2.1.

Point Radiance Spectroscopy Set-up

Figure 2a shows a schematic block-diagram of the experimental setup [Fig. 2b presents a view of the fiber positioning stages and the phantom box)]. Light from a tungsten halogen white light source (HL-2000 20 W, Ocean Optics, USA) was coupled to an 850-μm isotropic probe fiber (Medlight, Switzerland) that served as a spherical source [see inset of Fig. 2b]. The output power from the tip of the spherical diffuser was measured to be ∼3 mW (using a plane detector), hence, the total power coming from the source fiber was estimated to be ∼18 mW. The source fiber was positioned in a holder mounted on a x,y-translation stage with an additional z-axis control micrometer. A 600-μm core side firing fiber cleaved ∼43° at the distal end [see inset of Fig. 2b] was used as a radiance detector (Polymicro Technologies/Molex, USA). The fiber's numerical aperture (NA) based on a plane-cut tip was 0.24 (specified by the manufacturer). A protective cap (silica) on the fiber end preserved the total internal reflection condition upon immersing the fiber in a liquid. Both source and detector fibers were threaded through 1.1 mm (o.d.) stainless steel tubes. The detector fiber was mounted on a computer-controlled motorized rotation mount (Thorlabs, USA) that allowed complete 360 deg rotation with a 1 deg step. The detector fiber was connected to a computer interfaced spectrometer (USB-4000, Ocean Optics, USA) for signal acquisition in the 400 to 900 nm range. The integration time was 100 ms and four signal averaging was used. The sample (250-nm diameter Au colloid) was held in a 3.5-mm diameter thin walled quartz capillary tube, and the tube position was controlled in the x,y-plane by two translation stages. The source, detector, and tube were positioned in the middle of the phantom lucite box (18× 18×18 cm) with blackened walls. Experiments were conducted in air, water, and Intralipid-1%, all at room temperature (21°C).

Fig. 2

An experimental set-up for point-radiance measurements in liquid phantoms: (a) schematic, (b) a view of fiber positioning stages, and the phantom box. Inset in (b) a side-firing fiber (radiance detector) and a spherical diffuser (light source).

2.2.

Intralipid Phantom and 250-nm Gold Nanoparticles

Intralipid-1% was used as the background optical medium and was prepared by a volume dilution of a stock solution of Intralipid-20% (Sigma-Aldrich, Canada) with deionized water. The phantom box was completely filled with ∼1.8 L of Intralipd-1% solution. To focus the study on detection of Au NPs in highly scattering medium, the optical absorption of the Intralipid solution was not modified by adding dyes. We took an incremental approach to targeting the relevant prostate geometry by considering the localized optical inhomogeneities in an infinite medium. While it is relatively difficult to build a three-dimensional (3D) phantom model with easily adjustable optical properties of the background and a placement of localized inhomogeneities which would preserve the ease of the fiber manipulation, liquid phantoms allow an implementation of open access models with two-dimensional (2D) cylindrical symmetry (i.e., in-plane measurements). A localized inhomogeneity for the 2D phantom is approximated by a cylinder. Therefore, we started our study with a “borderless” model in order to focus on the properties of the turbid medium. However, due to the inherent 3D nature of photon scattering, the interaction between photons and the cylinder-shaped inhomogeneity can not be restricted to the in-plane.

Water-based 250-nm diameter Au colloid with a concentration of 3.8 × 10⁸ particle/ml (Ted Pella, USA) was used as the target of optical inhomogeneity. Results of a Mie theory calculation²³ of the extinction, scattering, and absorption efficiencies for a single 250-nm diameter Au particle in water are shown in Fig. 3a. Optical extinction is the sum of scattering and absorption. The extinction efficiency is defined as the extinction cross-section divided by the geometrical cross-section. Large particle size effects are noticeable in the scattering curve where the retardation effect is manifested in the appearance of the quadrupole resonance (∼620 nm), in addition to the dipole one (above 900 nm, not seen). The absorption curve undergoes relatively minor changes when compared with particles of smaller sizes. Another size-related effect is also evident—the particle becomes an approximately three times more efficient scatterer than an absorber. The measured extinction (1 cm cuvette, Cary 50) was converted into the extinction coefficient and is shown in Fig. 3b. Theoretical single particle extinction efficiency (C _ext) was converted into the extinction coefficient (μ_ext) using the particle density (N) in the Au colloid provided by the manufacturer using the following relation: μ_ext = N ·C _ext·πr ², where r is the radius of the particle. The experimental and theoretical extinction coefficients curves showed agreement within ∼10%.

2.3.

Methodology of Measurements

For each experiment, the source fiber and the radiance detector were positioned at a fixed separation distance, aligned vertically to maximize the signal, and an angular radiance profile was taken by rotating the detector. A set of two radiance profiles was acquired for each source-detector separation, one with the background medium alone (i.e., no sample) and a second with the Au NPs filled capillary tube (i.e., sample). The ratio of two profiles (no-sample/sample) was analyzed and reported. This ratio bears similarity to that normally used in spectroscopy for absorbance (A): A(λ) = log₁₀[I ₀(λ)/I _s(λ)], where I ₀ is the incident intensity, I _s is the transmitted intensity with the sample present and λ is the wavelength. Absorbance is replaced with optical extinction when the sample has scattering centers in addition to absorption. To emphasize the difference with traditional spectroscopy (in illumination and collection geometries), we report the ratio I _I(λ)/I _Au+w(λ) as a radiance extinction ratio of Au colloid (containing both Au and water, w) in the Intralipid solution. (Note, that we did not take the logarithm of the ratio). We posit that the ratio of these two radiance profiles should yield information on the spectral and spatial perturbation in the diffuse optical propagation due to the presence of a localized optical inhomogeneity. (In separate experiments, the effect of the quartz capillary tube was found to be negligible.) To separate the contributions from water and gold per se in the colloidal solution, an additional measurement was also conducted: water filled tube in Intralipid to produce I _I(λ)/I _w(λ). It also allowed to compare Au colloid filled tube in Intralipid with water filled tube in Intralipid via I _w(λ)/I _Au+w(λ). The first ratio elucidates the water effect and the second the effect of Au NPs.

One angular profile with selected parameters (360 positions with 1 deg step, 100 ms integration time, 4 averages) was acquired in 10 min. However, our data show that a 1 deg step is excessive and could easily be replaced by a ∼4 deg step without a loss of resolution. The signal/noise ratio can also be improved while keeping the total measurement cycle under 10 min.

3.1.

Side Firing Fiber Performance in Air and Water

The setup was initially tested in air and water backgrounds. The resulting angular radiance profiles plotted in polar coordinates and normalized to the maximum intensity are shown in Fig. 4 [in air, Fig. 4a and in water, Fig. 4b]. Detected spectra in air and water are influenced by the output of the white light source, fiber transmission characteristics, and the spectrometer response. However, the shape of the radiance profiles measured at all wavelengths was nearly identical. Hence, a wavelength of 520 nm was selected for comparison purposes. Angular detection of isotropic white light source with a side firing fiber [in air, Fig. 4a and water, Fig. 4b] produces a narrow lobe in polar coordinates whose width is a convolution of the point-like source with the full acceptance angle of the fiber. Hence, the lobe width is mostly determined by the numerical aperture of the fiber and the refractive index of the medium. The NA of the fiber is linked to the internal critical angle determined by the refractive indexes of the fiber core and fiber cladding and is a constant value: NA = n*sinθ = const where n is the refractive index of the surrounding medium and θ is the half-acceptance angle.²⁴ However, the NA of the side firing fiber may deviate from the plane-cut fiber due to complex refractions at a curved glass interface which yield two different acceptance angles in two orthogonal planes.²⁵ When the fiber is immersed into a medium with n>1 the acceptance angle decreases accordingly. Half-angle values extracted from the polar plots, 11 deg (air) and 5 deg (water), are smaller than corresponding values for the plane-cut fiber in air (14 deg) and water (8.3 deg). The values may serve as a first approximation of the true NA. As expected, the shape of radiance profiles in air and in water was preserved at all source-detector separations indicating a constant NA.

Fig. 4

Normalized to maximum values radiance profiles in (a) air, (b) water, and (c) Intralipid-1% at 520 nm for selected source-detector separations. No tube with chromophore.

3.2.

Gold Nanoparticles in Intralipid Phantom

Angular radiance profiles in Intralipid-1% normalized to the maximum intensity are shown in Fig. 4c. In the Intralipid preparations, water may account for up to 99% of the solution, depending on the concentration. Hence, the refractive index of Intralipid is expected to be similar to water. However, the profile measured in Intralipid-1% bears no resemblance to that in water [Fig. 4b]. For Intralipd-1%, the radiance profile widens significantly and acquires an off-centered circular-type feature. This is a manifestation of the multiple scattering events and a distribution of photons pathlengths that occur in highly scattering media such as, Intralipid. In order to be detected by the side firing fiber, photons must be approximately one scattering pathlength away from the outer interface of the fiber and inside the solid angle acceptance cone (∼ 10 deg), which for Intralipid is very similar to water.

The profiles measured in Intralipid-1% at various source-detector separations do not preserve the shape as seen in Fig. 4c. Anisotropy in the profiles observed at all distances is more pronounced at shorter ones. For example, Intralipid-10% has an anisotropy factor g ranging from 0.7 at 400 nm to ∼0.4 at 650 nm, indicating a preferential forward scattering.¹⁹ Our experimental radiance profiles agree qualitatively with the results of Monte Carlo simulation²⁶ and diffusion theory predications.²⁷ The response of radiance to the increase of the separation between the source and the detector demonstrated a decrease of radiance anisotropy (seen as a relative increase of the backscattered light). This is consistent with Monte Carlo simulations results and is linked to the Henyey–Greenstein distribution that describes the scattering phase function.²⁶ It follows that a reversal of the photon pathway will occur after multiple successive scattering events rather than from a single deflection at a single scattering event. An increase in the source-detector separation increases the longevity of the photon packet which is accompanied by an increase in the number of photons with path reversal and therefore, contributes to the backscattered signal.²⁶

Placing the sample into a background of Intralipid-1% perturbs a distribution of chromophores by introducing a localized optical inhomogeneity. To isolate the spectroscopic signature of the chromophore, we analyzed the ratio of the system response without the sample to the response with the sample at a given detector position. An analogy with data manipulation in typical spectroscopic measurements with a common spectrophotometer is helpful. A sample of interest is usually dissolved in a solvent (frequently, water) and placed in a cuvette surrounded by an outside medium. Because the outside medium is air, no correction is required. Therefore, the effect of the solvent, as well as the spectral profile of the light source and the spectrometer response, is taken into account by proper referencing to the blank (usually, cuvette with water). In our measurements, the surrounding medium is Intralipid and the solvent is water. Therefore, our measurements include an extra step of referencing to the surrounding medium (i.e., Intralipid) in addition to referencing to water.

The first set of translation measurements was conducted by keeping the source-detector separation constant at 12 mm with the detector always facing the source (i.e., no angular rotation) and the Au colloid sample positioned initially mid-way between the source and the detector. This corresponded to a zero offset from the source-detector direction. The sample was then translated orthogonally to the source-detector line with a 0.5 mm increment up to 18 mm from the source-detector direction, acquiring data at every position. Then, an Au colloid sample was replaced by the water sample and the measurements were repeated for the same sample positions. The radiance extinction ratios of Au colloid in Intralipid, [I _I(λ)/I _Au+w(λ)] and Au in Intralipid, [I _w(λ)/I _Au+w(λ)] (shifted vertically for clarity) are shown in Fig. 5 for a 0 mm offset.

Fig. 5

Individual radiance extinction ratios of Au colloid in Intralipid, (I _I/I _Au+w) and Au in Intralipid, (I _w/I _Au+w) (shifted vertically for clarity), source-detector separation 12 mm, source-sample separation 6 mm, 0 mm sample offset from the source-detector direction. The theoretical absorption efficiency of 250 nm Au is added for comparison.

The first remarkable feature is that the spectrum of Au NPs from Fig. 5 does not coincide with the extinction spectrum from Fig. 3, but with the absorption that is also shown on the plot. It can be understood in terms of independent scattering approximation.^{5, 17} Absorption and scattering coefficients of the system (Intralipid with Au NPs) can be considered as a linear combination of the optical properties of the background medium (Intralipid) and exogenous contrast agents (Au NPs). The scattering coefficient of Intralipid-1% can be estimated to be ∼64 cm⁻¹ from known values of the reduced scattering coefficient (∼16 cm⁻¹ at 500 nm from Fig. 1) and the anisotropy factor (g = 0.75 at 500 nm for Intralipid-20%).¹⁹ Comparing it with the maximum possible value of the scattering coefficient for Au NPs (0.75 cm⁻¹), it is clear that the total scattering coefficient of the Intralipid-1% with a Au NPs system should be dominated by Intralipid scattering. This is a rather simplistic approach, taken because the exact contribution of scattering and absorption coefficients to the measured radiance ratios is not known. The second feature is that the effect of water, observed as a characteristic dip at 750 nm, is removed after proper referencing to the water sample. Indeed, once the effect of water is removed, the experimentally obtained spectrum of Au NPs agrees with the calculated absorption (Fig. 5).

Fig. 3

Optical properties of 250 nm Au particles in water: (a) Mie theory-based calculated extinction, scattering, and absorption efficiencies, and (b) measured extinction coefficient (1 cm cuvette, Cary 50).

The results for some other offset values (with water effects removed) are shown in Fig. 6. Translation of the sample laterally introduces a change in the sample-detector separation. In Fig. 6, the first curve corresponds to a 0 mm offset and the last one to an 18 mm offset. It is evident that Au NPs can be detected at distances up to 18 mm, even when the detector is not facing the sample.

Fig. 6

Radiance extinction ratio of Au in Intralipid, (I _w/I _Au+w). Source-detector separation 12 mm, 0 to 18 mm sample offset from the mid-point in the source-detector direction.

To isolate the effect of the angular position from the radial distance, the tube with Au NPs was positioned at a constant distance of 6 mm from the detector keeping 12 mm as a source-detector separation and varying the sample's angle (0, 45, 90, 135, and 180 deg) relative to the source-detector direction. A 0 deg angle corresponded to the sample position between the source and the detector (i.e., on-axis). A detailed example is provided for the Au NPs sample placed at an angle of 135 deg. White light spectroscopy offers, in principle, a continuum of wavelengths for analysis. Since plasmonic enhanced absorption dominates scattering under the experimental conditions used, a wavelength of 520 nm (close to the maximum absorption of Au NPs) was chosen for the angular polar plots. Figure 7a shows two raw radiance profiles: one, for Intralipid only, and the other for the Au NPs sample present in Intralipid at a 135 deg angle. Placing the sample at 135 deg lowers the collected intensity at all detector angles. However, the angular distortion of the profile due to the sample is not obvious in Fig. 7a. Figure 7b shows the ratio of two profiles from part (a) that correspond to the extinction ratio I _I/I _Au+w, according to the previously described notation. If the sample would provide an isotropic reduction of the signal collected at all angles, the polar plot of the extinction ratio would be a circle. If the sample would provide a preferential reduction of the signal in the direction of the sample, then the ratio I _I/I _Au+w will show the maximum in this direction. Indeed, this type of distortion in a vicinity of 135^o is seen clearly in Fig. 7b. Water effects can be excluded from the angular profiles by analyzing I _w/I _Au+w. Figure 8 presents re-plotted I _w/I _Au+w for various angular positions of the sample on a linear x,y-scale. This representation allows better tracing of the sample location (marked by arrows) through the maxima in the profiles. Simple calculations show that a 3.5 mm diameter tube positioned at 6 mm distance from the detector will be seen in the ∼30 deg window. Given an estimated accuracy in the sample positioning (∼1 mm) and a 30 deg detection window, there is a good match between the targeted sample locations marked by arrows and the positions of the maxima in Fig. 8 for all angular positions, except 0 deg (not shown). The corresponding ratio for 0 deg looks almost flat with no pronounced maximum. Substitution of the fixed volume of Intralipd-1% with the equivalent volume of Au colloid between the source and the detector leads to two effects acting in opposite directions. Acting as a localized inclusion, water as opposed to Intralid, significantly reduces the scattering coefficient that increases the number of photons reaching the detector. Au NPs, on the other hand, increase the absorption coefficient acting as a sink for impinging photons and removing them from the subsequent diffusion process. As a result, it leads to the decrease in the signal collected by the detector. When both effects are almost of the same order, the sample is not detected in the Intralipid background. When the volume of water is reduced (via decreasing the diameter of the tube, for example) or absorption of Au NPs is increased, the profile of the radiance ratio at 0 deg will show the maximum as well. This was confirmed by performing similar experiments with 5-nm Au colloid that has an absorption coefficient higher than 250-nm Au colloid. The increase in the absorption coefficient came from a five-order increase in the particle density of the stock solution of 5-nm Au colloid, while the absorption efficiency of an individual particle dropped by a factor of ∼5 compared with a 250-nm Au colloid. Overall, experiments with 5-nm Au NPs reproduce qualitatively all major results observed for 250-nm Au NPs.

Fig. 7

(a) Polar plots of raw radiance profiles of Intralipid-1% alone and Au colloid in Intralipid-1% located at 135 deg (measured at 520 nm), (b) polar plot of radiance extinction ratio of Au colloid in Intralipid-1% (I _I/I _Au+w) [i.e., the ratio of the two profiles shown in (a)]. Angular position of the sample is denoted as a box.

Fig. 8

Radiance extinction ratio versus detection angle at 520 nm for different sample positions (shown by an arrow).

An analysis of curves from Fig. 8 reveals that a difference between “on-sample” value and “off-sample” value (corresponding to the maximum and the minimum on the curves) is quite consistent for all angles: 0.03 (45 deg), 0.04 (90 deg), 0.03 (135 deg), and 0.035 (180 deg). It indicates that a contrast value of 250-nm Au NPs with a density of 3.6 × 10⁸ particles/mL in Intralipid-1% is about 3% to 4% and does not depend on the observation angle. However, more investigations in this direction are required.

Figure 9 presents the radiance extinction ratio of 250-nm Au NPs in the solution of Intralipid diluted down to 0.016% and the optical extinction measured for the colloidal solution with a standard spectrometer (Cary 50). We performed dilutions of Intralipid-1% to confirm the “masking” effect of Intralipid on scattering of Au NPs. The source-detector separation was kept constant at 12 mm, and the sample was positioned mid-way between the source and the detector. As expected, at a certain concentration of the background medium (Intralipid-0.016%), we were able to recover the extinction spectrum of Au NP (Fig. 9) as was seen in Fig. 3, i.e., with both scattering and absorption contributing to the overall extinction. A decrease of the Intralipid concentration reduces the particle density that contributes to the value of the scattering coefficient. Taking the previously obtained value of 64 cm⁻¹ for the scattering coefficient of Intralipid-1%, the scattering coefficient of Intralipid-0.016% is estimated to be ∼1.0 cm⁻¹ at 500 nm. It starts to approach the one of the Au NPs (i.e., ∼ 0.75 cm⁻¹). This simple estimation supports the transition observed at the specific concentration. It has important implications for using Au NPs as contrast agents in scattering-based optical techniques. Due to the interplay between scattering coefficients of the background tissue and Au NPs, scattering signatures of individual Au NPs may be lost. The total scattering can be dominated by the background tissue scattering, and hence, the image contrast may be limited. It is understood, however, that this effect depends not only on a simple ratio of scattering coefficients of the background and the chromophore of interest, but on the effective optical thickness of the background. This has applications both for deep tissue imaging and confocal optical microscopy in highly scattering tissues. Because of the diffused light propagation regime, a complex geometrical/statistical model needs to be scrutinized thoroughly to estimate the value of the effective optical thickness. It is important to note that Au NPs with plasmon resonance in the visible range were used in this proof of principle investigation. It is understood that biological tissues would require nanoparticles with resonances in the biomedical transparency window (i.e., ∼650 to ∼1000 nm).

Fig. 9

Radiance extinction ratio of Au in Intralipid-0.016% and the measured (Cary 50) extinction for 250 nm Au colloid.

When translated to biological tissues, the approach is contingent on the ability to perform proper reference measurements in order to detect relative changes in tissue optical properties caused by any external treatment. In the context of the article, relative changes are brought by introducing localized exogenous chromophores (i.e., Au nanoparticles) as specific markers for diagnostic or treatment purposes. Considering prostate as a potential target and the two-fiber approach developed in the paper, we envisage the following methodology. An optical source fiber is inserted into the rectum and the detecting fiber into the urethra. Both fibers will be accommodated via specially designed catheters. The insertion depth of both fibers should be controlled. Once the desired targeted depth is reached, axial translation of both fibers with subsequent angular radiance acquisition measurements can offer potential 3D optical mapping. A baseline radiance profile would be obtained prior to any intervention. Systemically delivered and functionalized Au NPs with specific binding to tumor sites or nonfunctionalized Au NPs with preferential accumulation at tumor sites (due to the enhanced permeability and retention effect) will yield a perturbation in the radiance profile. The ratio approach described in the paper will be used for analysis. Additional studies are required to determine how the spatial extent of the perturbation would affect lower and upper limits of detection. Moreover, the maximum detection distance will depend on the optical attenuation of the prostate. To provide adequate illumination within the entire prostate (∼5 cm), more intense white light sources with output powers of several hundred milliwatts may be required.

To preserve the angular resolution, the detected signal must be radiance and not fluence. If the functionalities of the two fibers in the set-up are switched (i.e., illumination through the side firing fiber with rotation and detection via the isotropic spherical diffuser), multiple scattering will randomize photon pathways providing a nonselective isotropic illumination pattern. Therefore, the detected fluence will lose the specificity of the source-target interaction and therefore, the spatial content. However, a combination of two side firing fibers (used interchangeably as the source and the detector) may have some interesting properties by providing the absolute spatial coordinate in addition to the angle of the localized inhomogeneity based on simple geometrical considerations.