On the gEUD biological optimization objective for organs at risk in Photon Optimizer of Eclipse treatment planning system

Abstract Inverse planning optimization using biologically based objectives is becoming part of the intensity modulated optimization process. The performances and efficacy of the biologically based gEUD (generalized Equivalent Uniform Dose) objective implemented in the Photon Optimizer (PO) of Varian Eclipse treatment planning system have been here analyzed. gEUD is associated with the parameter a that accounts for the seriality of a structure, being higher for more serial organs. The PO was used to optimize volumetric modulated arc therapy (VMAT) plans on a virtual homogeneous cylindrical phantom presenting a target and an organ at risk (OAR). The OAR was placed at 4 mm, 1 and 2 cm distance, or cropped at 0, 2 and 4 mm from the target. Homogeneous target dose of 60 Gy in 20 fractions was requested with physical dose‐volume objectives, while OAR dose was minimized with the upper gEUD objective. The gEUD specific a parameter was varied from 0.1 to 40 to assess its impact to OAR sparing and target coverage. Actual head and neck and prostate cases, with one parotid and the rectum as test OAR, were also analyzed to translate the results in the more complex clinical environment. Increasing the a parameter value in the gEUD objective, the optimization achieved lower volumes of the OAR which received the highest dose levels. The maximum dose in the OAR was minimized well with a values up to 20, while further increase of a to 40 did not further improve the result. The OAR mean dose was reduced for the OAR located at 1 and 2 cm distance from the target, enforced with increasing a. For cropped OARs, a mean dose reduction was achieved for a values up to 3–5, but mean dose increased for higher a values. The optimal choice of the parameter a depends on the mutual OAR and target position, and seriality of the organ. Today no significant compendium of clinical and biological specific a and gEUD values are available for a wide range of OARs.

Intensity modulation radiotherapy planning, in both fixed beam setting (IMRT) and volumetric modulated arc setting (VMAT), uses inverse optimization processes generally based on physical dose or dose-volume (DV) parameters. However, the planning criteria based on physical dose (or DV) constraints are a crude surrogate of any biological index that would better reflect the clinical goals. This makes the physical DV surrogates possibly inadequate to describe the radiation response of the tissues, and suboptimal to obtain a dose distribution that would aim to reflect more biological objectives. 1,2 Dose-response models could be mechanistic, attempting to mathematically describe biological processes of cell survival, or phenomenological, empirically fitting available data. In the first group there are the normal tissue complication probability (NTCP) based model. The Lyman-Kutcher-Burman model 3 described the doseresponse curve with three parameters, based on uniform irradiation; in this case, dose volume histogram (DVH) reduction algorithms were necessary to account for the non-uniform dose distribution (an overview of those reduction models is, e.g., in 4 ). Differently, the Relative Seriality model 5 described the radiation response according to the damage and recovery of organ functional subunits. But the models which are the most used in the currently available biologically-based treatment planning belong to the phenomenological approach. In particular, the Equivalent Uniform Dose (EUD) concept proposed by Niemierko,6 and its extension to gEUD (generalized EUD), 7 provides a single metric for reporting non-uniform dose distribution, using gEUD as a single organ specific parameter to account for the biological response according to the delivered dose distribution in that organ.
The inclusion of biologically-based constraints in the optimizer cost function driving the inverse planning process, inherently incorporating a specific volume effect, could allow shaping the dose distribution by balancing the amount of volume receiving different dose levels. However, the result of an inverse planning optimization depends on the complex interplay of all the terms of the cost function. It is essential in the clinical practice to understand the effects of the biologically based objectives in controlling the dose distribution, and to know which is the desirable final dose distribution for a proper use of the underlying model.
The introduction of biologically based treatment planning, or a combination of physical and biological DV criteria in inverse planning objectives has been explored by the AAPM Task Group 166, 1   describing the commercially available solutions at the time of publication. A recent tool has been introduced in the new Photon Optimizer (PO), the inverse planning engine for both IMRT and VMAT implemented in the Eclipse TM planning system (Varian Medical Systems, Palo Alto, CA, USA) since its version 13.5, not described yet in the AAPM report. This tool makes available the gEUD objective as well as a variety of most general DV objectives in the same optimization process.
Aim of the present work is to investigate the results, from a clinical perspective, of the performance and efficacy of the biologically based gEUD objective in Eclipse TM in the inverse planning process, as it is implemented in the current optimization engine. Experiments were conducted for a simplified phantom with the aim to achieve some specific dose sparing inside given organs. The same was applied to clinical cases of head and neck (with a parotid as organ at risk, OAR) and prostate (with the rectum as OAR) to check and compare the consistency with real clinical application.

Dose
The gEUD is defined as: 6,7 gEUD ¼ X where v i is the fractional organ volume receiving a dose D i and a is a parameter that describes the volume effect. For a ! À1 (negative a values, down to À40 is available in practice), gEUD approaches the minimum dose, and can be used for tumors. | 107 critical structures. However, it is related to the parameter n describing the volume effect in the Lyman-Kutcher-Burman NTCP model, as n ¼ 1=a. This last parameter has been widely analyzed, and a summary overview can be found in Luxton et al. 8 The concept of the gEUD optimization during inverse planning optimization is depicted in Fig. 1: for the DVH on the left, the a parameter is equal to 1 and the optimization force is directed to reduce the volume receiving mid-dose levels, while, on the right DVH of the figure, the gEUD optimization with a high a parameter is shown to force the decrease in the structure volume receiving the higher dose levels. Regarding the specific implementation of the minimization of a convex optimization function (or non-convex of a global objective function), it is part of the non-disclosed implementation of the whole optimization engine.

2.B | The optimization objectives in PO
A number of different optimization objectives are available in PO (here used in its version 13.6). There are the physical constraints as Upper, Lower, and Mean objectives used, respectively, to: limit the dose level in a defined portion of the structure volume, define a minimum dose level that a certain target volume should receive, define the mean dose that should not be exceeded for the structure.
The biological objectives are: Upper gEUD, Lower gEUD, and Target gEUD. The parameter a can vary from +0.1 to +40 for Upper gEUD, from À40 to +1, excluding 0, for Lower gEUD and Target gEUD.
The exploration of the lower and target gEUD objectives is out of the scope of the present work, which aims to evaluate the capability of this tool to modulate, with one single objective, the shape of an OAR DVH. The target dose homogeneity was optimized in the current work with the only use of a lower and an upper physical DV constraint.
In the cost function, the different objectives are similarly handled in the Eclipse TM optimization engine as follows:

2.C | The phantom study design
A virtual phantom with homogeneous Hounsfield Unit (HU) assignment equal to 0 was generated in Eclipse. It had cylindrical shape of 30 cm diameter and 50 cm long. In the middle of the phantom, a cylindrical target was delineated, of 10 cm diameter and length.
As organs at risk (OAR), different cylinders (4 cm diameter and 5 cm long) were delineated on the left of the target: with target to OAR centres distance of 6.5 cm, cropped at the target Results on OAR dose distribution were reported as mean dose, gEUD (according to the varying a parameter), maximum point and near-to-maximum doses (as D 1% , D 2% , i.e., the dose received by 2% of the structure volume), D 20% , D 50% , V 15 Gy (volume receiving no more than 15 Gy dose level). | 109 and the same cropped 4 mm by the target. New plans were generated optimizing the test OAR with the mean objective, or the upper gEUD objective, varying the a parameter value (1, 2, 3, 5, and 10). The priority was not made changing, as well as all the other optimization objectives. During the optimization no interactions were allowed, while it was possible to hold each of the resolution levels to permit the optimizer to achieve a flat cost, as during the routine clinical procedure.

2.D | The clinical cases
The same parameters analyzed in the phantom study were here evaluated, and compared with those.

3.A | Phantom study
In Fig. 3 i.e., the structures for which the optimization was driven.
The requested value of 15 Gy for the gEUD was achieved for any value of the parameter a only when the OAR was located far from the target (2 cm distance in the exercise), where a homogeneous dose was requested with higher priority. In the cases where the OAR was located closer to the target, the requested gEUD value was achieved only for very small a value, while increasing with a.
The mean dose (and similarly D 50% ) to the same OAR structure decreased for all OAR-target distances, until an a value of 3-5; then, for a 10 and higher, the mean structure dose increases with a for OAR distances cropped 0 to 4 mm from the target, while for OAR positioned from 4 mm to 2 cm from the target, the mean dose continuously decreases. On the other hand, the behavior of the maximum and near-to-maximum doses is different and continuously decreases with a. However, the maximum dose reaches an approximate plateau (around an a value of 10-20), beyond which the optimizer is not able to significantly reduce the dose further.
The trade-off due to the increased OAR sparing for high doses achieved by increasing the a value, especially when the OAR structure is close to the target, could be twofold. On one side, there is a diminished target homogeneity and coverage, as highlighted in Table 1 with the Standard Deviation and V 95% parameter (volume receiving at least 95% of the prescription dose) for the target structure. This is evident for the OAR_0mmCrop, but also for the OAR_4mmCrop, while for the OAR + 2cm, the target coverage is not affected by the increased a  to the a = 20 case. Conversely, for a distant structure, for the same dose level requested, all the DVH smoothly decrease for a from 0.1 to its maximum value 40.
In the geometries studied, where an OAR is cropped to relatively distant, there is not much to gain from using an a parameter higher than 10 or 20. When using an a of 40, the maximal or near maximum dose of the OAR is nearly the same as that for a = 10 or a = 20, yet the mean dose is higher and target coverage is worse.
Comparing the plans optimized using the upper gEUD objective with a = 1 vs. the mean dose objective, differences were clearly present, showing that the different objectives (gEUD vs. mean dose) led to different terms in the cost function. Results are summarized in

3.B | Clinical cases
The dose distributions and DVHs of the clinical cases confirmed the general message reported for the phantom case. In Fig. 5

| DISCUSSION
The use of the biological optimization parameter called "upper gEUD" was evaluated for OAR structures at different distances from the target during VMAT optimization in the Eclipse TM PO optimizer.
It shows to be a powerful objective tool to improve the OAR sparing without compromising the target coverage and homogeneity when applied with an a value selected according to the structure seriality and target/OAR geometry.
Biological DV objectives have been explored for other planning systems or ad-hoc optimization engines, presenting similar results.
The first applications of the gEUD concept 10,11 showed that the The biological optimization using gEUD, for both target and OAR, has been used by Cabrera G. et al. 18

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Some published values of the n parameter of the Lyman-Kutcher-Burman NTCP model could be considered as a starting value for the gEUD optimization as a "true" biological solution. However, there is a lack of knowledge in which is the gEUD(a) tolerance value for each specific organ. Since the gEUD(a) value depends on the DVH shape, there is no correlation between e.g., the mean dose and the gEUD.
This makes more difficult a correct use of the gEUD objective, once applied the proper organ-specific a value, as there is no published data on gEUD(a) tolerance levels for specific organs.
In this view, in light of more specifically biological evaluations, the gEUD objective in Eclipse TM can be safely used since it reduces the OAR dose to all involved dose levels for a values from 1 to~5. For lar- ger a values, attention should be paid case by case, since, depending on the structures geometry and mutual locations, the DVH could be lower for some dose range and higher for other ranges.
For a more biologically conscious use of the gEUD-based optimization, and to give meaning to the gEUD dose in relation to a specific a parameter for each specific organ, we need clinical studies evaluating the patient toxicity related to gEUD and the a parameter for the most important critical structures. This will allow reducing better the doses to OAR, in the low or high dose range, where clinically and biologically it is more relevant in the specific structure, thanks to an improved knowledge of the biological and clinical effect of the radiation. For the moment, for the specific use of a, we could start from the fact that a = 1/n, and n values have been widely published and summarized. 8 The simplicity of the proposed phantom exercise allowed the understanding of the performance of the sole gEUD upper objective, without mixing or confounding different effects deriving from other sources anatomy related. However, the use of this tool to specific clinical cases was confirming the trends read in the phantom setting, now able to possibly distinguish between the tool performance and the anatomical specific features.

| CONCLUSIONS
The gEUD optimization objective implemented in the Eclipse PO optimizer has shown to be a powerful instrument to spare the OARs without reducing the target coverage. A better understanding of the correlation between the a parameter and the OAR radiobiology remains advisable.

CONF LICT OF I NTEREST
Stephen