Niklas Wahl

Development of the open‐source dose calculation and optimization toolkit matRad

Purpose We report on the development of the open‐source cross‐platform radiation treatment planning toolkit matRad and its comparison against validated treatment planning systems. The toolkit enables three‐dimensional intensity‐modulated radiation therapy treatment planning for photons, scanned protons and scanned carbon ions. Methods matRad is entirely written in Matlab and is freely available online. It re‐implements well‐established algorithms employing a modular and sequential software design to model the entire treatment planning workflow. It comprises core functionalities to import DICOM data, to calculate and optimize dose as well as a graphical user interface for visualization. matRad dose calculation algorithms (for carbon ions this also includes the computation of the relative biological effect) are compared against dose calculation results originating from clinically approved treatment planning systems. Results We observe three‐dimensional γ‐analysis pass rates ≥ 99.67% for all three radiation modalities utilizing a distance to agreement of 2 mm and a dose difference criterion of 2%. The computational efficiency of matRad is evaluated in a treatment planning study considering three different treatment scenarios for every radiation modality. For photons, we measure total run times of 145 s–1260 s for dose calculation and fluence optimization combined considering 4–72 beam orientations and 2608–13597 beamlets. For charged particles, we measure total run times of 63 s–993 s for dose calculation and fluence optimization combined considering 9963–45574 pencil beams. Using a CT and dose grid resolution of 0.3 cm3 requires a memory consumption of 1.59 GB–9.07 GB and 0.29 GB–17.94 GB for photons and charged particles, respectively. Conclusion The dosimetric accuracy, computational performance and open‐source character of matRad encourages a future application of matRad for both educational and research purposes.

Physically constrained voxel-based penalty adaptation for ultra-fast IMRT planning

Conventional treatment planning in intensity-modulated radiation therapy (IMRT) is a trial-and-error process that usually involves tedious tweaking of optimization parameters. Here, we present an algorithm that automates part of this process, in particular the adaptation of voxel-based penalties within normal tissue. Thereby, the proposed algorithm explicitly considers a priori known physical limitations of photon irradiation. The efficacy of the developed algorithm is assessed during treatment planning studies comprising 16 prostate and 5 head and neck cases. We study the eradication of hot spots in the normal tissue, effects on target coverage and target conformity, as well as selected dose volume points for organs at risk. The potential of the proposed method to generate class solutions for the two indications is investigated. Run-times of the algorithms are reported. Physically constrained voxel-based penalty adaptation is an adequate means to automatically detect and eradicate hot-spots during IMRT planning while maintaining target coverage and conformity. Negative effects on organs at risk are comparably small and restricted to lower doses. Using physically constrained voxel-based penalty adaptation, it was possible to improve the generation of class solutions for both indications. Considering the reported run-times of less than 20 s, physically constrained voxel-based penalty adaptation has the potential to reduce the clinical workload during planning and automated treatment plan generation in the long run, facilitating adaptive radiation treatments. PACS number(s): 87.55.de.Conventional treatment planning in intensity‐modulated radiation therapy (IMRT) is a trial‐and‐error process that usually involves tedious tweaking of optimization parameters. Here, we present an algorithm that automates part of this process, in particular the adaptation of voxel‐based penalties within normal tissue. Thereby, the proposed algorithm explicitly considers a priori known physical limitations of photon irradiation. The efficacy of the developed algorithm is assessed during treatment planning studies comprising 16 prostate and 5 head and neck cases. We study the eradication of hot spots in the normal tissue, effects on target coverage and target conformity, as well as selected dose volume points for organs at risk. The potential of the proposed method to generate class solutions for the two indications is investigated. Run‐times of the algorithms are reported. Physically constrained voxel‐based penalty adaptation is an adequate means to automatically detect and eradicate hot‐spots during IMRT planning while maintaining target coverage and conformity. Negative effects on organs at risk are comparably small and restricted to lower doses. Using physically constrained voxel‐based penalty adaptation, it was possible to improve the generation of class solutions for both indications. Considering the reported run‐times of less than 20 s, physically constrained voxel‐based penalty adaptation has the potential to reduce the clinical workload during planning and automated treatment plan generation in the long run, facilitating adaptive radiation treatments. PACS number(s): 87.55.de

Efficiency of analytical and sampling-based uncertainty propagation in intensity-modulated proton therapy

The sensitivity of intensity-modulated proton therapy (IMPT) treatment plans to uncertainties can be quantified and mitigated with robust/min-max and stochastic/probabilistic treatment analysis and optimization techniques. Those methods usually rely on sparse random, importance, or worst-case sampling. Inevitably, this imposes a trade-off between computational speed and accuracy of the uncertainty propagation. Here, we investigate analytical probabilistic modeling (APM) as an alternative for uncertainty propagation and minimization in IMPT that does not rely on scenario sampling. APM propagates probability distributions over range and setup uncertainties via a Gaussian pencil-beam approximation into moments of the probability distributions over the resulting dose in closed form. It supports arbitrary correlation models and allows for efficient incorporation of fractionation effects regarding random and systematic errors. We evaluate the trade-off between run-time and accuracy of APM uncertainty computations on three patient datasets. Results are compared against reference computations facilitating importance and random sampling. Two approximation techniques to accelerate uncertainty propagation and minimization based on probabilistic treatment plan optimization are presented. Runtimes are measured on CPU and GPU platforms, dosimetric accuracy is quantified in comparison to a sampling-based benchmark (5000 random samples). APM accurately propagates range and setup uncertainties into dose uncertainties at competitive run-times (GPU [Formula: see text] min). The resulting standard deviation (expectation value) of dose show average global [Formula: see text] pass rates between 94.2% and 99.9% (98.4% and 100.0%). All investigated importance sampling strategies provided less accuracy at higher run-times considering only a single fraction. Considering fractionation, APM uncertainty propagation and treatment plan optimization was proven to be possible at constant time complexity, while run-times of sampling-based computations are linear in the number of fractions. Using sum sampling within APM, uncertainty propagation can only be accelerated at the cost of reduced accuracy in variance calculations. For probabilistic plan optimization, we were able to approximate the necessary pre-computations within seconds, yielding treatment plans of similar quality as gained from exact uncertainty propagation. APM is suited to enhance the trade-off between speed and accuracy in uncertainty propagation and probabilistic treatment plan optimization, especially in the context of fractionation. This brings fully-fledged APM computations within reach of clinical application.

Analytical incorporation of fractionation effects in probabilistic treatment planning for intensity‐modulated proton therapy

PURPOSE We show that it is possible to explicitly incorporate fractionation effects into closed-form probabilistic treatment plan analysis and optimization for intensity-modulated proton therapy with analytical probabilistic modeling (APM). We study the impact of different fractionation schemes on the dosimetric uncertainty induced by random and systematic sources of range and setup uncertainty for treatment plans that were optimized with and without consideration of the number of treatment fractions. METHODS The APM framework is capable of handling arbitrarily correlated uncertainty models including systematic and random errors in the context of fractionation. On this basis, we construct an analytical dose variance computation pipeline that explicitly considers the number of treatment fractions for uncertainty quantitation and minimization during treatment planning. We evaluate the variance computation model in comparison to random sampling of 100 treatments for conventional and probabilistic treatment plans under different fractionation schemes (1, 5, 30 fractions) for an intracranial, a paraspinal and a prostate case. The impact of neglecting the fractionation scheme during treatment planning is investigated by applying treatment plans that were generated with probabilistic optimization for 1 fraction in a higher number of fractions and comparing them to the probabilistic plans optimized under explicit consideration of the number of fractions. RESULTS APM enables the construction of an analytical variance computation model for dose uncertainty considering fractionation at negligible computational overhead. It is computationally feasible (a) to simultaneously perform a robustness analysis for all possible fraction numbers and (b) to perform a probabilistic treatment plan optimization for a specific fraction number. The incorporation of fractionation assumptions for robustness analysis exposes a dose to uncertainty trade-off, i.e., the dose in the organs at risk is increased for a reduced fraction number and/or for more robust treatment plans. By explicit consideration of fractionation effects during planning, we demonstrate that it is possible to exploit this trade-off during optimization. APM optimization considering the fraction number reduced the dose in organs at risk compared to conventional probabilistic optimization neglecting the fraction number. CONCLUSION APM enables computationally efficient incorporation of fractionation effects in probabilistic uncertainty analysis and probabilistic treatment plan optimization. The consideration of the fractionation scheme in probabilistic treatment planning reveals the trade-off between number of fractions, nominal dose, and treatment plan robustness.

Analytical probabilistic modeling of RBE-weighted dose for ion therapy

Particle therapy is especially prone to uncertainties. This issue is usually addressed with uncertainty quantification and minimization techniques based on scenario sampling. For proton therapy, however, it was recently shown that it is also possible to use closed-form computations based on analytical probabilistic modeling (APM) for this purpose. APM yields unique features compared to sampling-based approaches, motivating further research in this context. This paper demonstrates the application of APM for intensity-modulated carbon ion therapy to quantify the influence of setup and range uncertainties on the RBE-weighted dose. In particular, we derive analytical forms for the nonlinear computations of the expectation value and variance of the RBE-weighted dose by propagating linearly correlated Gaussian input uncertainties through a pencil beam dose calculation algorithm. Both exact and approximation formulas are presented for the expectation value and variance of the RBE-weighted dose and are subsequently studied in-depth for a one-dimensional carbon ion spread-out Bragg peak. With V and B being the number of voxels and pencil beams, respectively, the proposed approximations induce only a marginal loss of accuracy while lowering the computational complexity from order [Formula: see text] to [Formula: see text] for the expectation value and from [Formula: see text] to [Formula: see text] for the variance of the RBE-weighted dose. Moreover, we evaluated the approximated calculation of the expectation value and standard deviation of the RBE-weighted dose in combination with a probabilistic effect-based optimization on three patient cases considering carbon ions as radiation modality against sampled references. The resulting global γ-pass rates (2 mm,2%) are [Formula: see text]99.15% for the expectation value and [Formula: see text]94.95% for the standard deviation of the RBE-weighted dose, respectively. We applied the derived analytical model to carbon ion treatment planning, although the concept is in general applicable to other ion species considering a variable RBE.

Schwingungen und Wellen

Wir kommen endlich zu einem Lieblingsthema vieler Physiker. Hier dreht sich alles um Vorgange, die schwingen und irgendwie periodisch sind. Dabei wird Energie standig von einer Form in eine andere umgewandelt, und zwar im Idealfall ohne Verluste. In der Praxis kommt so etwas naturlich nicht vor, aber inzwischen sollte klar sein, dass Physiker erst einmal idealisieren, um ein Problem anzugehen, und sich dann um eventuelle Abweichungen vom Idealfall kummern.

Zustandsänderungen und Kreisprozesse

Wir haben jetzt endlich alle Werkzeuge zusammen, um Zustandsanderungen zu betrachten. Dabei wollen wir sehen, wie sich Gase unter Anderungen ihrer Parameter verhalten. Wir betrachten hier ausschlieslich ideale Gase, da diese einerseits eine sehr gute Nahrung fur viele reale Gase darstellen, und weil sie durch die simple ideale Gasgleichung beschrieben werden. Eine kompliziertere Herangehensweise wurden unsere Erkenntnis nicht verbessern.

Temperatur und Wärme

Thermodynamik wird in manchen Texten auch „Warmelehre“ genannt. Es geht also viel um Temperatur und was eine Temperaturanderung in verschiedenen Stoffen oder Korpern bewirkt. Eine ganz alltagliche Erscheinung ware zum Beispiel, dass Eis ab einer gewissen Temperatur anfangt, zu schmelzen. Die Thermodynamik beschaftigt sich aber auch mit der Theorie von Gasen und z. B. damit, wie diese auf sogenannte Zustandsanderungen reagieren. Daraus ergeben sich auch ganz fundamentale Erkenntnisse, wie z. B. dass man kein Perpetuum Mobile bauen kann, also eine Maschine, die Energie aus dem „Nichts“ erzeugt. Euch sind viele Grosen der Thermodynamik aus dem Alltag bekannt: Temperatur, Druck und Volumen begegnen uns standig.

Beugung an Spalt und Gitter

Interferenzphanomene werden meist mithilfe von Spalt- oder Gitterexperimenten demonstriert. Bei diesen wird in der Regel monochromatisches (d. h. Lichtwellen gleicher Wellenlange) und koharentes Licht, heutzutage einfach durch Laser (siehe Exkurs 23.1) erzeugt, auf einen oder mehrere kleine Spaltblenden gerichtet und das Interferenzmuster auf einem Schirm hinter dem Spalt oder Gitter beobachtet. Das klingt zunachst nach einem sehr einfachen und unspektakularen Aufbau, jedoch darf man die Erkenntnisse dieser Experimente nicht unterschatzen.

Kräfte und Bewegung im Kraftfeld

Inertialsysteme, wie sie in Abschnitt 1.3 beschrieben sind, sind fur uns ganz streng genommen nicht alltaglich. Denn: Keiner von uns ist in einem Inertialsystem, wir erfahren durch die Erde standig eine Schwer- bzw.