with an equal amount of the Liposyn-dye suspension.We performed this dilution 10 times, which gave us dilutions ranging from 2° to 20 (or 1024).The sample was mixed using a magnetic stir plate, and we were careful to thoroughly mix the sample after each cell dilution.Although the optical properties changed slightly with each dilution, these discrepancies manifest themselves weakly in the emission phase at 10 MHz.Because of the changes in the optical coefficients, we used the average optical properties of all the measurements in the subsequent analysis; this is the reason for the rather large errors in the reduced-scattering coefficients of Table II.We also measured the optical properties at 635 rim with a laser diode in order to estimate the optical properties at 600 rim.  2 presents the changes in the emission phase at 10 M}lz resulting from the SCC titration measured at r 0.5 cm.The points represent the measured emission phase from the sample, which we corrected for the autofluorescence of the milk and the Liposyn.The solid line is a prediction ofthe emission phase, using the optical coefficients given in Table II.Note that in the high SCC range, the phase is essentially constant, which led us to believe that this represented cell densities where the bulk ofthe ethidium bromide was in a bound state.The fit we performed was one so-called "by eye."The values we used in the fit are listed in Table III.0.0538 0.0006 0.025 0.005 Figure 2--Response of the emission phase to a titration in the SCC.The points represent the measured phase and the line represents the prediction of the fluorescence-diffusion model.We used Eq. ( 7) to calculate the concentrations of the bound and free ethidium bromide populations in the sample.The solid line is a best "fit by eye," using the values given in Table ifi and the optical coefficients of Table II.The errors in phase are confined within the physical dimensions of the symbols.

Discussion of the Fitted Parameters
Although in some ways it is impossible to determine the actual values, each of the fitting parameters actually makes sense if we consider the work of So et al. [23].The additional binding sites provided by the cellular organelles should decrease the effective iç, since it is less likely for the ethidium bromide to bind to the cellular organelles than to the DNA.This of course, would increase the effective Kd.We are using the term 'effective' to imply the overall binding ofthe ethidium bromide to any target within the cell.In a pure DNA environment, we would normally expect less than 20 % ofthe 7x109 binding sites per bovine cell to provide targets for ethidium bromide [24], [25].However, we also would expect that the number of binding sites will also increase from the estimate of iO per cell since the ethidium bromide will bind to many targets other than DNA inside the cell.Finally, there is the shortened lifetime.We have observed in other experiments that the bound state lifetime of ethidium bromide in yeast cells is quite a bit lower than it is for DNA in solution.So et al. observed in mouse fibroblast cells that ethidium bromide bound to the cytoplasm, the nucleus, and the nucleoli [23].All of these additional binding sites lowered the average lifetime of the bound ethidium bromide.The average lifetime of all of the bound ethidium bromide turned out to be about 12 ns, which is what we measured in Figure 2. Consequently, the ratio of the quantum yields of the free to the bound states must now be about 1 .7/12.2 0.14 instead of 1.7/22 0.08.Factors such as the slight changes in the optical coefficients from dilution to dilution have a miniscule effect on this problem since the photon-density wave at 10 MHz is insensitive to changes in the scattering and in the absorption.
One final note about this plot is in order.There is some interplay between the number of binding sites and the effective Kd.However, lowering the effective Kd below 0.7 1iM provided no realistic means to compensate with the number of cells.Physically speaking, we expected the effective Kd to increase.The value of 7 tM offered the lowest effective Kd together with a reasonable number ofbinding cites per cell that could reproduce the data.We interpreted this to mean that as far as we could tell, this was the best fit.

Usefulness in Counting Cells
It is clear that the emission phase in Figure 2 tracked the changes in the cell density from within the multiple-scattering medium.The graph monitored the binding of not only the ethidium bromide to the DNA, but also the binding of the ethidium bromide to other cellular components.The question is, so what?It would be possible to construct a low-cost instrument capable ofdetecting the 5CC ofan undiluted milk sample.It would be relatively simple to Iranslate an emission phase into a SCC once a calibration curve has been acquired (as in Figure 2).Such an instrument would use a much smaller sample size, say at least a factor of 100 smaller than the 1 L sample we used.The main sacrifice we must make in reducing the sample volume is that it will be more difficult to measure the optical coefficients accurately.As we have shown, the effect of the uncertainty ofthe optical coefficients is minimal in this situation since we are looking at photon-density waves at 10 MHz.The reduced scattering of the milk should change in response to changes in the milk-fat content.The fat content of milk is one of the more important compositional quality factors of interest in the diary industry.A highly reflective sample holder could be used to simulate an infinite medium, and allow measurements ofthe optical properties.
Such an instrument could have two possible audiences.One would be the current testing facilities that test for milk 5CC.Currently, the 5CC is detennined by electronic cell counters and flow cytometers.However, it might also be possible to bring quantitative cell counting to the farm.Dairy farmers might benefit from being able to perform accurate somatic cell counting in milk samples as often as they see fit.Without an actual completed instrument, it is not clear that such ability will be economically helpful.A distinct advantage would be that it could be performed on individual quarters (i.e., one of the cow's four udders), something which testing facilities do not check.The accuracy ofthe method would be far superior to the subjective California mastitis test (CMT), which is one of the only mastitis detection machines on a farm.Of course, the CMT is also dirt cheap to perform (-$20 for enough reagent to test many animals).
Regardless, the key issue for such a farm instrument is undoubtedly cost.The price of such an instrument could be quite low.For example, one could use a $3 LED provided by Hewlett Packard, which outputs an amazing 120 mW across a 35 nm bandwidth centered at 472 nm.The modulation depth of this device at 10 MHz is at least 50%, dropping down to about 20% or so at 100 MHz.Ethidium bromide is very cheap, but also very toxic.It would be very nice to produce a unit that could be used as the milking occurs, but the use of a toxic dye might make this difficult.

5.3.
Implications for Tissue Spectroscopy Such a measurement is also possible in tissues.Of course, ethidium bromide may not be used in a patient!The spirit of the measurement provides hope that we could perform similar measurements in vivo with a suitable fluorophore.Any lifetime difference between bound and free states would provide a tremendous differentiation between the two states.One of the biggest problems in pharmaceutical research is finding out where in a tissue a drug actually settles.It is one thing to develop an anti-cancer drug that destroys cancer cells in a petri dish; it is another problem altogether to get it to achieve this objective in vivo.Ifthe drug itself is fluorescent, or if some fluorescent carrier can bring it to the target, it would be possible to study the binding ofthe drug to its target in vivo.This information, provided by a non-invasive in vivo measurement, could prove invaluable to the pharmaceutical industry in trying to observe where their drugs actually travel.
Although the results ofthe fitting in the previous section reflect an effective binding process of ethidium bromide to the cell, using multiple modulation frequencies would provide a means to select populations of binding sites based upon their fluorescence lifetimes.Each organelle or compound with a distinct lifetime could be extracted via this phase-sensitive filtering scheme.This principle is nothing new; it has been used before in frequency-domain fluorescence spectroscopy in non-scattering media.Regardless, the same strengths of frequency-domain lifetime spectroscopy in the cuvette or on the microscope slide apply to the turbid medium as well.

CONCLUSIONS
We have performed successful measurements of a titration in the number of cells by monitoring the binding of ethidium bromide to a conglomerate of cellular targets using the fluorescence lifetime as the contrast mechanism.The novelty of the measurement rested with the fact that we performed this measurement in an undiluted fresh milk sample, which had optical properties that were in the same range as those of soft tissues.We were able to quantitatively keep track of the number of cells within this multiple-scattering medium using a diffusion-based model, demonstrating that fluorescence lifetime spectroscopy may be performed in turbid media as in purely absorbing media.

a
[R][G] Kdwhere the brackets represent the concentration of the molecule in question.The dissociation constant Kd quantifies the dissociation of C into R and G.The K,, which is given in units of Molar, tells us that the lower the Kd, the tighter the binding.

Table I -
Spectroscopic Data for Ethidium Bromide in Free and DNA -Bound Forms

Table II -
Measured andExtrapolated Optical Coefficients ofthe Sample

Table ifi -
Fitted Parameters in Figure2