Bengt K. Lind

An algorithm for maximizing the probability of complication-free tumour control in radiation therapy

New radiobiological models are used to describe tumour and normal tissue reactions and to account for their dependence on the irradiated volume and inhomogeneities of the delivered dose distribution and cell sensitivity. The probability of accomplishing complication-free tumour control is maximized by an iterative algorithm. The algorithm is demonstrated by applying it to a one-dimensional (1D) tumour model but also to a more clinically relevant 2D case. The new algorithm is n-dimensional so it could simultaneously optimize the dose delivery in a 3D volume and in principle also select the ideal beam orientations, beam modalities (photons, electrons, neutrons, etc) and optimal spectral distributions of the corresponding modalities. To make calculation time reasonable, 2D-3D problems are most practical, and suitable beam orientations are preselected by the choice of irradiation kernel. The energy deposition kernel should therefore be selected in order to avoid irradiation through organs at risk. Clinically established dose response parameters for the tissues of interest are used to make the optimization as relevant as possible to the clinical problems at hand. The algorithm can be used even with a poorly selected kernel because it will always, as far as possible, avoid irradiating organs at risk. The generated dose distribution will be optimal with respect to the spatial distribution and assumed radiobiological properties of the tumour and normal tissues at risk for the kernel chosen. More specifically the probability of achieving tumour control without fatal complications in normal tissues is maximized. In the clinical examples a reduced tumour dose is seen at the border to sensitive organs at risk, but instead an increased dose just inside the tumour border is generated. The increased tumour dose has the effect that the dose fall-off is as steep as possible at the border to organs at risk.

A generalized pencil beam algorithm for optimization of radiation therapy

An iterative pencil beam algorithm for optimization of multidimensional radiation therapy dose plans has been developed. The algorithm allows the use of both physical and radiobiological treatment objective functions and allows arbitrary sampling such as straight Cartesian grids with linear or nonlinear sampling functions or random sampling. The algorithm can account for and optimally combine almost all the degrees of freedom at an advanced radiotherapy clinic, such as different beam modalities and spectra, beam directions, beam fluence distributions, and time-dose fractionations. The algorithm allows for external charged and neutral beams as well as intracavitary and interstitial sources to be optimally combined. A quantity termed the generalized fluence vector is introduced, combining fluences and energy fluences from external beams as well as the radiation source densities of intracavitary and interstitial sources or external source distributions. The positivity constraint on the generalized fluence can therefore be applied directly during the optimization procedure. The convergence properties and the required iteration time of the algorithm are discussed. Several examples with combinations of photon and electron beams of different energies and directions of incidence are presented. The optimization has been made with the treatment objective to maximize the probability of achieving tumor control without causing severe complications in healthy normal tissues.

Shaping of arbitrary dose distributions by dynamic multileaf collimation.

Traditionally, the shaping of non-uniform dose distributions has been performed by using wedges or compensating filters. The advent of high resolution multileaf collimators may largely eliminate the need for material attenuators for modification of the beam. This is achieved by a new technique for the shaping of arbitrary dose distributions by dynamic motion of the collimator leaves. By employing narrow elementary slit beams that correspond to the smallest possible opening of the multileaf collimator, the optimal density of such slit beams, i.e. opening density, can be determined automatically using a newly developed inversion algorithm. The present method has two major advantages (1) internal structures in the field can be created, controlled solely by steering the collimator leaves, (2) the opening density determined by the algorithm never gives rise to underdosage: this is important from a radiobiological point of view.

An adaptive control algorithm for optimization of intensity modulated radiotherapy considering uncertainties in beam profiles, patient set-up and internal organ motion

A new general beam optimization algorithm for inverse treatment planning is presented. It utilizes a new formulation of the probability to achieve complication-free tumour control. The new formulation explicitly describes the dependence of the treatment outcome on the incident fluence distribution, the patient geometry, the radiobiological properties of the patient and the fractionation schedule. In order to account for both measured and non-measured positioning uncertainties, the algorithm is based on a combination of dynamic and stochastic optimization techniques. Because of the difficulty in measuring all aspects of the intra- and interfractional variations in the patient geometry, such as internal organ displacements and deformations, these uncertainties are primarily accounted for in the treatment planning process by intensity modulation using stochastic optimization. The information about the deviations from the nominal fluence profiles and the nominal position of the patient relative to the beam that is obtained by portal imaging during treatment delivery, is used in a feedback loop to automatically adjust the profiles and the location of the patient for all subsequent treatments. Based on the treatment delivered in previous fractions, the algorithm furnishes optimal corrections for the remaining dose delivery both with regard to the fluence profile and its position relative to the patient. By dynamically refining the beam configuration from fraction to fraction, the algorithm generates an optimal sequence of treatments that very effectively reduces the influence of systematic and random set-up uncertainties to minimize and almost eliminate their overall effect on the treatment. Computer simulations have shown that the present algorithm leads to a significant increase in the probability of uncomplicated tumour control compared with the simple classical approach of adding fixed set-up margins to the internal target volume.

Stricture of the proximal esophagus in head and neck carcinoma patients after radiotherapy

It is well recognized that many patients with head and neck carcinoma have problems with food intake and malnutrition. The objective of the current study was to determine the clinical pattern of patients with nonneoplastic stricture of the upper esophagus after radiotherapy for head and neck carcinoma.

Long-term cardiac mortality following radiation therapy for Hodgkin's disease: analysis with the relative seriality model☆

PURPOSE (a) To assess the increased risk of death due to ischemic heart disease (IHD) in a group of patients treated for Hodgkins disease (HD) with radiation therapy (RT) as the primary treatment. (b) To quantify the dose response of IHD using a biophysical model. MATERIALS AND METHODS Patient material consisted of 157 patients diagnosed for HD between 1972 and 1985 who received RT as the primary treatment at Radiumhemmet, Karolinska Hospital. The general population formed the control group. The RT treatments were reconstructed based on the individual treatment data and simulator films. Individual clinical and dosimetrical data were analyzed with the relative seriality model. The material was also analyzed grouping the material according to dose-volume constraints. RESULTS Of the 157 patients, 13 (8.3%) died due to IHD. The standardized mortality ratio (SMR) was 5.0 (95% CI, 2.7-8.6). Analysis of dose-volume histograms (DVH) showed an increasing risk with increasing dose to a larger volume fraction. The observed individual clinical complication data could not be modeled unambiguously. The group analysis resulted in the dose-response parameters: D(50)=71 Gy, gamma=0.96 and s=1.0. CONCLUSIONS A significantly increased risk of death due to IHD following RT for HD was found. The risk was found to increase with higher dose and larger volume fraction irradiated.

Biologically effective uniform dose (D) for specification, report and comparison of dose response relations and treatment plans

Developments in radiation therapy planning have improved the information about the three-dimensional dose distribution in the patient. Isodose graphs, dose volume histograms and most recently radiobiological models can be used to evaluate the dose distribution delivered to the irradiated organs and volumes of interest. The concept of a biologically effective uniform dose (D) assumes that any two dose distributions are equivalent if they cause the same probability for tumour control or normal tissue complication. In the present paper the D concept both for tumours and normal tissues is presented, making use of the fact that probabilities averaged over both dose distribution and organ radiosensitivity are more relevant to the clinical outcome than the expected number of surviving clonogens or functional subunits. D can be calculated in complex target volumes or organs at risk either from the 3D dose matrix or from the corresponding dose volume histograms of the dose plan. The value of the D concept is demonstrated by applying it to two treatment plans of a cervix cancer. Comparison is made of the D concept with the effective dose (Deff ) and equivalent uniform dose (EUD) that have been suggested in the past. The value of the concept for complex targets and fractionation schedules is also pointed out.

Simultaneous optimization of dynamic multileaf collimation and scanning patterns or compensation filters using a generalized pencil beam algorithm.

A very flexible iterative method for simultaneous optimization of dynamic multileaf collimation, scanning patterns and compensation filters has been developed. The algorithm can account for and optimize almost all the degrees of freedom available in a modern radiation therapy clinic. The method has been implemented for three dimensional treatment planning. The algorithm has been tested for a number of cases where both traditional wedge filters and block collimators, and modern equipment such as scanned beams and multileaf collimators are available. It is shown that the algorithm can improve heavily on traditional uniform dose plans with respect to the probability of achieving tumor control without causing severe complications (P+) simply by finding the optimal beam weights and block collimator settings. By allowing more complex equipment to deliver the dose and by accounting for their increased flexibility during the optimization, the dose plan can be substantially improved with respect to the applied objective functions. It is demonstrated that flexible lateral collimation combined with compensators or scanned beams in most cases allow close to optimal dose delivery. Here both the calculation time and the amount of primary computer memory needed has been reduced by performing the dose calculations in a cone beam coordinate system allowing the use of approximately spatially invariant energy deposition kernels. A typical calculation time for optimization of a two-field technique in a three dimensional volume is about 20 s per iteration step on a Hewlett-Packard 735 workstation. A well converged solution is normally obtained within about 50-100 iterations or within 15-30 min.

Optimization of the Dose Level for a Given Treatment Plan to Maximize the Complication-free Tumor Cure

During the past decade, tumor and normal tissue reactions after radiotherapy have been increasingly quantified in radiobiological terms. For this purpose, response models describing the dependence of tumor and normal tissue reactions on the irradiated volume, heterogeneity of the delivered dose distribution and cell sensitivity variations can be taken into account. The probability of achieving a good treatment outcome can be increased by using an objective function such as P+, the probability of complication-free tumor control. A new procedure is presented, which quantifies P+ from the dose delivery on 2D surfaces and 3D volumes and helps the user of any treatment planning system (TPS) to select the best beam orientations, the best beam modalities and the most suitable beam energies. The final step of selecting the prescribed dose level is made by a renormalization of the entire dose plan until the value of P+ is maximized. The index P+ makes use of clinically established dose-response parameters, for tumors and normal tissues of interest, in order to improve its clinical relevance. The results, using P+, are compared against the assessments of experienced medical physicists and radiation oncologists for two clinical cases. It is observed that when the absorbed dose level for a given treatment plan is increased, the treatment outcome first improves rapidly. As the dose approaches the tolerance of normal tissues the complication-free cure begins to drop. The optimal dose level is often just below this point and it depends on the geometry of each patient and target volume. Furthermore, a more conformal dose delivery to the target results in a higher control rate for the same complication level. This effect can be quantified by the increased value of the P+ parameter.

Optimal radiation beam profiles considering the stochastic process of patient positioning in fractionated radiation therapy

We present a solution to the problem of finding optimal beam profiles in fractionated radiation therapy when taking the uncertainty in beam patient alignment into account. The problem was previously solved for the special cases of one single dose fraction and infinitely many fractions. For few fractions (<or=5), symmetry considerations reduce the problem so that it can be handled with ordinary numerical integration techniques. For the general case, including the frequently used 20-30 fractions, a Monte Carlo integration method has been developed. As may be expected, a linear response model for radiation sensitivity, based only on the total dose delivered, is insufficient for a large number of dose fractions with sharp beam edges. Under such circumstances the full linear quadratic model for cell survival has to be incorporated. The standard technique of opening up the fields to compensate for the positioning uncertainty is only feasible when the surrounding normal tissues tolerate radiation well. The present studies indicate that the probability of achieving tumour control without inducing severe injury to normal tissue can be increased if optimal non-uniform beams are used.