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

Wieser, Hans-Peter; Cisternas, Eduardo; Wahl, Niklas; Ulrich, Silke; Stadler, Alexander; Mescher, Henning; Müller, Lucas-Raphael; Klinge, Thomas; Gabryś, Hubert S.; Burigo, Lucas; Mairani, A.; Ecker, Swantje; Ackermann, B.; Ellerbrock, M.; Parodi, Katia; Jäkel, Oliver; Bangert, Mark

doi:10.1002/mp.12251

Cited by 228 publications

(256 citation statements)

References 38 publications

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“…Numerous DAO algorithms convert the plan's MLC positions,

\overset{l}{true}

, and aperture intensity,

\overset{w}{true}

, into equivalent fluence maps,

\overset{false\to}{τ} (\overset{false\to}{l}, \overset{false\to}{w})

, so that the precalculated pencil‐beam dose matrix, d , can continue to be used during optimization, to compute the objective function value and its gradient vector . One method of converting the aperture parameters into equivalent fluence maps is through the following approximate relationship:

τ_{j} (\overset{false\to}{l}, \overset{false\to}{w}) \approx \underset{ν}{false\sum} T_{j ν} (\overset{l}{true}) w_{ν},

where w ν is the intensity of aperture ν , and

T_{j ν} false(\overset{l}{true} false)

is a non‐convex piecewise linear function describing the fractional transmission through pencil‐beam j by aperture ν . An illustration of this transmission matrix is shown in Fig.…”

Section: Methodsmentioning

confidence: 99%

“…) and we can use the following piecewise approximation when evaluating Eq. () for each leaf in each aperture,

\begin{matrix} \frac{\partial {bold-italicT}_{μ j}^{T} (\overset{false\to}{l})}{\partial l_{k}^{false(μ false)}} \\ = \{\begin{matrix} \pm \frac{1}{h_{italicpb}}, & l e a f k o f a p e r t u r e μ (l_{k}^{(μ)}) c o i n c i d e s w i t h p e n c i l b e a m j \\ 0, & otherwise \end{matrix} \end{matrix}

with h pb being the width of the pencil beams. The sign (±) of this piecewise function will depend on whether the differentiated leaf k is a member of the left or right leaf bank, and whether a change in its position in the positive direction of motion will lead to the coinciding pencil‐beam becoming more exposed or blocked.…”

Section: Methodsmentioning

confidence: 99%

“…), the leaf will be considered to coincide with the pencil beam on the right unless the leaf is on the right boundary of the calculated pencil beam array (e.g., the leaf on the edge of pencil beam 16 in Fig. ) in which case it will be considered to coincide with the pencil beam on the left …”

Section: Methodsmentioning

confidence: 99%

“…Often a treatment plan must satisfy a variety of clinical dose–volume objectives such as a minimum PTV dose or a maximum dose to some volume of an OAR. Dose–volume objectives are typically included as a separate term in the objective function, such as the following for a minimum PTV dose objective:

\begin{matrix} f_{m i n - d v h}^{()(, italicptv)} (\overset{τ}{true}) \\ = p_{ptv} \underset{x \in P T V}{false\sum} Θ (d_{\min} - \underset{i}{false\sum} d_{xi} τ_{i}) {()(, d_{italicmin} - \sum_{i} {bold-italicd}_{italicxi} τ_{i})}^{2}, \end{matrix}

where Θ is the Heaviside function and d min is the minimum threshold dose . Note that a similar equation is used for maximum dose objectives in the PTV and OARs.…”

Section: Methodsmentioning

confidence: 99%

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A fast inverse direct aperture optimization algorithm for intensity‐modulated radiation therapy

et al. 2019

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Purpose The goal of this work was to develop and evaluate a fast inverse direct aperture optimization (FIDAO) algorithm for IMRT treatment planning and plan adaptation. Methods A previously proposed fluence map optimization algorithm called fast inverse dose optimization (FIDO) was extended to optimize the aperture shapes and weights of IMRT beams. FIDO is a very fast fluence map optimization algorithm for IMRT that finds the global minimum using direct matrix inversion without unphysical negative beam weights. In this study, an equivalent second‐order Taylor series expansion of the FIDO objective function was used, which allowed for the objective function value and gradient vector to be computed very efficiently during direct aperture optimization, resulting in faster optimization. To evaluate the speed gained with FIDAO, a proof‐of‐concept algorithm was developed in MATLAB using an interior‐point optimization method to solve the reformulated aperture‐based FIDO problem. The FIDAO algorithm was used to optimize four step‐and‐shoot IMRT cases: on the AAPM TG‐119 phantom as well as a liver, prostate, and head‐and‐neck clinical cases. Results were compared with a conventional DAO algorithm that uses the same interior‐point method but using the standard formulation of the objective function and its gradient vector. Results A substantial gain in optimization speed was obtained with the prototype FIDAO algorithm compared to the conventional DAO algorithm while producing plans of similar quality. The optimization time (number of iterations) for the prototype FIDAO algorithm vs the conventional DAO algorithm was 0.3 s (17) vs 56.7 s (50); 2.0 s (28) vs 134.1 s (57); 2.5 s (26) vs 180.6 s (107); and 6.7 s (20) vs 469.4 s (482) in the TG‐119 phantom, liver, prostate, and head‐and‐neck examples, respectively. Conclusions A new direct aperture optimization algorithm based on FIDO was developed. For the four IMRT test cases examined, this algorithm executed approximately 70–200 times faster without compromising the IMRT plan quality.

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“…Numerous DAO algorithms convert the plan's MLC positions,

\overset{l}{true}

, and aperture intensity,

\overset{w}{true}

, into equivalent fluence maps,

\overset{false\to}{τ} (\overset{false\to}{l}, \overset{false\to}{w})

τ_{j} (\overset{false\to}{l}, \overset{false\to}{w}) \approx \underset{ν}{false\sum} T_{j ν} (\overset{l}{true}) w_{ν},

where w ν is the intensity of aperture ν , and

T_{j ν} false(\overset{l}{true} false)

is a non‐convex piecewise linear function describing the fractional transmission through pencil‐beam j by aperture ν . An illustration of this transmission matrix is shown in Fig.…”

Section: Methodsmentioning

confidence: 99%

“…) and we can use the following piecewise approximation when evaluating Eq. () for each leaf in each aperture,

\begin{matrix} \frac{\partial {bold-italicT}_{μ j}^{T} (\overset{false\to}{l})}{\partial l_{k}^{false(μ false)}} \\ = \{\begin{matrix} \pm \frac{1}{h_{italicpb}}, & l e a f k o f a p e r t u r e μ (l_{k}^{(μ)}) c o i n c i d e s w i t h p e n c i l b e a m j \\ 0, & otherwise \end{matrix} \end{matrix}

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

\begin{matrix} f_{m i n - d v h}^{()(, italicptv)} (\overset{τ}{true}) \\ = p_{ptv} \underset{x \in P T V}{false\sum} Θ (d_{\min} - \underset{i}{false\sum} d_{xi} τ_{i}) {()(, d_{italicmin} - \sum_{i} {bold-italicd}_{italicxi} τ_{i})}^{2}, \end{matrix}

where Θ is the Heaviside function and d min is the minimum threshold dose . Note that a similar equation is used for maximum dose objectives in the PTV and OARs.…”

Section: Methodsmentioning

confidence: 99%

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A fast inverse direct aperture optimization algorithm for intensity‐modulated radiation therapy

et al. 2019

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“…For every patient, the same beam arrangement, scanning spot population scheme, and dose calculation engine were used for the three methods. The dose calculation for all scanning spots covering the CTV and a 5‐mm margin was performed by matRad, a MATLAB‐based three‐dimensional (3D) treatment planning toolkit. The dose calculation resolution was 2.5× 2.5× 2.5 mm.…”

Section: Methodsmentioning

confidence: 99%

Robust optimization for intensity‐modulated proton therapy with soft spot sensitivity regularization

Ruan

O’Connor

et al. 2019

Medical Physics

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Purpose Proton dose distribution is sensitive to uncertainties in range estimation and patient positioning. Currently, the proton robustness is managed by worst‐case scenario optimization methods, which are computationally inefficient. To overcome these challenges, we develop a novel intensity‐modulated proton therapy (IMPT) optimization method that integrates dose fidelity with a sensitivity term that describes dose perturbation as the result of range and positioning uncertainties. Methods In the integrated optimization framework, the optimization cost function is formulated to include two terms: a dose fidelity term and a robustness term penalizing the inner product of the scanning spot sensitivity and intensity. The sensitivity of an IMPT scanning spot to perturbations is defined as the dose distribution variation induced by range and positioning errors. To evaluate the sensitivity, the spatial gradient of the dose distribution of a specific spot is first calculated. The spot sensitivity is then determined by the total absolute value of the directional gradients of all affected voxels. The fast iterative shrinkage‐thresholding algorithm is used to solve the optimization problem. This method was tested on three skull base tumor (SBT) patients and three bilateral head‐and‐neck (H&N) patients. The proposed sensitivity‐regularized method (SenR) was implemented on both clinic target volume (CTV) and planning target volume (PTV). They were compared with conventional PTV‐based optimization method (Conv) and CTV‐based voxel‐wise worst‐case scenario optimization approach (WC). Results Under the nominal condition without uncertainties, the three methods achieved similar CTV dose coverage, while the CTV‐based SenR approach better spared organs at risks (OARs) compared with the WC approach, with an average reduction of [Dmean, Dmax] of [4.72, 3.38] GyRBE for the SBT cases and [2.54, 3.33] GyRBE for the H&N cases. The OAR sparing of the PTV‐based SenR method was comparable with the WC method. The WC method, and SenR approaches all improved the plan robustness from the conventional PTV‐based method. On average, under range uncertainties, the lowest [D95%, V95%, V100%] of CTV were increased from [93.75%, 88.47%, 47.37%] in the Conv method, to [99.28%, 99.51%, 86.64%] in the WC method, [97.71%, 97.85%, 81.65%] in the SenR‐CTV method and [98.77%, 99.30%, 85.12%] in the SenR‐PTV method, respectively. Under setup uncertainties, the average lowest [D95%, V95%, V100%] of CTV were increased from [95.35%, 94.92%, 65.12%] in the Conv method, to [99.43%, 99.63%, 87.12%] in the WC method, [96.97%, 97.13%, 77.86%] in the SenR‐CTV method, and [98.21%, 98.34%, 83.88%] in the SenR‐PTV method, respectively. The runtime of the SenR optimization is eight times shorter than that of the voxel‐wise worst‐case method. Conclusion We developed a novel computationally efficient robust optimization method for IMPT. The robustness is calculated as the spot sensitivity to both range and shift perturbations. The dose fidelity term is then regularized b...

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The dosimetric impact of stabilizing spinal implants in radiotherapy treatment planning with protons and photons: standard titanium alloy vs. radiolucent carbon‐fiber‐reinforced PEEK systems

Müller

Ryang

Oechsner

et al. 2020

J Applied Clin Med Phys

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Background: Throughout the last years, carbon-fibre-reinforced PEEK (CFP) pedicle screw systems were introduced to replace standard titanium alloy (Ti) implants for spinal instrumentation, promising improved radiotherapy (RT) treatment planning accuracy. We compared the dosimetric impact of both implants for intensity modulated proton (IMPT) and volumetric arc photon therapy (VMAT), with the focus on uncertainties in Hounsfield unit assignment of titanium alloy. Methods: Retrospective planning was performed on CT data of five patients with Ti and five with CFP implants. Carbon-fibre-reinforced PEEK systems comprised radiolucent pedicle screws with thin titanium-coated regions and titanium tulips. For each patient, one IMPT and one VMAT plan were generated with a nominal relative stopping power (SP) (IMPT) and electron density (ρ) (VMAT) and recalculated onto the identical CT with increased and decreased SP or ρ by AE6% for the titanium components. Results: Recalculated VMAT dose distributions hardly deviated from the nominal plans for both screw types. IMPT plans resulted in more heterogeneous target coverage, measured by the standard deviation σ inside the target, which increased on average by 7.6 AE 2.3% (Ti) vs 3.4 AE 1.2% (CFP). Larger SPs lead to lower target minimum doses, lower SPs to higher dose maxima, with a more pronounced effect for Ti screws. Conclusions: While VMAT plans showed no relevant difference in dosimetric quality between both screw types, IMPT plans demonstrated the benefit of CFP screws through a smaller dosimetric impact of CT-value uncertainties compared to Ti. Reducing metal components in implants will therefore improve dose calculation accuracy and lower the risk for tumor underdosage.

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

Cited by 228 publications

References 38 publications

A fast inverse direct aperture optimization algorithm for intensity‐modulated radiation therapy

A fast inverse direct aperture optimization algorithm for intensity‐modulated radiation therapy

Robust optimization for intensity‐modulated proton therapy with soft spot sensitivity regularization

The dosimetric impact of stabilizing spinal implants in radiotherapy treatment planning with protons and photons: standard titanium alloy vs. radiolucent carbon‐fiber‐reinforced PEEK systems

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