A linear programming approach to inverse planning in Gamma Knife radiosurgery

Sjölund, Jens; Riad, Stella; Hennix, M.; Nordström, Håkan

doi:10.1002/mp.13440

Cited by 32 publications

(76 citation statements)

References 57 publications

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“…The average dose deviation of our dose calculation from the LGP system was~0.8%. 21 In terms of the optimization model to be used in the MRL framework in our study, we chose the linear programming model proposed by Nordstr € o m H, which was originally developed for sector duration optimization, 14 since it was reported in a recent study that linear programming tended to yield shorter beam-on time than convex quadratic penalty approaches and convex moment-based approaches. 23 The objective function that is used at each round of optimization but with different sets of isocenter candidates is formulated as…”

Section: B Methods Of Our Choicementioning

confidence: 99%

“…This objective function can be expressed as a linear programming problem by introducing auxiliary variables. 14 The dual simplex algorithm was employed in our study to solve this linear programming problem. 24,25 After the optimization phase, sectors with nonzero beam-on time at a same isocenter need to be grouped into composite shots for delivery.…”

Section: B Methods Of Our Choicementioning

confidence: 99%

“…In terms of the optimization model to be used in the MRL framework in our study, we chose the linear programming model proposed by Nordstr

\overset{o}{true}

m H, which was originally developed for sector duration optimization, since it was reported in a recent study that linear programming tended to yield shorter beam‐on time than convex quadratic penalty approaches and convex moment‐based approaches . The objective function that is used at each round of optimization but with different sets of isocenter candidates is formulated as

\begin{matrix} {minimize}_{t} & \frac{ω_{TH}}{N_{T}} \sum_{i \in I_{T}} truemax ()(, D_{i} - D_{TH}, 0) + \frac{ω_{TL}}{N_{T}} \sum_{i \in I_{T}} truemax ()(, D_{TL} - D_{i}, 0) \\ + \frac{ω_{IS}}{N_{IS}} \sum_{i \in I_{italicIS}} truemax ()(, D_{i} - D_{IS}, 0) + \frac{ω_{OS}}{N_{OS}} \sum_{i \in I_{italicOS}} truemax ()(, D_{i} - D_{OS}, 0) \\ + \frac{ω_{O}}{N_{O}} \sum_{i \in I_{O}} truemax ()(, D_{i} - D_{O}, 0) \\ + ω_{italicBOT} \sum_{n = 1}^{N} {truemax}_{m = 1, 2, . ., 8} (\sum_{c = 1}^{3} t ()(, c, m, n)), \end{matrix}

subject t o t \geq 0

here,

t

is the be...…”

Section: Methodsmentioning

confidence: 99%

“…15 To address this issue, a sequential planning strategy has been employed by most of the existing GK inverse planning algorithms, including the inverse planning algorithm provided in the prevailing commercial treatment planning system for the Leksell GK units, named Leksell GammaPlan (LGP, Elekta Instrument AB Stockholm, Stockholm, Sweden). 11,13,14,[16][17][18][19] Specifically, isocenter locations are predetermined using a grassfire and sphere-packing (GSP) algorithm or some other geometric methods based on the geometry of the treatment targets. 13,16,18 Then, the shot shapes and durations are optimized at these predetermined locations to achieve a good dose distribution.…”

Section: Introductionmentioning

confidence: 99%

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A preliminary study on a multiresolution‐level inverse planning approach for Gamma Knife radiosurgery

et al. 2020

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Purpose: With many plan variables to determine, manual forward planning for Gamma Knife (GK) radiosurgery is very challenging. Inverse planning eases GK planning by determining the variables via solving an optimization problem. However, due to the vast search space, most inverse planning algorithms, including the one provided in Leksell GammaPlan (LGP) treatment planning system, have to predetermine the isocenter locations using some geometric methods and then optimize the shot shapes and durations at these preselected isocenters. This sequential planning scheme does not necessarily lead to optimal isocenter locations and hence globally optimal plans. In this study, we proposed a multiresolution-level (MRL) inverse planning approach, attempting to approach this large-scale GK optimization problem via an iterative method. Methods: In our MRL approach, several rounds of optimizations were performed with a progressively increased resolution used for isocenter candidates. At each round, an optimization problem was solved to optimize the beam-on time for each collimator and sector at each isocenter candidate. The isocenters that obtained nonzero beam-on times at the previous round and their neighbors on a finer resolution were used as new isocenter candidates for the next round of optimization. After plan optimization, shot sequencing was performed to group the optimized sectors to deliverable composite shots. Results: We have tested our MRL approach on six GK cases previously treated in our institution. For the five cases that have a single target, with similar target coverage obtained, our MRL inverse planning approach achieved better plan quality compared to manual forward planning and LGP inverse planning, with higher selectivity (0.73 AE 0.07 vs 0.72 AE 0.08 and 0.62 AE 0.10), lower gradient index (2.71 AE 0.25 vs 2.78 AE 0.24 and 3.00 AE 0.29), lower brainstem D 0.1cc dose (6.10 AE 4.46 Gy vs 8.87 AE 4.82 Gy and 9.17 AE 3.80 Gy), and shorter total beam-on time (62.1 AE 22.9 min vs 83.6 AE 28.2 min and 70.7 AE 16.7 min). For the case that have six targets, compared with manual planning and LGP inverse planning, our MRL approach achieved higher selectivity (0.68 vs 0.57 and 0.47) and lower gradient index (3.77 vs 4.51 and 5.11). The beam-on time of our plan was slightly longer than manual planning and LGP inverse planning (206.4 min vs 204.7 min and 199.3 min). We have also performed sector duration optimization at the isocenters determined by manual planning or the LGP inverse planning, and the resulting plan qualities were found to be inferior to our MRL approach for all the six cases. Conclusions: This preliminary study has demonstrated the efficacy and feasibility of our MRL inverse planning approach for GK radiosurgery.

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Section: B Methods Of Our Choicementioning

confidence: 99%

Section: B Methods Of Our Choicementioning

confidence: 99%

“…In terms of the optimization model to be used in the MRL framework in our study, we chose the linear programming model proposed by Nordstr

\overset{o}{true}

\begin{matrix} {minimize}_{t} & \frac{ω_{TH}}{N_{T}} \sum_{i \in I_{T}} truemax ()(, D_{i} - D_{TH}, 0) + \frac{ω_{TL}}{N_{T}} \sum_{i \in I_{T}} truemax ()(, D_{TL} - D_{i}, 0) \\ + \frac{ω_{IS}}{N_{IS}} \sum_{i \in I_{italicIS}} truemax ()(, D_{i} - D_{IS}, 0) + \frac{ω_{OS}}{N_{OS}} \sum_{i \in I_{italicOS}} truemax ()(, D_{i} - D_{OS}, 0) \\ + \frac{ω_{O}}{N_{O}} \sum_{i \in I_{O}} truemax ()(, D_{i} - D_{O}, 0) \\ + ω_{italicBOT} \sum_{n = 1}^{N} {truemax}_{m = 1, 2, . ., 8} (\sum_{c = 1}^{3} t ()(, c, m, n)), \end{matrix}

subject t o t \geq 0

here,

t

is the be...…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A preliminary study on a multiresolution‐level inverse planning approach for Gamma Knife radiosurgery

et al. 2020

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“…The Inverse Planning (IP) technique for GK SRS was proposed by multiple groups [1][2][3][4] and was not commercially available until Elekta released the GammaPlan® version 10.0 in 2010 [5]. The IP feature allowed the users to iteratively optimize desired target dose.…”

Section: Introductionmentioning

confidence: 99%

Tuning-Target-Guided Inverse Planning of Brain Tumors With Abutting Organs at Risk During Gamma Knife Stereotactic Radiosurgery

Xu¹,

Kubicek

Mulvihill

et al. 2020

Cureus

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Evaluating the impact of prescription isodose line on plan quality using Gamma Knife inverse planning

Kubicek²,

Mulvihill³

et al. 2021

J Applied Clin Med Phys

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The impact of selection of prescription isodose line (IDL) on plan quality has not been well evaluated during inverse planning (IP). In this study, a total of 180 IP plans at five levels of IDL were generated for 30 brain metastases (BMs). For each BM, one round of IP was performed with typical IP settings, followed by a quick fine‐tuning to ensure the same target coverage and comparable conformality index. The impact of the IDL on the quality metrics (selectivity, gradient index [GI], and treatment time) was evaluated. The decrease of selectivity and increase of GI meant inferior target dose conformality and more dose spillage. Additionally, a metric directly correlated to the treatment time was proposed. For all cases, the mean GI decreased monotonically as IDL decreased from 70% to 30%, and the decreasing rate was significantly different based on tumor size. The mean selectivity and number of shots decreased monotonically as IDL decreased for all the tumors. From 70% to 30% IDL, the decreasing rate of the mean selectivity was 2.8% (p = 0.020), 7.7% (p = 0.005), and 15.4% (p = 0.020) and that of the number of shots was 75.4% (p = 0.001), 73.2% (p = 0.001), and 50.7% (p = 0.009), for the large, medium, and small tumors, respectively. For the medium and small tumor groups, the mean treatment time increased monotonically when IDLs decreased (increasing rate was 80.0% [p = 0.002] for medium tumors [p = 0.001] and 130.8% [p = 0.001] for small tumors from 70% to 30%). For the large tumors, the mean treatment time was the shortest at 50% IDL (59.0 min) and higher at 70% (65.9 min) and 30% (71.9 min). Overall, the GammaPlan chose smaller sectors for plans with lower IDLs except for the large size group.

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A linear programming approach to inverse planning in Gamma Knife radiosurgery

Cited by 32 publications

References 57 publications

A preliminary study on a multiresolution‐level inverse planning approach for Gamma Knife radiosurgery

A preliminary study on a multiresolution‐level inverse planning approach for Gamma Knife radiosurgery

Tuning-Target-Guided Inverse Planning of Brain Tumors With Abutting Organs at Risk During Gamma Knife Stereotactic Radiosurgery

Evaluating the impact of prescription isodose line on plan quality using Gamma Knife inverse planning

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