## Abstract

We present for the first time experimental images of fluorescence lifetime distribution using model-based reconstruction. The lifetime distribution in our phantom experiments was realized through using an oxygen-sensitive dye [Sn(IV)Chlorin-e_{6}-Cl_{2}-3Na (SCCN)] whose lifetime varied with the oxygen concentration provided in the target and background media. The fluorescence tomographic data was obtained using our multi-channel frequency-domain system. Spatial maps of fluorescence lifetime were achieved with a finite element based reconstruction algorithm.

©2002 Optical Society of America

## 1. Introduction

Recently the idea of reconstruction-based fluorescence diffusion tomography has been developed for clinical applications such as breast cancer detection and tissue functional mapping [1–4]. This new imaging approach relies on the fact that the lifetime of fluorophores in tissue can potentially provide tissue functional information such as tissue oxygenation, pH, and enzyme [2–5]. It is also based on the fact that the fluorophores may preferentially accumulate in tumors, hence providing enhanced sensitivity for cancer detection [6,7]. In this type of indirect imaging method, a model-based reconstruction algorithm is crucial which allows for the formation of a spatial map of fluorophore concentration and/or lifetime in tissue.

This paper explores the possibility of fluorescence lifetime tomography (FLT) based on oxygen-sensitive dyes. Hohenberger *et al*. [8] have recently shown that the oxygen concentration for healthy and cancerous breast tissue is significantly different. They reported the values of oxygen concentration for healthy, fibroadenomas (benign lesions) and malignant lesions as 56, 63 and 44 mmHg, respectively. Fibroadenomas have higher oxygen content than the surrounding tissue because the solubility for oxygen of the fluid inside is presumably higher. Conversely, a malignant tumor has lower oxygen content than the surrounding tissue because of the high rate of mitosis. Mitosis requires a lot of energy from the cell that raises the cells metabolic rate. As the metabolic rate of the cell increases, oxygen use goes up and therefore the oxygen content in the malignant tumor is less than the surrounding tissue. It has also been shown in the literature [9–12] that the lifetimes of some fluorescent dyes are sensitive to the amount of oxygen present in solution/tissue. The more oxygen there is, the lower the lifetime: oxygen concentration and lifetime is quantitatively correlated by the well-known Stern-Volmer equation [13]. Thus tissue oxygen concentration maps can be derived from lifetime images obtained using FLT.

To date fluorescence reconstructions are largely limited to imaging of fluorophore concentration [14], or fluorescence-enhanced absorption [15]. In this paper we present successful quantitative reconstruction of lifetime distributions from frequency-domain measurements using tissue-like phantoms containing SCCN dye with varied oxygen content in the target and background. To the best of our knowledge, the results shown here are the first experimentally reconstructed images for which recovery of lifetime profile has been achieved with absolute ac excitation and fluorescent emission data.

## 2. Methods and Materials

#### 2.1. Reconstruction Algorithm

Based on a set of coupled diffusion equations that describe the propagation of both excitation and fluorescent emission light in tissues, our reconstruction approach casts image formation as a nonlinear optimization problem in which the optimization parameters are optical and fluorescent properties. While the details of our reconstruction algorithm can be found in Ref. 4, we outline a special formulation for the phantom study reported here. In frequency-domain, it is known that propagation of both excitation and fluorescent emission light in tissues can be described by the following coupled diffusion equations [3,16]:

where Φ_{x,m} is the photon density for excitation (subscript x) or fluorescent light (subscript m), D_{x,m} is the diffusion coefficient, μ_{ax,m} is the absorption coefficient due to contributions from both non-fluorescing chromophores and fluorescent dye, μ_{ax→m} is the absorption coefficient for the excitation light due to contribution from fluorescent dye, ω is the modulation frequency, c is the velocity of light in the medium, and η and τ are the fluorescent quantum yield and lifetime, respectively. S(r,ω) is the excitation source term in (1) which for a point source can be written as S = S_{o}δ(r - r_{o}), where S_{o} is the source strength and δ(r - r_{o}) is the Dirac-delta function for a source at r_{o}. The diffusion coefficient can be written as D_{x,m}(r) = 1/3[μ_{ax,m} (r) + [μ′_{sx,m}(r)] where μ′_{sx,m}(r) is the reduced scattering coefficient. In this study we use the non-zero photon density boundary conditions (BCs) or Type III BCs: -D_{x,m}∇Φ_{x,m} ∙ n̂ = αΦ_{x,m}, where n̂ is the unit normal vector for the boundary surface and α is a coefficient that is related to the internal reflection at the boundary.

Making use of finite element discretizations, we can obtain two matrix equations for Eqs. (1) and (2) and realize other derived matrix relations through differentiation, which lead to a set of equations capable of inverse problem solution:

where the elements of matrix [A_{x,m}] are ${\left({a}_{x,m}\right)}_{\mathrm{ij}}=<-{D}_{x,m}\nabla {\psi}_{j}\xb7\nabla {\psi}_{i}-\left({{\mu}_{a}}_{x,m}-\frac{\mathrm{i\omega}}{c}\right){\psi}_{j}{\psi}_{i}>$ where < > indicates integration over the problem domain; ψ_{i} and ψ_{j} are locally spatially-varying Lagrangian basis functions; the entries in column vectors {b_{x,m}} are ${\left({b}_{x}\right)}_{i}=-\u3008S{\psi}_{i}\u3009+\alpha {\displaystyle \sum _{j=1}^{M}}{\left({\Phi}_{x}\right)}_{j}\oint {\psi}_{j}{\psi}_{i}\mathrm{ds}$ and ${\left({b}_{m}\right)}_{i}=-<\eta {{\mu}_{a}}_{x\to m}{\displaystyle \sum _{j=1}^{N}}{\left({\Phi}_{x}\right)}_{j}{\psi}_{j}{\psi}_{i}\frac{1-\mathrm{i\omega \tau}}{1+{\omega}^{2}{\tau}^{2}}>+\alpha {\displaystyle \sum _{j=1}^{M}}{\left({\Phi}_{m}\right)}_{j}\oint {\psi}_{j}{\psi}_{i}\mathrm{ds}$ where ∮ expresses integration over the boundary surface where Type III BCs have been applied. χ expresses D_{x}, μ_{ax}, ημ_{ax→m}, or τ; ℑ_{x,m} is the Jacobian matrix that should be formed from ∂Φ_{x,m}/∂χ at the boundary measurement sites; Δχ is the update vectors for the optical and fluorescent property profiles; I is the identity matrix; λ may be a scalar or a diagonal matrix; and ${\mathrm{\Phi}}_{\mathrm{x},\mathrm{m}}^{\mathrm{o},\mathrm{c}}$ = {(${\mathrm{\Phi}}_{\mathrm{x},\mathrm{m}}^{\mathrm{o},\mathrm{c}}$)_{1},(${\mathrm{\Phi}}_{\mathrm{x},\mathrm{m}}^{\mathrm{o},\mathrm{c}}$)_{2}, ⋯ (${\mathrm{\Phi}}_{\mathrm{x},\mathrm{m}}^{\mathrm{o},\mathrm{c}}$)_{N}}^{T} and (${\mathrm{\Phi}}_{\mathrm{x},\mathrm{m}}^{\mathrm{o}}$)_{i} and (${\mathrm{\Phi}}_{\mathrm{x},\mathrm{m}}^{\mathrm{c}}$)_{i}, respectively, are observed and calculated photon density for i=1, 2, …, M boundary locations. Note that to estimate D_{x}, μ_{ax}, ημ^{ax→m}, and τ spatially we expand these quantities in a similar fashion to Φ as a finite sum of unknown coefficients multiplied by the locally defined Lagrangian basis functions. In FLT, images are formed by iteratively solving Eqs.3)–(5) and updating the optical and fluorescent property distributions from presumably uniform initial estimates of these properties.

#### 2.2. Experiments

Our experimental setup is an automated multi-channel frequency-domain imaging system that has been described in detail elsewhere [17,18]. In this system, an intensity-modulated 635-nm light from a 30 mW diode laser (Thorlabs) is sequentially sent to the phantom by sixteen 1-mm fiber optic bundles. For each source position, the diffused light is received at sixteen detector positions along the surface of the cylindrical phantom and sequentially delivered to a photomultiplier tube (PMT) (Hamamatsu R928). A second PMT is used to record the reference signal (<5% of the modulated light from the diode laser). The two PMTs are supplied by the radio-frequency (RF) generators (IFR Americas 2032A) at a modulated current of 100 MHz with 1.0 KHz shift. Both source and detector fiber bundles are firmly held by a black-painted metal ring structure. The multiplexing of the source/detector fibers are accomplished by two moving stages (Melles-Griot). dc, ac and phase shift signals are obtained using the standard heterodyne technique controlled by Fast Fourier Transform (FFT) Labview routines. Fluorescence signals are obtained through an 700 ± 10 nm interference filter placed in front of the detection PMT. For each experimental configuration, a total of 3×256 measurements (256 dc, ac and phases each) can be made. This requires about 8 minutes at the present time.

The oxygen-sensitive dye used (SCCN) was obtained from Frontier Scientific (Logan, UT) and used without further purification. The peak absorption and emission for this dye are near 635 and 694 nm, respectively. We used a 30 mm diameter cylindrical solid phantom (1% Intralipid + 10 mg/liter SCCN + 2% Agar) as the background medium which had
μ_{a} = 0.005 / mm and μ′_{s} =1.0/ mm . A glass tube (10 mm outer diameter, 9.5 mm inner diameter) was inserted as a target at different positions, as shown in Figs. 1a and 1b. The target tube contained a solution with the same amount of mixture of Intralipid and SCCN as the background. Thus both the target and background had the same scattering/absorption coefficients and fluorophore concentration. The lifetime contrast was introduced by varying the amount of oxygen content in the target and background. The gas delivery system, shown in Fig. 1c, was a simple home-made system designed to obtain only three differing oxygen concentrations where the oxygen partial pressure (pO_{2}) above the target solution was 0, 0.21, and 1.0 atm. Since we found that lowering the oxygen content of the target (0 atm) gave the greatest lifetime contrast with our system, we used 0 atm pO_{2} above the target and 1 atm pO_{2} above the background for all our experiments. In these experiments, nitrogen was bubbled into the target solution for a half hour while the background was simply open to air. Finally, we conducted an experiment with homogeneous phantom where the target and the background had the same oxygen concentration (1 atm). This experiment was aimed to see if the 0.5 mm thickness of the target tube and the absence of agar in the target have significant effect on our results.

## 3. Results and Discussion

The finite element mesh used for obtaining the results shown in this section consisted of 249 nodes and 448 triangle elements. The final images reported are the result of 20 iterations. Figure 2a presents the reconstructed lifetime image when the target was positioned at 3 o’clock, while Fig. 2b gives the lifetime profile along a cut-line through the centers of both the target and background as shown in Fig. 1a. As can be seen, the target is clearly detected. We note that the peak lifetime value of the target and the value of the background lifetime are in excellent agreement with the expected values of 1.14 and 0.80 ns for the target and background, respectively (the expected lifetime values of the dye solution at 0 and 1 atm pO_{2} were measured using a standard lifetime spectrometer). While the target is accurately located, the target size is underestimated in this case. The lifetime image and its profile for the target at a deeper location (12 o’clock) are shown in Figs. 3a and 3b. While we note that the target is correctly located and that the lifetime values of both the target and background are comparable to the expected values, we see that the overall quality of reconstruction in this case is worse than the image shown in Figs. 2a and 2b. We believe the degradation of image quality in this case is primarily attributed to the lower signal-to-noise ratio (SNR) available when the target is embedded at a larger depth from the boundary. This low SNR case also gives more artifacts around the boundary as we see in Fig. 3a. The recovered lifetime image for the homogeneous case is depicted in Fig. 4 where we can see that the target tube and agar concentration used do not affect our reconstructions significantly.

In summary, we have presented reconstruction of lifetime maps based an oxygen-sensitive dye in turbid media using ac excitation and fluorescent data. We have demonstrated quantitative imaging ability for recovering fluorescence lifetime in centimeter tissue-like phantoms. Thus oxygen concentration maps can be obtained for biomedical diagnosis. It should be pointed out that the reconstruction algorithm presented here is applicable to non-singlet delay of fluorescent dyes for detection of low oxygen concentration contrast [4]. Unlike the fluorescence lifetime imaging (FLIM) reported thus far [19], the lifetime tomography described here is built upon the model-based reconstruction method, thus suitable for imaging large tissues such as breast. This study represents our initial step toward *in vivo* fluorescence lifetime tomography. While the results presented are promising, we realize that improving SNR for FLT remains as a challenge.

## Acknowledgement

This research was supported in part by a grant from the Department of Defense (DOD) (BC 980050).

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