Convex reformulation of biologically-based multi-criteria intensity-modulated radiation therapy optimization including fractionation effects

Prediction of radiation pneumonitis using the effective α/β of lungs and heart in NSCLC patients treated with proton beam therapy

PURPOSE

Radiation pneumonitis (RP) remains a major complication in non-small cell lung cancer (NSCLC) patients undergoing radiochemotherapy (RCHT). Traditionally, the mean lung dose (MLD) and the volume of the total lung receiving at least 20 Gy (V20Gy) are used to predict RP in patients treated with normo-fractionated photon therapy. However, other models, including the actual dose-distribution in the lungs using the effective α/β model or a combination of radiation doses to the lungs and heart, have been proposed for predicting RP. Moreover, the models established for photons may not hold for patients treated with passively-scattered proton therapy (PSPT). Therefore, we here tested and validated novel predictive parameters for RP in NSCLC patient treated with PSPT.

METHODS

Data on the occurrence of RP, structure files and dose-volume histogram parameters for lungs and heart of 96 NSCLC patients, treated with PSPT and concurrent chemotherapy, was retrospectively retrieved from prospective clinical studies of two international centers. Data was randomly split into a training set (64 patients) and a validation set (32 patients). Statistical analyses were performed using binomial logistic regression.

RESULTS

The biologically effective dose (BED) of the'lungs - GTV' significantly predicted RP ≥ grade 2 in the training-set using both a univariate model (p = 0.019, AUCtrain = 0.72) and a multivariate model in combination with the effective α/β parameter of the heart (pBED = 0.006, [Formula: see text] = 0.043, AUCtrain = 0.74). However, these results did not hold in the validation-set (AUCval = 0.52 andAUCval = 0.50, respectively). Moreover, these models were found to neither outperform a model built with the MLD (p = 0.015, AUCtrain = 0.73, AUCval = 0.51), nor a multivariate model additionally including the V20Gy of the heart (pMLD = 0.039, pV20Gy,heart = 0.58, AUCtrain = 0.74, AUCval = 0.53).

CONCLUSION

Using the effective α/β parameter of the lungs and heart we achieved similar performance to commonly used models built for photon therapy, such as MLD, in predicting RP ≥ grade 2. Therefore, prediction models developed for photon RCHT still hold for patients treated with PSPT.

Personalized mid-course FDG-PET based adaptive treatment planning for non-small cell lung cancer using machine learning and optimization

Objective. Traditional radiotherapy (RT) treatment planning of non-small cell lung cancer (NSCLC) relies on population-wide estimates of organ tolerance to minimize excess toxicity. The goal of this study is to develop a personalized treatment planning based on patient-specific lung radiosensitivity, by combining machine learning and optimization.Approach. Sixty-nine non-small cell lung cancer patients with baseline and mid-treatment [18]F-fluorodeoxyglucose (FDG)-PET images were retrospectively analyzed. A probabilistic Bayesian networks (BN) model was developed to predict the risk of radiation pneumonitis (RP) at three months post-RT using pre- and mid-treatment FDG information. A patient-specific dose modifying factor (DMF), as a surrogate for lung radiosensitivity, was estimated to personalize the normal tissue toxicity probability (NTCP) model. This personalized NTCP was then integrated into a NTCP-based optimization model for RT adaptation, ensuring tumor coverage and respecting patient-specific lung radiosensitivity. The methodology was employed to adapt the treatment planning of fifteen NSCLC patients.Main results. The magnitude of the BN predicted risks corresponded with the RP severity. Average predicted risk for grade 1-4 RP were 0.18, 0.42, 0.63, and 0.76, respectively (p< 0.001). The proposed model yielded an average area under the receiver-operating characteristic curve (AUROC) of 0.84, outperforming the AUROCs of LKB-NTCP (0.77), and pre-treatment BN (0.79). Average DMF for the radio-tolerant (RP grade = 1) and radiosensitive (RP grade ≥ 2) groups were 0.8 and 1.63,p< 0.01. RT personalization resulted in five dose escalation strategies (average mean tumor dose increase = 6.47 Gy, range = [2.67-17.5]), and ten dose de-escalation (average mean lung dose reduction = 2.98 Gy [0.8-5.4]), corresponding to average NTCP reduction of 15% [4-27].Significance. Personalized FDG-PET-based mid-treatment adaptation of NSCLC RT could significantly lower the RP risk without compromising tumor control. The proposed methodology could help the design of personalized clinical trials for NSCLC patients.

Conic formulation of fluence map optimization problems

The convexity of objectives and constraints in fluence map optimization (FMO) for radiation therapy has been extensively studied. Next to convexity, there is another important characteristic of optimization functions and problems, which has thus far not been considered in FMO literature: conic representation. Optimization problems that are conically representable using quadratic, exponential and power cones are solvable with advanced primal-dual interior-point algorithms. These algorithms guarantee an optimal solution in polynomial time and have good performance in practice. In this paper, we construct conic representations for most FMO objectives and constraints. This paper is the first that shows that FMO problems containing multiple biological evaluation criteria can be solved in polynomial time. For fractionation-corrected functions for which no exact conic reformulation is found, we provide an accurate approximation that is conically representable. We present numerical results on the TROTS data set, which demonstrate very stable numerical performance for solving FMO problems in conic form. With ongoing research in the optimization community, improvements in speed can be expected, which makes conic optimization a promising alternative for solving FMO problems.

Robust dose-painting-by-numbers vs. nonselective dose escalation for non-small cell lung cancer patients

Purpose

Theoretical studies have shown that dose‐painting‐by‐numbers (DPBN) could lead to large gains in tumor control probability (TCP) compared to conventional dose distributions. However, these gains may vary considerably among patients due to (a) variations in the overall radiosensitivity of the tumor, (b) variations in the 3D distribution of intra‐tumor radiosensitivity within the tumor in combination with patient anatomy, (c) uncertainties of the 3D radiosensitivity maps, (d) geometrical uncertainties, and (e) temporal changes in radiosensitivity. The goal of this study was to investigate how much of the theoretical gains of DPBN remain when accounting for these factors. DPBN was compared to both a homogeneous reference dose distribution and to nonselective dose escalation (NSDE), that uses the same dose constraints as DPBN, but does not require 3D radiosensitivity maps.

Methods

A fully automated DPBN treatment planning strategy was developed and implemented in our in‐house developed treatment planning system (TPS) that is robust to uncertainties in radiosensitivity and patient positioning. The method optimized the expected TCP based on 3D maps of intra‐tumor radiosensitivity, while accounting for normal tissue constraints, uncertainties in radiosensitivity, and setup uncertainties. Based on FDG‐PETCT scans of 12 non‐small cell lung cancer (NSCLC) patients, data of 324 virtual patients were created synthetically with large variations in the aforementioned parameters. DPBN was compared to both a uniform dose distribution of 60 Gy, and NSDE. In total, 360 DPBN and 24 NSDE treatment plans were optimized.

Results

The average gain in TCP over all patients and radiosensitivity maps of DPBN was 0.54 ± 0.20 (range 0–0.97) compared to the 60 Gy uniform reference dose distribution, but only 0.03 ± 0.03 (range 0–0.22) compared to NSDE. The gains varied per patient depending on the radiosensitivity of the entire tumor and the 3D radiosensitivity maps. Uncertainty in radiosensitivity led to a considerable loss in TCP gain, which could be recovered almost completely by accounting for the uncertainty directly in the optimization.

Conclusions

Our results suggest that the gains of DPBN can be considerable compared to a 60 Gy uniform reference dose distribution, but small compared to NSDE for most patients. Using the robust DPBN treatment planning system developed in this work, the optimal DPBN treatment plan could be derived for any patient for whom 3D intra‐tumor radiosensitivity maps are known, and can be used to select patients that might benefit from DPBN. NSDE could be an effective strategy to increase TCP without requiring biological information of the tumor.

Optimal treatment plan adaptation using mid-treatment imaging biomarkers

Previous studies on personalized radiotherapy (RT) have mostly focused on baseline patient stratification, adapting the treatment plan according to mid-treatment anatomical changes, or dose boosting to selected tumor subregions using mid-treatment radiological findings. However, the question of how to find the optimal adapted plan has not been properly tackled. Moreover, the effect of information uncertainty on the resulting adaptation has not been explored. In this paper, we present a framework to optimally adapt radiation therapy treatments to early radiation treatment response estimates derived from pre- and mid-treatment imaging data while considering the information uncertainty. The framework is based on the optimal stopping in radiation therapy (OSRT) framework. Biological response is quantified using tumor control probability (TCP) and normal tissue complication probability (NTCP) models, and these are directly optimized for in the adaptation step. Two adaptation strategies are discussed: (1) uniform dose adaptation and (2) continuous dose adaptation. In the first strategy, the original fluence-map is simply scaled upwards or downwards, depending on whether dose escalation or de-escalation is deemed appropriate based on the mid-treatment response observed from the radiological images. In the second strategy, a full NTCP-TCP-based fluence map re-optimization is performed to achieve the optimal adapted plans. We retrospectively tested the performance of these strategies on 14 canine head and neck cases treated with tomotherapy, using as response biomarker the change in the 3'-deoxy-3'[(18)F]-fluorothymidine (FLT)-PET signals between the pre- and mid-treatment images, and accounting for information uncertainty. Using a 10% uncertainty level, the two adaptation strategies both yield a noteworthy average improvement in guaranteed (worst-case) TCP.

Split Common Coincidence Point Problem: A Formulation Applicable to (Bio)Physically-Based Inverse Planning Optimization

Inverse planning is a method of radiotherapy treatment planning where the care team begins with the desired dose distribution satisfying prescribed clinical objectives, and then determines the treatment parameters that will achieve it. The variety in symmetry, form, and characteristics of the objective functions describing clinical criteria requires a flexible optimization approach in order to obtain optimized treatment plans. Therefore, we introduce and discuss a nonlinear optimization formulation called the split common coincidence point problem (SCCPP). We show that the SCCPP is a suitable formulation for the inverse planning optimization problem with the flexibility of accommodating several biological and/or physical clinical objectives. Also, we propose an iterative algorithm for approximating the solution of the SCCPP, and using Bregman techniques, we establish that the proposed algorithm converges to a solution of the SCCPP and to an extremum of the inverse planning optimization problem. We end with a note on useful insights on implementing the algorithm in a clinical setting.

Prescription Value-Based Automatic Optimization of Importance Factors in Inverse Planning

Objective:

An automatic method for the optimization of importance factors was proposed to improve the efficiency of inverse planning.

Methods:

The automatic method consists of 3 steps: (1) First, the importance factors are automatically and iteratively adjusted based on our proposed penalty strategies. (2) Then, plan evaluation is performed to determine whether the obtained plan is acceptable. (3) If not, a higher penalty is assigned to the unsatisfied objective by multiplying it by a compensation coefficient. The optimization processes are performed alternately until an acceptable plan is obtained or the maximum iteration N_max of step (3) is reached.

Results:

Tested on 2 kinds of clinical cases and compared with manual method, the results showed that the quality of the proposed automatic plan was comparable to, or even better than, the manual plan in terms of the dose–volume histogram and dose distributions.

Conclusions:

The proposed algorithm has potential to significantly improve the efficiency of the existing manual adjustment methods for importance factors and contributes to the development of fully automated planning. Especially, the more the subobjective functions, the more obvious the advantage of our algorithm.

Derivation of mean dose tolerances for new fractionation schemes and treatment modalities

Avoiding toxicities in radiotherapy requires the knowledge of tolerable organ doses. For new, experimental fractionation schemes (e.g. hypofractionation) these are typically derived from traditional schedules using the biologically effective dose (BED) model. In this report we investigate the difficulties of establishing mean dose tolerances that arise since the mean BED depends on the entire spatial dose distribution, rather than on the dose level alone. A formula has been derived to establish mean physical dose constraints such that they are mean BED equivalent to a reference treatment scheme. This formula constitutes a modified BED equation where the influence of the spatial dose distribution is summarized in a single parameter, the dose shape factor. To quantify effects we analyzed 24 liver cancer patients for whom both proton and photon IMRT treatment plans were available. The results show that the standard BED equation-neglecting the spatial dose distribution-can overestimate mean dose tolerances for hypofractionated treatments by up to 20%. The shape difference between photon and proton dose distributions can cause 30-40% differences in mean physical dose for plans having identical mean BEDs. Converting hypofractionated, 5/15-fraction proton doses to mean BED equivalent photon doses in traditional 35-fraction regimens resulted in up to 10 Gy higher doses than applying the standard BED formula. The dose shape effect should be accounted for to avoid overestimation of mean dose tolerances, particularly when estimating constraints for hypofractionated regimens. Additionally, tolerances established for one treatment modality cannot necessarily be applied to other modalities with drastically different dose distributions, such as proton therapy. Last, protons may only allow marginal (5-10%) dose escalation if a fraction-size adjusted organ mean dose is constraining instead of a physical dose.

Radiobiological Optimization in Lung Stereotactic Body Radiation Therapy: Are We Ready to Apply Radiobiological Models?

Lung tumors are often associated with a poor prognosis although different schedules and treatment modalities have been extensively tested in the clinical practice. The complexity of this disease and the use of combined therapeutic approaches have been investigated and the use of high dose-rates is emerging as effective strategy. Technological improvements of clinical linear accelerators allow combining high dose-rate and a more conformal dose delivery with accurate imaging modalities pre- and during therapy. This paper aims at reporting the state of the art and future direction in the use of radiobiological models and radiobiological-based optimizations in the clinical practice for the treatment of lung cancer. To address this issue, a search was carried out on PubMed database to identify potential papers reporting tumor control probability and normal tissue complication probability for lung tumors. Full articles were retrieved when the abstract was considered relevant, and only papers published in English language were considered. The bibliographies of retrieved papers were also searched and relevant articles included. At the state of the art, dose–response relationships have been reported in literature for local tumor control and survival in stage III non-small cell lung cancer. Due to the lack of published radiobiological models for SBRT, several authors used dose constraints and models derived for conventional fractionation schemes. Recently, several radiobiological models and parameters for SBRT have been published and could be used in prospective trials although external validations are recommended to improve the robustness of model predictive capability. Moreover, radiobiological-based functions have been used within treatment planning systems for plan optimization but the advantages of using this strategy in the clinical practice are still under discussion. Future research should be directed toward combined regimens, in order to potentially improve both local tumor control and survival. Indeed, accurate knowledge of the relevant parameters describing tumor biology and normal tissue response is mandatory to correctly address this issue. In this context, the role of medical physicists and the AAPM in the development of radiobiological models is crucial for the progress of developing specific tool for radiobiological-based optimization treatment planning.

Frontiers in planning optimization for lung SBRT

Emerging data are showing the safety and the efficacy of Stereotactic Body Radiation therapy (SBRT) in lung cancer management. In this context, the very high doses delivered to the Planning Target Volume, make the planning phase essential for achieving high dose levels conformed to the shape of the target in order to have a good prognosis for tumor control and to avoid an overdose in relevant healthy adjacent tissue. In this non-systematic review we analyzed the technological and the physics aspects of SBRT planning for lung cancer. In particular, the aims of the study were: (i) to evaluate prescription strategies (homogeneous or inhomogeneous), (ii) to outline possible geometrical solutions by comparing the dosimetric results (iii) to describe the technological possibilities for a safe and effective treatment, (iv) to present the issues concerning radiobiological planning and the automation of the planning process.

A feasibility study of dynamic adaptive radiotherapy for nonsmall cell lung cancer

PURPOSE

The final state of the tumor at the end of a radiotherapy course is dependent on the doses given in each fraction during the treatment course. This study investigates the feasibility of using dynamic adaptive radiotherapy (DART) in treating lung cancers assuming CBCT is available to observe midtreatment tumor states. DART adapts treatment plans using a dynamic programming technique to consider the expected changes of the tumor in the optimization process.

METHODS

DART is constructed using a stochastic control formalism framework. It minimizes the total expected number of tumor cells at the end of a treatment course, which is equivalent to maximizing tumor control probability, subject to the uncertainty inherent in the tumor response. This formulation allows for nonstationary dose distributions as well as nonstationary fractional doses as needed to achieve a series of optimal plans that are conformal to the tumor over time, i.e., spatiotemporally optimal plans. Sixteen phantom cases with various sizes and locations of tumors and organs-at-risk (OAR) were generated using in-house software. Each case was planned with DART and conventional IMRT prescribing 60 Gy in 30 fractions. The observations of the change in the tumor volume over a treatment course were simulated using a two-level cell population model. Monte Carlo simulations of the treatment course for each case were run to account for uncertainty in the tumor response. The same OAR dose constraints were applied for both methods. The frequency of replanning was varied between 1, 2, 5 (weekly), and 29 times (daily). The final average tumor dose and OAR doses have been compared to quantify the potential dosimetric benefits of DART.

RESULTS

The average tumor max, min, mean, and D95 doses using DART relative to these using conventional IMRT were 124.0%-125.2%, 102.1%-114.7%, 113.7%-123.4%, and 102.0%-115.9% (range dependent on the frequency of replanning). The average relative maximum doses for the cord and esophagus, mean doses for the heart and lungs, and D05 for the unspecified tissue resulting 84%-102.4%, 99.8%-106.9%, 66.9%-85.6%, 58.2%-78.8%, and 85.2%-94.0%, respectively.

CONCLUSIONS

It is feasible to apply DART to the treatment of NSCLC using CBCT to observe the midtreatment tumor state. Potential increases in the tumor dose and reductions in the OAR dose, particularly for parallel OARs with mean or dose-volume constraints, could be achieved using DART compared to nonadaptive IMRT.

A radiobiology-based inverse treatment planning method for optimisation of permanent l-125 prostate implants in focal brachytherapy

Treatment plans for ten patients, initially treated with a conventional approach to low dose-rate brachytherapy (LDR, 145 Gy to entire prostate), were compared with plans for the same patients created with an inverse-optimisation planning process utilising a biologically-based objective. The 'biological optimisation' considered a non-uniform distribution of tumour cell density through the prostate based on known and expected locations of the tumour. Using dose planning-objectives derived from our previous biological-model validation study, the volume of the urethra receiving 125% of the conventional prescription (145 Gy) was reduced from a median value of 64% to less than 8% whilst maintaining high values of TCP. On average, the number of planned seeds was reduced from 85 to less than 75. The robustness of plans to random seed displacements needs to be carefully considered when using contemporary seed placement techniques. We conclude that an inverse planning approach to LDR treatments, based on a biological objective, has the potential to maintain high rates of tumour control whilst minimising dose to healthy tissue. In future, the radiobiological model will be informed using multi-parametric MRI to provide a personalised medicine approach.

Prostate Dose-painting Radiotherapy and Radiobiological Guided Optimisation Enhances the Therapeutic Ratio

AIMS

To describe the treatment of 11 patients with radiobiologically guided dose-painting radiotherapy and report on toxicity.

MATERIALS AND METHODS

Boost volumes were identified with functional magnetic resonance imaging scans in 11 patients with high-risk prostate cancer. Patients were treated using a dose-painting approach; the boost dose was limited to 86 Gy in 37 fractions, while keeping the rectal normal tissue complication probability to 5-6%. Rotational intensity-modulated radiotherapy was used with daily image guidance and fiducial markers.

RESULTS

The median dose to the prostate (outside the boost volume) and urethra was 75.4 Gy/37 fractions (range 75.1-75.8 Gy), whereas the median boost dose was 83.4 Gy (range 79.0-87.4 Gy). The tumour control probability (TCP) (Marsden model) increased from 71% for the standard plans to 83.6% [76.6-86.8%] for the dose-painting boost plans. The mean (Lyman-Kutcher-Burman) normal tissue complication probability for rectal bleeding was 5.2% (range 3.3-6.2%) and 5.2% for faecal incontinence (range 3.6-7.8%). All patients tolerated the treatment well, with a low acute toxicity profile. At a median follow-up of 36 months (range 24-50) there was no grade 3 late toxicity. Two patients had grade 2 late urinary toxicity (urethral stricture, urinary frequency and urgency), one patient had grade 1 and one grade 2 late rectal toxicity. The mean prostate-specific antigen at follow-up was 0.81 ng/ml after stopping hormone therapy; one patient relapsed biochemically at 32 months (2.70 ng/ml).

CONCLUSIONS

The toxicity for this radiobiological guided dose-painting protocol was low, but we have only treated a small cohort with limited follow-up time. The advantages of this treatment approach should be established in a clinical trial.

A DVH-guided IMRT optimization algorithm for automatic treatment planning and adaptive radiotherapy replanning

PURPOSE

To develop a novel algorithm that incorporates prior treatment knowledge into intensity modulated radiation therapy optimization to facilitate automatic treatment planning and adaptive radiotherapy (ART) replanning.

METHODS

The algorithm automatically creates a treatment plan guided by the DVH curves of a reference plan that contains information on the clinician-approved dose-volume trade-offs among different targets/organs and among different portions of a DVH curve for an organ. In ART, the reference plan is the initial plan for the same patient, while for automatic treatment planning the reference plan is selected from a library of clinically approved and delivered plans of previously treated patients with similar medical conditions and geometry. The proposed algorithm employs a voxel-based optimization model and navigates the large voxel-based Pareto surface. The voxel weights are iteratively adjusted to approach a plan that is similar to the reference plan in terms of the DVHs. If the reference plan is feasible but not Pareto optimal, the algorithm generates a Pareto optimal plan with the DVHs better than the reference ones. If the reference plan is too restricting for the new geometry, the algorithm generates a Pareto plan with DVHs close to the reference ones. In both cases, the new plans have similar DVH trade-offs as the reference plans.

RESULTS

The algorithm was tested using three patient cases and found to be able to automatically adjust the voxel-weighting factors in order to generate a Pareto plan with similar DVH trade-offs as the reference plan. The algorithm has also been implemented on a GPU for high efficiency.

CONCLUSIONS

A novel prior-knowledge-based optimization algorithm has been developed that automatically adjust the voxel weights and generate a clinical optimal plan at high efficiency. It is found that the new algorithm can significantly improve the plan quality and planning efficiency in ART replanning and automatic treatment planning.

A multicriteria framework with voxel-dependent parameters for radiotherapy treatment plan optimization

PURPOSE

To establish a new mathematical framework for radiotherapy treatment optimization with voxel-dependent optimization parameters.

METHODS

In the treatment plan optimization problem for radiotherapy, a clinically acceptable plan is usually generated by an optimization process with weighting factors or reference doses adjusted for a set of the objective functions associated to the organs. Recent discoveries indicate that adjusting parameters associated with each voxel may lead to better plan quality. However, it is still unclear regarding the mathematical reasons behind it. Furthermore, questions about the objective function selection and parameter adjustment to assure Pareto optimality as well as the relationship between the optimal solutions obtained from the organ-based and voxel-based models remain unanswered. To answer these questions, the authors establish in this work a new mathematical framework equipped with two theorems.

RESULTS

The new framework clarifies the different consequences of adjusting organ-dependent and voxel-dependent parameters for the treatment plan optimization of radiation therapy, as well as the impact of using different objective functions on plan qualities and Pareto surfaces. The main discoveries are threefold: (1) While in the organ-based model the selection of the objective function has an impact on the quality of the optimized plans, this is no longer an issue for the voxel-based model since the Pareto surface is independent of the objective function selection and the entire Pareto surface could be generated as long as the objective function satisfies certain mathematical conditions; (2) All Pareto solutions generated by the organ-based model with different objective functions are parts of a unique Pareto surface generated by the voxel-based model with any appropriate objective function; (3) A much larger Pareto surface is explored by adjusting voxel-dependent parameters than by adjusting organ-dependent parameters, possibly allowing for the generation of plans with better trade-offs among different clinical objectives.

CONCLUSIONS

The authors have developed a mathematical framework for radiotherapy treatment optimization using voxel-based parameters. The authors can improve the plan quality by adjusting voxel-based weighting factors and exploring the unique and large Pareto surface which include all the Pareto surfaces that can be generated by organ-based model using different objective functions.

Direct use of multivariable normal tissue complication probability models in treatment plan optimisation for individualised head and neck cancer radiotherapy produces clinically acceptable treatment plans

BACKGROUND AND PURPOSE

Recently, clinically validated multivariable normal tissue complication probability models (NTCP) for head and neck cancer (HNC) patients have become available. We test the feasibility of using multivariable NTCP-models directly in the optimiser for inverse treatment planning of radiotherapy to improve the dose distributions and corresponding NTCP-estimates in HNC patients.

MATERIAL AND METHODS

For 10 HNC cases, intensity-modulated radiotherapy plans were optimised either using objective functions based on the 'generalised equivalent uniform dose' (OFgEUD) or based on multivariable NTCP-models (OFNTCP). NTCP-models for patient-rated xerostomia, physician-rated RTOG grade II-IV dysphagia, and various patient-rated aspects of swallowing dysfunction were incorporated. The NTCP-models included dose-volume parameters as well as clinical factors contributing to a personalised optimisation process. Both optimisation techniques were compared by means of 'pseudo Pareto fronts' (target dose conformity vs. the sum of the NTCPs).

RESULTS

Both optimisation techniques resulted in clinically realistic treatment plans with only small differences. For nine patients the sum-NTCP was lower for the OFNTCP optimised plans (on average 5.7% (95%CI 1.7-9.9%, p<0.006)). Furthermore, the OFNTCP provided the advantages of fewer unknown optimisation parameters and an intrinsic mechanism of individualisation.

CONCLUSIONS

Treatment plan optimisation using multivariable NTCP-models directly in the OF is feasible as has been demonstrated for HNC radiotherapy.

(Radio)biological optimization of external-beam radiotherapy

“Biological optimization” (BIOP) means planning treatments using (radio)biological criteria and models, that is, tumour control probability and normal-tissue complication probability. Four different levels of BIOP are identified: Level I is “isotoxic” individualization of prescription dose D_presc at fixed fraction number. D_presc is varied to keep the NTCP of the organ at risk constant. Significant improvements in local control are expected for non-small-cell lung tumours. Level II involves the determination of an individualized isotoxic combination of D_presc and fractionation scheme. This approach is appropriate for “parallel” OARs (lung, parotids). Examples are given using our BioSuite software. Hypofractionated SABR for early-stage NSCLC is effectively Level-II BIOP. Level-III BIOP uses radiobiological functions as part of the inverse planning of IMRT, for example, maximizing TCP whilst not exceeding a given NTCP. This results in non-uniform target doses. The NTCP model parameters (reflecting tissue “architecture”) drive the optimizer to emphasize different regions of the DVH, for example, penalising high doses for quasi-serial OARs such as rectum. Level-IV BIOP adds functional imaging information, for example, hypoxia or clonogen location, to Level III; examples are given of our prostate “dose painting” protocol, BioProp. The limitations of and uncertainties inherent in the radiobiological models are emphasized.

Radiobiological model-based bio-anatomical quality assurance in intensity-modulated radiation therapy for prostate cancer

A bio-anatomical quality assurance (QA) method employing tumor control probability (TCP) and normal tissue complication probability (NTCP) is described that can integrate radiobiological effects into intensity-modulated radiation therapy (IMRT). We evaluated the variations in the radiobiological effects caused by random errors (r-errors) and systematic errors (s-errors) by evaluating TCP and NTCP in two groups: patients with an intact prostate (G(intact)) and those who have undergone prostatectomy (G(tectomy)). The r-errors were generated using an isocenter shift of ±1 mm to simulate a misaligned patient set-up. The s-errors were generated using individual leaves that were displaced inwardly and outwardly by 1 mm on multileaf collimator field files. Subvolume-based TCP and NTCP were visualized on computed tomography (CT) images to determine the radiobiological effects on the principal structures. The bio-anatomical QA using the TCP and NTCP maps differentiated the critical radiobiological effects on specific volumes, particularly at the anterior rectal walls and planning target volumes. The s-errors showed a TCP variation of -40-25% in G(tectomy) and -30-10% in G(intact), while the r-errors were less than 1.5% in both groups. The r-errors for the rectum and bladder showed higher NTCP variations at ±20% and ±10%, respectively, and the s-errors were greater than ±65% for both. This bio-anatomical method, as a patient-specific IMRT QA, can provide distinct indications of clinically significant radiobiological effects beyond the minimization of probable physical dose errors in phantoms.

A practical approach to assess clinical planning tradeoffs in the design of individualized IMRT treatment plans

BACKGROUND AND PURPOSE

To investigate the tradeoffs between organ at risk sparing and tumour coverage for IMRT treatment of lung tumours, and to develop a tool for clinical use to graphically represent these tradeoffs.

MATERIAL AND METHODS

For 5 patients with inoperable non-small cell lung cancer (NSCLC) different IMRT plans were generated using a standard TPS. The plans were automatically generated for a range of IMRT settings (weights and dose levels of the objective functions) and were systematically evaluated, focusing on the tradeoffs between organ at risk (OAR) dose and target coverage. A method to analyze and visualize planning tradeoffs was developed and evaluated.

RESULTS

Lung and oesophagus were identified as the critical organs at risk for NSCLC, the sparing of which strongly influences PTV coverage. Systematically analyzing the tradeoffs between these organs revealed that the sparing of these organs was approximately linearly related to PTV coverage parameters. Using this property, a tool was developed to graphically present the tradeoffs between the sparing of these organs at risk and the PTV coverage. The tool is an effective method to visualize the tradeoffs.

CONCLUSIONS

A tool was developed to assist IMRT plan design and selection. The clear presentation of the tradeoffs between OAR dose and coverage facilitates the optimization process and offers additional information to the clinician for a patient specific choice of the optimal IMRT plan.

An approach to multiobjective optimization of rotational therapy. II. Pareto optimal surfaces and linear combinations of modulated blocked arcs for a prostate geometry

PURPOSE

The purpose of this work is twofold: To further develop an approach to multiobjective optimization of rotational therapy treatments recently introduced by the authors [J. Pardo-Montero and J. D. Fenwick, "An approach to multiobjective optimization of rotational therapy," Med. Phys. 36, 3292-3303 (2009)], especially regarding its application to realistic geometries, and to study the quality (Pareto optimality) of plans obtained using such an approach by comparing them with Pareto optimal plans obtained through inverse planning.

METHODS

In the previous work of the authors, a methodology is proposed for constructing a large number of plans, with different compromises between the objectives involved, from a small number of geometrically based arcs, each arc prioritizing different objectives. Here, this method has been further developed and studied. Two different techniques for constructing these arcs are investigated, one based on image-reconstruction algorithms and the other based on more common gradient-descent algorithms. The difficulty of dealing with organs abutting the target, briefly reported in previous work of the authors, has been investigated using partial OAR unblocking. Optimality of the solutions has been investigated by comparison with a Pareto front obtained from inverse planning. A relative Euclidean distance has been used to measure the distance of these plans to the Pareto front, and dose volume histogram comparisons have been used to gauge the clinical impact of these distances. A prostate geometry has been used for the study.

RESULTS

For geometries where a blocked OAR abuts the target, moderate OAR unblocking can substantially improve target dose distribution and minimize hot spots while not overly compromising dose sparing of the organ. Image-reconstruction type and gradient-descent blocked-arc computations generate similar results. The Pareto front for the prostate geometry, reconstructed using a large number of inverse plans, presents a hockey-stick shape comprising two regions: One where the dose to the target is close to prescription and trade-offs can be made between doses to the organs at risk and (small) changes in target dose, and one where very substantial rectal sparing is achieved at the cost of large target underdosage. Plans computed following the approach using a conformal arc and four blocked arcs generally lie close to the Pareto front, although distances of some plans from high gradient regions of the Pareto front can be greater. Only around 12% of plans lie a relative Euclidean distance of 0.15 or greater from the Pareto front. Using the alternative distance measure of Craft ["Calculating and controlling the error of discrete representations of Pareto surfaces in convex multi-criteria optimization," Phys. Medica (to be published)], around 2/5 of plans lie more than 0.05 from the front. Computation of blocked arcs is quite fast, the algorithms requiring 35%-80% of the running time per iteration needed for conventional inverse plan computation.

CONCLUSIONS

The geometry-based arc approach to multicriteria optimization of rotational therapy allows solutions to be obtained that lie close to the Pareto front. Both the image-reconstruction type and gradient-descent algorithms produce similar modulated arcs, the latter one perhaps being preferred because it is more easily implementable in standard treatment planning systems. Moderate unblocking provides a good way of dealing with OARs which abut the PTV. Optimization of geometry-based arcs is faster than usual inverse optimization of treatment plans, making this approach more rapid than an inverse-based Pareto front reconstruction.

The equivalence of multi-criteria methods for radiotherapy plan optimization

Several methods can be used to achieve multi-criteria optimization of radiation therapy treatment planning, which strive for Pareto-optimality. The property of the solution being Pareto optimal is desired, because it guarantees that no criteria can be improved without deteriorating another criteria. The most widely used methods are the weighted-sum method, in which the different treatment objectives are weighted, and constrained optimization methods, in which treatment goals are set and the algorithm has to find the best plan fulfilling these goals. The constrained method used in this paper, the 2p element of c (2-phase element-constraint) method is based on the element-constraint method, which generates Pareto-optimal solutions. Both approaches are uniquely related to each other. In this paper, we will show that it is possible to switch from the constrained method to the weighted-sum method by using the Lagrange multipliers from the constrained optimization problem, and vice versa by setting the appropriate constraints. In general, the theory presented in this paper can be useful in cases where a new situation is slightly different from the original situation, e.g. in online treatment planning, with deformations of the volumes of interest, or in automated treatment planning, where changes to the automated plan have to be made. An example of the latter is given where the planner is not satisfied with the result from the constrained method and wishes to decrease the dose in a structure. By using the Lagrange multipliers, a weighted-sum optimization problem is constructed, which generates a Pareto-optimal solution in the neighbourhood of the original plan, but fulfills the new treatment objectives.

Comparing planning time, delivery time and plan quality for IMRT, RapidArc and Tomotherapy

The purpose of this study is to examine plan quality, treatment planning time, and estimated treatment delivery time for 5- and 9-field sliding window IMRT, single and dual arc RapidArc, and tomotherapy. For four phantoms, 5- and 9-field IMRT, single and dual arc RapidArc and tomotherapy plans were created. Plans were evaluated based on the ability to meet dose-volume constraints, dose homogeneity index, radiation conformity index, planning time, estimated delivery time, integral dose, and volume receiving more than 2 and 5 Gy. For all of the phantoms, tomotherapy was able to meet the most optimization criteria during planning (50% for P1, 67% for P2, 0% for P3, and 50% for P4). RapidArc met less of the optimization criteria (25% for P1, 17% for P2, 0% for P3, and 0% for P4), while IMRT was never able to meet any of the constraints. In addition, tomotherapy plans were able to produce the most homogeneous dose. Tomotherapy plans had longer planning time, longer estimated treatment times, lower conformity index, and higher integral dose. Tomotherapy plans can produce plans of higher quality and have the capability to conform dose distributions better than IMRT or RapidArc in the axial plane, but exhibit increased dose superior and inferior to the target volume. RapidArc, however, is capable of producing better plans than IMRT for the test cases examined in this study.