2.1.

Imaging System

We have constructed a $140\text{-}\mathrm{MHz}$ frequency-domain system to study the fluorescence properties of VEGF/Cy7. The excitation source consists of a pigtailed $690\text{-}\mathrm{nm}$ laser diode (Thorlabs Incorporated, Newton, New Jersey) sequentially delivered to nine multimode fibers distributed on a hand-held probe (see Fig. 1 ) using a $1\times 9$ optical switch (Piezosystem, Jena, Germany). The optical probe surface was painted black to make an absorption boundary with an effective reflection coefficient approximately equal to zero.³¹ The laser output at the optical probe was $18\mathrm{mW}$ . 14 fiber bundles (Fiber Instrument Sales Incorporated, Oriskany, New York), each $3\mathrm{mm}$ in diameter and distributed throughout the probe, sequentially collected the fluorescence and excitation light with an optical bandpass filter placed in and out of the light path, respectively. A shared detection assembly sampled received photons at each fiber bundle location. The assembly consisted of a sealed photomultiplier tube (model number R928, Hamamatsu, Bridgewater, New Jersey) plus associated optics that was linearly translated across the array of fiber bundle tips with a stepper motor (Applied Motion Products, Watsonville, California). Details of the assembly, denoted at the collimation system and filter (CSF) in Fig. 1, are shown in Fig. 2 . The experimental time for collection of one set of data from nine source locations and 14 detection locations was approximately $3\min$ . A sketch of the optical probe is shown in Fig. 2, where the smaller filled circles are sources and the larger filled circles are the fiber bundle detectors. Only source-detector pairs with separations greater than $1.2\mathrm{cm}$ were used for the image reconstruction process, enabling use of a diffusion approximation model.

Fig. 1

Diagram of the frequency-domain system with optical probe and arrangements for imaging experiments. Legend: OS is oscillator; LD is laser diode; LO is local oscillator; BP is bandpass; Pre-amp is preamplifier; Amp is amplifier; CSF is collimation system and filter; PMT is photomultiplier tube; and PC is personal computer. Measurement and reference signals are collected by the computer, and the optical switches are controlled by the same computer. Four laser diodes were in the system, but only one was used for the reported experiments.

Fig. 2

(a) The diagram of detection optics (CSF in Fig. 1). (b) Diagram of the optical probe.

To maximize sensitivity and imaging depth, the design of the detection optics must ensure that the residual excitation and stray light produce responses that are at or below the system electronic and detector noise floors. Different optical designs have been reported to achieve high signal-to-noise ratios.^{32, 33, 34} Hwang ³² reviewed approaches for efficient collection of fluorescence signals in phantom and animal studies. Several optical filter designs were employed to achieve high optical densities for collection of weak fluorescent signals. Our system employed several measures to achieve rejection of nonfluorescent signals in excess of $70\mathrm{dB}$ . First, the photomultiplier tube (PMT) aperture was restricted to match the incident focused light beam, and all detection optics were mounted in black lens tubes (Thorlabs Incorporated, Newton, New Jersey) encased within a light-sealed flat-black enclosure with the fiber bundles. Second, for fluorescence measurements, a dual-stage interference filter integrated on a single substrate (model number HQ800/60 M, Chroma Technologies, Rockingham, Vermont) removed excitation and stray light. The broadband filter was designed for greater than $100\mathrm{dB}$ isolation at 690 wavelength (spectrophotometer-limited measurement of better than $70\mathrm{dB}$ ), and all other optics were antireflection-coated to prevent spurious reflections that could affect the rejection efficiency.

Strict control of the collimation of the incident light on the excitation filters to within $+∕-5\mathrm{deg}$ is critical for rejection performance. Because the large $3\text{-}\mathrm{mm}$ detector fiber bundles used to improve light collection efficiency increase beam divergence, near-infrared achromatic lenses with long focal lengths of 30 and $35\mathrm{mm}$ (AC254-035-B and AC254-030-B, Thorlabs, Newton, New Jersey) were used to achieve the required degree of collimation. The effectiveness of the optical rejection was verified by temporary addition of an absorptive filter that did not change the noise floor of the system over the full range of PMT bias voltages. The combination of high collection efficiency fiber bundles and low-loss, high-rejection optics enabled high sensitivity detection of sub- $25\text{-}\mathrm{nM}$ fluorescent targets to depths of two centimeters.

2.2.

Phantom Preparation

Phantom studies were performed to validate our approach. In these experiments, a 0.6% Intralipid solution (Fresenius Kabi, Uppsala, Sweden) infused with $2\mathrm{nM}$ of Cy7 fluorescent dye (GE Healthcare, Waukesha, Wisconsin) was used to emulate a semi-infinite turbid background medium. The background medium yielded calibrated optical properties of absorption coefficient ${\mu }_a=0.013{\mathrm{cm}}^{-1}$ and reduced scattering coefficient ${\mu }_s^{\prime }=6.5{\mathrm{cm}}^{-1}$ at the excitation wavelength $\left(690\mathrm{nm}\right)$ , and ${\mu }_a=0.019{\mathrm{cm}}^{-1}$ and ${\mu }_s^{\prime }=5.25{\mathrm{cm}}^{-1}$ at the emission wavelength $\left(776\mathrm{nm}\right)$ (see Table 1 ). Calibration of source strengths and detector gains as well as the Intralipid optical properties was performed by using a least-squares fitting procedure.²¹ Briefly, in this calibration the excitation power of different source positions, gains of different detector positions, and the slopes of amplitude and phase measurements versus source-detector separations were estimated by fitting the measured data using a semi-infinite diffusion model with an absorption boundary condition.²¹ The background absorption and reduced scattering coefficients were readily obtained from the estimated slopes of amplitude and phase measurements.

Table 1

Optical properties of background 0.6 % Intralipid and Cy7 dye. The absorption coefficient is μa , μs′ is the reduced scattering coefficient, and ε is the extinction coefficient. Maximum extinction coefficient of Cy7 in water is 0.20cm−1μM−1 at 747nm .

The spectral dependence of the Cy7 extinction coefficient was measured by an 8453 UV-visible diode array spectrometer (Hewlett-Packard, Waldbronn, Germany) and values are listed in Table 1. The targets consisted of transparent cylindrical glass tubes of $1.0\mathrm{cm}$ diameter and $0.6\mathrm{cm}$ height (volume, $\pi {\mathrm{r}}^2\mathrm{h}$ , $0.47{\mathrm{cm}}^3$ ) filled with 0.6% Intralipid and Cy7 concentrations of $10\text{to}100\mathrm{nM}$ . The tubes were submerged one by one in the Intralipid background solution as depicted in Fig. 1. An adjustable micrometer stage was used to control the depth of the target. For phantoms and tumors, the center location of the target was aligned with the center of the probe, which was also the position of the central source of the probe shown in Fig. 2. The lateral alignment was performed by adjusting the target position to intercept the laser output from the central source position while viewing the target with a hand-held mirror held at $45\mathrm{deg}$ to the probe prior to Intralipid submersion. The spot size of the laser beam was $4\mathrm{mm}$ at the measured target depths. Through this process, the depth of the target was precisely controlled and the $x$ and $y$ positions were controlled to within $2\mathrm{mm}$ as determined by the divergence of the beam at the measured depths. Our dual-zone mesh imaging algorithm, used for accurately reconstructing fluorophore concentration, is discussed in Sec. 3.2.

2.3.

Mouse Tumors

SCID/Ncr (Balb/c background) mice were injected with 5 million MDA231luc cells²⁶ at the mammary fat pad, and tumors grew to approximately $1\mathrm{cm}$ size in a few weeks. Tumor-bearing mice were injected intravenously via the retro-orbital sinus with scVEGF/Cy7 conjugate (injection dose is listed in Table 2 ), which was allowed to circulate for one hour prior to sacrificing for imaging experiments. The scVEGF/Cy7, characterized by a fluorescence peak at $776\mathrm{nm}$ , was prepared by conjugating the derivative of a single-chain (sc) VEGF with Cy7 as described for scVEGF/Cy5.5 in Ref. 26. Animal protocol was approved by the Institutional Animal Care and Use Committee of University of Connecticut. During the experiment, the euthanized mouse was placed on a thin glass plate, head-to-tail along the $y$ axis, with the mammary fat pad facing the imaging probe, as shown in Fig. 1. The mouse and the plate were submerged in the intralipid and imaged using the same procedures as in the phantom experiments.

Table 2

Concentrations of scVEGF/Cy-7 injected into two mice.

Because of the requirement for a matching medium for diffuse optical imaging and the slower data acquisition speed of our system, the mice were euthanized before imaging to avoid unnecessary pressure to live animals. Backer ²⁶ reported that the near-infrared fluorescence images persist for several hours after scVEGF/Cy injection and remain nearly constant for at least $7\text{days}$ . This is because the Cy5.5 dye remains inside the cell long after the protein is digested. scVEGF-based tracers are internalized by endothelial cells via VEGFR-2 (vascular endothelial growth factor receptor-2)-mediated endocytosis.²⁶ Because of internalization, Cy5.5 fluorescence can be detected in tumor cryosections and in harvested tumors.²⁶ Thus our fluorescence measurements made immediately after euthanization should closely represent what would be anticipated under in-vivo conditions.

3.1.

Structural Parameters Estimation

Earlier, we demonstrated a novel technique for simultaneous estimation of target structural parameters and image reconstruction of fluorophore concentration.²⁰ A brief description of the theory is given here for the sake of completeness. The fluorescence fluence excited by a point source located at $r_S$ and detected by a point-like detector located at $r_d$ can be expressed as³⁵:

The ratio of the fluorescence fluences excited by a source at $r_s$ and detected by two detectors at $r_{d1}$ and $r_{d2}$ can be obtained as:

From Eq. 2 we can see that the only difference between the numerator and the denominator is the term $G_{\mathrm{fl}}$ , which depends on the positions of the two different detectors and position of the target. This observation was validated by simulations and phantom experiments as reported in Ref. 20. For convenience, we define two variables to describe the ratio of the fluorescence fluences: the amplitude of the ratio $R$ and the phase of the ratio $\Delta \Psi$ , which can be written as:

Both parameters are functions of the target depth $\left(Z\right)$ and size.³⁵ For the low contrast targets, the weak fluorescence signal from the target is embedded with the background signals. Difficulties have been faced to extract the useful target structural parameters from the total fluorescence signal, which is the summation of the background and target fluorescence signals. In our data processing for phantoms, the measured background signal was subtracted from the total signal, and the real and imaginary parts of the subtracted signal were used for amplitude and phase calculation. For the mouse experiments where background signal subtraction was not feasible, we used longer separated source-detector pairs (nearly $1.5\mathrm{cm}$ ) as per the observations in Ref. 20. After the background signals were subtracted from the target signal and/or the closer source-detector pair contributions were removed, the amplitude and phase were calculated for each measurement. The phase for a measurement is given by

A small constant number $\zeta$ of about 0.003 was added to the denominator (real part of fluorescence fluency) of Eq. 5 to improve the robustness of phase calculation in the presence of noise. This empirical approach is often used in signal processing to condition the weak signals, and it is very similar in concept to a regulation approach for conditioning an ill-conditioned matrix by adding a small empirical number to the diagonal of the matrix. The new equation for phase $\left(\Psi \right)$ is given as:

After the amplitudes and phases were calculated for each source-detector pair, the ratios of amplitudes and phases for all pairs of measurements were taken for structural parameter calculations.

Using an extrapolated boundary condition with a semi-infinite geometry, the amplitude and phase of the fluorescence photon density wave for a known target at any position can be generated analytically.³¹ Therefore, the amplitude ratio $\left(R\right)$ and phase difference $\Delta \Psi$ at any two positions can be calculated.^{35, 36} When multiple sources and detectors are present, different combinations of any two detectors for a given source can be selected to obtain the ratios of fluorescence fluences. Because our optical probe consists of nine sources and 14 detectors, for each source a total of 91 $\left(C_2^{14}\right)$ phase differences and 91 amplitude ratios can be obtained. Thus a total of 1638 $(91\times 2\times 9)$ measurements can be taken to determine the structural parameters, which is an overdetermined problem because we have a total of 252 ( $(9\times 14\times 2)$ : 126 amplitudes and 126 phases) measurements. Multiple ratios, analytically obtained, from a known target with known fluorophore concentration and known target structural parameters (location and size) were fitted to the multiple ratios of the measured experimental data from a target with unknown structural parameters (location and size). A chi-square $\left({\chi }^2\right)$ fitting technique was used to calculate the error between the analytically generated data and the experimentally measured data. The simplex downhill optimization^{36, 37} method was used for error minimization by varying the unknown target structural parameters. The final target structural parameters were obtained when the algorithm converged with error less than a certain limit.

3.2.

Functional Parameter and Image Reconstruction

To reconstruct absorption and/or fluorescence images, a normalized Born approximation has been widely used.^{2, 38, 39} This normalization eliminates unknown system parameters, i.e., source strengths, gains of different detectors, background optical properties of the tissue, coupling efficiency to the tissue, etc. In our earlier paper,²⁰ we normalized the target fluorescence measurement with the background fluorescence data for image reconstruction. This normalization method works well only for targets embedded in a homogeneous medium of high target-to-background contrast. For targets embedded in both homogeneous and heterogeneous media, normalization of the fluorescence measurement with the excitation data has been shown to work well,^{38, 39} because this procedure minimizes the background scattering and absorption, and reconstructs the intrinsic fluorophore concentration of the target. This normalized Born ratio is adopted in this study and is given as:

For inversion, a dual-zone mesh method was used to reconstruct the fluorophore concentrations. Because the target center is available from the structural parameters, we divide the imaging region into two parts, the background (B) and target (L) region.²⁰ We then discretized the target region of imaging volume $2.5\times 2.5\times 1.0\mathrm{cm}$ into a finer grid $(0.1\times 0.1\times 0.5\mathrm{cm})$ , and the background region of volume $6.0\times 6.0\times 4.0\mathrm{cm}$ into a coarser grid $(1.0\times 1.0\times 0.5\mathrm{cm})$ . Equation 7 can be expressed as a matrix equation when multiple measurements are available:

Depth ( $z$ -axis) estimations of the target position were found to be accurate to within 10%. The estimates of $x$ and $y$ coordinates, however, had larger errors that increased with the depth of the target. The typical deviations of the $x$ and $y$ positions from the expected positions were $0.02\text{to}1.25\mathrm{cm}$ in both directions with $0.2\text{-}\mathrm{cm}$ experimental uncertainty due to the laser beam size at the measured depths (Sec. 2.2). In our calculations, the targets were assumed to be spherical targets and the radii of the reconstructed targets ranged from 10 to 50% of the true target size.²⁰ The errors in the location estimations were lower for cylindrical Cy7 tube phantoms and higher for mouse tumors. Because of the $x$ - and $y$ -location uncertainties of up to $1.25\mathrm{cm}$ , the fine-mesh target volume in the reconstructions was fixed to $2.5\times 2.5\times 1.0\mathrm{cm}$ .

Our dual-zone mesh method is robust to structure estimation errors in $x$ and $y$ dimensions but sensitive to depth.^{22, 23, 40} If a target was reconstructed at an inaccurate depth, the fluorophore concentration would be either under-reconstructed or over-reconstructed. Because the structural estimation algorithm introduced in Ref. 20 and validated in this work is accurate in estimating depth, the approach provides sufficient accuracy for use with the dual-zone mesh method for imaging reconstruction.

4.1.

Phantom Studies

An example of a fluorescence image of a $50\text{-}\mathrm{nM}$ Cy7 target of diameter $1.0\mathrm{cm}$ and height $0.6\mathrm{cm}$ in a $2\text{-}\mathrm{nM}$ Cy7 background and 0.6% Intralipid medium is shown in Fig. 3 . The Born normalization we used here eliminates the unknown-background optical properties, so the particular background medium does not affect the image reconstruction. From the structural parameter calculation, it was found that the target was located at $1.6\mathrm{cm}$ depth ( $z$ axis). Because the target size estimate was not accurate (an error of 25% in this particular case) image reconstruction was performed over the entire volume with a finer mesh at $1.6\mathrm{cm}$ depth and a coarse mesh at all other depths. In Fig. 3, the first depth slice is reconstructed at $0.6\mathrm{cm}$ from the probe surface and the last slice is at $3.6\mathrm{cm}$ . The spatial dimensions of each slice are $6\times 6\mathrm{cm}$ , corresponding to the probe size used. The thickness of each slice corresponds to $0.5\mathrm{cm}$ in depth. The fluorescence image appeared at the third slice of the fine mesh region $(z=1.6\mathrm{cm})$ . The percentage of the true target fluorophore concentration reconstructed at $1.6\mathrm{cm}$ depth is 86% $\left(43\mathrm{nM}\right)$ .

Fig. 3

Reconstructed fluorescence image of a $50\text{-}\mathrm{nM}$ Cy7 target in $2.0\text{-}\mathrm{nM}$ background at $1.6\text{-}\mathrm{cm}$ reconstructed depth. The first slice is reconstructed at $0.6\mathrm{cm}$ depth and the last one is at $3.6\mathrm{cm}$ . The increment in each slice is $0.5\mathrm{cm}$ in depth.

To quantify our approach, one set of experiments was performed for targets with fluorophore concentrations of $10\text{to}100\mathrm{nM}$ at different depths $\left(0.5\text{to}2.0\mathrm{cm}\right)$ . The target depth was controlled by a micrometer stage, as explained earlier. We estimated the target depth from the chi-square fitting technique as shown in Fig. 4 , and the estimated depth was used for fluorescence image reconstruction. The $x$ axis shows the experimental depth measured from the micrometer stage, and the $y$ axis shows the depths estimated from fitting. The results demonstrate that the techniques are able to reconstruct target depths with concentrations as low as $50\mathrm{nM}$ for depths up to $2\mathrm{cm}$ , and $25\mathrm{nM}$ at depths up to $1.5\mathrm{cm}$ . Each measurement at a particular depth for a given target was repeated three times, and the parameters were reconstructed for all the measurements. The reconstructed depths in Fig. 4 are the means of the three measurements with the standard deviations shown as error bars.

Fig. 4

The reconstructed depth using the optical estimation algorithm plotted against the experimentally measured depth for different concentrations of targets at several depths.

The fluorescence images were reconstructed at the estimated depths obtained from chi-square fitting (from Fig. 4). Figure 5 shows the fluorophore concentrations reconstructed at different depths (from Fig. 4) for various target concentrations. The data clearly shows that the techniques were able to reconstruct the concentration of fluorescence targets located at depths up to $2.0\mathrm{cm}$ for concentrations as low as $25\mathrm{nM}$ . Although we could not reconstruct the target depth for the $25\text{-}\mathrm{nM}$ target at $2.0\mathrm{cm}$ , we were able to reconstruct the fluorescence image at the $2.0\text{-}\mathrm{cm}$ expected experimental depth, and the reconstructed fluorophore concentration was $16\mathrm{nM}$ (64%). As shown in Fig. 5, the images at $0.5\mathrm{cm}$ depth are over-reconstructed, and the fluorophore concentration reconstruction decreases with increasing target depth. The maximum difference in reconstructed fluorophore concentrations across different depths for a given target is within $\pm 20\mathrm{\%}$ .

Fig. 5

The concentrations of fluorophores reconstructed at reconstructed depths for the cases shown in Fig. 4.

To compare the effect of different background media on image reconstruction, one experiment was done with the same cylindrical tube filled with $100\text{-}\mathrm{nM}$ Cy7, prepared similarly as mentioned in Sec. 2.2, inserted in chicken breast. The size of the chicken breast was bigger than that of our optical probe, and the probe was in direct contact with it without any matching fluid. The chicken breast had calibrated optical properties of absorption coefficient ${\mu }_a=0.025{\mathrm{cm}}^{-1}$ and reduced scattering coefficient ${\mu }_s^{\prime }=2.5{\mathrm{cm}}^{-1}$ at the excitation wavelength $\left(690\mathrm{nm}\right)$ , and ${\mu }_a=0.022{\mathrm{cm}}^{-1}$ and ${\mu }_s^{\prime }=2.19{\mathrm{cm}}^{-1}$ at the emission wavelength $\left(776\mathrm{nm}\right)$ . From the structural parameter calculations, the target depth was estimated to be $1.15\mathrm{cm}$ , and the fluorescence concentration reconstructed at this depth was $92\mathrm{nM}$ (shown in Fig. 6 ). In comparison to the Cy7 images in Intralipid background, the background media (Intralipid or chicken breast) did not affect fluorescence image reconstruction.

Fig. 6

Reconstructed fluorescence image of a $100\text{-}\mathrm{nM}$ Cy7 target embedded in chicken breast. The first slice is reconstructed at $0.65\mathrm{cm}$ depth and the last one is at $3.65\mathrm{cm}$ . The increment in each slice is $0.5\mathrm{cm}$ in depth.

4.2.

Imaging with scVEGF/Cy7 Tracer

To demonstrate the capability of our approach to image deeply seated tumors in realistic samples, tumor-bearing mice were injected with $100\mu \mathrm{l}$ of either $16\text{-}\mu \mathrm{M}$ or $19\text{-}\mu \mathrm{M}$ solution of scVEGF/Cy7 (as shown in Table 2). The molecular specificity of this conjugate, which binds to and is internalized by VEGF receptors expressed in high number on endothelial cells in angiogenic vasculature, facilitates the visualization of tumor angiogenesis. Mice were sacrificed one hour postinjection, placed in Intralipid solution, and imaged. The mice were positioned as shown in Fig. 1.

Figure 7 shows the depth estimation for the mouse tumors translated to different depths from the optical probe by the micrometer stage. We could reliably estimate the tumor depth up to $1.5\mathrm{cm}$ from the probe surface. For comparison, depth estimates in the phantom experiments were reliable to depths of $2.0\mathrm{cm}$ for $50\text{-}\mathrm{nM}$ Cy7 tubes and to $1.5\mathrm{cm}$ for $25\text{-}\mathrm{nM}$ Cy7 tubes. The fluorescence images were reconstructed at the estimated depths and shown in Figs. 8 and 9 for mouse 1 and 2, respectively, where the color bar is in nanomolar scale. Although the structural parameters were not accurately reconstructed at $2.0\mathrm{cm}$ , we were still able to reconstruct the fluorophore concentration at the $2.0\text{-}\mathrm{cm}$ expected experimental depth, similar to the case for the $25\text{-}\mathrm{nM}$ Cy7 tube at $2.0\mathrm{cm}$ depth in the phantom experiments. The fluorophore concentration reconstructed at $2.0\mathrm{cm}$ was much lower than that reconstructed at other depths. The maximum fluorophore concentrations in tumors reconstructed at different depths are listed in Table 3 , with the average values computed within the full width at half maximum (FWHM) given in parentheses. These concentrations are comparable to estimates based on tumor uptake of radio-labeled scVEGF-based probes.²⁶ Typical uptake for such tracers in the tumors is $\sim 2$ to 3% of the injected dose. Injection of $100\mu \mathrm{l}$ of either $16\text{-}\mu \mathrm{M}$ or $19\text{-}\mu \mathrm{M}$ solution of scVEGF/Cy7 $\left(1.6\text{to}1.9\mathrm{nM}\right)$ should therefore lead to accumulation of $32\text{to}58\mathrm{pM}$ of tracer in tumors. For a tumor about $1\mathrm{cm}$ in diameter, this would correspond to a concentration in the $10\text{to}50\text{-}\mathrm{nM}$ range, which is close to the range of reconstructed values shown in Table 3.

Fig. 7

Plot of the reconstructed depths for the tumors in two mice versus experimentally measured depths.

Fig. 8

Reconstructed fluorescence images of tumor marked with VEGF/Cy7 conjugate in mouse 1 at different reconstructed depths: (a) $0.43\mathrm{cm}$ , (b) $1.02\mathrm{cm}$ , (c) $1.46\mathrm{cm}$ , and (d) $2.0\mathrm{cm}$ . The rest of the slices in each figure correspond to coarse mesh in the background region. The depth is shown in the title of each subimage.

Fig. 9

Reconstructed fluorescence images of tumor marked with VEGF/Cy7 conjugate for mouse 2 at different reconstructed depths: (a) $0.51\mathrm{cm}$ , (b) $1.05\mathrm{cm}$ , (c) $1.53\mathrm{cm}$ , and (d) $2.0\mathrm{cm}$ . The rest of the slices in each figure correspond to coarse mesh in the background region. The depth is shown in the title of each subimage.

Table 3

Maximum fluorophore concentrations reconstructed at different depths from mouse tumors; average values at FWHM are shown in the parentheses.

By examining the images obtained from mice, we can see that the background artifact level was higher in the first two layers when the target was located in a deeper range as shown in Figs. 8 and 9. Because the fluorescence signals generated from a deeper target were much weaker than that from a shallower target, the signal-to-background fluorescence ratio was lower in the former case, which resulted in a higher background artifact level in reconstructed images.