2.1.

Phantom Design, Fabrication, and Preparation

In the aforementioned prior work, a human retinal vasculature image was captured by a commercial fundus camera (Fig. 1). This image was segmented to generate a digital geometric model of a two-dimensional (2-D) vascular network with varying vessel size and density. The segmentation process involved image enhancement and thresholding-based conversion to a binary map using Adobe Photoshop^® software (Adobe Systems Inc., San Jose, California). In order to convert this 2-D planar model into a full 3-D representation and incorporate circular vessel cross sections, several 2-D maps were edited using a morphological image erosion technique, and stacked with $70\text{-}\mu \mathrm{m}$ $z$-spacing to vary inplane vessel width, resulting in vertically discretized circular channel profiles. The final design was converted into the stereolithographic file format using MATLAB^® for 3-D printing.

An SLA 3-D printer (Form $1+$, FormLab, Somerville, Massachusetts) was used to fabricate phantoms for this study. This printer consists of three major parts: an ultraviolet (UV) beam scanner, a resin tank, and a building stage. The UV beam scanner fabricates thin layers of cured photoreactive resin (based on the object’s initial design in the $x\text{-}y$ plane, parallel to the building stage) to form the entire 3-D shape of an object. Prior to printing, a gentle shaking of the resin container was performed to prevent particle settling. During the printing process, drops of resin are exposed to the focused UV light, resulting in crosslinking and formation of a solid, polymerized structure. After the formation of each layer, the building stage translates in the $z$ direction within the resin tank. The 3-D printer provides a nominal feature size resolution of $300\mu \mathrm{m}$ and user-selectable layer thicknesses of 25, 50, or $100\mu \mathrm{m}$. We found the $50\text{-}\mu \mathrm{m}$ resolution setting to be optimal for this study. The printing speed is fixed based on the nominal selected layer resolution ($50\mu \mathrm{m}$ in this case). Several stock materials incorporating different color pigments and turbidity levels were used (FormLab, Somerville, Massachusetts).

There are a number of fabrication challenges to printing phantoms with channels of submillimeter diameters and arbitrarily irregular orientation and shape. First of all, removing uncured resin from irregular channels is both essential and difficult to accomplish effectively. Phantoms were cleaned by repeated flushing of the channels with isopropanol solution. Second, the smallest size and depth of 3-D-printed vascular channels were limited by the 3-D printer capability. To evaluate this limit, we printed a phantom with seven cylindrical channels having nominal diameters and depths of 0.5 to 1.1 mm and 350 μm, respectively. Printing was repeated three times for different channel orientations with respect to the printing bed: parallel, perpendicular, and 45 deg. An x-ray microtomography, or $\mu \text{-}\mathrm{CT}$, system (SCANCO Medical $\mu \mathrm{CT}$ 100, Switzerland) was used to evaluate the quality of printed phantom morphology.

Ensuring that phantom optical properties are biologically relevant is a critical part of demonstrating tissue phantom suitability. Toward this end, we printed thin slabs ($4.0\mathrm{cm}\times 4.0\mathrm{cm}\times 2.0\mathrm{mm}$) and characterized their optical properties using spectrophotometry. Diffuse transmittance and reflectance were measured in the wavelength range of 400 to 1200 nm with a 5 nm interval using a dual-beam integrating sphere spectrophotometer (Lambda 1050, Perkin Elmer, Waltham, Massachusetts). The absorption coefficient, ${\mu }_{\mathrm{a}}$, and reduced scattering coefficient, ${\mu }_{\mathrm{s}}^{\prime }$, were calculated at each wavelength from the measured transmittance and reflectance, using the inverse adding-doubling method.²³

To mimic the optical properties of blood, we utilized a commercially available human ${\mathrm{HbO}}_2$ solution for calibrating CO-oximeters (Multi-4™ L2, Instrumentation Laboratory Co., Bedford, Massachusetts), which contains a total Hb concentration in the normal range of human blood ($\sim 13.8\mathrm{g}/\mathrm{dL}$). Yeast, an oxygen-consuming microorganism, can be added to this solution to induce dynamic desaturation, the conversion of ${\mathrm{HbO}}_2$ to HHb.²⁴ Solutions of ${\mathrm{HbO}}_2$ and ${\mathrm{HbO}}_2+2\%$ yeast were injected into the vascular channels of the phantoms for HRI measurement.

2.2.

Hyperspectral Reflectance Imaging System

A diagram of our near-infrared HRI system, which was described briefly by Wang et al.,²² is shown in Fig. 2. It uses a 100 W quartz tungsten–halogen fiber-optic light source (Oriel Instruments, Stratford, Connecticut) for illumination. The illumination light was delivered through a liquid light guide (Newport Corporation, Irvine, California) of 5 mm diameter, collimated and expanded to a beam diameter of 15 mm, and homogenized using a diffuser before applying to the sample. The reflected light from the sample was collected through a macrovideo zoom lens (18–108 mm focal length, $f/2.5$, Edmund Optics, Barrington, New Jersey), collimated by a 5 mm lens, then filtered by a liquid crystal tunable filter (LCTF, CRI Varispec, Perkin Elmer, Waltham, Massachusetts), working in the range of 650 to 1000 nm, with bandwidths of 7 to 10 nm. Filtered light was detected by a Peltier-cooled, high-sensitivity, visible–near-infrared CCD camera (Pixis 1024, Princeton Instruments, Trenton, New Jersey). A LabView interface was used to control the LCTF and the camera (wavelength range, wavelength step size, and exposure time).

Fig. 2

Diagram of the HRI system.

2.3.

Imaging Procedure and Data Processing

Reflectance images of $1024\times 1024$ pixels over a $4.5\mathrm{cm}\times 4.5\mathrm{cm}$ field of view were taken sequentially in the wavelength range of 650 to 1000 nm at 10 nm intervals. For each experiment, reference images of a Spectralon^® standard of similar size to the phantom were taken using the same experimental settings as in phantom imaging. Data were then analyzed using custom routines written in MATLAB^®. The algorithm is briefly described as follows: (1) Raw reflectance images were normalized by reference standard images, wavelength by wavelength, to remove spectral signal variations due to system/equipment properties and to correct for illumination nonuniformity; (2) $2\times 2$ binning was applied to the normalized images to reduce noise; (3) an absorbance spectrum, $A(\lambda )$, was calculated for each pixel as²⁵

2.4.

Hyperspectral Reflectance Imaging Measurements

The HRI system and 3-D-printed phantoms with Hb-filled channels were utilized for oximetry measurements. Three different experimental schemes were followed, as listed in Table 1.

Table 1

Hyperspectral reflectance imaging (HRI) vascular phantom experimental schemes.

To evaluate the results of HRI oximetry, spectroscopic measurements (Lambda 1050, Perkin Elmer, Waltham, Massachusetts) were also performed on samples extracted from the same batch used to fill phantom channels (1.3 mm diameter, 350 μm to 3 mm depth with 5 mm separation between cylindrical channels). Desaturation over time was then calculated from spectrophotometry data, and results were correlated with the HRI-generated estimates. Three separate measurements showed a mean difference of 8% between corresponding timepoints, indicating moderately good agreement, with differences possibly due to the simplicity of our oximetry estimation algorithms, absorption by the matrix material, or variations in the yeast oxygen consumption rate.

3.1.

Phantom Optical Properties

Different off-the-shelf photoreactive resins were analyzed through optical property measurements before selecting the optimal material, and no additional materials (chromophores and scatterers) were added. Results were compared with optical properties of biological tissues such as bovine retina,²⁷ gray brain matter,²⁸ and Caucasian skin²⁹ (Fig. 3). The 3-D printer manufacturer's "white" resin was shown to provide biologically relevant scattering levels, and thus was selected for use in the remainder of the measurements in this study. The formulation of this resin, including pigment and additive concentrations, is proprietary and thus was not available to the authors. To further investigate the white resin’s scattering properties, a clear photoreactive resin (FormLabs, Somerville, Massachusetts) was obtained, and different concentrations of titanium dioxide (${\mathrm{TiO}}_2$) particles (Sigma Aldrich, Saint Louis, Missouri) were added. Turbidity levels of the prepared samples were measured using spectrophotometry. The clear resin with 0.05% ${\mathrm{TiO}}_2$ by weight showed a similar scattering distribution as that obtained from the white resin; the root mean square error (RMSE) between these two distributions was $\sim 0.02{\mathrm{mm}}^{-1}$ over the wavelength range of 650 to 1000 nm based on 5 nm intervals. White resin showed a lower absorption than biological tissues; however, Hb was added in phantom channels to provide a biologically relevant chromophore. Polymerized resin optical property stability was shown to be excellent over a period of eight months (Fig. 3). An RMSE of $~0.0015{\mathrm{mm}}^{-1}$ for ${\mu }_a$ and 0.024 mm−1 for ${\mu }_s^{\prime }$ was observed between the first and last measurements in the wavelength range of 650 to 1000 nm at 5 nm intervals.

Fig. 3

(a) Absorption coefficient and (b) reduced scattering coefficient of a white 3-D-printed slab. Results of measurements over a period of 8 months after 3-D printing are compared to biological tissues.^27–29

3.2.

Phantom Morphology Validation

The results of our printing quality assessment in cylindrical channel phantoms are shown in Table 2. Samples were printed in three orientations: horizontal, 45 deg, and vertical with respect to the printing bed. Horizontally oriented channels showed the poorest printing quality among these samples. The printer failed to create patent channels when the specified diameter was less than $900\mu \mathrm{m}$. The smallest patent channel achievable was measured at $500\mu \mathrm{m}$ in diameter, and an average size deviation of $\sim 60\%$ from the designed values was observed. Vertically oriented channels were the highest quality, with the smallest patent channel having a diameter of $\sim 450\mu \mathrm{m}$, and the average size deviation between the 3-D-printed channels and the designed parameters measured as $\sim 8\%$.

Table 2

Geometry validation results: cylindrical channel phantoms.

Two different phantoms incorporating image-based vascular structures were designed and fabricated. Geometry validation was performed using $\mu \text{-}\mathrm{CT}$ imaging and advanced visualization software (3-D Slicer, Isomics Inc., Cambridge, Massachusetts; Netfabb GmbH, Lupburg, Germany). A set of $\mu \text{-}\mathrm{CT}$ images captured from a defective two-layer vascular phantom is shown in Fig. 4. Areas with unshaped channels and surface leakage are marked in the cross-sectional images [Figs. 4(a) and 4(b)]. Several factors such as printer resolution limitations, poor channel cleaning, air bubble accumulation in the resin tank, or sample orientation may result in an imperfect product. Another set of $\mu \text{-}\mathrm{CT}$ cross-sectional images and a 3-D view of an intact two-layer phantom, printed under the identical specifications and conditions as before, are shown in Fig. 5. Table 3 shows validation results for both one- and two-layer phantoms. For the one-layer vascular network phantom, a minimum channel thickness (height) of $750\mu \mathrm{m}$ was achieved and channels were consistently formed deeper and with smaller size than designed. While simple cylindrical channels printed in an orientation perpendicular to the printing show a mean error of of 8% (Table 2, cylindrical channel phantom), phantoms printed in arbitrary orientations have lower resolution due to layer thickness limitations. Even with these larger diameter channels, the two-layer phantom channels proved difficult to fill with Hb solution in a reasonable time frame and thus were increased in diameter slightly (830 to $920\mu \mathrm{m}$; Table 3) to facilitate this process. The results illustrate the potential variability in samples fabricated with features approaching the printer resolution limit and indicate the necessity of using a nondestructive imaging method (e.g., $\mu \text{-}\mathrm{CT}$), to ensure 3-D-printed phantom quality.

Table 3

Geometry validation results: vascular phantoms.

Fig. 4

$\mu$-Computed tomography ($\mu \text{-}\mathrm{CT}$) validation of a defective phantom: (a) cross-sectional image of two-layer phantom, arrows point to the unshaped channels; (b) cross-sectional image from the same phantom with a surface leakage, where the arrow points to the leaking area; and (c) 3-D view with bottom layer omitted for clarity.

Fig. 5

$\mu \text{-}\mathrm{CT}$ validation of viable phantoms: cross-sectional images of (a) one-layer and (b) two-layer vascular phantoms and (c) a 3-D view of the two-layer phantom.

3.3.

Oximetry in One-layer Phantom

The one-layer vascular phantom was filled with a solution of ${\mathrm{HbO}}_2$ and 2% yeast (Table 1, configuration 1). Photographs of this phantom 30 and 120 min after solution injection are shown in Fig. 6. The change in apparent color of the Hb solution qualitatively suggests that desaturation has occurred.

Fig. 6

Photographs of one-layer vascular phantom at (a) 30 min and (b) 120 min after solution injection.

HRI measurements were performed for 30 time points over about 6 h (until oxygenation change of $<0.5\%$ was observed over 30 min) to monitor the process of desaturation. From each set of HRI spectral images, an absorbance map was calculated [Eq. (1)] and fractional contributions of the primary chromophores–${\mathrm{HbO}}_2$, HHb, water, and cured resin—were solved using a spectral unmixing NNLS algorithm [Eq. (2)]. A set of images derived from HRI data captured 75 min after adding yeast to the ${\mathrm{HbO}}_2$ solution is shown in Fig. 7. Figure 8 shows calculated absorbance spectra as well as chromophore contribution fitting results for channel regions with high- and low-channel densities and a nonchannel region of the same phantom. The ${\mathrm{SO}}_2$ map [Fig. 7(d)] is marked with three regions of interest (ROIs), representing (1) high-channel density, (2) low-channel density, and (3) nonchannel regions, which indicate the location of spectral data presented in Fig. 8.

Fig. 7

One-layer phantom chromophore concentrations and saturation maps 75 min after adding the ${\mathrm{HbO}}_2+\mathrm{yeast}$ solution: (a) ${\mathrm{HbO}}_2$, (b) deoxyhemoglobin (HHb), (c) total Hb, (e) water, and (f) cured resin. The hemoglobin saturation levels (${\mathrm{SO}}_2$) map (d) is marked with three regions of interest (ROIs) used to generate results in Fig. 8.

Fig. 8

Sample HRI spectral data measured from the one-layer vascular phantom 75 min after solution injection, including absorbance curves for regions with (a) high- and low-channel densities and nonchannel area (the effect of phantom matrix is removed from the absorbance data for demonstration purpose) and (b–d) chromophore contributions after NNLS unmixing. Results are shown for channel regions with (b) relatively high and (c) low densities, and (d) a nonchannel area.

In locations where phantom channel density was greatest, higher ${\mathrm{HbO}}_2$, HHb, and total Hb concentrations tended to be measured within the channels. This is due to the interaction of diffuse photons with a larger fractional volume of Hb-filled channels; similar variations in estimated chromophore contribution are also seen in Figs. 8(b) and 8(c). The influence of channel density can be observed in the ${\mathrm{SO}}_2$ map (Fig. 7) as well, though to a lesser extent. Higher ${\mathrm{SO}}_2$ values tended to be measured in regions of greater vessel density—the maximum variation in ${\mathrm{SO}}_2$ with vessel density was approximately 6%, 13%, and 17% at mean saturation levels of 65%, 40%, and 12%, respectively. This variation may indicate a minor spectral attenuation effect or a spectral unmixing error with Hb concentration. Alternately, some of this variation may be attributable to differences in yeast and dissolved oxygen content stemming from the injection process, which can take up to 15 min to completely fill all channels. Since the phantom was filled with an Hb solution from one batch, yeast concentration remains almost uniform within the phantom channels.

In spite of a lack of Hb in nonchannel locations, calculations indicated some residual Hb concentration in these regions, due to scattered light being absorbed in adjacent channel regions. The ${\mathrm{SO}}_2$ distribution in Fig. 7(d) shows a saturation range of 50% to 65% in nonchannel regions due to the aforementioned scattering from adjacent channels combined with the fact that this is a ratiometric parameter where both components of the ratio are similarly low. A sharp drop-off in ${\mathrm{SO}}_2$ is seen toward the edges of the phantom; this is essentially an unmixing artifact caused by crosstalk between the HHb and resin absorbance signatures. No ${\mathrm{HbO}}_2$ absorption is seen in this region, yet HHb concentration is nonzero, which leads to a zero oxygenation value.

To further investigate light propagation in regions with different channel densities, a 3-D-printed phantom incorporating 14 parallel cylindrical channels with 1.3 mm diameters and varied regional densities (with edge-to-edge channel spacing of 0.2 to 2.5 mm) was designed and fabricated. HRI was performed on this phantom with Hb–yeast solution-filled channels. For ROIs in both channel and nonchannel locations, higher absorbance and chromophore content estimates were observed in areas where channel density was greater, similar to results in vascular phantoms. Also, ${\mathrm{SO}}_2$ levels were calculated for ROIs with different channel densities and compared with spectrophotometry data. Comparing HRI measurements of ROIs with different channel densities showed a maximum ${\mathrm{SO}}_2$ difference of $\sim 8\%$ for a mean saturation level of 45%.

3.4.

Oximetry in Two-Layer Phantom

Biological tissue contains blood vessels of varied saturation levels (e.g., arteries and veins) at a range of depths. Toward accurate representation of these characteristics, the vascular networks in the two-layer phantom were each filled with a different Hb solution (Table 1, configurations 2 and 3). HRI was conducted on the phantom for each experimental configuration, and data were recorded for more than 30 time points over about 8 h.

Links to the transient ${\mathrm{SO}}_2$ results for two-layer phantoms are provided in Fig. 9, with the still images representing data acquired 4 h after filling phantom channels with the Hb solution. For the experimental configuration 2, both the top and bottom layers are fully oxygenated at the beginning of the experiment. Therefore, the ${\mathrm{SO}}_2$ video starts with a fully saturated frame (${\mathrm{SO}}_2=99\pm 1\%$). The ${\mathrm{SO}}_2$ level decays gradually due to the yeast oxygen consumption in the top layer channels (channel region final mean ${\mathrm{SO}}_2=28\pm 12\%$). Inhomogeneities seen in the ${\mathrm{SO}}_2$ frames are primarily correlated with channel morphology, with higher ${\mathrm{SO}}_2$ values seen in regions where fewer superficial layer vessels are located. Similarly, for experimental configuration 3, the ${\mathrm{SO}}_2$ video starts with an almost fully saturated frame (${\mathrm{SO}}_2=97\pm 1\%$) and continues toward desaturation more quickly in nonvessel areas (channel region final mean ${\mathrm{SO}}_2=63\pm 6\%$). Since HRI is more sensitive to superficial channels, a higher equilibrium saturation level is observed at the final time point compared with configuration 2. Desaturation of Hb solution inside the deeper channels over time lowers perceived ${\mathrm{SO}}_2$ values of the bulk phantom. Additionally, it is noteworthy that the highly saturated superficial vasculature is readily visible against the lower saturation background in Fig. 9(b) (Video 2); however, in Fig. 9(a) (Video 1), the desaturated superficial vasculature does not appear with high contrast against the highly oxygenated background. This phenomenon will require further elucidation in future studies.

Fig. 9

HRI-calculated ${\mathrm{SO}}_2$ data in two-layer phantoms, 4 h after yeast mixing for (a) experimental configuration 2 (Video 1, AVI, 1.2 MB) [URL: http://dx.doi.org/10.1117/1.JBO.20.12.121312.1] and (b) configuration 3 (Video 2, AVI, 1.5 MB) [URL: http://dx.doi.org/10.1117/1.JBO.20.12.121312.2].

Desaturation over time was calculated from a channel region in the HRI images for both one- and two-layer phantoms (Fig. 10). Solutions in the variable layer started from near 100% saturation and constantly decreased until they reached a stable level, where almost all ${\mathrm{HbO}}_2$ had apparently been converted to HHb. The equilibrium saturation level for configuration 1 was almost zero percent (${\mathrm{SO}}_2$ dropped from 90% to 0% over 6 h), while in the two-layer phantom, a significantly higher saturation was observed at the equilibrium state ($\sim 30\%$ and $\sim 65\%$ for configurations 2 and 3, respectively), due to the presence of a constantly oxygenated vascular layer. Comparing the saturation levels of the configurations 2 and 3 shows that the system was roughly twice as sensitive to the saturation level of the top layer as to the bottom layer.

Fig. 10

Phantoms oxygen desaturation over time. In configurations 2 and 3, ${\mathrm{SO}}_2$ values are fixed at approximately 100% in the bottom and top layers, respectively.

3.5.

Spectral Variations in Penetration Depth

Due to the decrease in scattering with wavelength, variations in visualization of deeper channels were noted in two-layer phantom experiments. Normalized reflectance images at $\lambda =650\mathrm{nm}$ and $\lambda =1000\mathrm{nm}$ and a corresponding saturation map (experimental configuration 2, desaturated stable state) are shown in Fig. 11 (Video 3), along with spectrally varying reflectance images over this range at 10 nm intervals. Reflectance images at longer wavelengths show improved visualization of channels. Arrows show the location of a second-layer channel filled with highly oxygenated Hb solution. This channel was not covered by the first layer vascular mesh; thus diffuse reflectance from this channel was less affected by the first vascular layer. Consequently, an inhomogeneity in the saturation map was seen after full desaturation of the first layer. This result illustrates the potential to use wavelength-specific or narrow-band imaging to complement and elucidate ${\mathrm{SO}}_2$ measurements performed with HRI.

Fig. 11

Normalized reflectance images at (a) $\lambda =650\mathrm{nm}$ and (b) $\lambda =1000\mathrm{nm}$ (Video 3, AVI, 1.3 MB) [URL: http://dx.doi.org/10.1117/1.JBO.20.12.121312.3] and (c) ${\mathrm{SO}}_2$ map at 8 h after adding yeast to the ${\mathrm{HbO}}_2$ solution (experimental configuration 2). Arrows indicate the effect of deep channel on both reflectance image and saturation map.

As a further investigation of depth selectivity and wavelength dependence in HRI, a phantom incorporating a tilted vascular array was designed and fabricated with 3-D printing. Channel depth varied from 0.5 to 2.8 mm in this phantom, as verified by $\mu \text{-}\mathrm{CT}$ imaging. Channels of the phantom were filled with a Hb-yeast solution (Table 1, configuration 4). HRI was conducted on the phantom and data were recorded for more than 3 h in order to study different ${\mathrm{SO}}_2$ levels. Figure 12 shows results from these experiments, including representative reflectance images, a representative ${\mathrm{SO}}_2$ map, and a graph of estimated ${\mathrm{SO}}_2$ levels as a function of network region depth and time. A greater depth of penetration and better vessel visualization were found at longer wavelengths as illustrated in Figs. 12(a) and 12(b). Also, a significant deviation between the ${\mathrm{SO}}_2$ levels of channels located at different depths was observed [Fig. 12(c)]. An underestimation of ${\mathrm{SO}}_2$ levels for deeper areas was observed.

Fig. 12

Vascular phantom with tilted channels: normalized reflectance images at (a) 650 nm and (b) 1000 nm; (c) ${\mathrm{SO}}_2$ level versus depth for different time points after adding yeast to Hb solution; and (d) ${\mathrm{SO}}_2$ map at 105 min after adding yeast to the Hb solution [ROIs used to generate the graph (c) are marked on the map].

In order to provide a more idealized investigation of the effect of depth variation on HRI measurements, experiments were repeated in a 3-D-printed phantom with eight cylindrical channels with diameters of 1.3 mm at depths from 0.35 to 3.5 mm. A decrease in channel contrast and predicted chromophore content versus depth was observed due to limited light penetration. For instance, the estimated ${\mathrm{HbO}}_2$ contribution of the 3-mm-deep channel were three and four times smaller than those for the shallowest channel at 99% and 60% Hb saturation levels, respectively. Consequently, a decrease of calculated ${\mathrm{SO}}_2$ levels was also seen for deeper channels at different time points, similar to the results of the tilted vascular phantom. A maximum 14% deviation from the mean ${\mathrm{SO}}_2$ value was observed among 10 measurements performed at Hb saturation levels between 99% and 0%. The variation in ${\mathrm{SO}}_2$ with depth may be due, at least in part, to the defocusing effect of scattering for deeper channels, which reduces the intensity of the maximum pixels in the deeper channels compared with shallower ones.