Investigations into the feasibility of optical-CT 3D dosimetry with minimal use of refractively matched fluids

Abstract

Purpose:

In optical-CT, the use of a refractively matched polyurethane solid-tank in place of a fluid bath has the potential to greatly increase practical convenience, reduce cost, and possibly improve the efficacy of flood corrections. This work investigates the feasibility of solid-tank optical-CT imaging for 3D dosimetry through computer simulation.

Methods:

A matlab ray-tracing simulation platform, ScanSim, was used to model a parallel-source telecentric optical-CT imaging system through a polyurethane solid-tank containing a central cylindrical hollow into which PRESAGE radiochromic dosimeters can be placed. A small amount of fluid fills the 1–5 mm gap between the dosimeter and the walls of the tank. The use of the solid-tank reduces the required amount of fluid by approximately 97%. To characterize the efficacy of solid-tank, optical-CT scanning simulations investigated sensitivity to refractive index (RI) mismatches between dosimeter, solid-tank, and fluid, for a variety of dosimeter (RI = 1.5–1.47) and fluid (RI = 1.55–1.0) combinations. Efficacy was evaluated through the usable radius (r_u) metric, defined as the fraction of the radius of the dosimeter where measured dose is predicted to be within 2% of the ground truth entered into the simulation. Additional simulations examined the effect of increasing gap size (1–5 mm) between the dosimeter and solid-tank well. The effects of changing the lens tolerance (0.5°–5.0°) were also investigated.

Results:

As the RI mismatch between the dosimeter and solid-tank increased from 0 to 0.02, the usable radius decreased from 97.6% to 50.2%. The optimal fluid RI decreased nonlinearly from 1.5 to 1.34 as the mismatch increased and was up to 9% lower than the tank. Media mismatches between the dosimeter and solid-tank also exacerbate the effects of changing the gap size, with no easily quantifiable relationship with usable radius. Generally, the optimal fluid RI value increases as gap size increases and is closely matched to the dosimeter at large gap sizes (>3 mm). Increasing the telecentric lens tolerance increases the usable radius for all refractive media combinations and improves the maximum usable radius of mismatched media to that of perfectly matched media for tolerances >5.0°. The maximum usable radius can be improved up to a factor of 2 when lens tolerances are small (<1.0°).

Conclusions:

Dry solid-tank optical-CT imaging in a telecentric system is feasible if the dosimeter RI is a close match with the solid-tank (<0.01 difference), providing accurate dose measurements within ±2% of true dose to over 80% of the dosimeter volume. In order to achieve accurate measurements over 96% of the dosimeter volume (representing out to 2 mm from the dosimeter edge), the dosimeter-tank RI mismatch must be less than 0.005. Optimal results occur when the RI of the dosimeter and tank is the same, in which case the fluid will have the same RI. If mismatches between the tank and dosimeter RI occur, the RI of the matching fluid needs to be fine tuned to achieve the highest usable radius.

1. INTRODUCTION

Optical-CT scanning has long relied on immersion of samples in refractively matched fluid baths to mitigate refraction artifacts.^1–3 Refractive index (RI) matching is a time-consuming trial-and-error process of mixing two liquids, whose RIs bracket the sample RI, that can take up to several hours when large quantities of fluid are required.⁴ The use of PRESAGE^® dosimeters by Heuris, Inc. (Skillman, NJ) with high RIs necessitates the use of fluids with similar RIs. These high RI fluids tend to be viscous, rendering them susceptible to thermal convection currents and “swirls” of altered RI that mandate a wait period between mixing and scanning to allow the sample to settle. This waiting period is also used to allow any dust motes or airborne particulates that may have accumulated in the fluid to settle so they will not be seen in the projections and cause artifacts in the final image.^4,5 High viscosity also presents problems during scans, since fast sample rotation will cause vortices and other motion artifacts.⁴ All of these factors severely limit the throughput of current optical-CT systems^6–12 and open the door for novel scanner design that could eliminate many of these factors.

Dry scanning (or “free space scanning”) systems generally seek accurate optical-CT scanning in air rather than refractively matched fluid. Several types of dry scanners have been proposed and evaluated before,^13–15 but results showed large imaging artifacts or large dose discrepancies outside of a small central volume of the dosimeter.^4,16,17 In light of these results, we propose a third type of optical-CT system that could potentially overcome the limitations of fluid-based systems and produce more encouraging results than free space scanning systems. For the system explored in this work, “dry scanning” is a slight misnomer, as scanning still requires small amounts (∼10 ml) of refractively matched fluid between the solid-tank walls and the dosimeter. Even so, this represents a substantial improvement over the several liters of fluid required for the current system, so the appellation seems appropriate. The proposed dry scanner offers some key benefits over traditional fluid bath setups, both in practical convenience and cost. Because the solid-tank has a similar refractive index to the PRESAGE^® (Refs. 18–21) radiochromic dosimeters used, refraction artifacts are minimized without requiring large quantities of refractively matched fluid. In addition to cost saving, this makes a dry scanning system much easier to use and maintain by mitigating the limitations of the use of large quantities of high RI fluids.

2. METHODS

An example of the type of scanning system simulated in this work is the novel Duke Fresnel optical-CT scanner (DFOS)²² shown in Fig. 1, which is similar to the Duke large field-of-view optical-CT scanner (DLOS),^5,6 but the fluid bath is replaced with a molded polyurethane block called a “solid-tank.” The solid-tank has a central cylindrical well to hold the dosimeter and turntable and has similar dimensions to the replaced fluid bath. Imaging is done with telecentric lenses and collimators,^8,11,12 and scanning procedures are the same.^6,23 The prototype DFOS scanner is essentially monochromatic due to the presence of a narrow bandpass filter (633 ± 5 nm).

FIG. 1.

Top-down view of DFOS and DLOS. DFOS uses Fresnel lenses and replaces the fluid bath with a solid-tank made of polyurethane, reducing the required amount of refractively matched fluid by approximately 97%.

The ScanSim optical-CT simulation tool was described in a prior work.^5,14 It is a matlab based ray-tracing software that simulates the entire optical-CT acquisition and reconstruction process for 3D dosimetry, including pre- and postirradiation correction. In the present work, ScanSim’s capabilities were expanded to accommodate the geometry and physics of dry scanning [see Fig. 2(A)]. Parameters for the solid-tank well size and refractive index were added to the simulation, and an extra media interface representing the solid-tank-fluid boundary added to the supporting functions for ray tracing. In ScanSim, ray tracing records the path inside the dosimeter and surrounding media, the relative intensity loss due to transmission losses at boundaries, and attenuation based on optical density.^5,14 The accuracy of the ScanSim software was carefully validated through independent hand calculation of individual ray paths. In addition, a basic verification by comparison against measurement was performed [Fig. 2(B)]. Here, a dose of 4 Gy was delivered in a single 6 MV arc with a static field size of 4 × 4 cm to a cylindrical PRESAGE dosimeter of size 10 cm diameter. The dosimeter was scanned with DLOS and a “measured” dose profile extracted from the reconstructed data. This arc treatment delivery was simulated in ScanSim by inputting an idealized OD distribution corresponding to the dose distribution of this rotationally symmetric treatment. The corresponding “simulated” measured dose profile was then calculated by ScanSim [Fig. 2(B)]. A slight left–right misalignment of the delivery isocenter is observed in the figure, but the ability of the simulation to model the measured dose distribution, including the edge artifacts, is clear.

FIG. 2.

(A) A diagram illustrating ray tracing in the ScanSim simulation of a solid-tank scanner. Rays originate normal to the y axis (simulating a telecentric light source) in the solid-tank (RI = n1) and propagate through a fluid gap (RI = n2) and into the dosimeter (RI = n3). Information about the ray intensity, transmission coefficients, and attenuation is updated at each media boundary. (B) A comparison of simulated and measured line profiles through a static arc delivery (shown in the inset), demonstrating ScanSim’s ability to accurately reproduce measured data including edge artifacts.

Because total internal reflection is a larger concern with the extra media interface and greater range of refractive indices allowed, this effect was accommodated for all media interfaces. Total internal reflection occurs when the angle of incidence on a media interface is greater than the critical angle dictated by the refractive index of the two media,

$${\displaystyle {\theta }_c=arcsin\left(\frac{n_2}{n_1}\right).}$$ (1)

At each media interface, the angle of incidence is compared to the critical angle for the boundary. If the incident angle exceeds the critical angle, that ray was declared scattered and nonrecoverable, and the ray truncated at the point of incidence. The prior version of ScanSim did not account for scatter rejection by the telecentric collimators and lenses used with this system, and all rays were declared detectable regardless of their angle of incidence on the detector or magnitude of intensity loss.⁵ In the updated telecentric version, rays are only declared detectable if their angle of incidence on the detector is less than or equal to the telecentric lens tolerance. Any rays not meeting this criterion, including those subjected to total internal reflection, are considered rejected, and their intensity values set to zero. Rejected rays are visualized on the ray-tracing output diagram with dotted lines for scattered events and “X” marks for total internal reflection.

2.A. Simulation parameters

The controlled variables of the simulations were the refractive indices of the dosimeter (1.5–1.47) and surrounding fluid (1.55–1.33), the gap size between the dosimeter and the solid-tank well (1.0–5.0 mm), and the telecentric lens tolerance (0.5°–5.0°). Gap size refers to the difference between the solid-tank well radius, r_t, and the dosimeter radius, r₀, and is a measure of how tightly the dosimeter fits into the solid-tank well. The RIs of all liquids simulated in this work were determined in-house using a refractometer under specialized lab lighting at ∼600 nm. The simulated RI values for the PRESAGE dosimeters and the polyurethane solid-tank were determined as that of the RI fluid (measured by refractometer) that yielded minimum refraction artifacts at 633 nm in DLOS projection images.

All scanning configurations were simulated with 0.2 mm ray spacing and a uniform dose distribution of 5 Gy to the total dosimeter volume. The ray spacing value was chosen to provide good sampling of the dose distribution without requiring lengthy calculation times—since each ray path is calculated independently, calculation times are very dependent on the number of rays, which is determined by the ray spacing. A uniform dose distribution was chosen to make measurement of the usable radius more straightforward. In practice, it is feasible to obtain measured optical-CT images of a uniformly irradiated dosimeter for a wide range of dose levels (up to 20 Gy). Total signal loss at the detector can be avoided by restricting the delivered dose so that the maximum attenuation in the dosimeter matches the dynamic range of the detector.²⁴ While ScanSim is capable of algebraic reconstruction techniques, this method is slow and computationally intensive, making it inefficient for the hundreds of consecutive simulations and reconstructions required for this study. Filtered backprojection was used as a faster reconstruction alternative. At present, ScanSim can only simulate symmetrical dose distributions. ScanSim calculates a single 2D projection which is then duplicated for the other projection angles to generate a sinogram corresponding to a full optical-CT acquisition. The sinogram is then fed into matlab’s iradon filtered backprojection algorithm using the default Ram-Lak filter. While a flood field correction is common practice in real-world optical-CT scanning, it was unnecessary to include in the simulation because the mathematical model is an idealized water bath with no imperfections like scratches, smudges, or debris.

The simulated dosimeter parameters are common to PRESAGE^® radiochromic dosimeters^18–20 used in Imaging and Radiation Oncology Core (IROC) head phantoms in order to maintain clinical relevancy. The fixed dosimeter properties⁵ were radius, r₀ = 50 mm, OD sensitivity = 0.023 cm⁻¹ Gy⁻¹, and unirradiated background OD = 0.003 cm⁻¹. The refractive indices (ranging from 1.47 to 1.5) and other simulated dosimeter properties were chosen based on the measured properties of a sample of PRESAGE^® dosimeter formulations.¹⁹

The simulated solid-tank parameters were chosen based on the physical solid-tank system DFOS. The refractive index of the solid-tank was fixed for all simulations at RI_t = 1.5 to match the refractive index of the DFOS solid-tank polyurethane formulation.

2.B. Scanning configurations

Three scanning configurations were simulated. Fixed and controlled variables for each configuration are summarized in Table I. Scanning configurations fall into three categories.

TABLE I.

Scanning configuration summary. Each scanning configuration fits into one of three categories: optimal media matching, effect of gap size, or telecentric lens tolerance.

Category	Fixed variables	Controlled variables
Optimal media matching	Solid-tank RI = 1.5	Dosimeter RI (1.5–1.48)Fluid RI (1.55–1.33)
	Gap size = 1.0 mm
	Lens tolerance = 1.0°
Effect of gap size	Solid-tank RI = 1.5	Dosimeter RI (1.5–1.48)
			Lens tolerance = 1.0°	Fluid RI (1.51–1.45)
		Gap size (1.0–5.0 mm)
Telecentric lens tolerance	Solid-tank RI = 1.5	Dosimeter RI (1.5–1.48)
		Gap size = 1.0 mm	Fluid RI (1.51–1.33)
			Lens tolerance (0.5°–5.0°)

Optimal media matching: These simulations attempt to determine the appropriate choice of RI-matched fluid based on the dosimeter and solid-tank RI. For each chosen dosimeter-tank RI pair, the fluid RI value was varied.

Effect of gap size: These simulations evaluate the effect of scanner geometry on our chosen metric. We attempt to determine an optimal fluid RI choice based on the dosimeter and solid-tank RI and the “fit” of the dosimeter in the solid-tank well by changing the gap size parameter. For each dosimeter-tank pair, a gap size was chosen and the fluid RI varied. These simulations were repeated for each gap size in the specified range.

Telecentric lens tolerance: These simulations evaluate the effect of increasing or decreasing the telecentric lens tolerance on our metric. For each dosimeter-tank pair, a telecentric lens tolerance was chosen and the fluid RI varied. These simulations were repeated for each telecentric lens tolerance in the specified range.

2.C. Metrics for evaluation

The primary metric used to evaluate the accuracy of the system is the usable radius, r_u. The usable radius is the distance in millimeters from the center of the dosimeter at which the measured and true dose differ by less than 2%. The reference dose for percentage difference is D_max. Because all scanning configurations were evaluated with a simulated uniform dose distribution of 5 Gy to the total dosimeter volume, D_max = 5 Gy, this value is expressed as the percentage ratio of the usable radius to the dosimeter radius $\left(r_u/r_0\ast 100\right)$ for dimensionless comparison.

Other terms used in the analysis involve the following

Optimal fluid RI: the fluid refractive index required to achieve the maximum usable radius for a given dosimeter-tank pair with the current scanning configuration.

Maximum usable radius: the usable radius achieved with optimal media matching for the given scanning configuration.

Recoverable refraction: when rays refracted at an initial media interface are refracted back into telecentric alignment before reaching the detector.

3. RESULTS AND DISCUSSION

3.A. Optimal media matching

Results showing the usable radius for a range of fluid RI choices and dosimeters are displayed in Fig. 3. A scanning scenario with perfectly matched dosimeter and solid-tank produces the highest maximum usable radius, with a linear decrease in maximum usable radius as the dosimeter RI decreases.

FIG. 3.

Telecentric systems are very sensitive to RI mismatches and refraction artifacts. Each dosimeter has an optimal fluid RI value that produces the largest usable radius. Gap size = 1 mm, solid-tank RI = 1.5, and lens tolerance = 1.0°.

When the fluid’s refractive index is greater than the dosimeter’s, there is a sharp falloff in the usable radius for a telecentric system caused by unrecoverable refraction on the edges of the dosimeter. As rays exit the dosimeter into a fluid with a higher refractive index, they are bent toward the normal in accordance with Snell’s law. Near the edges of the dosimeter, the angle of the normal line is such that these rays are bent even further out of alignment with the telecentric axis. This effect occurs in reverse as the fluid refractive index matches the dosimeter and continues to decrease, and eventually, those refracted rays are bent away from the normal enough to come into telecentric alignment, causing a sharp peak in the usable radius. The rays near the center of the dosimeter are not deflected as much by media mismatches because their incident angles are much smaller, so they generally remain detectable for all scenarios. Because of this recoverable refraction effect, the optimal fluid RI is not a match with either the dosimeter or the solid-tank but occurs at a lower refractive index than either, as shown in Fig. 4.

FIG. 4.

Optimal fluid RI for telecentric system. Optimal fluid RI is not a match with dosimeter RI or solid-tank RI except in cases of perfectly matching RI. Solid-tank RI = 1.5, gap size = 1.0 mm, and lens tolerance = 1.0°.

Once the fluid RI continues to decrease past the optimal value, rays continue to be refracted toward telecentric alignment, creating the milder decrease in usable radius shown in Fig. 3.

The maximum usable radius decreases from 97.6% to 50.2% over a change of 0.02 in dosimeter refractive index, indicating that telecentric dry scanning is extremely sensitive to media mismatches between the dosimeter and solid-tank. Figure 5 displays the relationship between the maximum usable radius and the RI of the dosimeter. Mismatches between the tank and dosimeter cause more refraction, which decreases the number of rays detected by the telecentric lens.

FIG. 5.

In a telecentric system, the maximum usable radius for dosimeters of various RIs increases linearly as the dosimeter RI approaches that of the solid-tank. Solid-tank RI = 1.5, gap size = 1.0 mm, lens tolerance = 1.0°, and fluid RI = optimal value.

Ray-tracing diagrams demonstrating standard results for various media combinations in a telecentric system are provided in Appendix B, Figs. 14–18 [available in supplementary material (Ref. 25)].

3.B. The effect of gap size

Figure 6 shows the effect of changing gap size on the usable radius for selected dosimeter RIs in a telecentric system. For a given dosimeter RI, the combination of gap size and fluid RI has a significant effect on the usable radius.

FIG. 6.

The effect of gap size on the usable radius for various dosimeter RIs is difficult to quantify—as gap size widens, a higher RI fluid is typically required to recover high fraction of the usable radius.

Generally, the optimal fluid RI increases as the gap size increases, becoming more closely matched to the dosimeter at large (>3 mm) gap sizes. The results suggest that the maximum usable radius depends on gap size in addition to dosimeter-tank mismatch. At larger gap sizes, refraction effects (including recoverable refraction) are amplified by the increased amount of fluid traveled by a light ray. As a result, changing the gap size by a small amount can cause substantial increases in the usable radius. For example, in Fig. 6, for dosimeter RI = 1.49, the usable radius increases from 47.2% with a gap size of 1 mm to 84.4% with a gap size of 1.5 mm for the exact same RI combination of RI_t = 1.5, RI_dosimeter = 1.49, and RI_fluid = 1.47. Both the solid-tank and dosimeter are made from precision molds, so consistent geometry and gap-size can be maintained. These results indicate that optimal results occur when the RI of the dosimeter and tank is the same, in which case the fluid will have the same RI. If mismatches between the tank and dosimeter RI occur, the RI of the matching fluid needs to be fine tuned to achieve the highest R_u. Care would need to be taken to optimize and standardize the size of the original molds.

Figure 7 shows how the optimal fluid RI relates to gap size for mismatched dosimeter-tank RIs. Consistent with earlier results, as the gap size increases, the optimal fluid RI becomes more closely matched to the dosimeter. At small gap sizes, the optimal fluid RI is much lower than the dosimeter RI.

FIG. 7.

The solid-tank system is very sensitive to small changes in gap size, requiring the fluid RI to be carefully adjusted if there is a RI mismatch between the dosimeter and solid-tank. In these cases, the optimal fluid RI approaches that of the dosimeter at large gap sizes. Solid-tank RI = 1.5 and lens tolerance = 1.0°.

Figures 11–13 in Appendix A [available in supplementary material (Ref. 25)] show an alternate arrangement of the data for these dosimeters examining the relationship between usable radius and gap size for various fluid RIs. Ray tracings demonstrating some of these results are provided in Appendix B, Figs. 18 and 19.

3.C. Telecentric lens tolerance

The usable radius for various refractive media combinations at different telecentric lens tolerances is shown in Fig. 8. At higher tolerance (>5°), a telecentric system behaves similarly to an ideal system because it is accepting much more refracted light that would be rejected at a lower tolerance. Here, we are assuming that refracted rays are perfectly localized by the detector system; in reality (or in a physical system), the acceptance of nonparallel rays would cause some geometric (and therefore dosimetric) uncertainty in dosimeter readout at the periphery of the dosimeter.

FIG. 8.

As the telecentric lens tolerance increases, the maximum usable radius for mismatched media increases as more light that would previously have been rejected is allowed to contribute to the image. Perfectly matched media produce the same maximum usable radius regardless of telecentric lens tolerance. Gap size = 1 mm and solid-tank RI = 1.5.

Figure 9 compares the maximum usable radius for matched and mismatched dosimeters at different telecentric lens tolerances. For perfectly matched media, the usable radius remains at 97.6% for all telecentric lens tolerances. For mismatched dosimeter-tank RI and high telecentricity (low tolerance), the maximum usable radius increases rapidly from 68.8% at 0.5° to 89.8% at 1.0°. The maximum usable radius for mismatched media approaches that of perfectly matched media at large telecentric lens tolerances (>2.0°), indicating that increasing the lens tolerance by slightly spoiling of the telecentric beam with a diffuser or increasing the aperture stops in the lens can recover the usable radius in situations where the solid-tank and dosimeter are slightly mismatched. However, this method presents a trade-off between usable radius and resolution—at large telecentric lens tolerances, refracted rays incident on the detector will be incorrectly reconstructed under the assumption of straight-line travel through the sample.

FIG. 9.

When the dosimeter and solid-tank have different RIs, increasing the telecentric lens tolerance can recover the usable radius.

3.D. Unique artifacts

At certain refractive media combinations, a unique ring artifact appears in the reconstructed image, as shown in Fig. 10.

FIG. 10.

Ring artifacts in reconstructed image and corresponding ray-tracing diagram. The outer ring is caused by recoverable refraction near the edges. Solid lines are rays accepted by the telecentric lens, and dotted lines are rejected. The gap size is 1 mm, so it is not visible in the ray tracing. Dosimeter RI = 1.48, fluid RI = 1.45, solid-tank RI = 1.5, gap size = 1 mm, and telecentric tolerance = 1.0°.

This outer ring in Fig. 10 corresponds to rays near the edge of the dosimeter being detected while those on either side do not due to the geometry and media RI combinations. The inner ring represents the central core of rays that experience little deflection and are generally detectable at all media combinations. The ring disappears when the fluid RI decreases to the optimal value, making it a potentially useful landmark for trial-and-error fluid matching.

4. CONCLUSIONS

The aims of this paper were to investigate the feasibility of dry telecentric optical-CT imaging and determine optimal design and scanning parameters for such a system by simulating common scanning configurations. Our results show that dry optical-CT imaging is feasible in situations when the dosimeter and solid-tank have closely matched refractive indices or if data are not required in the periphery of the dosimeter. If the magnitude of dosimeter-tank RI mismatch is less than −0.01, a dry telecentric scanning system will produce dose measurements within ±2% of the true dose across over 80% of the dosimeter radius. To produce accurate dose measurements across 95% of the dosimeter radius with a dry telecentric system, the dosimeter-tank mismatch must be less than −0.005. In situations with dosimeter-tank RI mismatches greater than −0.01, dose measurements in the periphery will be inaccurate. If a close match cannot be obtained, increasing the telecentric lens tolerance is the easiest method to recover the usable radius. Gap size is the most difficult parameter to adjust on the fly as it is determined by the dosimeter and solid-tank molds. In practice, adjusting the RI of the fluid can compensate for losses in usable radius due to gap size. Due to the sensitivity of the solid-tank system to small changes in gap-size (when there is RI mismatch between the dosimeter and solid-tank), care should be taken to standardize the dosimeter mold for both the solid-tank system and the dosimeters.

The simulation tool ScanSim may be helpful in guiding design considerations for optical-CT solid-tank scanners, especially in the optimal choice of RI of the small amount of fluid still required for dry scanning. The optimal fluid RI choice is not immediately obvious in situations when the dosimeter and tank are not refractively matched, as it is a function of both the dosimeter-tank RI mismatch and the gap size. If mismatches between the tank and dosimeter RI occur, the RI of the matching fluid needs to be fine tuned to achieve the highest R_u. Generally, if the gap size is large (>5 mm), the optimal fluid RI choice will be slightly lower than the dosimeter RI. At small gap sizes (1–3 mm), the optimal fluid RI choice is considerably lower than the dosimeter RI.