Pascal Storchi

Optical diffusion in layered media

In highly scattering media, light energy fluence rate distributions can be described by diffusion theory. Boundary conditions, appropriate to the diffusion approximation, are derived for surfaces where reflection of diffuse light occurs. Both outer surfaces and interfaces separating media with different indices of refraction can be treated. The diffusion equation together with its boundary conditions is solved using the finite element method. This numerical method allows much freedom of geometry.

iCycle: Integrated, multicriterial beam angle, and profile optimization for generation of coplanar and noncoplanar IMRT plans

PURPOSE To introduce iCycle, a novel algorithm for integrated, multicriterial optimization of beam angles, and intensity modulated radiotherapy (IMRT) profiles. METHODS A multicriterial plan optimization with iCycle is based on a prescription called wish-list, containing hard constraints and objectives with ascribed priorities. Priorities are ordinal parameters used for relative importance ranking of the objectives. The higher an objective priority is, the higher the probability that the corresponding objective will be met. Beam directions are selected from an input set of candidate directions. Input sets can be restricted, e.g., to allow only generation of coplanar plans, or to avoid collisions between patient/couch and the gantry in a noncoplanar setup. Obtaining clinically feasible calculation times was an important design criterium for development of iCycle. This could be realized by sequentially adding beams to the treatment plan in an iterative procedure. Each iteration loop starts with selection of the optimal direction to be added. Then, a Pareto-optimal IMRT plan is generated for the (fixed) beam setup that includes all so far selected directions, using a previously published algorithm for multicriterial optimization of fluence profiles for a fixed beam arrangement Breedveld et al. [Phys. Med. Biol. 54, 7199-7209 (2009)]. To select the next direction, each not yet selected candidate direction is temporarily added to the plan and an optimization problem, derived from the Lagrangian obtained from the just performed optimization for establishing the Pareto-optimal plan, is solved. For each patient, a single one-beam, two-beam, three-beam, etc. Pareto-optimal plan is generated until addition of beams does no longer result in significant plan quality improvement. Plan generation with iCycle is fully automated. RESULTS Performance and characteristics of iCycle are demonstrated by generating plans for a maxillary sinus case, a cervical cancer patient, and a liver patient treated with SBRT. Plans generated with beam angle optimization did better meet the clinical goals than equiangular or manually selected configurations. For the maxillary sinus and liver cases, significant improvements for noncoplanar setups were seen. The cervix case showed that also in IMRT with coplanar setups, beam angle optimization with iCycle may improve plan quality. Computation times for coplanar plans were around 1-2 h and for noncoplanar plans 4-7 h, depending on the number of beams and the complexity of the site. CONCLUSIONS Integrated beam angle and profile optimization with iCycle may result in significant improvements in treatment plan quality. Due to automation, the plan generation workload is minimal. Clinical application has started.

Calculation of a pencil beam kernel from measured photon beam data

Usually, pencil beam kernels for photon beam calculations are obtained by Monte Carlo calculations. In this paper, we present a method to derive a pencil beam kernel from measured beam data, i.e. central axis depth doses, phantom scatter factors and off-axis ratios. These data are usually available in a radiotherapy planning system. The differences from other similar works are: (a) the central part of the pencil beam is derived from the measured penumbra of large fields and (b) the dependence of the primary photon fluence on the depth caused by beam hardening in the phantom is taken into account. The calculated pencil beam will evidently be influenced by the methods and instruments used for measurement of the basic data set. This is of particular importance for an accurate prediction of the absorbed dose delivered by small fields. Comparisons with measurements show that the accuracy of the calculated dose distributions fits well in a 2% error interval in the open part of the field, and in a 2 mm isodose shift in the penumbra region.

Automatic calculation of three-dimensional margins around treatment volumes in radiotherapy planning

Following the publication of ICRU Report 50, the concepts of GTV (gross tumour volume). CTV (clinical target volume) and PTV (planning target volume) are being used in radiotherapy planning with increasing frequency. In 3D planning, the GTV (or CTV) is normally outlined by the clinician in CT or MRI slices. The PTV is determined by adding margins to these volumes. Since manual drawing of an accurate 3D margin in a set of 2D slices is extremely time consuming, software has been developed to automate this step in the planning. The target volume is represented in a 3D matrix grid with voxel values one inside and zero outside the target volume. It is expanded by centering an ellipsoid at every matrix element within the volume. The shape of the ellipsoid reflects the size of the margins in the three main orthogonal directions. Finally, the PTV contours are determined from the 50% iso-value lines of the expanded volume. The software tool has been in clinical use since the end of 1994 and has mostly been applied to the planning of prostate irradiations. The accuracy is better than can be achieved manually and the workload has been reduced considerably (from 4 h manually to approximately 1 min automatically).

A novel approach to multi-criteria inverse planning for IMRT

Treatment plan optimization is a multi-criteria process. Optimizing solely on one objective or on a sum of a priori weighted objectives may result in inferior treatment plans. Manually adjusting weights or constraints in a trial and error procedure is time consuming. In this paper we introduce a novel multi-criteria optimization approach to automatically optimize treatment constraints (dose-volume and maximum-dose). The algorithm tries to meet these constraints as well as possible, but in the case of conflicts it relaxes lower priority constraints so that higher priority constraints can be met. Afterwards, all constraints are tightened, starting with the highest priority constraints. Applied constraint priority lists can be used as class solutions for patients with similar tumour types. The presented algorithm does iteratively apply an underlying algorithm for beam profile optimization, based on a quadratic objective function with voxel-dependent importance factors. These voxel-dependent importance factors are automatically adjusted to reduce dose-volume and maximum-dose constraint violations.

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.

Treatment precision of image-guided liver SBRT using implanted fiducial markers depends on marker?tumour distance

The purpose of this study is to assess the accuracy of day-to-day predictions of liver tumour position using implanted gold markers as surrogates and to compare the method with alternative set-up strategies, i.e. no correction, vertebrae and 3D diaphragm-based set-up. Twenty patients undergoing stereotactic body radiation therapy (SBRT) with abdominal compression for primary or metastatic liver cancer were analysed. We determined the day-to-day correlation between gold marker and tumour positions in contrast-enhanced CT scans acquired at treatment preparation and before each treatment session. The influence of marker-tumour distance on the accuracy of prediction was estimated by introducing a method extension of the set-up error paradigm. The distance between gold markers and the centre of the tumour varied between 5 and 96 mm. Marker-guidance was superior to guiding treatment using other surrogates, although both the random and systematic components of the prediction error SD depended on the tumour-marker distance. For a marker-tumour distance of 4 cm, we observed σ = 1.3 mm and Σ = 1.6 mm. The 3D position of the diaphragm dome was the second best predictor. In conclusion, the tumour position can be predicted accurately using implanted markers, but marker-guided set-up accuracy decreases with increasing distance between implanted markers and the tumour.

Calculation models for determining the absorbed dose in water phantoms in off-axis planes of rectangular fields of open and wedged photon beams

Beam models are proposed for the calculation of the dose in off-axis planes of rectangular photon fields, when the data set used in the treatment planning system is based on the simple storage model of Milan and Bentley. For open beams the model separates the off-axis ratio into an envelope profile and two boundary profiles. The envelope profile gives the field intensity of the maximal position of the jaws and has rotational symmetry. The boundary profiles describe the boundaries of the field actually formed by the jaws. In the case of a wedged beam, the model also separates the off-axis ratio into envelope profiles and boundary profiles. To determine these profiles for the non-wedge direction from open beam profiles, the wedge thickness is converted to an equivalent water thickness. In the case of an asymmetric field, the boundary profiles are shifted to the field centre. Results of calculation with these models have been compared with measurements and the simple multiplication of profiles, which has often been used with the Milan-Bentley model. The new models agree within a few per cent with the measurements and are a great improvement compared to the simple multiplication of profiles.

A model to determine the initial phase space of a clinical electron beam from measured beam data.

Advanced electron beam dose calculation models for radiation oncology require as input an initial phase space (IPS) that describes a clinical electron beam. The IPS is a distribution in position, energy and direction of electrons and photons in a plane in front of the patient. A method is presented to derive the IPS of a clinical electron beam from a limited set of measured beam data. The electron beam is modelled by a sum of four beam components: a main diverging beam, applicator edge scatter, applicator transmission and a second diverging beam. The two diverging beam components are described by weighted sums of monoenergetic diverging electron and photon beams. The weight factors of these monoenergetic beams are determined by the method of simulated annealing such that a best fit is obtained with depth-dose curves measured for several field sizes at two source-surface distances. The resulting IPSs are applied by the phase-space evolution electron beam dose calculation model to calculate absolute 3D dose distributions. The accuracy of the calculated results is in general within 1.5% or 1.5 mm; worst cases show differences of up to 3% or 3 mm. The method presented here to describe clinical electron beams yields accurate results, requires only a limited set of measurements and might be considered as an alternative to the use of Monte Carlo methods to generate full initial phase spaces.

Automated non-coplanar beam direction optimization improves IMRT in SBRT of liver metastasis

PURPOSE To investigate whether automatically optimized coplanar, or non-coplanar beam setups improve intensity modulated radiotherapy (IMRT) treatment plans for stereotactic body radiotherapy (SBRT) of liver tumors, compared to a reference equi-angular IMRT plan. METHODS For a group of 13 liver patients, an in-house developed beam selection algorithm (Cycle) was used for generation of 3D-CRT plans with either optimized coplanar-, or non-coplanar beam setups. These 10 field, coplanar and non-coplanar setups, and an 11 field, equi-angular coplanar reference setup were then used as input for generation of IMRT plans. For all plans, the PTV dose was maximized in an iterative procedure by increasing the prescribed PTV dose in small steps until further increase was prevented by constraint violation(s). RESULTS For optimized non-coplanar setups, D(PTV, max) increased by on average 30% (range 8-64%) compared to the corresponding reference IMRT plan. Similar increases were observed for D(PTV, 99%) and gEUD(a). For optimized coplanar setups, mean PTV dose increases were only approximately 4%. After re-scaling all plans to the clinically applied dose, optimized non-coplanar configurations resulted in the best sparing of organs at risk (healthy liver, spinal cord, bowel). CONCLUSION Compared to an equi-angular beam setup, computer optimized non-coplanar setups do result in substantial improvements in IMRT plans for SBRT of liver tumors.