Optimization of intensity-modulated radiation therapy with biological objectives

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.

Modeling Radiotherapy Induced Normal Tissue Complications: An Overview beyond Phenomenological Models

An overview of radiotherapy (RT) induced normal tissue complication probability (NTCP) models is presented. NTCP models based on empirical and mechanistic approaches that describe a specific radiation induced late effect proposed over time for conventional RT are reviewed with particular emphasis on their basic assumptions and related mathematical translation and their weak and strong points.

Modulated photon radiotherapy (XMRT): an algorithm for the simultaneous optimization of photon beamlet energy and intensity in external beam radiotherapy (EBRT) planning

This is a proof of principle study on an algorithm for optimizing external beam radiotherapy in terms of both photon beamlet energy and fluence. This simultaneous beamlet energy and fluence optimization is denoted modulated photon radiotherapy (XMRT). XMRT is compared with single-energy intensity modulated radiotherapy (IMRT) for five clinically relevant test geometries to determine whether treating beamlet energy as a decision variable improves the dose distributions. All test geometries were modelled in a cylindrical water phantom. XMRT optimized the fluence for 6 and 18 MV beamlets while IMRT optimized with only 6 MV and only 18 MV. CERR (computational environment for radiotherapy research) was used to calculate the dose deposition matrices and the resulting dose for XMRT and IMRT solutions. Solutions were compared via their dose volume histograms and dose metrics, such as the mean, maximum, and minimum doses for each structure. The homogeneity index (HI) and conformity number (CN) were calculated to assess the quality of the target dose coverage. Complexity of the resulting fluence maps was minimized using the sum of positive gradients technique. The results showed XMRT's ability to improve healthy-organ dose reduction while yielding comparable coverage of the target relative to IMRT for all geometries. All three energy-optimization approaches yielded similar HI and CNs for all geometries, as well as a similar degree of fluence map complexity. The dose reduction provided by XMRT was demonstrated by the relative decrease in the dose metrics for the majority of the organs at risk (OARs) in all geometries. Largest reductions ranged between 5% to 10% in the mean dose to OARs for two of the geometries when compared with both single-energy IMRT schemes. XMRT has shown potential dosimetric benefits through improved OAR sparing by allowing beam energy to act as a degree of freedom in the EBRT optimization process.

SORS: a new software for the simulation of radiotherapy schedule

We present a software for choosing the best radiotherapy treatment schedule for head and neck cancers as a beginning radiotherapy plan or a temporarily interrupted plan. Its application occurs according to two modalities: the first adopts the best estimates for model parameters; the second takes into account the parameters' uncertainty too. In both cases, the choice becomes the schedule with the highest uncomplicated tumor control probability (UTCP). In the UTCP valuation, the normal tissue complication probability (NTCP) of each organ is related to the gravity of its possible late injury. For NTCP calculation, it has been adopted the empirical LKB (Lyman-Kutcher-Burman) model corrected for dose/fraction via linear-quadratic model and the incomplete repair effect. The tumor control probability (TCP) model is Poisson based and contains corrections for dose/fraction and regrowth effect; optionally, it can be accounted for the incomplete repair effect as well. At the end of processing, a detailed file with all informations about UTCP, TCP and single organ NTCP is furnished for every examined schedule. Moreover, a useful 3-D graphic representation of the schedule's UTCP is available, allowing the physician to easily understand the schedules with the highest radiotherapeutic efficacy. The open source characteristic allows the program to adapt to the individual clinical case as well as to be a valid support in radiobiological research.

Planning and delivery of intensity-modulated radiation therapy

Intensity modulated radiation therapy (IMRT) is an advanced form of external beam radiation therapy. IMRT offers an additional dimension of freedom as compared with field shaping in three-dimensional conformal radiation therapy because the radiation intensities within a radiation field can be varied according to the preferences of locations within a given beam direction from which the radiation is directed to the tumor. This added freedom allows the treatment planning system to better shape the radiation doses to conform to the target volume while sparing surrounding normal structures. The resulting dosimetric advantage has shown to translate into clinical advantages of improving local and regional tumor control. It also offers a valuable mechanism for dose escalation to tumors while simultaneously reducing radiation toxicities to the surrounding normal tissue and sensitive structures. In less than a decade, IMRT has become common practice in radiation oncology. Looking forward, the authors wonder if IMRT has matured to such a point that the room for further improvement has diminished and so it is pertinent to ask what the future will hold for IMRT. This article attempts to look from the perspective of the current state of the technology to predict the immediate trends and the future directions. This article will (1) review the clinical experience of IMRT; (2) review what we learned in IMRT planning; (3) review different treatment delivery techniques; and finally, (4) predict the areas of advancements in the years to come.

On the parameter describing the generalised equivalent uniform dose (gEUD) for tumours

The purpose of the present work was to estimate the parameter 'a' describing the generalised equivalent uniform dose (gEUD) for tumours and its dependence on radiobiological parameters. The consequences of uncertainties in a on the gEUD were also studied. An estimate of a was found by requiring that, for a given target dose distribution, the mechanistic EUD (based on radiobiological linear quadratic modelling) equals gEUD. The estimate of a was found to depend on the dose distribution, and decreased with factors that increase the slope of the cell survival curve (i.e. decreasing alpha/beta values and increasing alpha values). Furthermore, the parameter a was estimated for 35 prostate cancer IMRT plans of varying dose distributions, for two sets of previously published radiobiological parameters: (1) alpha=0.15 Gy(-1) and alpha/beta=3 Gy, and (2) alpha=0.26 Gy(-1) and alpha/beta=10 Gy. The estimated values of a ranged from -25.6 to -22.4 for all combinations of dose distributions and parameter sets. Uncertainties in a were found to give only small uncertainties in gEUD. Although the current work shows limitations of the gEUD model for tumours, gEUD may still be preferable for biological treatment plan optimization, evaluation and reporting.

Towards an objective evaluation of tolerances for beam modeling in a treatment planning system

The performance of a convolution/superposition based treatment planning system depends on the ability of the dose calculation algorithm to accurately account for physical interactions taking place in the tissue, key components of the linac head and on the accuracy of the photon beam model. Generally the user has little or no control over the performance of the dose calculation algorithm but is responsible for the accuracy of the beam model within the constraints imposed by the system. This study explores the dosimetric impact of limitations in photon beam modeling accuracy on complex 3D clinical treatment plans. A total of 70 photon beam models was created in the Pinnacle treatment planning system. Two of the models served as references for 6 MV and 15 MV beams, while the rest were created by perturbing the reference models in order to produce specific deviations in specific regions of the calculated dose profiles (central axis and transverse). The beam models were then used to generate 3D plans on seven CT data sets each for four different treatment sites (breast and conformal prostate, lung and brain). The equivalent uniform doses (EUD) of the targets and the principal organs at risk (OARs) of all plans ( approximately 1000) were calculated and compared to the EUDs delivered by the reference beam models. In general, accurate dosimetry of the target is most greatly compromised by poor modeling of the central axis depth dose and the horns, while the EUDs of the OARs exhibited the greatest sensitivity to beam width accuracy. Based on the results of this analysis we suggest a set of tolerances to be met during commissioning of the beam models in a treatment planning system that are consistent in terms of clinical outcomes as predicted by the EUD.

The Tradeoff Between Treatment Plan Quality and Required Number of Monitor Units in Intensity-modulated Radiotherapy

PURPOSE

To provide a mathematical approach for quantifying the tradeoff between intensity-modulated radiotherapy (IMRT) complexity and plan quality.

METHODS AND MATERIALS

We solve a multi-objective program that includes IMRT complexity, measured as the number of monitor units (MU) needed to deliver the plan using a multileaf collimator, as an objective. Clinical feasibility of plans is ensured by the use of hard constraints in the formulation. Optimization output is a Pareto surface of treatment plans, which allows the tradeoffs between IMRT complexity, tumor coverage, and tissue sparing to be observed. Paraspinal and lung cases are presented.

RESULTS

Although the amount of possible MU reduction is highly dependent on the difficulty of the underlying treatment plan (difficult plans requiring a high degree of intensity modulation are more sensitive to MU reduction), in some cases the number of MU can be reduced more than twofold with a <1% increase in the objective function.

CONCLUSIONS

The largely increased number of MU and irradiation time in IMRT is sometimes unnecessary. Tools like the one presented should be considered for integration into daily clinical practice to avoid this problem.