Automation of Radiation Treatment Planning—IV. Derivation of a Mathematical Expression for the per cent Depth Dose Surface of Cobalt 60 Beams and Visualisation of Multiple Field Dose Distributions

In‐vivo dosimetry techniques are currently being applied only by a few Centers because they require time‐consuming implementation measurements, and workload for detector positioning and data analysis. The transit in‐vivo dosimetry performed by the electronic portal imaging device (EPID) avoids the problem of solid‐state detector positioning on the patient. Moreover, the dosimetric characterization of the recent Elekta aSi EPIDs in terms of signal stability and linearity make these detectors useful for the transit in‐vivo dosimetry with 6, 10 and 15 MV photon beams. However, the implementation of the EPID transit dosimetry requires several measurements. Recently, the present authors have developed an in‐vivo dosimetry method for 3D CRT based on correlation functions defined by the ratios between the transit signal, normalsnormalt(w,L), by the EPID and the phantom midplane dose, normalDnormalm(w,L), at the source to axis distance (SAD) as a function of the phantom thickness, w, and the square field dimensions, L. When the phantom midplane was positioned at distance, d, from the SAD, the ratios normalsnormalt(w,L)/snormalt'(d,w,L) were used to take into account the variation of the scattered photon contributions on the EPID as a function of d and L.The aim of this paper is the implementation of a procedure that uses generalized correlation functions obtained by nine Elekta Precise linac beams. The procedure can be used by other Elekta Precise linacs equipped with the same aSi EPIDs, assuming the stabilities of the beam output factors and the EPID signals. The procedure here reported avoids measurements in solid water equivalent phantoms needed to implement the in‐vivo dosimetry method in the radiotherapy department. A tolerance level ranging between ±5% and ±6% (depending on the type of tumor) was estimated for the comparison between the reconstructed isocenter dose, Diso, and the computed dose, Diso,TPS, by the treatment planning system (TPS).PACS number: 87.55.Qr; 87.56.Fc

Section: Methodsmentioning

confidence: 99%

Correlation functions for Elekta aSi EPIDs used as transit dosimeter for open fields

Cilla

Fidanzio

Greco

et al. 2010

“…The photon component of the rectangular‐field percent depth dose was interpolated from a set of square‐field photon‐dose components. The side of the equivalent square used for interpolation was determined using the method of Sterling et al, (15)

L_{e q} = 2 L W / (L + W)

. For rectangular fields,

β_{f}

is estimated by interpolating a value for the equivalent square field from

β_{f}

values for square fields.…”

Section: Methodsmentioning

confidence: 99%

Calculating percent depth dose with the electron pencil‐beam redefinition algorithm

Price

Hogstrom

Antolak

et al. 2007

In the present work, we investigated the accuracy of the electron pencil‐beam redefinition algorithm (PBRA) in calculating central‐axis percent depth dose in water for rectangular fields. The PBRA energy correction factor C(E) was determined so that PBRA‐calculated percent depth dose best matched the percent depth dose measured in water. The hypothesis tested was that a method can be implemented into the PBRA that will enable the algorithm to calculate central‐axis percent depth dose in water at a 100‐cm source‐to‐surface distance (SSD) with an accuracy of 2% or 1‐mm distance to agreement for rectangular field sizes ≥2×2 cm. Preliminary investigations showed that C(E), determined using a single percent depth dose for a large field (that is, having side‐scatter equilibrium), was insufficient for the PBRA to accurately calculate percent depth dose for all square fields ≥2×2 cm. Therefore, two alternative methods for determining C(E) were investigated. In Method 1, C(E), modeled as a polynomial in energy, was determined by fitting the PBRA calculations to individual rectangular‐field percent depth doses. In Method 2, C(E) for square fields, described by a polynomial in both energy and side of square W [that is, C=C(E,W)], was determined by fitting the PBRA calculations to measured percent depth dose for a small number of square fields. Using the function C(E, W), C(E) for other square fields was determined, and C(E) for rectangular field sizes was determined using the geometric mean of C(E) for the two measured square fields of the dimension of the rectangle (square root method). Using both methods, PBRA calculations were evaluated by comparison with measured square‐field and derived rectangular‐field percent depth doses at 100‐cm SSD for the Siemens Primus radiotherapy accelerator equipped with a 25×25‐cm applicator at 10 MeV and 15 MeV. To improve the fit of C(E) and C(E, W) to the electron component of percent depth dose, it was necessary to modify the PBRA's photon depth dose model to include dose buildup. Results showed that, using both methods, the PBRA was able to predict percent depth dose within criteria for all square and rectangular fields. Results showed that second‐ or third‐order polynomials in energy (Methods 1 and 2) and in field size (Method 2) were typically required. Although the time for dose calculation using Method 1 is approximately twice that using Method 2, we recommend that Method 1 be used for clinical implementation of the PBRA because it is more accurate (most measured depth doses predicted within approximately 1%) and simpler to implement.PACS number: 87.53.Fs

“…For a rectangular field with width a and length b , Sterling's formula1

E S^{S t e r l i n g} (a, b) = \frac{2 a b}{a + b},

was historically the first widely used, explicit ES formula for such a purpose. It remains the primary choice in current medical physics practice.…”

Section: Introductionmentioning

confidence: 99%

Using weighted power mean for equivalent square estimation

Zhou

et al. 2017

PurposeEquivalent Square (ES) enables the calculation of many radiation quantities for rectangular treatment fields, based only on measurements from square fields. While it is widely applied in radiotherapy, its accuracy, especially for extremely elongated fields, still leaves room for improvement. In this study, we introduce a novel explicit ES formula based on Weighted Power Mean (WPM) function and compare its performance with the Sterling formula and Vadash/Bjärngard's formula.MethodsThe proposed WPM formula is ESWPMa,b=)(wanormalα+1−wbnormalα1/α for a rectangular photon field with sides a and b. The formula performance was evaluated by three methods: standard deviation of model fitting residual error, maximum relative model prediction error, and model's Akaike Information Criterion (AIC). Testing datasets included the ES table from British Journal of Radiology (BJR), photon output factors (S cp) from the Varian TrueBeam Representative Beam Data (Med Phys. 2012;39:6981–7018), and published S cp data for Varian TrueBeam Edge (J Appl Clin Med Phys. 2015;16:125‐148).ResultsFor the BJR dataset, the best‐fit parameter value α = −1.25 achieved a 20% reduction in standard deviation in ES estimation residual error compared with the two established formulae. For the two Varian datasets, employing WPM reduced the maximum relative error from 3.5% (Sterling) or 2% (Vadash/Bjärngard) to 0.7% for open field sizes ranging from 3 cm to 40 cm, and the reduction was even more prominent for 1 cm field sizes on Edge (J Appl Clin Med Phys. 2015;16:125–148). The AIC value of the WPM formula was consistently lower than its counterparts from the traditional formulae on photon output factors, most prominent on very elongated small fields.ConclusionThe WPM formula outperformed the traditional formulae on three testing datasets. With increasing utilization of very elongated, small rectangular fields in modern radiotherapy, improved photon output factor estimation is expected by adopting the WPM formula in treatment planning and secondary MU check.