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An analytical formalism for the assessment of dose uncertainties due to positioning uncertainties.

ABSTRACT: PURPOSE:To present an analytical formalism for the in depth assessment of uncertainties of field output factors in small fields related to detector positioning based on dose profile measurements. Additionally, a procedure for the propagation of these uncertainties was developed. METHODS:Based on the assumption that one dimensional and two dimensional second-order polynomial functions can be fitted to dose profiles of small photon beams, equations for the calculation of the expectation value, the variance, and the standard deviation were developed. The following fitting procedures of the dose profiles were considered: A one-dimensional case (1D), a quasi two-dimensional case (2Dq) based on independently measured line profiles and a full 2D case (2Df) which also considers cross-correlations in a two-dimensional dose distribution. A rectangular and a Gaussian probability density function (PDF) characterizing the probability of possible positions of the detector relative to the maximum dose were used. Uncertainty components such as the finite resolution of the scanning water phantom, the reproducibility of the determination of the position of the maximum dose, and the reproducibility of the collimator system were investigated. This formalism was tested in a 0.5 x 0.5 cm2 photon field where dose profiles were measured using a radiochromic film, a synthetic diamond detector, and an unshielded diode detector. Additionally, the dose distribution measured with the radiochromic film was convoluted with a convolution kernel mimicking the active volume of the unshielded diode. RESULTS:Analytic expressions for the calculation of uncertainties on field output factors were found for the 1D, the 2Dq, and the 2Df case. The uncertainty of the field output factor related to the relative position of the detector to the maximum dose increased quadratically with increasing limits of possible detector positions. Analysis of the radiochromic film showed that the 2Dq case gave a more conservative assessment of the uncertainty compared to the 2Df case with a difference of < 0.1%. The 2Dq case applied to the film measurements agreed well with the same approach as was applied to the unshielded diode. The investigated uncertainty components propagated to an uncertainty of the field output factors of 0.5% and 0.4% for the synthetic diamond and the unshielded diode, respectively. Additionally, the expectation value was lower than the maximum dose. The difference was 0.4% and 0.3% for the synthetic diamond and the unshielded diode, respectively. CONCLUSIONS:The assessment of uncertainties of field output factors related to detector positioning is feasible using the proposed formalism. The 2Dq case is applicable when using online detectors. Accurate positioning in small fields is essential for accurate dosimetry as its related uncertainty increases quadratically. The observed drop of the expectation value needs to be considered in small field dosimetry.

SUBMITTER: Lechner W

PROVIDER: S-EPMC7078844 | biostudies-literature | 2020 Mar

REPOSITORIES: biostudies-literature

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An analytical formalism for the assessment of dose uncertainties due to positioning uncertainties.

Lechner Wolfgang W Georg Dietmar D Palmans Hugo H

Medical physics 20200126 3

<h4>Purpose</h4>To present an analytical formalism for the in depth assessment of uncertainties of field output factors in small fields related to detector positioning based on dose profile measurements. Additionally, a procedure for the propagation of these uncertainties was developed.<h4>Methods</h4>Based on the assumption that one dimensional and two dimensional second-order polynomial functions can be fitted to dose profiles of small photon beams, equations for the calculation of the expecta ...[more]

PMID: 31880323

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Project description:PurposeTo examine the equivalent uniform dose (EUD) formalism using the universal survival curve (USC) applicable to high-dose stereotactic body radiotherapy (SBRT).Materials and methodsFor nine non-small-cell carcinoma cell (NSCLC) lines, the linear-quadratic (LQ) and USC models were used to calculate the EUD of a set of hypothetical two-compartment tumor dose-volume histogram (DVH) models. The dose was varied by ±5%, ±10%, and ±20% about the prescription dose (60 Gy/3 fractions) to the first compartment, with fraction volume varying from 1% and 5% to 30%. Clinical DVHs of 21 SBRT treatments of NSCLC prescribed to the 70-83% isodose lines were also considered. The EUD of non-standard SBRT dose fractionation (EUDSBRT) was further converted to standard fractionation of 2 Gy (EUDCFRT) using the LQ and USC models to facilitate comparisons between different SBRT dose fractionations. Tumor control probability (TCP) was then estimated from the LQ- and USC-EUDCFRT.ResultsFor non-standard SBRT fractionation, the deviation of the USC- from the LQ-EUDSBRT is largely limited to 5% in the presence of dose variation up to ±20% to fractional tumor volume up to 30% in all NSCLC cell lines. Linear regression with zero constant yielded USC-EUDSBRT = 0.96 × LQ-EUDSBRT (r2 = 0.99) for the clinical DVHs. Converting EUDSBRT into standard 2‑Gy fractions by the LQ formalism produced significantly larger EUDCFRT than the USC formalism, particularly for low [Formula: see text] ratios and large fraction dose. Simplified two-compartment DVH models illustrated that both the LQ- and USC-EUDCFRT values were sensitive to cold spot below the prescription dose with little volume dependence. Their deviations were almost constant for up to 30% dose increase above the prescription. Linear regression with zero constant yielded USC-EUDCFRT = 1.56 × LQ-EUDCFRT (r2 = 0.99) for the clinical DVHs. The clinical LQ-EUDCFRT resulted in median TCP of almost 100% vs. 93.8% with USC-EUDCFRT.ConclusionA uniform formalism of EUD should be defined among the SBRT community in order to apply it as a single metric for dose reporting and dose-response modeling in high-dose-gradient SBRT because its value depends on the underlying cell survival model and the model parameters. Further investigations of the optimal formalism to derive the EUD through clinical correlations are warranted.

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An analytical formalism for the assessment of dose uncertainties due to positioning uncertainties.

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An analytical formalism for the assessment of dose uncertainties due to positioning uncertainties.

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