Adaptive fractionation at the MR-linac.

Objective. Fractionated radiotherapy typically delivers the same dose in each fraction. Adaptive fractionation (AF) is an approach to exploit inter-fraction motion by increasing the dose on days when the distance of tumor and dose-limiting organs at risk (OAR) is large and decreasing the dose on unfavorable days. We develop an AF algorithm and evaluate the concept for patients with abdominal tumors previously treated at the MR-linac in 5 fractions.Approach. Given daily adapted treatment plans, inter-fractional changes are quantified by sparing factorsδtdefined as the OAR-to-tumor dose ratio. The key problem of AF is to decide on the dose to deliver in fractiont, givenδtand the dose delivered in previous fractions, but not knowing futureδts. Optimal doses that maximize the expected biologically effective dose in the tumor (BED10) while staying below a maximum OAR BED3constraint are computed using dynamic programming, assuming a normal distribution overδwith mean and variance estimated from previously observed patient-specificδts. The algorithm is evaluated for 16 MR-linac patients in whom tumor dose was compromised due to proximity of bowel, stomach, or duodenum.Main Results. In 14 out of the 16 patients, AF increased the tumor BED10compared to the reference treatment that delivers the same OAR dose in each fraction. However, in 11 of these 14 patients, the increase in BED10was below 1 Gy. Two patients with large sparing factor variation had a benefit of more than 10 Gy BED10increase. For one patient, AF led to a 5 Gy BED10decrease due to an unfavorable order of sparing factors.Significance. On average, AF provided only a small increase in tumor BED. However, AF may yield substantial benefits for individual patients with large variations in the geometry.

Aperture shape optimization for IMRT treatment planning.

We propose an algorithm for aperture shape optimization (ASO) for step and shoot delivery of intensity-modulated radiotherapy. The method is an approach to direct aperture optimization (DAO) that exploits gradient information to locally optimize the positions of the leafs of a multileaf collimator. Based on the dose-influence matrix, the dose distribution is locally approximated as a linear function of the leaf positions. Since this approximation is valid only in a small interval around the current leaf positions, we use a trust-region-like method to optimize the leaf positions: in one iteration, the leaf motion is confined to the beamlets where the leaf edges are currently positioned. This yields a well-behaved optimization problem for the leaf positions and the aperture weights, which can be solved efficiently. If, in one iteration, a leaf is moved to the edge of a beamlet, the leaf motion can be confined to the neighboring beamlet in the next iteration. This allows for large leaf position changes over the course of the algorithm. In this paper, the ASO algorithm is embedded into a column-generation approach to DAO. After a new aperture is added to the treatment plan, we use the ASO algorithm to simultaneously optimize aperture weights and leaf positions for the new set of apertures. We present results for a paraspinal tumor case, a prostate case and a head and neck case. The computational results indicate that, using this approach, treatment plans close to the ideal fluence map optimization solution can be obtained.

Relating two techniques for handling uncertainties in IMRT optimization.

Radiotherapy treatment planning is associated with uncertainties. Examples are uncertainties in the tumour location due to organ movement or the inter/intra observer variability in target definition. Different approaches to incorporate uncertainties into IMRT optimization have been proposed. In this note, we point out a relation between two previously published methods: the coverage probability approach and the concept of optimizing the expectation value of an objective function that depends on a set of random variables. Both concepts are generally different, but turn out to be equivalent in special cases.

Simulation and visualization of dose uncertainties due to interfractional organ motion.

In this paper, we deal with the effects of interfractional organ motion during radiation therapy. We consider two problems: first, treatment plan evaluation in the presence of motion, and second, the incorporation of organ motion into IMRT optimization. Concerning treatment plan evaluation, we face the problem that the delivered dose cannot be predicted with certainty at the time of treatment planning but is associated with uncertainties. We present a method to simulate stochastic properties of the dose distribution. This provides the treatment planner with information about motion-related risks of different plans and may support the decision for or against a treatment plan. This information includes the display of probabilities of individual voxels to receive doses from a therapeutical interval or above critical levels, as well as a diagram that shows the variability of the dose volume histogram. Concerning the incorporation of organ motion into IMRT planning, we further analyse the approach of inverse planning based on probability distributions of possible patient geometries. We consider three different sources of uncertainty, namely uncertainty about the amplitude of motion, a systematic error and a random error. We analyse the impact of these sources of uncertainty on the optimized treatment plans for prostate cancer.

Incorporating organ movements in inverse planning: assessing dose uncertainties by Bayesian inference.

We present a method to calculate dose uncertainties due to inter-fraction organ movements in fractionated radiotherapy, i.e. in addition to the expectation value of the dose distribution a variance distribution is calculated. To calculate the expectation value of the dose distribution in the presence of organ movements, one estimates a probability distribution of possible patient geometries. The respective variance of the expected dose distribution arises for two reasons: first, the patient is irradiated with a finite number of fractions only and second, the probability distribution of patient geometries has to be estimated from a small number of images and is therefore not exactly known. To quantify the total dose variance, we propose a method that is based on the principle of Bayesian inference. The method is of particular interest when organ motion is incorporated in inverse IMRT planning by means of inverse planning performed on a probability distribution of patient geometries. In order to make this a robust approach, it turns out that the dose variance should be considered (and minimized) in the optimization process. As an application of the presented concept of Bayesian inference, we compare three approaches to inverse planning based on probability distributions that account for an increasing degree of uncertainty. The Bayes theorem further provides a concept to interpolate between patient specific data and population-based knowledge on organ motion which is relevant since the number of CT images of a patient is typically small.

Inclusion of organ movements in IMRT treatment planning via inverse planning based on probability distributions.

In this paper, we investigate an off-line strategy to incorporate inter-fraction organ motion in IMRT treatment planning. It was suggested that inverse planning could be based on a probability distribution of patient geometries instead of a single snap shot. However, this concept is connected to two intrinsic problems: first, this probability distribution has to be estimated from only a few images; and second, the distribution is only sparsely sampled over the treatment course due to a finite number of fractions. In the current work, we develop new concepts of inverse planning which account for these two problems.

Time-delay autosynchronization of the spatiotemporal dynamics in resonant tunneling diodes.

The double barrier resonant tunneling diode exhibits complex spatiotemporal patterns including low-dimensional chaos when operated in an active external circuit. We demonstrate how autosynchronization by time-delayed feedback control can be used to select and stabilize specific current density patterns in a noninvasive way. We compare the efficiency of different control schemes involving feedback in either local spatial or global degrees of freedom. The numerically obtained Floquet exponents are explained by analytical results from linear stability analysis.