Dynamically accumulated dose and 4D accumulated dose for moving tumors

Heng Li, Yupeng Li, Xiaodong Zhang, Xiaoqiang Li, Wei Liu, Michael T. Gillin, X. Ronald Zhu

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

Purpose: The purpose of this work was to investigate the relationship between dynamically accumulated dose (dynamic dose) and 4D accumulated dose (4D dose) for irradiation of moving tumors, and to quantify the dose uncertainty induced by tumor motion. Methods: The authors established that regardless of treatment modality and delivery properties, the dynamic dose will converge to the 4D dose, instead of the 3D static dose, after multiple deliveries. The bounds of dynamic dose, or the maximum estimation error using 4D or static dose, were established for the 4D and static doses, respectively. Numerical simulations were performed (1) to prove the principle that for each phase, after multiple deliveries, the average number of deliveries for any given time converges to the total number of fractions (K) over the number of phases (N); (2) to investigate the dose difference between the 4D and dynamic doses as a function of the number of deliveries for deliveries of a pulsed beam; and (3) to investigate the dose difference between 4D dose and dynamic doses as a function of delivery time for deliveries of a continuous beam. A Poisson model was developed to estimate the mean dose error as a function of number of deliveries or delivered time for both pulsed beam and continuous beam. Results: The numerical simulations confirmed that the number of deliveries for each phase converges to KN, assuming a random starting phase. Simulations for the pulsed beam and continuous beam also suggested that the dose error is a strong function of the number of deliveries andor total deliver time and could be a function of the breathing cycle, depending on the mode of delivery. The Poisson model agrees well with the simulation. Conclusions: Dynamically accumulated dose will converge to the 4D accumulated dose after multiple deliveries, regardless of treatment modality. Bounds of the dynamic dose could be determined using quantities derived from 4D doses, and the mean dose difference between the dynamic dose and 4D dose as a function of number of deliveries andor total deliver time was also established.

Original languageEnglish (US)
Pages (from-to)7359-7367
Number of pages9
JournalMedical Physics
Volume39
Issue number12
DOIs
StatePublished - Dec 2012
Externally publishedYes

Fingerprint

Neoplasms
Uncertainty
Respiration

Keywords

  • 4D CT
  • 4D planning
  • interplay effect

ASJC Scopus subject areas

  • Biophysics
  • Radiology Nuclear Medicine and imaging

Cite this

Li, H., Li, Y., Zhang, X., Li, X., Liu, W., Gillin, M. T., & Zhu, X. R. (2012). Dynamically accumulated dose and 4D accumulated dose for moving tumors. Medical Physics, 39(12), 7359-7367. https://doi.org/10.1118/1.4766434

Dynamically accumulated dose and 4D accumulated dose for moving tumors. / Li, Heng; Li, Yupeng; Zhang, Xiaodong; Li, Xiaoqiang; Liu, Wei; Gillin, Michael T.; Zhu, X. Ronald.

In: Medical Physics, Vol. 39, No. 12, 12.2012, p. 7359-7367.

Research output: Contribution to journalArticle

Li, H, Li, Y, Zhang, X, Li, X, Liu, W, Gillin, MT & Zhu, XR 2012, 'Dynamically accumulated dose and 4D accumulated dose for moving tumors', Medical Physics, vol. 39, no. 12, pp. 7359-7367. https://doi.org/10.1118/1.4766434
Li, Heng ; Li, Yupeng ; Zhang, Xiaodong ; Li, Xiaoqiang ; Liu, Wei ; Gillin, Michael T. ; Zhu, X. Ronald. / Dynamically accumulated dose and 4D accumulated dose for moving tumors. In: Medical Physics. 2012 ; Vol. 39, No. 12. pp. 7359-7367.
@article{6f79f09b20ed411c8875ea5da572980b,
title = "Dynamically accumulated dose and 4D accumulated dose for moving tumors",
abstract = "Purpose: The purpose of this work was to investigate the relationship between dynamically accumulated dose (dynamic dose) and 4D accumulated dose (4D dose) for irradiation of moving tumors, and to quantify the dose uncertainty induced by tumor motion. Methods: The authors established that regardless of treatment modality and delivery properties, the dynamic dose will converge to the 4D dose, instead of the 3D static dose, after multiple deliveries. The bounds of dynamic dose, or the maximum estimation error using 4D or static dose, were established for the 4D and static doses, respectively. Numerical simulations were performed (1) to prove the principle that for each phase, after multiple deliveries, the average number of deliveries for any given time converges to the total number of fractions (K) over the number of phases (N); (2) to investigate the dose difference between the 4D and dynamic doses as a function of the number of deliveries for deliveries of a pulsed beam; and (3) to investigate the dose difference between 4D dose and dynamic doses as a function of delivery time for deliveries of a continuous beam. A Poisson model was developed to estimate the mean dose error as a function of number of deliveries or delivered time for both pulsed beam and continuous beam. Results: The numerical simulations confirmed that the number of deliveries for each phase converges to KN, assuming a random starting phase. Simulations for the pulsed beam and continuous beam also suggested that the dose error is a strong function of the number of deliveries andor total deliver time and could be a function of the breathing cycle, depending on the mode of delivery. The Poisson model agrees well with the simulation. Conclusions: Dynamically accumulated dose will converge to the 4D accumulated dose after multiple deliveries, regardless of treatment modality. Bounds of the dynamic dose could be determined using quantities derived from 4D doses, and the mean dose difference between the dynamic dose and 4D dose as a function of number of deliveries andor total deliver time was also established.",
keywords = "4D CT, 4D planning, interplay effect",
author = "Heng Li and Yupeng Li and Xiaodong Zhang and Xiaoqiang Li and Wei Liu and Gillin, {Michael T.} and Zhu, {X. Ronald}",
year = "2012",
month = "12",
doi = "10.1118/1.4766434",
language = "English (US)",
volume = "39",
pages = "7359--7367",
journal = "Medical Physics",
issn = "0094-2405",
publisher = "AAPM - American Association of Physicists in Medicine",
number = "12",

}

TY - JOUR

T1 - Dynamically accumulated dose and 4D accumulated dose for moving tumors

AU - Li, Heng

AU - Li, Yupeng

AU - Zhang, Xiaodong

AU - Li, Xiaoqiang

AU - Liu, Wei

AU - Gillin, Michael T.

AU - Zhu, X. Ronald

PY - 2012/12

Y1 - 2012/12

N2 - Purpose: The purpose of this work was to investigate the relationship between dynamically accumulated dose (dynamic dose) and 4D accumulated dose (4D dose) for irradiation of moving tumors, and to quantify the dose uncertainty induced by tumor motion. Methods: The authors established that regardless of treatment modality and delivery properties, the dynamic dose will converge to the 4D dose, instead of the 3D static dose, after multiple deliveries. The bounds of dynamic dose, or the maximum estimation error using 4D or static dose, were established for the 4D and static doses, respectively. Numerical simulations were performed (1) to prove the principle that for each phase, after multiple deliveries, the average number of deliveries for any given time converges to the total number of fractions (K) over the number of phases (N); (2) to investigate the dose difference between the 4D and dynamic doses as a function of the number of deliveries for deliveries of a pulsed beam; and (3) to investigate the dose difference between 4D dose and dynamic doses as a function of delivery time for deliveries of a continuous beam. A Poisson model was developed to estimate the mean dose error as a function of number of deliveries or delivered time for both pulsed beam and continuous beam. Results: The numerical simulations confirmed that the number of deliveries for each phase converges to KN, assuming a random starting phase. Simulations for the pulsed beam and continuous beam also suggested that the dose error is a strong function of the number of deliveries andor total deliver time and could be a function of the breathing cycle, depending on the mode of delivery. The Poisson model agrees well with the simulation. Conclusions: Dynamically accumulated dose will converge to the 4D accumulated dose after multiple deliveries, regardless of treatment modality. Bounds of the dynamic dose could be determined using quantities derived from 4D doses, and the mean dose difference between the dynamic dose and 4D dose as a function of number of deliveries andor total deliver time was also established.

AB - Purpose: The purpose of this work was to investigate the relationship between dynamically accumulated dose (dynamic dose) and 4D accumulated dose (4D dose) for irradiation of moving tumors, and to quantify the dose uncertainty induced by tumor motion. Methods: The authors established that regardless of treatment modality and delivery properties, the dynamic dose will converge to the 4D dose, instead of the 3D static dose, after multiple deliveries. The bounds of dynamic dose, or the maximum estimation error using 4D or static dose, were established for the 4D and static doses, respectively. Numerical simulations were performed (1) to prove the principle that for each phase, after multiple deliveries, the average number of deliveries for any given time converges to the total number of fractions (K) over the number of phases (N); (2) to investigate the dose difference between the 4D and dynamic doses as a function of the number of deliveries for deliveries of a pulsed beam; and (3) to investigate the dose difference between 4D dose and dynamic doses as a function of delivery time for deliveries of a continuous beam. A Poisson model was developed to estimate the mean dose error as a function of number of deliveries or delivered time for both pulsed beam and continuous beam. Results: The numerical simulations confirmed that the number of deliveries for each phase converges to KN, assuming a random starting phase. Simulations for the pulsed beam and continuous beam also suggested that the dose error is a strong function of the number of deliveries andor total deliver time and could be a function of the breathing cycle, depending on the mode of delivery. The Poisson model agrees well with the simulation. Conclusions: Dynamically accumulated dose will converge to the 4D accumulated dose after multiple deliveries, regardless of treatment modality. Bounds of the dynamic dose could be determined using quantities derived from 4D doses, and the mean dose difference between the dynamic dose and 4D dose as a function of number of deliveries andor total deliver time was also established.

KW - 4D CT

KW - 4D planning

KW - interplay effect

UR - http://www.scopus.com/inward/record.url?scp=84870865970&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84870865970&partnerID=8YFLogxK

U2 - 10.1118/1.4766434

DO - 10.1118/1.4766434

M3 - Article

VL - 39

SP - 7359

EP - 7367

JO - Medical Physics

JF - Medical Physics

SN - 0094-2405

IS - 12

ER -