Thomas Bortfeld

X-RAY FIELD COMPENSATION WITH MULTILEAF COLLIMATORS

PURPOSE It has been proposed that conformal therapy can be carried out with static ports that are each individually compensated to deliver an optimal total dose distribution. If this proposal is to be implemented, one must have a means of compensating or modulating the fluence distributions within the boundaries of individual treatment fields. A theory was developed and implemented to achieve this goal. METHODS AND MATERIALS The theory allowed creation of a leaf-setting sequence for a desired level of field-modulation precision. This method of beam modulation was experimentally verified using radiographic film to integrate the dose delivered by the sequence of discrete static multileaf collimator-defined subfields. RESULTS Beam profiles were generated that matched the planned beam profiles to within the specified degree of precision. CONCLUSION This methodology is a candidate for implementation of inverse planning for conformal therapy.

Correlation between CT numbers and tissue parameters needed for Monte Carlo simulations of clinical dose distributions

We describe a new method to convert CT numbers into mass density and elemental weights of tissues required as input for dose calculations with Monte Carlo codes such as EGS4. As a first step, we calculate the CT numbers for 71 human tissues. To reduce the effort for the necessary fits of the CT numbers to mass density and elemental weights, we establish four sections on the CT number scale, each confined by selected tissues. Within each section, the mass density and elemental weights of the selected tissues are interpolated. For this purpose, functional relationships between the CT number and each of the tissue parameters, valid for media which are composed of only two components in varying proportions, are derived. Compared with conventional data fits, no loss of accuracy is accepted when using the interpolation functions. Assuming plausible values for the deviations of calculated and measured CT numbers, the mass density can be determined with an accuracy better than 0.04 g cm(-3). The weights of phosphorus and calcium can be determined with maximum uncertainties of 1 or 2.3 percentage points (pp) respectively. Similar values can be achieved for hydrogen (0.8 pp) and nitrogen (3 pp). For carbon and oxygen weights, errors up to 14 pp can occur. The influence of the elemental weights on the results of Monte Carlo dose calculations is investigated and discussed.

A unified approach for inversion problems in intensity-modulated radiation therapy.

We propose and study a unified model for handling dose constraints (physical dose, equivalent uniform dose (EUD), etc) and radiation source constraints in a single mathematical framework based on the split feasibility problem. The model does not impose on the constraints an exogenous objective (merit) function. The optimization algorithm minimizes a weighted proximity function that measures the sum of the squares of the distances to the constraint sets. This guarantees convergence to a feasible solution point if the split feasibility problem is consistent (i.e., has a solution), or, otherwise, convergence to a solution that minimally violates the physical dose constraints and EUD constraints. We present computational results that demonstrate the validity of the model and the power of the proposed algorithmic scheme.

The multiple-sets split feasibility problem and its applications for inverse problems

The multiple-sets split feasibility problem requires finding a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. It can be a model for many inverse problems where constraints are imposed on the solutions in the domain of a linear operator as well as in the operators range. It generalizes the convex feasibility problem as well as the two-sets split feasibility problem. We propose a projection algorithm that minimizes a proximity function that measures the distance of a point from all sets. The formulation, as well as the algorithm, generalize earlier work on the split feasibility problem. We offer also a generalization to proximity functions with Bregman distances. Application of the method to the inverse problem of intensity-modulated radiation therapy treatment planning is studied in a separate companion paper and is here only described briefly.

Number and orientations of beams in intensity‐modulated radiation treatments

The fundamental question of how many equispaced coplanar intensity-modulated photon beams are required to obtain an optimum treatment plan is investigated in a dose escalation study for a typical prostate tumor. Furthermore, optimization of beam orientations to improve dose distributions is explored. A dose-based objective function and a fast gradient technique are employed for optimizing the intensity profiles (inverse planning). An exhaustive search and fast simulated annealing techniques (FSA) are used to optimize beam orientations. However, to keep computation times reasonable, the intensity profiles for each beam arrangement are still optimized using inverse planning. A pencil beam convolution algorithm is employed for dose calculation. All calculations are performed in three-dimensional (3D) geometry for 15 MV photons. DVHs, dose displays, TCP, NTCP, and biological score functions are used for evaluation of treatment plans. It is shown that for the prostate case presented here, the minimum required number of equiangular beams depends on the prescription dose level and ranges from three beams for 70 Gy plans to seven to nine beams for 81 Gy plans. For the highest dose level (81 Gy), beam orientations are optimized and compared to equiangular spaced arrangements. It is shown that (1) optimizing beam orientations is most valuable for a small numbers of beams (< or = 5) and the gain diminishes rapidly for higher numbers of beams; (2) if sensitive structures (for example rectum) are partially enclosed by the target volume, beams coming from their direction tend to be preferable, since they allow greater control over dose distributions; (3) while FSA and an exhaustive search lead to the same results, computation times using FSA are reduced by two orders of magnitude to clinically acceptable values. Moreover, characteristics of and demands on biology-based and dose-based objective functions for optimization of intensity-modulated treatments are discussed.

An experimental investigation on intra-fractional organ motion effects in lung IMRT treatments

Respiration-induced tumour motion can potentially compromise the use of intensity-modulated radiotherapy (IMRT) as a dose escalation tool for lung tumour treatment. We have experimentally investigated the intra-fractional organ motion effects in lung IMRT treatments delivered by multi-leaf collimator (MLC). An in-house made motor-driven platform, which moves sinusoidally with an amplitude of 1 cm and a period of 4 s, was used to mimic tumour motion. Tumour motion was simulated along cranial-caudal direction while MLC leaves moved across the patient from left to right, as in most clinical cases. The dose to a point near the centre of the tumour mass was measured according to geometric and dosimetric parameters from two five-field lung IMRT plans. For each field, measurement was done for two dose rates (300 and 500 MU min(-1)), three MLC delivery modes (sliding window, step-and-shoot with 10 and 20 intensity levels) and eight equally spaced starting phases of tumour motion. The dose to the measurement point delivered from all five fields was derived for both a single fraction and 30 fractions by randomly sampling from measured dose values of each field at different initial phases. It was found that the mean dose to a moving tumour differs slightly (<2-3%) from that to a static tumour. The variation in breathing phase at the start of dose delivery results in a maximum variation around the mean dose of greater than 30% for one field. The full width at half maximum for the probability distribution of the point dose is up to 8% for all five fields in a single fraction, but less than 1-2% after 30 fractions. In general, lower dose rate can reduce the motion-caused dose variation and therefore might be preferable for lung IMRT when no motion mitigation techniques are used. From the two IMRT cases we studied where tumour motion is perpendicular to MLC leaf motion, the dose variation was found to be insensitive to the MLC delivery mode.

Decomposition of pencil beam kernels for fast dose calculations in three‐dimensional treatment planning

A method for the calculation of three-dimensional dose distributions for high-energy photon beams is presented. The main features are (i) the calculation is fast enough to allow interactive three-dimensional treatment planning, and (ii) irregularly shaped or compensated fields, which are required to fit three-dimensional dose distributions to target volumes, are adequately taken into consideration. The method is based on the pencil beam convolution technique and shares its features concerning accuracy. A considerable gain in speed is achieved by decomposing the pencil beam kernel into three separated terms, thus reducing the required number of two-dimensional convolutions. The convolutions are performed in the frequency domain via the fast Hartley transform. Using these techniques, the calculation time for the convolutions is only about 8 s on a DEC VAX station 3100. This is one-fourth to one-third of the calculation time for the ray tracing through the three-dimensional CT data set, which has to be performed in any case. Results of the calculation are compared with measurements in a homogeneous phantom for 15 MV photons. Two irregular fields shaped with a multileaf collimator are considered. The deviations between measured and calculated absolute dose values are smaller than +/- 2%.

Realization and verification of three-dimensional conformal radiotherapy with modulated fields

PURPOSE We describe the experimental demonstration of the delivery of a three-dimensional conformal radiotherapy dose distribution using in-field modulation of nine fixed-gantry fields. METHODS AND MATERIALS Two-dimensional in-field modulation profiles, varying from field to field, were realized by quasi-dynamic multileaf collimation using the prototype of a commercially available multileaf collimator installed on a medical linear accelerator. The profiles were calculated to deliver an optimal dose distribution for a patient with a prostate carcinoma. The target volume surface was invaginated and bifurcated. The calculated dose distribution was delivered to a homogeneous polystyrene phantom consisting of 1 cm thick slices that were cut to match the patients outer contour. Seven therapy verification films were placed between the phantom slices. RESULTS Analysis of the films revealed a degree of conformation of the high-dose region to the target shape that would not be possible with unmodulated conformal therapy. However, small observed spatial displacements of the dose distribution confirm the need for very accurate positioning. CONCLUSIONS It is feasible to deliver clinically relevant, three-dimensional dose distributions that conform to invaginated and bifurcated target volumes using fields modulated by multileaf collimators.

Optimized planning using physical objectives and constraints.

Intensity-modulated radiation therapy (IMRT) allows one to achieve a better conformation of the high-dose region to the prescribed tumor target volume than uniform beam therapy, especially in complex treatment situations. Still, perfect conformation is impossible. Hence the goal of optimized IMRT planning or inverse planning is to find the beam profiles that yield the optimum among the physically achievable treatment plans. The principal physical advantage of IMRT is best exploited if the optimization is driven by physical criteria. This article presents an overview of such physical, yet clinically relevant, criteria along with optimization algorithms that take these criteria into account. Practical computer implementations are described, which allow one to perform the optimization in an interactive manner within a few minutes. The application of these methods to some complex clinical example cases is presented, and the results are compared with uniform beam treatment plans and with biologically optimized plans.

A TREATMENT PLANNING INTER-COMPARISON OF PROTON AND INTENSITY MODULATED PHOTON RADIOTHERAPY

PURPOSE A comparative treatment planning study has been undertaken between standard photon delivery techniques,b intensity modulated photon methods and spot scanned protons in order to investigate the merits and limitations of each of these treatment approaches. METHODS Plans for each modality were performed using CT scans and planning information for nine patients with varying indications and lesion sites and the results have been analysed using a variety of dose and volume based parameters. RESULTS Over all cases, it is predicted that the use of protons could lead to a reduction of the total integral dose by a factor three compared to standard photon techniques and a factor two compared to IM photon plans. In addition, in all but one Organ at Risk (OAR) for one case, protons are predicted to reduce both mean OAR dose and the irradiated volume at the 50% mean target dose level compared to both photon methods. However, when considering the volume of an OAR irradiated to 70% or more of the target dose, little difference could be shown between proton and intensity modulated photon plans. On comparing the magnitude of dose hot spots in OARs resulting from the proton and IM photon plans, more variation was observed, and the ranking of the plans was then found to be case and OAR dependent. CONCLUSIONS The use of protons has been found to reduce the medium to low dose load (below about 70% of the target dose) to OARs and all non-target tissues compared to both standard and inversely planned photons, but that the use of intensity modulated photons can result in similar levels of high dose conformation to that afforded by protons. However, the introduction of inverse planning methods for protons is necessary before general conclusions on the relative efficacy of photons and protons can be drawn.