Radiotherapy Dose Accumulation Routine (RADAR)- A novel dose accumulation script with built-in uncertainty

Abstract

Purpose:

To incorporate uncertainty into dose accumulation for reirradiation.

Methods:

The RAdiotherapy Dose Accumulation Routine (RADAR) script for the Eclipse treatment planning system (Varian Medical Systems) is described and the voxel-wise ellipsoid search algorithm is introduced as a means of incorporating uncertainty. RADAR is first demonstrated on a test patient reirradiated to the spine illustrating the effect of the uncertainty algorithm. A summary of initial evaluation testing by 11 users, each of whom ran a separate spine reirradiation case, follows. Finally, RADAR run times are reported for different conditions.

Results:

In the demonstration case in which a 3mm ellipsoid search was used, maximum RADAR 2 Gy equivalent (EQD2) accumulated spinal cord dose increased from 7244 cGy to 12689 cGy because the ellipsoid search pulled dose from closer to the adjacent target structure. When the ellipsoid search was restricted to voxels within the spinal cord, the maximum accumulated cord dose was reduced to 6523 cGy and did not exceed the sum of the maximum EQD2 spinal cord doses of the individual plans (6730 cGy). In the evaluation cases, the RADAR EQD2 maximum dose for the spinal cord increased an average of 31.6% with uncertainty applied compared to a conventional dose accumulation and decreased an average of 16.7% compared to a conventional dose accumulation when the uncertainty calculation was restricted to voxels within the spinal cord. RADAR run times depend on the number of plans being added and the type of uncertainty being used.

Conclusion:

RADAR offers a novel way to directly account for uncertainty in dose accumulation by means of a voxel-wise ellipsoid search algorithm. EQD2 dose accumulation with and without dose discounts is also available.

Introduction

Reirradiation[1] is becoming more common in the modern radiotherapy clinic [2–5]. Part of the standard reirradiation workflow involves the analysis of previous treatments and their effect on the current delivery [6]. The task of the medical physicist is to assemble a holistic picture of the accumulated dose that the patient has received to the degree that may be relevant for the current treatment course. This in turn guides the physician in their choice of prescription doses and organ at risk (OAR) tolerance doses.

There is much in the literature about dose accumulation and the inherent uncertainty of relying on a rigid or deformable registration to accurately relate voxels of one course with voxels of another[3] [7–10]. Validation of registration algorithms is therefore important prior to its use in dose accumulation in a single course or in the reirradiation setting [11–15]. If this is not done correctly then the reported cumulative dose distribution may yield an inaccurate dose/volume metric which could potentially misguide clinical decisions[16, 17].

Evaluating the geometrical accuracy of a deformable image registration (DIR) algorithm is challenging because ground truth is often missing in a clinical use case, especially on a patient specific level. Lowther et al created in silico deformations using a B-spline DIR algorithm as reference, and evaluated the accuracy of a commercial demons DIR algorithm against the reference algorithm [18]. A voxel-based dose error map resulting from DIR was constructed by calculating the dose discrepancies between the assessed and reference algorithms, plus the inverse consistency error. Subsequently, dose was accumulated between fractions accounting for such an error map, and a dose volume histogram (DVH) was produced with uncertainty envelopes reflecting the DIR uncertainty. While this method is a powerful tool to evaluate patient specific accuracy of a DIR algorithm, the major limitation is that it provides a nominal accumulated dose at each voxel without a measure of the uncertainty brought from the intrinsic nature of constructing in silico deformations with only one simulation and a particular reference DIR algorithm. A complimentary approach developed by Amstutz et al modeled the uncertainty of DIR by analyzing the results from 5 different DIR algorithms[19]. The distributions of the differences were calculated on a voxel level for the first fraction, and utilized to estimate dose uncertainties for future fractions in combination with the dose distribution. However, when the tumor responds to treatment and experiences a substantial volume change, the accuracy of the model would be compromised. Furthermore, the model may be limited to the DIR algorithms applied in the evaluation, not guaranteed transferable to other algorithms. An easily explainable and less-resource-demanding algorithm that can account for DIR uncertainty is still in need for the standard application of dose accumulation.

In this report, we describe a novel application called RAdiotherapy Dose Accumulation Routine (RADAR) that accounts for registration uncertainty when performing a dose accumulation. Uncertainty is accounted for by “smearing” the prior dose distribution either by a fixed amount or on an OAR specific basis. In this way one can obtain a robust yet realistic dose accumulation without adding doses that are unreasonably far apart anatomically. The inclusion of uncertainty reduces the risk of taking the registration too literally when adding doses. RADAR also gives the option of accumulating Linear-Quadratic equivalent doses in 2 Gy fractions (EQD2 conversion) that applies a templated α/β to OARs of interest. It also optionally applies organ-specific dose discounts depending on how long ago the previous dose was delivered. RADAR has been developed as a plugin script for the Eclipse treatment planning system (Varian Medical Systems, Palo Alto, CA).

Methods

In this section, the program is described in detail. In the subsequent section, RADAR is illustrated using a representative spine SBRT case, and initial evaluation testing by prospective end users is described. Finally, some limitations of the program encountered in the testing are described.

RADAR design

RADAR allows the user to accumulate dose voxel by voxel in the standard fashion or with uncertainty using a novel voxel search method described below. The output of the program is an accumulated dose distribution on the current CT scan represented as an Eclipse plan with no beams. The name of the RADAR output plan and the course in which it resides is specified by the user. The uncertainty algorithm as well as the EQD2 and dose discount features are described below.

Dose Accumulation With Uncertainty- the ellipsoid search

The process of applying uncertainty to a previously treated plan is as follows. For corresponding voxels of the previous plans (as determined by the image registration), RADAR does not add the dose for that voxel as it would in a typical dose accumulation but rather determines the maximum dose $D_{ϵ}$ within an ellipsoid centered on that voxel and passes that to the accumulation. This will be referred to as an “ellipsoid search”.

$${D_{ϵ}(x_i,y_i,z_i)}^{prev}={MAX}_{x^{\prime }=x_i\pm {ϵ}_{x,}{y}^{\prime }=y_i\pm {ϵ}_y,z^{\prime }=z_i\pm {ϵ}_z}\left[{D(x^{\prime },y^{\prime },z^{\prime })}^{prev}\right]$$

where ${ϵ}_{x,}{ϵ}_{y,}{ϵ}_{z,}$ are the radii of an ellipsoid centered on $x_i,y_i,z_i$. These “search radii” are user defined and can be global or structure specific. The accumulated dose at a given voxel $i$ in the current scan associated with a voxel $i_{prev}^{\prime }$ in a previous scan $prev$ through the image registration is then given by

$${D\left(x_i,y_i,z_i\right)}^{accum}={D\left(x_i,y_i,z_i\right)}^{current}+\sum _{prev}{D_{ϵ}(x_{i_{prev}^{\prime }},y_{i_{prev}^{\prime }},z_{i_{prev}^{\prime }})}^{prev}$$

where the sum is over all courses of prior treatment in the accumulation.

Structure Matching

One can imagine a voxel of the current scan existing within a certain OAR. If the ellipsoid search around the corresponding voxel of the previous scan is large enough, dose may be pulled from a nearby target structure which would be excessive. Therefore, it may be desirable to limit the ellipsoid search to an area within the corresponding OAR of that scan, ensuring that the maximum accumulated dose for a particular OAR does not exceed the sum of the maximum doses to that OAR from the individual plans. For this reason, a “structure matching” option, illustrated in figure 1, is available for the ellipsoid search which truncates the search to only include voxels within the same OAR as the corresponding voxel of the current scan. The user has the option to choose which structures would be subject to this restriction. There are 3 potential use cases for structure matching depending on the proximity of the voxel in the previous scan to the OAR of interest:

1. The previous voxel is inside the OAR of interest (voxel v_i’ in figure 1). In this case the ellipsoid search in the previous scan is truncated to include only the voxels contained within that OAR.

2. The previous voxel is outside the OAR of interest but within 1 search radius from the surface (voxel v_i” in figure 1). In this case the centroid of the ellipsoid is moved from its original position to the nearest surface voxel of the OAR of interest, again only taking voxels inside the OAR into account. This is called a “jump search”.

3. The previous voxel is farther from the OAR than 1 search radius (voxel v_i”’ in figure 1). In that case the search is done locally with no geometric truncation, but the dose returned is capped at the maximum dose of that OAR for that plan.

Figure 1-.

An illustration of the RADAR uncertainty calculation for the 3 use cases encountered when using structure matching. The OAR of interest is represented by the rectangular structure for the previous course (blue) and the current course (orange).

EQD2 Dose Summation and Dose Discount

RADAR users have the option of performing a 2 Gy equivalent (EQD2) dose summation. In these cases, the program will default to a templated α/β ratio for each structure and the summation will be an EQD2 equivalent rather than a direct physical dose summation. For each voxel v_i in the current scan, the α/β ratio used for the accumulation is dependent on the structure in the current scan in which that voxel resides. If a voxel resides in unspecified tissue, a site default α/β ratio is used.

The program additionally offers the option of a “dose discount” for EQD2 dose summations that takes into account the time elapsed between past and current treatments. The discounts are stored as templates in the program allowing the user to choose between different discount paradigms as dictated by the clinical scenario. For this exercise, the dose discount table used was based on a publication by K. Paradis et al [20].

RADAR initial evaluation testing by end users

A group of 11 treatment planners was recruited to each run a retrospective dose accumulation for a unique spine patient with multiple courses using RADAR under different conditions (search on/off, structure matching on/off, EQD on/off, dose discount on/off) and provide feedback. Results were compiled and reviewed by the implementation team and feedback was elicited about the user experience. Limitations of RADAR were also evaluated and addressed. Runtimes were also recorded. This helped the implementation team in building in features to make the software safer and more user friendly following our software development guidelines [21].

Results

RADAR illustrative case- SBRT spine

A patient previously treated with multiple courses to the spine was retrospectively analyzed using RADAR.

This patient received multiple courses of treatment to different areas of the spine but for purposes of illustration we focus on a series of 3 treatments to the T9 area (see figure 2) connected via rigid registration for simplicity. They are listed below in chronological order.:

1. Treatment A (2020): An AP-PA treatment to the T8-T11 region of 800 cGy x 1 fraction

2. Treatment B (2021): A 9 field IMRT treatment to T8-T10 of 800 cGy x 5 fractions

3. Treatment C: (2022): A 9 field IMRT treatment to T9 of 800 cGy x 5 fractions

FIGURE 2.

Sagittal projections for the 3 treatment courses of the illustrative case.

For the purposes of this illustration, Treatment C will be considered the “current” treatment and Treatments A and B will be considered “previous” treatments.

For the RADAR dose accumulations performed for these 3 plans, a search radius of 3mm was chosen for the spinal cord in each of the 3 directions. For simplicity of illustration, ellipsoid searches were not performed for other structures.

Dose accumulation with ellipsoid search

An illustrative RADAR analysis was performed for the following 3 use cases:

1. without uncertainty

2. with uncertainty (ellipsoid search) turned on and structure matching turned off

3. with uncertainty and structure matching turned on.

The effect of structure matching is shown in figure 3 with structure matching for the spinal cord turned on (left) and off (right). As can be seen in the figure, the spinal cord region is cooler with structure matching on compared to being off.

Figure 3-.

A visual comparison of EQD2 dose accumulation with structure matching turned on (left) and turned off (right). It can clearly be seen that the spinal cord region is cooler with structure matching on.

Table 1 lists the maximum dose to the spinal cord (EQD2) reported by RADAR for the 3 use cases above plus, for comparison, the sum of the maximum spinal cord doses (EQD2) from each of the 3 individual plans which might be inferred if dose accumulation was not available. Results are shown without and with the dose discount applied.

Table 1.

Spinal cord dose maxima (in EQD2) for RADAR sample case.

	Spinal cord maximum dose (EQD2)
	DD off (cGy)	DD on (cGy)
RADAR- no ellipsoid search	7244.3	5452.5
RADAR- ellipsoid w/structure matching off	12689.0	10430.0
RADAR- ellipsoid w/structure matching on	6523.4	4925.0
Sum of max cord dose for plans A, B, and C	6730.0	5067.5

Maxima are shown in the first 3 rows for no ellipsoid search, ellipsoid search with structure matching, ellipsoid search without structure matching. The fourth row shows the EQD2 sum of spinal cord maxima from the individual plans for comparison. Results are compared for dose discount (DD) off and on.

When the dose accumulation is performed without uncertainty (row 1, “RADAR- no ellipsoid search”), the maximum 2 Gy equivalent (EQD2) cord dose is 7244.3 cGy which would typically be reported for a standard rigid dose accumulation. In this use case, the accumulation is driven only by the rigid registration so any misalignment of the spinal cord structures in the registration is not accounted for. When uncertainty is applied (row 2, “RADAR- ellipsoid w/structure matching off”) the maximum spinal cord dose increases to 12689 cGy. This is because for this case the ellipsoid search pulls dose that is outside the spinal cord and closer to or inside the target potentially identifying an area adjacent to the spinal cord that received a high dose in a previous course. When the ellipsoid search is repeated with structure matching turned on (row 3, “RADAR- ellipsoid search with structure matching on”), the dose decreases to 6523.4 cGy since it restricts the search only to voxels within the spinal cord of the previous courses. For a structure such as the spinal cord the user would then have information that the spinal cord likely received a dose closer to 65 Gy but was close to a high dose region. One may lower the planned dose in that area as an added precaution, especially if this were a more mobile structure such as the esophagus. In this way the ellipsoid search with and without structure matching acts as a “probe” of the dose distribution. Finally, when the 2 Gy equivalent individual spinal cord maxima are added as may be the case without DICOM data of the previous treatments (row 4 “Sum of max cord dose for plans A, B, and C”) the result is slightly higher (6730 cGy) than structure matching because this is not a true dose accumulation and the maxima are not at the same location.

The process was repeated, this time with the dose discount feature turned on. (column 2 of table 1). The results are predictably lower. The dose discounts applied based on the Michigan table [20] for the spinal cord dose were 50% for Treatment A and 25% for treatment B.

RADAR initial evaluation testing by end users

For the 11 cases retrospectively tested by treatment planners, the maximum dose determined by RADAR for spinal cord, cauda equina, and esophagus with and without structure matching was compared to the sum of the maximum doses of the individual plans. The search radii used for this exercise (in cm) were as follows:

Cord: (0.3, 0.3, 0.3)

Cauda equina: (0.3, 0.3, 0.3)

Esophagus: (0.5, 0.5, 0.5)

In table 2, the average dose indices returned by RADAR (EQD2) with uncertainty turned on are compared to a conventional dose accumulation, simulated by running RADAR without uncertainty. As can be seen in the first column of results, with uncertainty turned on the average indices shown are increased relative to the conventional result as expected. With structure matching activated (fourth column of results), the average indices are lower than the conventional dose accumulation. This is because no effort is made to restrict dose to within the OAR of interest in a conventional dose accumulation and the OAR may pull dose from a nearby PTV if the registration is not perfect or there are slight differences in contouring (which RADAR can flag using overlap metrics for each OAR).

Table 2.

The difference between RADAR with uncertainty and a conventional dose accumulation (determined by running RADAR without uncertainty) for the evaluation testing cases (the conventional result is subtracted from the RADAR result).

		RADAR (w/uncertainty) vs conventional dose accumulation
Structure	Index(EQD2)	Structure matching off			Structure matching on
		avg	min	max	avg	min	max
Spinal Cord (N=9)	Dmax	31.6%	0.5%	73.7%	−16.7%	−35.6%	0.8%
	D0.035cc	32.7%	0.7%	65.3%	−8.6%	−29.3%	5.9%
Cauda Equina (N=3)	Dmax	10.5%	0.3%	30.6%	−6.3%	−19.3%	0.3%
	D0.035cc	9.2%	0.5%	26.5%	−7.8%	−23.7%	26.5%
Esophagus (N=9)	Dmax	8.1%	0.7%	20.4%	−8.9%	−23.8%	6.1%
	D0.035cc	11.4%	0.8%	39.7%	−3.5%	−24.9%	39.2%

Results refer to EQD2 accumulations. With structure matching off, RADAR increases these common metrics however with structure matching on, the results are lower than the conventional dose accumulation on the average.

In these tests, the average run time for RADAR when 2 plans were being summed was on the order of 2 minutes without structure matching. Run time increased to 2 minutes, 40 seconds when structure matching was turned on. As the number of plans increased, the effect of structure matching on the run time was more pronounced. The average run time with structure matching turned on for 3 plans was 6 minutes, 40 seconds. One tester had 5 plans and the average run time when structure matching was turned on was approximately 100 minutes. Turning on EQD2 or dose discount did not have a significant effect on the run time.

Limitations of RADAR

The initial evaluation testing by treatment planners revealed certain limitations of RADAR, described below.

The Integral Dose Effect

Because of the inherent nature of the ellipsoid search method of uncertainty estimation, voxels of previous plans are assigned a higher dose for the accumulation than they originally had. This increases the integral dose of OAR’s in which they reside, thereby inflating volumetric constraints such as V20Gy or D5cc. The larger the search radius, the larger the effect. Figure 4 shows the effect of increasing the search radius on maximum dose and D5cc for the bowel in a sample case. One can see that the Dmax value is less affected than D5cc which can climb very quickly as the search radius increases because of the inflated integral dose associated with the uncertainty algorithm. It can be clinically meaningful to use the ellipsoid search for quantities such as Dmax, and to an acceptable extent, D0.035cc to account for uncertainty. However, metrics involving larger volumes such as 5%, 5cc, or more may become unrealistically high due to the increase in integral dose. We have therefore decided to use RADAR searches only to determine Dmax and D0.035cc, or other such “max-like” metrics, with uncertainty applied in the initial release and a warning message was added to that effect. This feature will be further explored and considered to determine an acceptable course of action for volumetric constraints.

Figure 4-.

The effect of increasing the search radius on Dmax and D5cc of the bowel (physical dose). The first set of bars represent the initial values of these quantities and the successive sets of bars represent the increase of these quantities as the search radius is increased from 1mm to 10mm, first without structure matching (U-1mm through U-10mm) and then with (R-1mm-R10mm). The largest effect of increasing the search radius is on the D5cc value.

The Voxelization Effect

Dose accumulations in RADAR are calculated on a voxel-by-voxel basis. When structure matching is turned on for a certain OAR, it ensures that no voxels within that OAR have any doses higher than the sum of the maximum doses of the individual OARs. If a DVH is created in the Eclipse planning system for this structure however, it uses a finer grid to sample doses and may therefore interpolate between a voxel contained inside the OAR and one just outside the OAR which may have a higher dose due to target proximity. Therefore, even though all the voxels residing inside the OAR satisfy the maximum dose restriction, in certain instances the Eclipse DVH algorithm may show a maximum dose tail which violates this rule.

Discussion

Uncertainty in dose accumulation is an ongoing area of interest. In a recent multicenter trial, DICOM plan data was provided to participating institutions for 2 cases: head and neck and lung. Cumulative dose assessments were returned by 24 participants, 20 of which were dose summations by rigid (n=15) or deformable (n=5) registration. Large variations in reported doses were found, especially in near maximum doses[22].

The quality of the dose accumulation is dependent on the quality of the underlying image registration. In a study examining the composite dose to the spinal cord it was shown that changes of 3 mm to a rigid registration for spine reirradiation could increase the maximum spinal cord dose by over 50% [23]. Brock et al recommended quality checks for registrations [11], and there are more coarse accumulation methods available if a dose accumulation is not possible due to registration quality. Murray et al developed a support tool for reirradiation (STRIDeR) which optimized OAR dose in the reirradiation setting using previously delivered dose as background dose. If the deformable registration was not deemed trustworthy, OAR dose maxima from the original plans were used instead [24, 25]. RADAR provides a novel way to intuitively incorporate uncertainty into the dose accumulation process such that a more informed decision can be made regarding how much dose can safely be delivered in the setting of reirradiation.

Through the search radii, RADAR relies on a specification of uncertainty for each organ at risk which combines the effects of registration uncertainty (which would differ between rigid and deformable registration) and expected organ motion and is therefore fertile ground for additional research and analysis. The question naturally arises in dose accumulation as to how far apart the maximum doses of a specific OAR from 2 different scans have to be when registered so that the user can safely assume they do not overlap. This is different for each OAR and naturally leads to the concept of the ellipsoid search. Given the estimated distance or ellipsoid size, RADAR is pulling the maximum dose from that area to ensure that the same piece of tissue is likely within the ellipsoid. There are other uncertainties such as delivery uncertainty that also play a part in determining the actual dose that is assumed to have been delivered. Azcona et al defined an “Evaluation Target Volume” (ETV) for dose accumulation over a single course which was an expansion of the GTV in the reference plan to include DIR uncertainty, intraobserver variability, imaging and delivery uncertainty[26]. With RADAR, a nominal delivery uncertainty can be added to the search radius since it is user defined but more investigation is needed to decide if the ellipsoid search is the best way to address this particular type of uncertainty when accumulating doses over multiple courses in which the delivery uncertainty may vary.

In this report we used a search radius of 3mm in each direction[27] for illustration which may not be clinically ideal. The selection of search radii, as related to the uncertainty, has direct impact on the cumulative dose distribution and dosimetric indices extracted from the composite plan. If they are too small the dosimetric indices in the RADAR composite plan may not adequately reflect the potential for toxicity. If they are too large then an overly conservative estimate of high cumulative dose to an OAR may prevent delivery of adequate salvage dose in the current course of treatment which will in turn decrease the probability of local control or long term survival. Spine SBRT is a good example of this. Other than registration uncertainties, there is also internal motion of the spinal cord itself. Oztek et al recommended a PRV margin of 1.5–2mm to account for spinal cord motion for SBRT of spine metastases based on MRI studies. Meyer et al used a 2mm spherical search to smear previously delivered spinal cord dose in an automated planning study for spine SBRT[28]. There are many such studies that can be used to reach a clinical consensus [29, 30] and that consensus will evolve. We also leave open the possibility that there will be different radii for different directions. For instance, the potential Superior-Inferior (SI) motion of the spinal cord could be different than the Left-Right (LR) and Anterior-Posterior (AP) motion [31, 32].

When considering registration uncertainty alone, one protection against search radii pulling dose from target structures introduced into the program is structure matching. For voxels within the spinal cord contour, it is reasonable to assume that the true corresponding piece of tissue in the prior treatment would likely reside in the spinal cord contour of the previous scan, assuming precise contouring. This applies for all OAR’s and is the basis of the structure matching concept which in effect incorporates contouring information into the uncertainty analysis. Some concerns with this approach are that contouring uncertainties or variations may unrealistically restrict the search area. This is one of the reasons that RADAR reports the overlap percentage, as well as the 95% Hausdorff distance(HD), and Mean Distance to Agreement (MDA) of matched structure pairs, which alerts the user that corresponding structures have a low overlap and may be reflective of differing contouring styles. The user should closely examine cases in which the overlap percentage is low (or HD and MDA are large) and make a decision regarding use of structure matching or the size of the search radius in order to not unrealistically bias the composite OAR dose. Although the voxel based ellipsoid search with structure matching may not be the most realistic way to account for all uncertainties such as setup error or lost/added tissue, it is a start and RADAR can be enhanced with more comprehensive uncertainty calculations in the future.

RADAR is a complex program with many parameters. As such it should be templated so that the user does not have to struggle with setting parameters and deciding on structure matching parameters on a tight planning timeline, yet still reap the benefits of the program. The alpha testing was very helpful in determining what parts of the program to lock down for clinical use. Locked down parameters would only be accessible to superusers who are more intimately familiar with the program and are under less time pressure.

An effective reirradiation workflow must be clearly defined[20, 33]. Since the uncertainty algorithm and the structure matching functionality are untested in a clinical setting it was decided for the initial clinical release to analyze cases using dose accumulation without uncertainty, with uncertainty, and with uncertainty and structure matching. The results would be compared such that the effects of the uncertainty feature and of structure matching would be clearly understood on a case by case basis until there was enough accumulated experience to use these new features exclusively. A number of cases are being run preclinically in this fashion which will be described in a forthcoming report on clinical implementation.

Future directions for RADAR include determination of uncertainty at the voxel level [34] [35] and exploring other options for application of uncertainty such as a convolution of doses for each voxel using a specific convolution kernel rather than a search for the maximum dose within an ellipsoid. The kernel would be dependent on the local uncertainty determined at each voxel.

CONCLUSIONS

RADAR provides a novel way to include uncertainty in the dose accumulation such that dose can be added with incorporation of uncertainty. Uncertainty parameters are structure-specific and user defined and provide the flexibility to progressively tune these parameters over time which is the subject of ongoing work. EQD2 summation as well as the ability to apply a dose discount are also included as the use of dose accumulation through RADAR necessitates establishment of radiobiologically consistent cumulative dose constraints.

[Data Availability Statement for this Work]

Research data are not available at this time.