Including Volume Effects in Biological Treatment Plan Optimization for Carbon Ion Therapy: Generalized Equivalent Uniform Dose-Based Objective in TRiP98

We describe a way to include biologically based objectives in plan optimization specific for carbon ion therapy, beyond the standard voxel-dose-based criteria already implemented in TRiP98, research planning software for ion beams. The aim is to account for volume effects—tissue architecture-dependent response to damage—in the optimization procedure, using the concept of generalized equivalent uniform dose (gEUD), which is an expression to convert a heterogeneous dose distribution (e.g., in an organ at risk (OAR)) into a uniform dose associated with the same biological effect. Moreover, gEUD is closely related to normal tissue complication probability (NTCP). The multi-field optimization problem here takes also into account the relative biological effectiveness (RBE), which in the case of ion beams is not factorizable and introduces strong non-linearity. We implemented the gEUD-based optimization in TRiP98, allowing us to control the whole dose–volume histogram (DVH) shape of OAR with a single objective by adjusting the prescribed gEUD₀ and the volume effect parameter a, reducing the volume receiving dose levels close to mean dose when a = 1 (large volume effect) while close to maximum dose for a >> 1 (small volume effect), depending on the organ type considered. We studied the role of gEUD₀ and a in the optimization, and we compared voxel-dose-based and gEUD-based optimization in chordoma cases with different anatomies. In particular, for a plan containing multiple OARs, we obtained the same target coverage and similar DVHs for OARs with a small volume effect while decreasing the mean dose received by the proximal parotid, thus reducing its NTCP by a factor of 2.5. Further investigations are done for this plan, considering also the distal parotid gland, obtaining a NTCP reduction by a factor of 1.9 for the proximal and 2.9 for the distal one. In conclusion, this novel optimization method can be applied to different OARs, but it achieves the largest improvement for organs whose volume effect is larger. This allows TRiP98 to perform a double level of biologically driven optimization for ion beams, including at the same time RBE-weighted dose and volume effects in inverse planning. An outlook is presented on the possible extension of this method to the target.

Potential Defects and Improvements of Equivalent Uniform Dose Prediction Model Based on the Analysis of Radiation-Induced Brain Injury

PURPOSE

To study the impact of dose distribution on volume-effect parameter and predictive ability of equivalent uniform dose (EUD) model, and to explore the improvements.

METHODS AND MATERIALS

The brains of 103 nasopharyngeal carcinoma patients treated with IMRT were segmented according to dose distribution (brain and left/right half-brain for similar distributions but different sizes; V _D with different D for different distributions). Predictive ability of EUD_{V D} (EUD of V _D ) for radiation-induced brain injury was assessed by receiver operating characteristics curve (ROC) and area under the curve (AUC). The optimal volume-effect parameter a of EUD was selected when AUC was maximal (mAUC). Correlations between mAUC, a and D were analyzed by Pearson correlation analysis. Both mAUC and a in brain and half-brain were compared by using paired samples t-tests. The optimal D _V and V _D points were selected for a simple comparison.

RESULTS

The mAUC of brain/half-brain EUD was 0.819/0.821 and the optimal a value was 21.5/22. When D increased, mAUC of EUD_{V D} increased, while a decreased. The mAUC reached the maximum value when D was 50-55 Gy, and a was always 1 when D ≥55 Gy. The difference of mAUC/a between brain and half-brain was not significant. If a was in range of 1 to 22, AUC of brain/half-brain EUD_{V55 Gy} (0.857-0.830/0.845-0.830) was always larger than that of brain/half-brain EUD (0.681-0.819/0.691-0.821). The AUCs of optimal dose/volume points were 0.801 (brain D_{2.5 cc}), 0.823 (brain V_{70 Gy}), 0.818 (half-brain D_{1 cc}), and 0.827 (half-brain V_{69 Gy}), respectively. Mean dose (equal to EUD_{V D} with a = 1) of high-dose volume (V_{50 Gy}-V_{60 Gy}) was superior to traditional EUD and dose/volume points.

CONCLUSION

Volume-effect parameter of EUD is variable and related to dose distribution. EUD with large low-dose volume may not be better than simple dose/volume points. Critical-dose-volume EUD could improve the predictive ability and has an invariant volume-effect parameter. Mean dose may be the case in which critical-dose-volume EUD has the best predictive ability.

Variance-based sensitivity analysis for uncertainties in proton therapy: A framework to assess the effect of simultaneous uncertainties in range, positioning, and RBE model predictions on RBE-weighted dose distributions

PURPOSE

Treatment plans in proton therapy are more sensitive to uncertainties than in conventional photon therapy. In addition to setup uncertainties, proton therapy is affected by uncertainties in proton range and relative biological effectiveness (RBE). While to date a constant RBE of 1.1 is commonly assumed, the actual RBE is known to increase toward the distal end of the spread-out Bragg peak. Several models for variable RBE predictions exist. We present a framework to evaluate the combined impact and interactions of setup, range, and RBE uncertainties in a comprehensive, variance-based sensitivity analysis (SA).

MATERIAL AND METHODS

The variance-based SA requires a large number (10⁴ -10⁵ ) of RBE-weighted dose (RWD) calculations. Based on a particle therapy extension of the research treatment planning system CERR we implemented a fast, graphics processing unit (GPU) accelerated pencil beam modeling of patient and range shifts. For RBE predictions, two biological models were included: The mechanistic repair-misrepair-fixation (RMF) model and the phenomenological Wedenberg model. All input parameters (patient position, proton range, RBE model parameters) are sampled simultaneously within their assumed probability distributions. Statistical formalisms rank the input parameters according to their influence on the overall uncertainty of RBE-weighted dose-volume histogram (RW-DVH) quantiles and the RWD in every voxel, resulting in relative, normalized sensitivity indices (S = 0: noninfluential input, S = 1: only influential input). Results are visualized as RW-DVHs with error bars and sensitivity maps.

RESULTS AND CONCLUSIONS

The approach is demonstrated for two representative brain tumor cases and a prostate case. The full SA including ∼ 3 × 10 4 RWD calculations took 39, 11, and 55 min, respectively. Range uncertainty was an important contribution to overall uncertainty at the distal end of the target, while the relatively smaller uncertainty inside the target was governed by biological uncertainties. Consequently, the uncertainty of the RW-DVH quantile D₉₈ for the target was governed by range uncertainty while the uncertainty of the mean target dose was dominated by the biological parameters. The SA framework is a powerful and flexible tool to evaluate uncertainty in RWD distributions and DVH quantiles, taking into account physical and RBE uncertainties and their interactions. The additional information might help to prioritize research efforts to reduce physical and RBE uncertainties and could also have implications for future approaches to biologically robust planning and optimization.

A comparison of mechanism-inspired models for particle relative biological effectiveness (RBE)

BACKGROUND AND SIGNIFICANCE

The application of heavy ion beams in cancer therapy must account for the increasing relative biological effectiveness (RBE) with increasing penetration depth when determining dose prescriptions and organ at risk (OAR) constraints in treatment planning. Because RBE depends in a complex manner on factors such as the ion type, energy, cell and tissue radiosensitivity, physical dose, biological endpoint, and position within and outside treatment fields, biophysical models reflecting these dependencies are required for the personalization and optimization of treatment plans.

AIM

To review and compare three mechanism-inspired models which predict the complexities of particle RBE for various ion types, energies, linear energy transfer (LET) values and tissue radiation sensitivities.

METHODS

The review of models and mechanisms focuses on the Local Effect Model (LEM), the Microdosimetric-Kinetic (MK) model, and the Repair-Misrepair-Fixation (RMF) model in combination with the Monte Carlo Damage Simulation (MCDS). These models relate the induction of potentially lethal double strand breaks (DSBs) to the subsequent interactions and biological processing of DSB into more lethal forms of damage. A key element to explain the increased biological effectiveness of high LET ions compared to MV x rays is the characterization of the number and local complexity (clustering) of the initial DSB produced within a cell. For high LET ions, the spatial density of DSB induction along an ion's trajectory is much greater than along the path of a low LET electron, such as the secondary electrons produced by the megavoltage (MV) x rays used in conventional radiation therapy. The main aspects of the three models are introduced and the conceptual similarities and differences are critiqued and highlighted. Model predictions are compared in terms of the RBE for DSB induction and for reproductive cell survival.

RESULTS AND CONCLUSIONS

Comparisons of the RBE for DSB induction and for cell survival are presented for proton (¹ H), helium (⁴ He), and carbon (¹² C) ions for the therapeutically most relevant range of ion beam energies. The reviewed models embody mechanisms of action acting over the spatial scales underlying the biological processing of potentially lethal DSB into more lethal forms of damage. Differences among the number and types of input parameters, relevant biological targets, and the computational approaches among the LEM, MK and RMF models are summarized and critiqued. Potential experiments to test some of the seemingly contradictory aspects of the models are discussed.

Rapid implementation of the repair-misrepair-fixation (RMF) model facilitating online adaption of radiosensitivity parameters in ion therapy

INTRODUCTION

Treatment planning for ion therapy must account for physical properties of the beam as well as differences in the relative biological effectiveness (RBE) of ions compared to photons. In this work, we present a fast RBE calculation approach, based on the decoupling of physical properties and the [Formula: see text] ratio commonly used to describe the radiosensitivity of irradiated cells or organs.

MATERIAL AND METHODS

In the framework of the mechanistic repair-misrepair-fixation (RMF) model, the biological modeling can be decoupled from the physical dose. This was implemented into a research treatment planning system for carbon ion therapy.

RESULTS

The presented implementation of the RMF model is very fast, allowing online changes of [Formula: see text]. For example, a change of [Formula: see text] including a complete biological modeling and a recalculation of RBE for [Formula: see text] voxel takes 4 ms on a 4 CPU, 3.2 GHz workstation.

DISCUSSION AND CONCLUSION

The derived decoupling within the RMF model allows fast changes in [Formula: see text], facilitating online adaption by the user. This provides new options for radiation oncologists, facilitating online variations of the radiobiological input parameters during the treatment plan evaluation process as well as uncertainty and sensitivity analyses.