Comparative Evaluation of Curve-fitting Techniques for Electronic Portal Imaging Device-based Multileaf Collimator Picket Fence Analysis

Abstract

Purpose:

The primary objective of this study was to identify the most suitable curve-fitting method for picket fence analysis by comparing commonly used mathematical fitting approaches with film-based reference measurements.

Materials and Methods:

A picket fence test was planned on an Elekta Synergy linear accelerator equipped with an MLCi2 multileaf collimator (40 leaf pairs) using 6-mm slit widths and five pickets with a nominal field geometry of 0.6 cm × 24 cm, covering 24 leaf pairs per picket. For analysis, only the central 20 opposing leaf pairs in each picket were evaluated, yielding a total of 100 analyzed peaks. The identical picket fence plan was delivered to both the electronic portal imaging device (EPID) and Gafchromic film. EPID images were exported as TIFF files and analyzed using PTW MEPHYSTO software to obtain peak coordinates, followed by manual determination of peak center position, maximum amplitude, and full width at half maximum (FWHM).

Results:

Mean FWHM values were 6.90 mm (Gaussian), 5.69 mm (Lorentzian), 6.29 mm (pseudo-Voigt), 6.92 mm (manual), and 6.56 mm (film). Gaussian fitting and manual measurements demonstrated systematic overestimation of FWHM relative to film, while Lorentzian fitting showed the largest deviation and highest root mean square error (RMSE).

Conclusion:

Based on percentage error, RMSE, and Bonferroni-corrected nonparametric statistical analysis, pseudo-Voigt curve fitting provides the most accurate and consistent estimation of slit width in EPID-based picket fence analysis.

INTRODUCTION

Multileaf collimators (MLCs) play a critical role in modern radiotherapy by enabling accurate beam shaping and intensity modulation. The dosimetric and geometric accuracy of MLC leaf positioning directly influences target coverage and normal tissue sparing, particularly in advanced treatment techniques such as intensity-modulated radiotherapy (IMRT) and volumetric-modulated arc therapy (VMAT). Consequently, routine and reliable quality assurance (QA) of MLC performance is essential to ensure safe and accurate dose delivery.[1,2]

Among the various MLC QA tools, the picket fence test is widely employed for evaluating leaf positioning accuracy and interleaf consistency. Originally developed using radiographic film, the picket fence test has been successfully adapted to electronic portal imaging devices (EPIDs), enabling rapid acquisition, digital analysis, and improved spatial resolution.[1,3] EPID-based picket fence images are commonly analyzed using commercial QA software; however, these tools often rely on predefined algorithms and threshold-based detection methods, which may not fully characterize the underlying shape of measured intensity profiles.[4,5]

EPID-based picket fence profiles are influenced by multiple physical factors, including detector spatial resolution, radiation scatter, MLC transmission, and finite leaf edge geometry. As a result, measured slit profiles deviate from an ideal rectangular shape and typically exhibit rounded peaks with extended tails.[4,6] Under such conditions, direct or manual determination of parameters such as the full width at half maximum (FWHM) can be sensitive to noise and operator-dependent variations, potentially affecting the robustness and reproducibility of the analysis.

In such situations, direct point-based or threshold-based measurements may be inadequate for reliable parameter estimation, particularly in the presence of noise and asymmetric profile tails. Analytical curve fitting has been shown to improve the robustness and repeatability of peak characterization by utilizing the full profile shape rather than discrete intensity points, enabling more accurate determination of peak position and width parameters.[7,8,9,10]

Analytical curve-fitting techniques provide a systematic and objective approach for characterizing measured profiles by approximating the data using mathematical models with physically meaningful parameters. By fitting analytical functions to EPID intensity profiles, both the peak center (associated with leaf positioning accuracy) and FWHM (related to effective slit width) can be consistently estimated. Gaussian, Lorentzian, and Voigt-based functions are widely used in medical physics and spectroscopy to model detector response, scatter-dominated distributions, and combined broadening effects, respectively.[7,8,9]

The Gaussian function primarily represents detector-related blurring and electronic noise, while the Lorentzian function is more sensitive to long-range scatter and transmission-induced profile tails. The Voigt function, defined as the convolution of Gaussian and Lorentzian components, provides a more comprehensive description by accounting for both effects simultaneously.[8,9] Despite their relevance, systematic comparisons of these curve-fitting approaches for EPID-based MLC picket fence analysis remain limited.

In this study, EPID-based picket fence profiles acquired on an Elekta Synergy linear accelerator were analyzed using Gaussian, Lorentzian, and pseudo-Voigt curve-fitting techniques and compared with manual measurements and Gafchromic film–derived reference data. Performance was assessed using FWHM estimation, peak center determination, and goodness-of-fit metrics. Statistical comparison of methods was performed using the Friedman rank test for repeated measures, followed by Wilcoxon signed-rank post hoc analysis with Bonferroni correction to identify significant differences among fitting approaches.[11,12] The primary aim of this work is to identify the most suitable curve-fitting method for reliable picket fence analysis in clinics lacking access to commercial MLC QA software.

MATERIALS AND METHODS

Picket fence planning and electronic portal imaging device image acquisition

A picket fence test was planned using the Monaco treatment planning system (Elekta AB, Stockholm, Sweden) for an Elekta Synergy linear accelerator equipped with an MLCi2 MLC. The test pattern consisted of five equidistant pickets with a nominal slit width of 6 mm and 40 mm spacing between adjacent pickets as illustrated in Figure 1. The 6 mm slit width was selected because the MLCi2 system does not allow leaf openings smaller than 6 mm, making it the minimum achievable and clinically relevant slit width for this configuration. For each picket evaluated 20 opposing leaf pairs, resulting in a total of 100 slit profiles (peaks). The plan was exported through the MOSAIQ oncology information system and delivered.

Figure 1.

Representative picket fence slit from the treatment planning geometry. The full picket fence pattern consisted of five equidistant pickets with 40 mm inter-picket spacing and a nominal slit width of 6 mm. Each picket spanned 24 opposing multileaf collimator leaf pairs, of which the central 20 leaf pairs were included in the quantitative analysis

Each slit was delivered with 3 monitor units. Portal images were acquired using an EPID positioned at a source-to-detector distance (SDD) of 160 cm and exported in TIFF format for analysis. The EPID has a matrix size of 1024 × 1024 pixels corresponding to an active imaging area of 41 cm × 41 cm at the detector plane, which projects to approximately 26 cm × 26 cm at isocenter (100 cm SDD).

Based on this geometry, the effective pixel size was determined to be approximately 0.25 mm at the isocenter and 0.40 mm at 160 cm SDD, accounting for geometric magnification.[13] This spatial calibration was applied to convert pixel-based measurements into physical distances for profile and FWHM analysis.

Initial profile extraction using PTW MEPHYSTO

The exported EPID images were analyzed using physikalisch-technische werkstätten (PTW) MEPHYSTO software (PTW Freiburg, Germany). One- dimensional cross-plane intensity profiles, oriented parallel to the MLC leaf motion, were extracted for each slit. As illustrated in Figure 2, profiles were generated for all five pickets, with 20 opposing leaf pairs analyzed per picket, resulting in a total of 100 individual EPID profiles.

Figure 2.

Electronic portal imaging device-measured picket fence image and corresponding cross-plane intensity profiles extracted for all evaluated multileaf collimator leaf pairs. Multiple horizontal sampling lines (left panel) were used to generate cross-plane profiles across the five pickets, resulting in an ensemble of slit profiles for each picket (right panel). These profiles represent all 20 opposing leaf pairs per picket and form the dataset used for quantitative slit width (full width at half maximum) and peak center analysis

EPID resolution is fixed by the detector matrix and field size, while film resolution is determined by scanner dpi. In both cases, the sampling was sufficient to ensure multiple data points across the FWHM, enabling reliable curve fitting.

For each profile, manual measurements of the peak center position, maximum intensity, and FWHM were obtained directly within the MEPHYSTO environment. These manually derived parameters were used as the baseline reference for subsequent comparison with Gaussian, Lorentzian, and pseudo-Voigt curve-fitting analyses, enabling evaluation of systematic differences between manual and model-based approaches.

For manual FWHM determination, one-dimensional intensity profiles were extracted across each slit using the central axis of the image. The maximum intensity value of the profile was identified, and the half-maximum level was calculated as 50% of this value.

The positions corresponding to the half-maximum on both sides of the peak were determined using linear interpolation between adjacent data points to improve spatial accuracy. The FWHM was then calculated as the distance between these two positions.

All measurements were performed on normalized profiles to ensure consistency across datasets.

Curve coordinate export and analytical fitting

Extracted EPID profile coordinates were exported from MEPHYSTO to Microsoft Excel for further analysis. For each profile, x–y scatter plots of measured intensity versus position were generated. Analytical curve fitting was then performed using Gaussian, Lorentzian, and pseudo-Voigt functions.

Curve fitting was implemented using least-squares minimization, where the sum of squared differences (χ²) between measured and calculated values was minimized. The Excel Solver tool was used to optimize fitting parameters, including peak amplitude, peak center position, and width parameters. Gaussian fitting was performed first, followed by Lorentzian fitting, and finally pseudo-Voigt fitting by combining Gaussian and Lorentzian components. For pseudo-Voigt fitting, Gaussian and Lorentzian contributions were optimized to determine the effective Gaussian parameters.

Systematic EPID overestimation in small field and slit-width measurements has been widely reported and attributed to detector scatter and spatial blurring; therefore, institutionally validated correction factors derived from prior radiation field analyzer (RFA) measurements using a small-field detector and Gafchromic film were applied.[5,6,14]

EPID overestimation of slit width was characterized as part of institutional QA protocols using a comparative measurement approach. MLC-defined slit openings ranging from 6 mm to 20 mm were generated using a picket fence delivery pattern and measured using EPID, Gafchromic EBT3 film, and a microSilicon diode detector for RFA. For each slit width, beam profiles were analyzed using PTW software to determine the FWHM consistently across all measurement systems under identical geometric conditions.

EPID overestimation was defined as the systematic deviation between EPID-derived slit width and the corresponding reference values obtained from film and diode measurements, quantified as the absolute difference. A linear regression analysis was performed between EPID measurements and RFA reference values, and the relationship was modeled using a linear equation.

In the present study, these institutionally established correction factors were applied to account for EPID-related overestimation effects.

Curve-fitting models and mathematical formulation

Gaussian function

The Gaussian function is expressed as:[7]

where

• A is the peak amplitude,

• μ is the peak center position, and

• σ is the standard deviation.

The FWHM of the Gaussian function is given by:

Gaussian fitting primarily reflects detector-related spatial blurring and random noise contributions.

Lorentzian function

The Lorentzian function is defined as:[7,8]

where

• A is the peak amplitude,

• x₀ is the peak center position, and

• γ is the half-width at half-maximum parameter

The corresponding FWHM is:

FWHW=2γ

Lorentzian fitting is particularly sensitive to long-tailed distributions caused by scatter and MLC transmission effects.

Voigt and pseudo-voigt function

The Voigt function represents the convolution of Gaussian and Lorentzian components:[8,9]

Due to computational complexity, a pseudo-Voigt approximation is commonly employed, expressed as a weighted linear combination:

where

• η is the Lorentzian fraction (0≤η≤1).

The Voigt or pseudo-Voigt FWHM reflects the combined influence of detector response and scatter-related broadening, providing a more physically representative description of EPID-based picket fence profiles.

Goodness-of-fit evaluation

To evaluate fitting performance, the following goodness-of-fit metrics were calculated for each fitted profile:

• Coefficient of determination (R²), indicating the proportion of variance explained by the model

  

  where y_i are the measured EPID intensity values, ŷ_i are the fitted values, ȳ is the mean of the data, and n is the number of data points. A value of R² close to 1 indicates a model that explains most of the variance.

• Root mean square error (RMSE), reflecting the average deviation between measured and fitted values

  

• Chi-square (χ²) and reduced Chi-square (χ²ᵣ), calculated under equal weighting assumptions.

Lower RMSE and χ²ᵣ values were interpreted as indicators of improved agreement between fitted and measured profiles.

Film irradiation and analysis

To provide an independent reference, the same picket fence plan was delivered to Gafchromic EBT3 film [Figure 3] placed at the isocenter with 5 cm slab phantom above and 5 cm below for buildup and backscatter. Irradiations were performed at 100 cm SSD.

Figure 3.

Gafchromic film showing a five-picket multileaf collimator pattern with clearly visible narrow irradiated bands (Picket 1–5). Lower plot shows the Corresponding cross-plane dose profiles extracted from the film, illustrating distinct peaks for each picket used for full-width at half maximum analysis

Irradiated films were scanned using an Epson flatbed scanner at 300 dpi, corresponding to a spatial sampling resolution of approximately 0.085 mm per pixel.

As the study focused on geometric FWHM rather than absolute dosimetry, the analysis was performed using normalized intensity profiles. Accordingly, absolute dose calibration[15] was not required, as the evaluation was based on relative profile shape.

To ensure spatial accuracy and reduce scanner-related artifacts, all films were consistently positioned at the center of the scanner bed during acquisition. Potential sources of uncertainty include scanner response variability, film non-uniformity, and signal-to-noise limitations.

The uncertainty in film-derived FWHM is primarily governed by the scanner sampling resolution and is therefore on the order of the effective pixel size (~0.085 mm). This high-resolution dataset served as the reference standard for validating the EPID-based curve-fitting techniques.

Statistical comparison with film reference

Parametric analysis (paired Student’s t-test)

For each curve-fitting method (manual, Gaussian, Lorentzian, pseudo-Voigt), paired FWHM values from EPID profiles were compared with corresponding FWHM values from film measurements. A two-tailed paired Student’s t-test was performed using Microsoft Excel. P < 0.05 was considered statistically significant for assessing differences under the assumption of normality.

Nonparametric analysis (Wilcoxon signed-rank test with Bonferroni correction)

Given potential deviations from normal distribution, a Wilcoxon signed-rank test was also applied to compare each EPID curve-fitting method with film-derived FWHM values. To correct for multiple comparisons across methods, the Bonferroni correction was applied:

where α = 0.05, and m is the number of pairwise comparisons. Adjusted significance thresholds were used to interpret P values. All statistical tests were performed using Microsoft Excel.

Friedman rank test

To compare the performance of multiple analysis methods across repeated measurements without assuming normality, the Friedman rank test was employed. This nonparametric test is appropriate for blocked experimental designs in which the same subjects (or measurement instances) are evaluated under multiple conditions.

Let

N be the number of blocks (here, number of slit profiles, n = 100,

k be the number of treatments or methods compared (here, manual, Gaussian, Lorentzian, and pseudo-Voigt, k = 4),

j be the average rank of the jth method across all blocks.

The Friedman test statistic is defined as:

Under the null hypothesis that all methods perform equivalently, the statistic χ²_F X²_F follows a Chi-square distribution with k − 1 degrees of freedom for sufficiently large n.

In this study, the Friedman test was applied to percentage FWHM error values obtained from each method relative to film-based reference measurements. A statistically significant Friedman test result (P < 0.05) indicated the presence of systematic differences among methods, justifying further pairwise post hoc comparisons.

Data synthesis and interpretation

The extracted FWHM values, peak centers,[16,17] and goodness-of-fit metrics from EPID analyses (manual and curve-fitting models) were compared against film-derived values to evaluate agreement and systematic deviations. Combined use of parametric and non-parametric statistics provided complementary perspectives on method performance. Interpretation of results focused on identifying the most reliable analytical approach for EPID-based picket fence QA, particularly in contexts where commercial software is frequently used but may not account for full profile shape characteristics.

RESULTS

Full-width at half maximum and peak center measurements

The mean FWHM and peak center values obtained using different analysis methods are summarized in Table 1, while the distribution of FWHM values across all 100 slit profiles is illustrated in Figure 4. The film-based measurement yielded a mean FWHM of 6.56 mm and was used as the reference standard.

Table 1.

Mean full width at half maximum, peak center position, and goodness-of-fit metrics for electronic portal imaging devices-based picket fence analysis using Gaussian, Lorentzian, and pseudo-Voigt fitting, compared with manual electronic portal imaging devices and Gafchromic film reference measurements (100 profiles)

Parameter	Gaussian	Lorentzian	Pseudo-Voigt	Manual	Film
Mean FWHM (mm)	6.9	5.69	6.29	6.92	6.56
Mean inter-peak distance (mm)	39.85	39.15	39.92	39.82	39.76
Mean R2	0.9912	0.9713	0.9957	-	-
Mean RMSE	2.96	5.7	1.47	-	-

FWHM: Full width at half maximum, RMSE: Root mean square error

Figure 4.

Box-and-whisker plot summarizing full width at half maximum (FWHM) values derived from all 100 slit profiles for Gaussian, Lorentzian, pseudo-Voigt, and manual electronic portal imaging device-based methods, with Gafchromic film used as the reference. The boxes indicate the interquartile range, the central line denotes the median, whiskers represent the full data range, and the cross marker shows the mean FWHM for each technique

Among EPID-based methods, Gaussian fitting (mean FWHM = 6.90 mm) and manual measurement (6.92 mm) produced consistently larger FWHM values compared with film, indicating systematic overestimation of slit width. This trend is also evident in Figure 4, where both methods show higher median values and relatively narrow interquartile ranges above the film distribution. In contrast, Lorentzian fitting resulted in a lower mean FWHM (5.69 mm), reflecting systematic underestimation, with its distribution clearly shifted below the film reference in Figure 4.

The pseudo-Voigt fitting method demonstrated the closest agreement with film, yielding a mean FWHM of 6.29 mm. As shown in Figure 4, the pseudo-Voigt distribution exhibits substantial overlap with the film measurements and a reduced spread compared with the other EPID-based techniques, indicating improved consistency across the full set of 100 profiles.

For the pseudo-Voigt fits, the Lorentzian fraction (η) was consistently small across all slit profiles, with an average value of η = 0.105. This indicates that the EPID picket fence profiles were predominantly Gaussian in nature, with a minor but non-negligible Lorentzian contribution arising from scatter and MLC transmission effects.

Mean inter-peak distances were consistent across all methods, with values ranging between 39.80 and 39.92 mm, indicating stable peak localization irrespective of the fitting approach. Peak centers were determined independently for each fitting method, and inter-peak distances were subsequently calculated as the separation between adjacent peak center positions within the same method.

Goodness-of-fit analysis

All curve-fitting methods demonstrated high coefficients of determination, with R² values exceeding 0.97 for all models. The pseudo-Voigt method achieved the highest mean R² (0.9957), followed by Gaussian (0.9912) and Lorentzian (0.9713).

The RMSE values [Figure 5] demonstrated clear differences among the fitting models. Pseudo-Voigt fitting produced the lowest RMSE (1.47), followed by Gaussian fitting (2.96), while Lorentzian fitting showed the highest RMSE (5.7), indicating the least agreement with the measured EPID intensity profiles. The reduced RMSE observed with pseudo-Voigt fitting reflects its improved representation of the measured profile shape compared with single-component models.[7,8,9,10]

Figure 5.

Root mean square error between the measured electronic portal imaging device profile data and the corresponding Gaussian, Lorentzian, and pseudo-Voigt curve fits, calculated across all 100 profiles, illustrating the relative goodness-of-fit of each model to the original measured data. RMSE: Root mean square error

Percentage error relative to film

Percentage error analysis using film as the reference revealed that pseudo-Voigt fitting yielded the lowest mean FWHM error (2.6%), followed by Gaussian fitting (4.2%) and manual analysis (4.35%), while Lorentzian fitting exhibited the highest mean error (9%). As shown in Figure 6, the pseudo-Voigt method also demonstrated the narrowest interquartile range and the smallest spread of errors, indicating improved consistency across all 100 slit profiles. In contrast, Lorentzian fitting displayed a wider error distribution with larger variability and outliers. Per-leaf-pair analysis further confirmed that pseudo-Voigt FWHM values consistently tracked film measurements more closely than the other methods across all 100 peaks, with reduced systematic bias relative to Gaussian, Lorentzian, and manual approaches.

Figure 6.

Box-and-whisker plot showing the percentage full-width at half maximum error of EPID-based analysis methods relative to the film reference for all 100 slit profiles. The distributions compare Gaussian versus film (G vs. F), Lorentzian vs film (L vs. F), pseudo-Voigt versus film (PV vs. F), and manual versus film (M vs. F). Boxes represent the interquartile range with median values indicated, whiskers denote the data spread, and markers show mean values and outliers, illustrating the relative bias and variability of each method with respect to the film reference. FWHM: Full width at half maximum

Statistical analysis

Student’s t-test comparisons between EPID-based methods and film demonstrated statistically significant differences for all fitting approaches (Gaussian, Lorentzian, pseudo-Voigt, and manual), with P < 0.01.

Paired comparisons between EPID-derived FWHM values and film measurements showed statistically significant differences for all methods (P < 0.001). The Friedman rank test applied to percentage error data across all methods demonstrated a statistically significant overall difference (χ² test, P = 0.000662, N = 100).

Subsequent Wilcoxon signed-rank post hoc tests, with Bonferroni correction applied for three comparisons (α = 0.0167), confirmed that pseudo-Voigt fitting differed significantly from Gaussian (P = 0.0057), Lorentzian (P = 6.9 × 10^⁻5), and manual methods (P = 0.0074).

DISCUSSION

Routine QA of MLC performance is essential for maintaining geometric and dosimetric accuracy in modern radiotherapy techniques such as IMRT and VMAT. The picket fence test remains one of the most widely adopted tools for evaluating MLC leaf positioning accuracy due to its simplicity and sensitivity to systematic and random leaf errors. With the increasing adoption of EPID-based QA, analysis methodologies must be both robust and interpretable, particularly for institutions without access to advanced commercial QA software.[1,18]

Recent studies have highlighted both the strengths and limitations of conventional EPID-based picket fence analysis. Barnes et al. demonstrated that while EPID-based picket fence tests are effective for routine QA, basic threshold-or peak-detection-based analysis may not adequately characterize subtle profile distortions or systematic biases in slit-width estimation.[1] Similarly, Kalavagunta et al. emphasized that qualitative or simplistic weekly picket fence tests may be insufficient to capture clinically relevant MLC deviations, advocating for more quantitative and reproducible analysis approaches.[2] The clinical importance of accurate MLC positioning has been further demonstrated by Ceylan et al., who showed that small leaf position errors detected in picket fence tests can significantly affect gamma index pass rates in patient-specific QA.[3]

In this context, the present study systematically evaluated manual, Gaussian, Lorentzian, and pseudo-Voigt curve-fitting methods for EPID-based picket fence analysis, using Gafchromic film as an independent reference standard. The results clearly demonstrate that the choice of curve-fitting model significantly influences FWHM estimation, even when all methods exhibit high apparent goodness-of-fit.

Gaussian fitting and manual FWHM determination consistently overestimated slit width relative to film. This behavior is consistent with earlier evaluations of QA software systems, where Gaussian-based or threshold-based algorithms were shown to be sensitive to detector blur and noise near profile shoulders.[4,6] Manual measurements are additionally affected by operator subjectivity, particularly in EPID profiles with rounded peaks and shallow gradients.

Conversely, Lorentzian fitting systematically underestimated slit width, which can be explained by the mathematical properties of the Lorentzian function. Lorentzian profiles place greater weight on extended tails, resulting in a narrower half-maximum region and consequently smaller FWHM values. Similar limitations of pure Lorentzian models have been reported in spectroscopic and surface analysis literature, where Lorentzian-only fitting was shown to inadequately represent mixed broadening phenomena.[7]

Figure 7 illustrates representative EPID slit profiles fitted using Gaussian, Lorentzian, and pseudo-Voigt models. The Gaussian fit [Figure 7a] reproduces the peak maximum but overestimates the FWHM due to broadening at the profile shoulders, a behavior consistent with the intrinsic blur and optical spread of amorphous silicon EPIDs.[4,5,6] In contrast, the Lorentzian fit [Figure 7b] yields a narrower half-maximum region and systematically underestimates FWHM, reflecting its emphasis on long-range tails rather than detector-dominated peak cores.[7,8] The pseudo-Voigt model [Figure 7c], combining Gaussian and Lorentzian components, provides the closest agreement with measured EPID profiles across the full spatial range [Figure 7d]. The small Lorentzian fraction (η ≈0.105) indicates that the profiles are predominantly Gaussian with a minor scatter-related contribution, consistent with mixed broadening mechanisms in EPID imaging.[7,8,9,10]

Figure 7.

Representative electronic portal imaging device slit intensity profile illustrating curve-fitting approaches. (a) Measured profile overlaid with a Gaussian fit, (b) measured profile with a Lorentzian fit, (c) measured profile with a pseudo-Voigt fit, and (d) combined comparison showing the measured data with all three fitting models across the same spatial range

The pseudo-Voigt fitting approach demonstrated the closest agreement with film measurements, yielding the lowest mean percentage error, smallest RMSE, and highest R² values among all tested methods. This finding is physically intuitive, as EPID slit profiles are influenced by a combination of Gaussian-like detector response and electronic noise, as well as Lorentzian-like scatter and MLC transmission effects.[7,8,9,10] The observed mean pseudo-Voigt Lorentzian fraction (η ≈ 0.105) confirms that EPID picket fence profiles exhibit mixed broadening, validating the use of pseudo-Voigt fitting over single-component models for routine MLC QA.

In addition to individual slit analysis, the full central cross-line EPID intensity profile provides a global view of fitting performance across all pickets [Figure 8]. The measured profile and corresponding pseudo-Voigt fits show close agreement over peak maxima, shoulders, and inter-picket regions, indicating that the pseudo-Voigt model consistently captures the combined detector and scatter effects across the entire field. The uniform peak separation and stable fitting behavior across all slits further support the robustness of the pseudo-Voigt approach for comprehensive MLC positioning assessment in EPID-based picket fence QA.

Figure 8.

Full central cross-line electronic portal imaging device intensity profile showing measured data overlaid with pseudo-Voigt fits for all picket openings. Each peak is independently modeled to represent the combined detector response across the entire profile

Multiple statistical methods were used to provide a comprehensive evaluation of EPID performance in picket fence QA. Since the objective involved assessing not only differences but also agreement and variability between measurement methods, complementary statistical metrics were applied. The paired t-test assessed the significance of differences, R² quantified agreement, RMSE measured absolute deviation, and percentage error provided a clinically relevant estimate of relative difference. Together, these metrics ensure a balanced and robust assessment of EPID-based slit width measurements in relation to picket fence QA requirements.

From a statistical standpoint, the Friedman rank test confirmed significant differences among the evaluated methods, justifying further post hoc analysis. The Friedman test is particularly appropriate in this setting because it does not assume normality and accounts for repeated measurements across multiple methods.[11] Subsequent Wilcoxon signed-rank tests with Bonferroni correction demonstrated that pseudo-Voigt fitting remained significantly superior to Gaussian, Lorentzian, and manual approaches even under conservative multiple-comparison control.

Clinically, these findings have important implications. Although all methods yielded statistically significant differences relative to film, clinical relevance depends on the magnitude and direction of error rather than statistical significance alone.[12] Systematic over-or underestimation of slit width may mask subtle MLC deviations or generate false positives, potentially affecting QA decision-making.

In this study, EPID slit-width overestimation was not re-evaluated, as the primary objective was to compare curve-fitting models rather than detector response characteristics. Instead, previously validated institutional correction factors derived from RFA measurements with a small-field detector and Gafchromic film were applied. This approach allowed the observed differences among fitting methods to be attributed primarily to model performance rather than known EPID broadening effects.[14]

The observed FWHM-based slit width measurements and EPID–film agreement are consistent with clinically accepted tolerances for MLC QA. In routine radiotherapy QA, MLC positional accuracy is generally expected to be within ± 1 mm, as recommended in international QA guidelines for dynamic MLC delivery.

In this context, the deviations observed in the present study fall within clinically relevant limits and are capable of detecting small but meaningful MLC positional errors. The sensitivity of the proposed method, particularly in identifying variations in the range of approximately 0.5–1 mm, aligns well with the requirements of picket fence-based QA verification.

Although direct comparison with identical FWHM-based curve-fitting approaches in literature is limited, previous studies on EPID-based MLC QA have similarly reported systematic EPID overestimation in small fields due to detector scatter and spatial blurring, supporting the findings of the present study.

The primary aim of the picket fence test is to assess MLC positional accuracy by detecting leaf positioning errors. In this study, the proposed EPID-based curve-fitting approach demonstrated high sensitivity to variations in slit width through quantitative FWHM analysis. Considering the effective EPID spatial resolution (~0.25 mm at isocenter) and the use of interpolation and curve fitting techniques, the method is capable of resolving sub-pixel variations in profile shape. Consequently, MLC positional deviations on the order of 0.5 mm can be reliably detected, while 1 mm errors are clearly distinguishable. This level of sensitivity is consistent with clinical QA requirements and supports the applicability of the method for precise MLC performance evaluation.

The proposed EPID-based curve-fitting approach is expected to be generally applicable to other MLC systems and EPID technologies, as it relies on fundamental characteristics of beam profile acquisition and analysis. While this study was performed on a specific MLC design and EPID configuration, the methodology is based on relative intensity profiles and geometric FWHM determination, which are not inherently system-specific.

The accuracy of spatial measurements is inherently limited by the detector sampling interval (pixel pitch), as well as interpolation during image processing and potential EPID positioning variations. These factors introduce a small uncertainty in FWHM determination, on the order of the effective pixel size at the respective acquisition geometry, which has been accounted for in the analysis.

However, differences in MLC leaf width, leaf end design, transmission characteristics, and EPID detector resolution may influence the measured profiles and fitting accuracy. Therefore, appropriate system-specific calibration and validation may be required when extending this approach to other platforms. Despite these considerations, the overall framework remains adaptable and can be implemented across a range of clinical systems with suitable adjustments.

The proposed tool is a low-cost alternative to commercial MLC QA software; however, the processing time is higher compared to simple visual inspection. For the analysis of approximately 100 slit profiles, an initial setup and familiarization phase is required. After this stage, the workflow becomes more efficient due to the repetitive and standardized nature of the analysis.

On average, the complete evaluation of 100 slit profiles requires approximately 1 h after measurement, which is considered acceptable for routine weekly or monthly MLC QA.

These findings align well with the broader QA philosophy outlined in AAPM TG-142 and subsequent EPID QA literature, which emphasize reproducibility, traceability, and sensitivity to clinically meaningful deviations.[6,18,19,20] By combining EPID-based acquisition with physically motivated curve fitting and appropriate statistical analysis, the proposed approach offers a low-cost, reproducible, and quantitative enhancement to routine picket fence QA.

CONCLUSION

This study compared different curve-fitting approaches for EPID-based picket fence analysis using Gafchromic film as a reference standard for validation. The findings demonstrate that different fitting models can significantly influence slit width estimation, even when statistical goodness-of-fit appears high.

Among the evaluated methods, pseudo-Voigt fitting showed the best overall agreement with the reference measurements, with lower deviation compared to Gaussian and Lorentzian approaches.

The results indicate that appropriate model selection is critical for accurate EPID-based MLC QA. The observed level of agreement suggests that the proposed approach is capable of detecting clinically relevant MLC positional variations within acceptable QA tolerances.

In conclusion, the study highlights the importance of selecting an appropriate analytical model for reliable EPID-based picket fence evaluation and supports the use of pseudo-Voigt fitting for improved consistency in MLC QA.

Conflicts of interest

There are no conflicts of interest.

Funding Statement

Nil.