3.1.

Choice of Material

Optical properties (e.g., reflectivity, scattering, and absorption) reveal heterogeneities in tissue and allow separation of dissimilar tissue types. A number of previous research efforts have focused on providing mathematical and experimental details for calibration and fabrication of the scattering and absorption properties in phantoms,^5,30,31 mainly by means of mixing an appropriate weight fraction of scattering agents [e.g., titanium dioxide (TiO₂)] and absorption agents (e.g., India ink).³² A common material for tissue-mimicking phantoms is polydimethylsiloxane (PDMS) due to its tunability for scattering and absorption.^33,34 PDMS is particularly useful for phantoms that mimic highly stretchable organs, such as the bladder.²⁹

Our strategy to introduce birefringence in a tissue-mimicking phantom relies on the photoelastic property of PDMS, which varies as a function of the curing ratio and stretch. Photoelasticity describes the induced macroscopic birefringence in a material undergoing a large elastic deformation.³⁵ When subject to a mechanical force, the polymer chains in soft materials, such as hydrogels and elastomers, increase in alignment and exhibit optical anisotropy, which causes a difference between the refractive indices ($\mathrm{\Delta }n$, or birefringence) for different polarization states. The high elasticity of PDMS allows for large deformation with minimal stress relaxation. As a result, PDMS-based structures can be repeatedly stretched without losing their induced birefringence over time.³⁶ Figure 2 shows representative PS-OCT-generated retardation maps of single layer, homogeneous PDMS phantoms in relaxed and stretched states. The phantoms shown in Figs. 2(a) and 2(b) were made with a 15:1 weight ratio of base to curing agent, comprised 0.2 weight ratio (w%) ${\mathrm{TiO}}_2$ and had an initial (relaxed or unstretched) thickness of 1.5 mm.

Fig. 2

Retardation maps of PDMS in relaxed (a) and stretched (b) states. Retardation plots show the cross-sectional plane of the PDMS. Yellow and white triangles point to the location of the top and bottom surface of the phantom, respectively. $\text{Scale bar}=0.2\mathrm{mm}$. (c) Imaging system setup for measuring phantom birefringence.

3.2.

Design and Preparation of Birefringent Slab Phantoms

To characterize the stretch-induced birefringence of PDMS phantoms, we first prepared several single layer, scattering phantoms (i.e., slab phantoms) from Sylgard 184 silicone elastomer (Dow Silicones Corporation) by mixing the base solution (part A) and the curing agent (part B) at specific curing ratios. In this study, we prepared PDMS phantoms with four curing ratios (weight ratios of part A to part B): 10:1, 15:1, 20:1, and 25:1. We also added ${\mathrm{TiO}}_2$ to mimic tissue scattering. The weight ratios used included 0.04, 0.15, 0.2, and 0.3 w% and were chosen based on values of the light attenuation coefficient (AC) determined in previous literatures for the different layers in bladder tissues.²⁸ Each solution was degassed in a desiccator before being transferred to a plastic mold to cure at 80°C for 2.5 h.

3.3.

General Procedure for Measuring Birefringence in Slab Phantoms

We then used the testing setup shown in Fig. 2(c) to measure the retardation as a function of applied stretch. The PDMS phantom was secured into two clamps with an initial clamp separation of 6 mm, which we refer to as the “original length.” One clamp was held stationary by mounting it to a force gauge (FG-3007, Nidec-Shimpo, Inc.); the other clamp was mounted onto a translational stage and allowed to move away in 2.5-mm increments using the micrometer, which controlled the amount of stretch. The imaging location was centered on the phantom and remained unchanged for a given stretching experiment. The phantom was imaged when relaxed and then at each stretch increment. From the PS-OCT image, we determined the thickness and birefringence for each phantom and experimental condition in the following manner (Fig. 3):

Fig. 3

Flow diagram for calculation of phantom birefringence.

We further determined the stress $\sigma$ applied for each amount of stretch from force measurements recorded by the force gauge using the following equation:

3.4.

Characterization of Slab Phantom Birefringence

The optical anisotropy of PDMS is determined by the number of cross-linked polymer chains in a unit area, which can be adjusted by varying the weight ratio of the base solution (part A) and the curing agent (part B). Theoretical prediction and experimental data of birefringence induced in PDMS have been studied recently,³⁵ albeit with very modest amount of stretch. As a result, the published birefringence levels are too low to be useful in mimicking values of tissue birefringence. In this study, we explored a wider range of stretch values in slab PDMS phantoms of varying curing ratios and measured the induced birefringence under each condition.

To characterize the amount of stretch, we defined a parameter, the length ratio, which equals the elongated length divided by the original length. For each curing ratio, the induced birefringence versus stretch relationship was measured and plotted as a function of length ratio, as shown in Fig. 4(a) for phantoms with an initial thickness of 1.5 mm. Each data point represents the average birefringence and standard deviation measurements from five measurement repeats. Note that error bars are not shown for data points with very low standard deviations, as in these cases the error bars are smaller than the extent of the data point. The results reveal that PDMS phantoms made with lower curing ratios (i.e., 10:1) have greater stiffness and are therefore more resistant to deformation. The maximum achievable elongation, that is, the point at which the phantom starts to slip out of the clamp, is lowest for 10:1 phantoms, followed by that for 15:1; meanwhile, 20:1 and 25:1 phantoms exhibit greater stretchability and can reach more than five times their original length. We reason that both the increase in stiffness as well as the decrease in stickiness contribute to the slipping that happens at lower curing ratios, such as the 10:1.

Fig. 4

(a) Birefringence versus stretch and (b) birefringence versus stress relationships at different curing ratios, characterized with 1.5-mm-thick phantoms with 0.2 w% ${\mathrm{TiO}}_2$.

In our experiments, all four curing ratios exhibited birefringence changes with stretch. At lower curing ratios, the induced birefringence increases at a faster rate with stretch than at higher curing ratios. However, because of the low stretchability of low curing-ratio phantoms, higher values of birefringence could ultimately be obtained in stretched phantoms made with higher curing ratios. For example, the largest birefringence we induced ($2.1\times {10}^{-4}$) over the range of length ratios we explored was achieved with 20:1 phantoms, when stretched to approximately five times the original length. Notably, birefringence levels we induced in PDMS are within the range of those in tissues that exhibit weak birefringence, including the normal and diseased bladder (see Sec. 2), retinal nerve ($\mathrm{\Delta }n=1.2\times {10}^{-4}$),³⁷ and tumor in breast tissue ($\mathrm{\Delta }n=1.8\times {10}^{-4}$).³⁸ We also report the birefringence properties of another silicone-based polymer, Dragon Skin (Smooth-On, Inc.). Under the same stretching conditions, the 1.5-mm-thick Dragon Skin phantom showed negligible changes in birefringence, and we therefore concluded that the Dragon Skin does not exhibit a stretch-induced birefringent property.

We also measured the force exerted on the PDMS phantom as we performed the stretching experiments and determined the changes of birefringence as a function of stress, as shown in Fig. 4(b). The stress measurement is determined by both the force and the original cross-sectional area, which is related to the original phantom thickness, ($L_{2,0}$). Stress measurements on the Dragon Skin were also performed; however, the elasticity of Dragon Skin is much lower than PDMS, and thus exhibited negligible birefringence changes over the applicable range of stress.

Tissue-mimicking phantoms are particularly useful for testing tools and procedures in a mock surgical environment. As manipulation of tissue with surgical tools can cause local changes in the measured birefringence at the manipulation site, we also tested whether the use of PDMS to mimic tissue birefringence allows resemblance of such changes. We used a tweezer to press perpendicularly on a layer of stretched PDMS (15:1 curing ratio, 1.5-mm thick) and, without piercing the phantom, we imaged it from the opposite side of the tweezer at two cross-sectional imaging planes: (1) the plane, including the tweezer, i.e., the manipulation site, and (2) a parallel imaging plane located 1-mm away from the tweezer. We pressed from the opposite side of the imaging surface to allow better visualization of the effect on measured retardation (if imaged from the same side, the tweezer would cast a shadow and prevent changes directly underneath the tweezer to be visualized). The 1-mm-away imaging plane was used to study the whether the effect of manipulation can change the birefringence measurements from the surrounding regions. As shown in Fig. 5(a), a local birefringence change can be observed as a change in the retardation mapping, when comparing the cross-sectional images resulted from no manipulation and when manipulation was applied. In this case, the retardation increases more rapidly along the axis of manipulation than the surrounding PDMS and untouched PDMS. To quantify the amount of change in birefringence, we took birefringence measurements from 20 A-scans centered at the manipulation site and 20 A-scans from the corresponding lateral location of the untouched PDMS. The locations of the 20 A-scans are indicated by the white dashed line in Fig. 5(a). We observed a 38.6% and 35.6% increase at a 0- ($\mathrm{\Delta }n=1.40\times {10}^{-4}$) and 1-mm distance ($\mathrm{\Delta }n=1.37\times {10}^{-4}$) from the manipulation site, respectively, when compared with untouched PDMS ($\mathrm{\Delta }n=1.01\times {10}^{-4}$).

Fig. 5

(a) Retardation maps of cross section of PDMS when no manipulation is applied (left image), and when there is manipulation applied: at an imaging plane that includes the tweezer (0 mm from manipulation site, middle image) and a parallel imaging plane that is 1-mm away from the tweeze (right image). The orange triangle indicates the location of the tweezer, which simulates manipulation with surgical tool. The white dashed lines indicate location where birefringence measurements were taken. (b) Birefringence versus stretch at varying ${\mathrm{TiO}}_2$ (w%), characterized with 1.5-mm-thick phantoms made with 20:1 curing ratio.

A major advantage of using PDMS as the birefringent material is that it is optically clear, which grants easy control of the scattering properties. By means of tuning the volume of scattering in each representative layer, we can achieve realistic tissue contrast in conventional B-scan intensity images. To confirm that the induced birefringence measured with PS-OCT is not dependent on the amount of scatterers, we conducted stretching experiments with slab phantoms comprising 0.1 w% to 0.5 w% ${\mathrm{TiO}}_2$, while keeping all other factors constant (i.e., curing ratio and thickness). The results suggest that there is no significant difference in the rate of birefringence increase with scatterer weight ratio, as shown in Fig. 5(b). This result confirms that we can tune the scattering of the phantom, as is necessary to mimic different types of biological tissue, without altering the birefringence levels.

4.1.

Relevant Properties of the Human Bladder

To mimic the layered structure of the bladder wall under PS-OCT imaging, there are three important design criteria for each layer: thickness, AC, and level of birefringence. When imaged from the lumen side, the three layers in the healthy bladder can be distinctively visualized and have thicknesses of $50\mu \mathrm{m}$, $400\mu \mathrm{m}$, 1.6 mm, and ACs of 0.8, 3.5, and $1.5{\mathrm{mm}}^{-1}$, respectively.^28,29 Since the urothelium is a cell layer, it does not exhibit any birefringence, which is consistent with our finding of negligible birefringence in Section 2. In contrast, the collagen-rich LP layer and the smooth muscle in the MP layer both exhibit birefringence in healthy bladders. In early stage cancerous development, bladder tumors, such as in the case of CIS, have reduced contrast between the urothelium and LP on the OCT image, which causes them to lose their distinct stratification and appear as a fused layer. Dimming in the OCT intensity and near complete loss of birefringence can also be observed as the result of cancer development,³⁹ which is consistent with our finding of negligible birefringence in the fused CIS layer of the diseased bladder in Sec. 2. The table in Fig. 6(a) summarizes these general characteristics and inspires our phantom design.

Fig. 6

(a) Overall design of desired thickness, AC, and birefringence in each layer of the bladder under normal and tumor conditions. (b) Induced birefringence in 15:1 phantoms with different initial thicknesses (solid line: 1.5-mm-thick phantom and dashed line: 1-mm-thick phantom). Pink shaded region: birefringence values observed in normal bladder LP. Gray shaded region: thickness values observed in normal bladder LP. Overlap region shows birefringence and thickness values to be achieved in the LP layer of normal bladder phantoms. (c) Fabrication steps for normal (left) and diseased (right) bladder phantoms.

To generate layers that do not exhibit birefringence with stretch, we chose to use the Dragon Skin as the material for nonbirefringent regions, since it does not exhibit photoelasticity but is still highly elastic. Hence, Dragon Skin was used for the urothelium layer of the healthy bladder phantom. Similarly, we chose to use multiple layers of Dragon Skin with ACs ranging from 1.8 to $2.2{\mathrm{mm}}^{-1}$ (lower AC near the MP and higher AC at the top) to represent the fused appearance of the urothelium and LP layers in the CIS-mimicking phantom, given that these layers also exhibit negligible birefringence in the diseased case. The varying AC levels were achieved by adding different weight ratios of ${\mathrm{TiO}}_2$, of which the relationship has been previously established.²⁸

Because of the presence of collagen and smooth muscle fibers, respectively, both the LP and MP layers of the healthy bladder exhibit birefringence. Hence, both layers should be fabricated from PDMS. To determine the curing ratios to use for these layers, we consider the graph in Fig. 6(b), where we compared the birefringence of stretched phantoms with initial thicknesses of 1 (dashed line) and 1.5 mm (solid line) and reported the change of thickness of the phantom ($L_2$) as a function of length ratio. The red shaded region denotes the range of birefringence values associated with a healthy bladder LP, while the gray shaded region denotes the thickness value of a typical LP layer. We chose to use a curing ratio of 15:1 for the LP layer, as it is capable of achieving birefringence values that fall within the range for healthy LP with modest length ratios. Although we could not measure the birefringence of the MP layer directly with PS-OCT due to the high attenuation of light when reaching that depth, we chose to use a curing ratio of 25:1 to reflect the non-negligible, but lower expected birefringence in that layer in healthy tissue. Because CIS is a superficial tumor that does not extend to the MP, we chose to use the same recipe for the MP of the diseased phantom as for the healthy phantom.

4.2.

Phantom Fabrication Procedure

Figure 6(c) shows the steps taken to fabricate the healthy and CIS phantoms. First, the MP layers of both phantoms were fabricated by pouring ${\mathrm{TiO}}_2$-infused PDMS (0.15 w%) into a standard mold (e.g., a petri dish) and letting it cure. Note that we did not tightly control the thickness of this layer because it is typically too thick to visualize in OCT, so its actual thickness does not matter so long as it exceeds 1.6 mm when stretched. Our choice of a high curing ratio for this layer (25:1) ensures that it can stretch well. For the healthy phantom, the LP layer was added and cured atop the MP by pouring another layer of PDMS with ${\mathrm{TiO}}_2$ (0.3 w%). Its thickness was controlled by weight versus volume calibration. Finally, to create a thin urothelium layer, a ${\mathrm{TiO}}_2$-inflused Dragon Skin solution (0.04 w%) was first thinned with NOVOCS solution (Smooth-On, Inc.) at 100 w% (i.e. part A + part B : NOVOCS = 1:1) and then sprayed onto the LP layer with a Badger air brush (200-BWH) and Badger air compressor (AS180-12) at the rate of one second per spray coating, until the thickness reached the design criterion for the urothelium ($\sim 90\mu \mathrm{m}$).²⁸ To fabricate the combined urothelium and LP layers in the disease phantom, the same air brushing technique was used. In this case, multiple coatings of Dragon Skin were applied with ACs ranging from 0.15 w% to 0.2 w%: the AC of the solutions decreased progressively from near the MP toward the tissue surface. Sonication was used during Dragon Skin preparation to ensure evenly dispersed ${\mathrm{TiO}}_2$ particles. All Dragon Skin layers were allowed to cure at room temperature for 6 h.

4.3.

Measurements in the Final Phantoms

OCT intensity and PS-OCT retardation images of the final normal and diseased phantoms are shown in Fig. 7. In this image, both phantoms were stretched to a length ratio of nearly four. Intensity and retardation versus depth plots, averaged laterally in the boxed regions (and calculated from the surface of the phantom to 500 pixels below the surface), are shown next to the OCT intensity cross-sectional images on the left. Both the intensity and the retardation map can visually differentiate the normal from the diseased condition, suggesting that the design criteria have been met successfully. The achieved thicknesses of the layers and measured birefringence are reported on the plot. Specifically, in the normal bladder phantom, we achieved birefringence levels of $3.11\times {10}^{-7}$, $1.05\times {10}^{-4}$, and $4.50\times {10}^{-5}$ in the urothelium, LP, and MP layers. In the diseased phantom, the values for the fused layer and MP are $4.61\times {10}^{-6}$ and $3.59\times {10}^{-5}$.

Fig. 7

B-scan and retardation maps of (a) normal and (b) diseased bladder phantoms. Plots of averaged intensity and retardation versus depth plots are shown for the regions boxed with yellow solid line. Scale bar = 0.2 mm.