Role of the parameters involved in the plan optimization based on the generalized equivalent uniform dose and radiobiological implications

Risk adaptive planning with biology-based constraints may lead to higher tumor control probability in tumors of the canine brain: A planning study

BACKGROUND

Classical radiation protocols are guided by physical dose delivered homogeneously over the target. Protocols are chosen to keep normal tissue complication probability (NTCP) at an acceptable level. Organs at risk (OAR) adjacent to the target volume could lead to underdosage of the tumor and a decrease of tumor control probability (TCP). The intent of our study was to explore a biology-based dose escalation: by keeping NTCP for OAR constant, radiation dose was to be maximized, allowing to result in heterogeneous dose distributions.

METHODS

We used computed tomography datasets of 25 dogs with brain tumors, previously treated with 10x4 Gy (40 Gy to PTV D50). We generated 3 plans for each patient: A) original treatment plan with homogeneous dose distribution, B) heterogeneous dose distribution with strict adherence to the same NTCPs as in A), and C) heterogeneous dose distribution with adherence to NTCP <5%. For plan comparison, TCPs and TCP equivalent doses (homogenous target dose which results in the same TCP) were calculated. To enable the use of the generalized equivalent uniform dose (gEUD) metric of the tumor target in plan optimization, the calculated TCP values were used to obtain the volume effect parameter a.

RESULTS

As intended, NTCPs for all OARs did not differ from plan A) to B). In plan C), however, NTCPs were significantly higher for brain (mean 2.5% (SD±1.9, 95%CI: 1.7,3.3), p<0.001), optic chiasm (mean 2.0% (SD±2.2, 95%CI: 1.0,2.8), p=0.010) compared to plan A), but no significant increase was found for the brainstem. For 24 of 25 of the evaluated patients, the heterogenous plans B) and C) led to an increase in target dose and projected increase in TCP compared to the homogenous plan A). Furthermore, the distribution of the projected individual TCP values as a function of the dose was found to be in good agreement with the population TCP model.

CONCLUSION

Our study is a first step towards risk-adaptive radiation dose optimization. This strategy utilizes a biologic objective function based on TCP and NTCP instead of an objective function based on physical dose constraints.

Multi-organ spatial stratification of 3-D dose distributions improves risk prediction of long-term self-reported severe symptoms in oropharyngeal cancer patients receiving radiotherapy: development of a pre-treatment decision support tool

Purpose

Identify Oropharyngeal cancer (OPC) patients at high-risk of developing long-term severe radiation-associated symptoms using dose volume histograms for organs-at-risk, via unsupervised clustering.

Material and methods

All patients were treated using radiation therapy for OPC. Dose-volume histograms of organs-at-risk were extracted from patients' treatment plans. Symptom ratings were collected via the MD Anderson Symptom Inventory (MDASI) given weekly during, and 6 months post-treatment. Drymouth, trouble swallowing, mucus, and vocal dysfunction were selected for analysis in this study. Patient stratifications were obtained by applying Bayesian Mixture Models with three components to patient's dose histograms for relevant organs. The clusters with the highest total mean doses were translated into dose thresholds using rule mining. Patient stratifications were compared against Tumor staging information using multivariate likelihood ratio tests. Model performance for prediction of moderate/severe symptoms at 6 months was compared against normal tissue complication probability (NTCP) models using cross-validation.

Results

A total of 349 patients were included for long-term symptom prediction. High-risk clusters were significantly correlated with outcomes for severe late drymouth (p <.0001, OR = 2.94), swallow (p = .002, OR = 5.13), mucus (p = .001, OR = 3.18), and voice (p = .009, OR = 8.99). Simplified clusters were also correlated with late severe symptoms for drymouth (p <.001, OR = 2.77), swallow (p = .01, OR = 3.63), mucus (p = .01, OR = 2.37), and voice (p <.001, OR = 19.75). Proposed cluster stratifications show better performance than NTCP models for severe drymouth (AUC.598 vs.559, MCC.143 vs.062), swallow (AUC.631 vs.561, MCC.20 vs -.030), mucus (AUC.596 vs.492, MCC.164 vs -.041), and voice (AUC.681 vs.555, MCC.181 vs -.019). Simplified dose thresholds also show better performance than baseline models for predicting late severe ratings for all symptoms.

Conclusion

Our results show that leveraging the 3-D dose histograms from radiation therapy plan improves stratification of patients according to their risk of experiencing long-term severe radiation associated symptoms, beyond existing NTPC models. Our rule-based method can approximate our stratifications with minimal loss of accuracy and can proactively identify risk factors for radiation-associated toxicity.

Effective optimization strategy for large optimization volume object, remaining volume at risk (RVR):α-value selection and usage from generalized equivalent uniform dose (gEUD) curve deviation perspective

Objective.A large optimization volume for intensity-modulated radiation therapy (IMRT), such as the remaining volume at risk (RVR), is traditionally unsuitable for dose-volume constraint control and requires planner-specific empirical considerations owing to the patient-specific shape. To enable less empirical optimization, the generalized equivalent uniform dose (gEUD) optimization is effective; however, the utilization of parametera-values remains elusive. Our study clarifies thea-value characteristics for optimization and to enable effectivea-value use.Approach.The gEUD can be obtained as a function of itsa-value, which is the weighted generalized mean; its curve has a continuous, differentiable, and sigmoid shape, deforming in its optimization state with retained curve characteristics. Using differential geometry, the gEUD curve changes in optimization is considered a geodesic deviation intervened by the forces between deforming and retaining the curve. The curvature and gradient of the curve are radically related to optimization. The vertex point (a=a_k) was set and thea-value roles were classified into the following three parts of the curve with respect to thea-value: (i) high gradient and middle curvature, (ii) middle gradient and high curvature, and (iii) low gradient and low curvature. Then, a strategy for multiplea-values was then identified using RVR optimization.Main results.Eleven head and neck patients who underwent static seven-field IMRT were used to verify thea-value characteristics and curvature effect for optimization. The lowera-value (i) (a= 1-3) optimization was effective for the whole dose-volume range; in contrast, the effect of highera-value (iii) (a= 12-20) optimization addressed strongly the high-dose range of the dose volume. The middlea-value (ii) (arounda=a_k) showed intermediate but effective high-to-low dose reduction. Thesea-value characteristics were observed as superimpositions in the optimization. Thus, multiple gEUD-based optimization was significantly superior to the exponential constraints normally applied to the RVR that surrounds the PTV, normal tissue objective (NTO), resulting in up to 25.9% and 8.1% improvement in dose-volume indices D2% and V10Gy, respectively.Significance.This study revealed an appropriatea-value for gEUD optimization, leading to favorable dose-volume optimization for the RVR region using fixed multiplea-value conditions, despite the very large and patient-specific shape of the region.

Using biologically based objectives to optimize boost intensity-modulated radiation therapy planning for brainstem tumors in dogs

Irradiated brain tumors commonly progress at the primary site, generating interest in focal dose escalation. The aim of this retrospective observational study was to use biological optimization objectives for a modeling exercise with simultaneously-integrated boost IMRT (SIB-IMRT) to generate a dose-escalated protocol with acceptable late radiation toxicity risk estimate and improve tumor control for brainstem tumors in dogs safely. We re-planned 20 dog brainstem tumor datasets with SIB-IMRT, prescribing 20 × 2.81 Gy to the gross tumor volume (GTV) and 20 × 2.5 Gy to the planning target volume. During the optimization process, we used biologically equivalent generalized equivalent uniform doses (gEUD) as planning aids. These were derived from human data, calculated to adhere to normal tissue complication probability (NTCP) ≤5%, and converted to the herein used fractionation schedule. We extracted the absolute organ at risk dose-volume histograms to calculate NTCP of each individual plan. For planning optimization, gEUD(a = 4)  = 39.8 Gy for brain and gEUD(a = 6.3)  = 43.8 Gy for brainstem were applied. Mean brain NTCP was low with 0.43% (SD ±0.49%, range 0.01-2.04%); mean brainstem NTCP was higher with 7.18% (SD ±4.29%, range 2.87-20.72%). Nevertheless, NTCP of < 10% in brainstem was achievable in 80% (16/20) of dogs. Spearman's correlation between relative GTV and NTCP was high (ρ = 0.798, P < .001), emphasizing increased risk with relative size even with subvolume-boost. Including biologically based gEUD values into optimization allowed estimating NTCP during the planning process. In conclusion, gEUD-based SIB-IMRT planning resulted in dose-escalated treatment plans with acceptable risk estimate of NTCP < 10% in the majority of dogs with brainstem tumors. Risk was correlated with relative tumor size.

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

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.

Risk-optimized proton therapy to minimize radiogenic second cancers

Proton therapy confers substantially lower predicted risk of second cancer compared with photon therapy. However, no previous studies have used an algorithmic approach to optimize beam angle or fluence-modulation for proton therapy to minimize those risks. The objectives of this study were to demonstrate the feasibility of risk-optimized proton therapy and to determine the combination of beam angles and fluence weights that minimizes the risk of second cancer in the bladder and rectum for a prostate cancer patient. We used 6 risk models to predict excess relative risk of second cancer. Treatment planning utilized a combination of a commercial treatment planning system and an in-house risk-optimization algorithm. When normal-tissue dose constraints were incorporated in treatment planning, the risk model that incorporated the effects of fractionation, initiation, inactivation, repopulation and promotion selected a combination of anterior and lateral beams, which lowered the relative risk by 21% for the bladder and 30% for the rectum compared to the lateral-opposed beam arrangement. Other results were found for other risk models.

Mathematical formulation of energy minimization - based inverse optimization

Purpose: To introduce the concept of energy minimization-based inverse optimization for external beam radiotherapy.

Materials and Methods: Mathematical formulation of energy minimization-based inverse optimization is presented. This mathematical representation is compared to the most commonly used dose–volume based formulation used in inverse optimization. A simple example on digitally created phantom is demonstrated. The phantom consists of three sections: a target surrounded by high and low density regions. The target is irradiated with two beams passing through those regions. Inverse optimization with dose–volume and energy minimization-based objective functions is performed. The dosimetric properties of the two optimization results are evaluated.

Results: Dose–volume histograms for all the volumes of interest used for dose optimization are compared. Energy-based optimization results in higher maximum dose to the volumes that are used as dose-limiting structures. However, the average and the integral doses delivered for the volumes outside of the target are larger with dose–volume optimization.

Conclusion: Mathematical formulation of energy minimization-based inverse optimization is derived. The optimization applied on the digital phantom shows that energy minimization-based approach tends to deliver somewhat higher maximum doses compared to standard of care, realized with dose–volume based optimization. At the same time, however, the energy minimization-based optimization reduces much more significantly the average and the integral doses.

Biological optimization in volumetric modulated arc radiotherapy for prostate carcinoma

PURPOSE

To investigate the potential benefits achievable with biological optimization for modulated volumetric arc (VMAT) treatments of prostate carcinoma.

METHODS AND MATERIALS

Fifteen prostate patient plans were studied retrospectively. For each case, planning target volume, rectum, and bladder were considered. Three optimization schemes were used: dose-volume histogram (DVH) based, generalized equivalent uniform dose (gEUD) based, and mixed DVH/gEUD based. For each scheme, a single or dual 6-MV, 356° VMAT arc was used. The plans were optimized with Pinnacle(3) (v. 9.0 beta) treatment planning system. For each patient, the optimized dose distributions were normalized to deliver the same prescription dose. The quality of the plans was evaluated by dose indices (DIs) and gEUDs for rectum and bladder. The tallied DIs were D(1%), D(15%), D(25%), and D(40%), and the tallied gEUDs were for a values of 1 and 6. Statistical tests were used to quantify the magnitude and the significance of the observed differences. Monitor units and treatment times for each optimization scheme were also assessed.

RESULTS

All optimization schemes generated clinically acceptable plans. The statistical tests indicated that biological optimization yielded increased organs-at-risk sparing, ranging from ~1% to more than ~27% depending on the tallied DI, gEUD, and anatomical structure. The increased sparing was at the expense of longer treatment times and increased number of monitor units.

CONCLUSIONS

Biological optimization can significantly increase the organs-at-risk sparing in VMAT optimization for prostate carcinoma. In some particular cases, however, the DVH-based optimization resulted in superior treatment plans.