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ABSTRACT: In this paper we look at the development of radiation therapy treatment planning from a mathematical point of view. Historically, planning for Intensity-Modulated Radiation Therapy (IMRT) has been considered as an inverse problem. We discuss first the two fundamental approaches that have been investigated to solve this inverse problem: Continuous analytic inversion techniques on one hand, and fully-discretized algebraic methods on the other hand. In the second part of the paper, we review another fundamental question which has been subject to debate from the beginning of IMRT until the present day: The rotation therapy approach versus fixed angle IMRT. This builds a bridge from historic work on IMRT planning to contemporary research in the context of Intensity-Modulated Arc Therapy (IMAT).
Physica Medica 05/2011; 28(2):109-18. · 1.07 Impact Factor
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ABSTRACT: The purpose of this work is to investigate robust 4D optimization techniques which account for respiratory motion uncertainties. Two robust optimization techniques were applied to generate 4D optimized lung treatment plans. The probabilistic optimization approach minimizes the dose variance in the target volume while the worst case optimization minimizes a weighted combination of the nominal and worst case dose distributions which occur in the presence of respiratory motion variation. The two 4D optimization approaches were compared with a margin-based midventilation planning approach in five lung patients. Respiratory motion amplitude and baseline variations were quantified from tidal volume measurements during planning 4D CT acquisition. A similar target coverage was obtained for all three approaches, although the 4D optimization methods tended to be better at sparing the organs at risk. Both robust planning methods are suited for automatic determination of treatment plans which ensure target dose conformality under respiratory motion variations, while minimizing the dose burden of healthy lung tissue.
Medical Physics 08/2009; 36(7):3059-71. · 2.83 Impact Factor
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ABSTRACT: Treatment plans optimized for intensity modulated proton therapy (IMPT) may be very sensitive to setup errors and range uncertainties. If these errors are not accounted for during treatment planning, the dose distribution realized in the patient may by strongly degraded compared to the planned dose distribution. The authors implemented the probabilistic approach to incorporate uncertainties directly into the optimization of an intensity modulated treatment plan. Following this approach, the dose distribution depends on a set of random variables which parameterize the uncertainty, as does the objective function used to optimize the treatment plan. The authors optimize the expected value of the objective function. They investigate IMPT treatment planning regarding range uncertainties and setup errors. They demonstrate that incorporating these uncertainties into the optimization yields qualitatively different treatment plans compared to conventional plans which do not account for uncertainty. The sensitivity of an IMPT plan depends on the dose contributions of individual beam directions. Roughly speaking, steep dose gradients in beam direction make treatment plans sensitive to range errors. Steep lateral dose gradients make plans sensitive to setup errors. More robust treatment plans are obtained by redistributing dose among different beam directions. This can be achieved by the probabilistic approach. In contrast, the safety margin approach as widely applied in photon therapy fails in IMPT and is neither suitable for handling range variations nor setup errors.
Medical Physics 02/2009; 36(1):149-63. · 2.83 Impact Factor
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ABSTRACT: Developments in radiotherapy treatment planning and optimization by medical physicists and the American Association of Physicists in Medicine are reviewed, with emphasis on recent work in optimization. It is shown that medical physicists have played a vital role in the creation of innovative treatment planning techniques throughout the past century, most significantly since the advent of computerized tomography for three-dimensional (3D) imaging and high-powered computers capable of 3D planning and optimization. Some early advances in 3D planning made by physicists include development of novel planning algorithms, beam's-eye-view, virtual simulation, dose-volume histogram analysis tools, and bioeffect modeling. Most of the recent developments have been driven by the need to develop treatment planning for conformal radiotherapy, especially intensity modulated radiation therapy. These advances include inverse planning, handling the effects of motion and uncertainty, biological planning, and multicriteria optimization.
Medical Physics 12/2008; 35(11):4911-23. · 2.83 Impact Factor
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ABSTRACT: Treatment plans optimized for intensity modulated proton therapy (IMPT) may be sensitive to range variations. The dose distribution may deteriorate substantially when the actual range of a pencil beam does not match the assumed range. We present two treatment planning concepts for IMPT which incorporate range uncertainties into the optimization. The first method is a probabilistic approach. The range of a pencil beam is assumed to be a random variable, which makes the delivered dose and the value of the objective function a random variable too. We then propose to optimize the expectation value of the objective function. The second approach is a robust formulation that applies methods developed in the field of robust linear programming. This approach optimizes the worst case dose distribution that may occur, assuming that the ranges of the pencil beams may vary within some interval. Both methods yield treatment plans that are considerably less sensitive to range variations compared to conventional treatment plans optimized without accounting for range uncertainties. In addition, both approaches--although conceptually different--yield very similar results on a qualitative level.
Physics in Medicine and Biology 06/2007; 52(10):2755-73. · 2.83 Impact Factor
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ABSTRACT: For intensity modulated radiotherapy (IMRT) of deep-seated tumours, dosimetric variations of the original static dose profiles due to breathing motion can be primarily considered as blurring effects known from conventional radiotherapy. The purpose of this dosimetric study was to clarify whether these results are transferable to superficial targets and to quantify the additional effect of fractionation. A solid polystyrene phantom and an anthropomorphic phantom were used for film and ion chamber dose measurements. The phantoms were installed on an electric driven device and moved with a frequency of 6 or 12 cycles per minute and an amplitude of 4 mm or 10 mm. A split beam geometry of two adjacent asymmetric fields and an IMRT treatment plan with 12 fields for irradiation of the breast were investigated. For the split beam geometry the dose modifications due to unintended superposition of partial fields were reduced by fractionation and completely smoothed out after 20 fractions. IMRT applied to the moving phantom led to a more homogeneous dose distribution compared to the static phantom. The standard deviation of the target dose which is a measure of the dose homogeneity was 10.3 cGy for the static phantom and 7.7 cGy for a 10 mm amplitude. The absolute dose values, measured with ionization chambers, remained unaffected. Irradiation of superficial targets by IMRT in the step-and-shoot technique did not result in unexpected dose perturbations due to breathing motion. We conclude that regular breathing motion does not jeopardize IMRT of superficial target volumes.
Physics in Medicine and Biology 04/2006; 51(6):N117-26. · 2.83 Impact Factor
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ABSTRACT: One aim of adaptive radiotherapy (ART) is the observation of organ motion followed by a subsequent adaptation of the treatment plan. One way of achieving this goal is a kV x-ray source mounted at a linear accelerator in combination with a flat-panel imager. Two imaging hardware configurations were evaluated for their potential for online tracking and the subsequent correction of organ motion by using fluoroscopic images: x-ray tube positioned with (A) 90 degrees and (B) 180 degrees offset to the MV beam. For one lung case two IMRT plans with five coplanar beams and the table positioned at 0 degrees were optimized for two multileaf collimators (MLCs) with 10 mm and 2.75 mm leaf width. Respiratory motion, modelled by rigid transformation in the lungs, was investigated for different amplitudes. The 3D dose distributions for different cases (no movement, uncorrected movement, correction for the movement perpendicular to the respective kV beam) were evaluated with the help of dose volume histograms (DVHs) and a modified conformity (Baltas et al 1998 Int. J. Radiat. Oncol. Biol. Phys. 40 515-24) and coverage index using the 90% isodose. For the corrected treatment plans the influence of the observed displacement vector caused by organ movement was accounted for by a respective displacement of the target point. For the simulated movement with a small amplitude (3 mm) in the anterior-posterior (AP) direction the dose distributions resulting from the correction of the displacement vector using imaging system A or B showed similar results for both systems and were in good agreement with the dose distribution of the static (not moving) patient. Increasing the amplitude in the AP direction to 6 mm or even 9 mm leads for both amplitudes and both MLCs to almost the same conformity and coverage index as the static dose distribution if imaging system B is used for the online correction. For the dose distribution obtained with correction based on imaging system A the deviation between the optimal and the corrected dose distribution is increasing with increasing amplitude. For the MLC with the smaller leaf width the difference between the optimal and the corrected dose distributions is always significantly larger than for the less conformal dose distributions created by the MLC with the 10 mm leaves. These results can be explained by the fact that system A cannot observe movement in the AP-LR plane perpendicular to the MV beam and therefore cannot correct for these movements whereas system B only fails to observe the motion in the beam direction which for photon irradiation has less impact on the dose distribution.
Physics in Medicine and Biology 10/2005; 50(17):4087-96. · 2.83 Impact Factor
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ABSTRACT: We investigate an off-line strategy to incorporate inter fraction organ movements in IMRT treatment planning. Nowadays, imaging modalities located in the treatment room allow for several CT scans of a patient during the course of treatment. These multiple CT scans can be used to estimate a probability distribution of possible patient geometries. This probability distribution can subsequently be used to calculate the expectation value of the delivered dose distribution. In order to incorporate organ movements into the treatment planning process, it was suggested that inverse planning could be based on that probability distribution of patient geometries instead of a single snapshot. However, it was shown that a straightforward optimization of the expectation value of the dose may be insufficient since the expected dose distribution is related to several uncertainties: 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 order to obtain a robust treatment plan these uncertainties should be considered and minimized in the inverse planning process. In the current paper, we calculate a 3D variance distribution in addition to the expectation value of the dose distribution which are simultaneously optimized. The variance is used as a surrogate to quantify the associated risks of a treatment plan. The feasibility of this approach is demonstrated for clinical data of prostate patients. Different scenarios of dose expectation values and corresponding variances are discussed.
Medical Physics 09/2005; 32(8):2471-83. · 2.83 Impact Factor
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Jan Unkelbach
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ABSTRACT: Die vorliegende Arbeit beschreibt ein Verfahren zur Berücksichtigung von Organbewegungen in der Bestrahlungsplanung für die fraktionierte intensitätsmodulierte Strahlentherapie (IMRT). Organbewegungen werden durch ein mathematisches Modell beschrieben welches die Grundlage der Bestrahlungsplan-Optimierung darstellt. Das Modell enthält Zufallsvariablen um die stochastische Natur von Organbewegungen zu beschreiben. Die vorausgesagte Dosisverteilung im Patienten muss daher ebenfalls als Zufallsvariable aufgefasst werden und wird durch einen Erwartungswert der Dosis und dessen Varianz charakterisiert. Zur Optimierung des Bestrahlungsplans unter Berücksichtigung des Bewegungsmodells wird der Erwartungswert einer quadratischen Kostenfunktion minimiert, der sich als Summe der Dosisvarianz und der quadratischen Differenz von Solldosis und Erwartungswert der Dosis darstellen lässt. Die daraus resultierenden Bestrahlungspläne haben die Eigenschaft, dass Bereiche in denen Tumorgewebe nur relativ selten lokalisiert ist mit einer geringeren Dosis bestrahlt werden. Dies wird ausgeglichen durch eine Dosisüberhöhung in benachbarten Bereichen, so dass sich durch den Einfluss der Bewegung im Verlauf der gesamten Therapie eine näherungsweise homogene Gesamtdosisverteilung im Tumor ergibt. Das Verfahren erlaubt eine potentiell bessere Schonung von angrenzenden gesunden Geweben im Vergleich zur Sicherheitsrand-Methode. The presented thesis describes an off-line approach to incorporate organ motion into the treatment plan optimization for fractionated intensity modulated radiotherapy (IMRT). Organ movement is described in terms of a mathematical model that represents the basis of the treatment plan optimization process. The motion model contains random variables in order to describe the stochastic nature of organ movements. As a consequence, the predicted dose distribution in the patient must be considered as a random variable as well. It is characterized by the expectation value and the variance of the dose. For treatment plan optimization incorporating the motion model, the expectation value of a quadratic cost function is minimized, which can be expressed as the sum of the variance of the dose and the quadratic difference of expected and prescribed dose. The resulting treatment plans show a reduction of the dose in regions where tumor tissue is only rarely present. This is compensated for by delivering a higher dose to neighboring regions that are mostly occupied by tumor tissue. Due to organ movement during the course of treatment, a widely homogeneous cumulative dose distribution is delivered to the tumor. This method, compared to the standard safety margin approach, potentially allows for a better sparing of healthy tissues from dose burden.
