A novel procedure for determining the optimal MLC configuration parameters in treatment planning systems based on measurements with a Farmer chamber

Modelling of the multi-leaf collimator (MLC) in treatment planning systems (TPS) is crucial for the dose calculation accuracy of intensity-modulated radiation therapy plans. However, no standardised methodology for their configuration exists to date. In this study we present a method that separates the effect of each dosimetric characteristic of the MLC, offering comprehensive equations for the determination of the configuration parameters used in the TPS model. The main advantage of the method is that it only requires prior knowledge of the nominal leaf width and is based on doses measured with a Farmer chamber, which is a very well established and robust methodology. Another significant advantage is the required time, since measuring the tests takes only about 30 minutes per energy. Firstly, we provide a theoretical general formalism in terms of the primary fluence constructed from the transmission map obtained from an MLC model for synchronous and asynchronous sweeping beams. Secondly, we apply the formalism to the RayStation TPS as a proof of concept and we derive analytical expressions that allow the determination of the configuration parameters (leaf tip width, tongue-and-groove width, x-position offset and MLC transmission) and describe how they intertwine. Finally, we apply the method to Varian’s Millennium120 and HD120 MLCs in a TrueBeam linear accelerator for different energies and determine the optimal configuration parameters. The proposed procedure is much faster and streamlined than the typical trial-and-error methods and increases the accuracy of dose calculation in clinical plans. Additionally, the procedure can be useful for standardising the MLC configuration process and it exposes the limitations of the implemented MLC model, providing guidance for further improvement of these models in TPSs.


Introduction
Intensity Modulated Radiation Therapy (IMRT) has been widely adopted as the treatment technique of choice for the majority of photon beam treatments in radiation oncology (Guckenberger et al 2017) since it allows for the delivery of complexly shaped dose distributions that help reduce dose to critical structures surrounding target volumes. In order to achieve optimal agreement between planned dose distributions calculated by the treatment planning system (TPS) and measured dose distributions as delivered by the linear accelerator, the configuration of the multi-leaf collimator (MLC) in the TPS constitutes a crucial element. Current MLC designs share two basic mechnanical features: a rounded-leaf end to obtain a consistent penumbra in all leaf positions (Boyer and Li 1997) and a tongue-and-groove (TG) arrangement of adjacent leaves to reduce inter-leaf leakage (Yu 1998 where k is a constant that relates fluence values to dose units. The total primary fluence can be computed from transmission maps following an approach similar to Yu (1998). Thus, because of their symmetry and constant leaf speed, the delivered primary fluence for these tests ϕ SG can be approximated as the integral of the transmission map T(x, y) under a leaf pair with a given width w leaf and across a distance d in the leaf motion direction: To characterise the sweeping gap beams the dosimetric leaf separation or dosimetric leaf gap (DLG) is often used. This parameter accounts for the increased transmission through the rounded leaf ends as well as for the MLC calibration and can be modelled by retracting the leaves a certain offset δ equal to half the DLG, which results in an effective gap that can be expressed as: The fluence ϕ SG can be split into two different contributions. The first contribution corresponds to the fluence across open leaves with an effective gap size gap eff . The second contribution is the integrated transmission T across the closed leaf section, which depends on both the distance d travelled by the sweeping gap and the gap size. Hence, for a certain leaf of width w leaf , ϕ SG can be expressed as: Consequently, D SG depends linearly on the effective leaf gap, as described by many authors: Therefore, D SG also depends linearly on the nominal leaf gap: where These parameters λ and γ can be experimentally obtained and k and δ can be determined as: Let us consider next the asynchronous sweeping gap field (aSG) in which adjacent leaves are displaced from each other a certain amount s as illustrated in figure 1, and all leaf pairs move at constant speed while keeping the same nominal gap and MLC shape (Hernandez et al 2017). By introducing this shift between adjacent leaves, the tongue and groove regions are exposed, effectively reducing the total primary fluence with respect to the SG test by a certain amount ∆ϕ TG (s) at each side of the leaves: Thus, for the aSG fields: For s = 0 no tongue-and-groove effect is present and D aSG (0) corresponds identically to the usual sweeping gap test D SG . The fluence reduction caused by the tongue-and-groove can be readily obtained from equation (10) as: Graphical representation of the MLC model in the RayStation treatment planning system for both (a) sweeping gap and (b) asynchronous sweeping gap fields. Straight lines represent the nominal leaf edges and the fluence is illustrated with dark and light grey shaded areas corresponding to regions with transmission T and √ T respectively. Only the regions corresponding to a leaf pair have been shaded.
The previous expression is the generalisation of the function A(s) used previously (Hernandez et al 2018) in terms of fluence to facilitate a more comprehensive and general interpretation.

Description of the RayStation MLC model
The MLC model in the RayStation TPS is characterised by a set of user-definable configuration parameters (RaySearch Labs 2017). A brief description of these parameters is given here: (a) Transmission T: A single configuration value T for the transmission is used as input for defining the model. Thus, this transmission value should be taken as an average of the interleaf and intraleaf transmissions. (b) Tongue-and-groove width w TG : The tongue-and-groove region is centered at the leaf side and the width w TG is added both outwards (tongue) and inwards (groove). A transmission value of √ T is assigned to this tongue-and-groove region, which has a total width of twice the w TG . (c) Leaf tip width l tip : The width of a region starting at the leaf tip where a higher transmission value is used to model the increased transmission through the rounded leaf end. In this region a transmission of √ T is assigned and neither the tongue nor the groove are modelled.
where the ± sign depends on the MLC bank considered. At the central axis (x = 0) the position offset is equal to x off .

Application to the RayStation MLC model 2.3.1. Sweeping gap tests (SG)
Let us investigate the doses for the sweeping gap tests as calculated by the MLC model described in the previous section. These measurements are typically carried out at the central axis, therefore the gain and curvature parameters can be omitted and the position offset equals x off . The fluence ϕ SG delivered by the SG field tests can be obtained integrating the transmission map for the central leaf (as indicated in Eq 2). This is equivalent to calculating ϕ SG as the sum of the products of the area and the transmission for all the regions under the central leaf as depicted in Fig 2(a): As introduced in equation (4) the dose produced by a sweeping gap without tongue-and-groove is indistinguishable from a simple MLC model that uses an effective leaf gap to account for the increased transmission through the rounded leaf tip. From equations (4) and (13) it can be deduced that (see details in Supplementary Materials (stacks.iop.org/PMB/65/155006/mmedia)): where the last term can be interpreted as twice an offset δ i introduced by the leaf tip model: And the total offset δ, as defined in equation (3), can be related to the configuration parameters in the RayStation MLC model as: Hence, the calculated doses for the SG tests are equal to the doses predicted when no leaf tip model is considered and the leaf positions are shifted by a distance δ = x off + δ i . The parameter x off can be understood as an offset due to the MLC positioning calibration (δ cal ) and δ i can be interpreted as an intrinsic offset providing the same equivalent fluence as the additional transmission at the leaf tip considered by the MLC model in the TPS.

Asynchronous sweeping gap tests (aSG)
To investigate the fluence reduction caused by the TG effect, the fluence for the aSG fields is evaluated. In this model three different regions can be distinguished depending on the relative amounts of s, l tip and gap * , defined as gap * = gap + 2x off .
(a) 0 < s ≤ l tip : since no TG is modelled at the leaf tip, there is no fluence reduction for distances between adjacent leaves smaller than the leaf tip width, hence ϕ aSG (s) = ϕ SG and ∆ϕ TG (s) = 0 . (b) l tip < s ≤ gap * + l tip . This situation corresponds to the illustration in figure 2(b). Using equation (2) and accumulating the fluence under the central leaf pair, the fluence can be computed with respect to the ϕ SG (s) given in equation (13) as (see details in Supplementary Materials): And the fluence reduction results into: This expression shows that in this region the fluence reduction increases linearly with the excess distance over the leaf tip. The slope of the linear relationship is a known function of the transmission T and the width w TG . Note that the fluence reduction caused by the TG effect does not depend on the gap size of the sweeping gap under consideration. (c) gap * + l tip < s. In this region opposing leaves begin to interdigitate and the fluence reduction reaches a maximum that no longer depends on the distance s between neighbouring leaves: Therefore, the fluence reduction is constant and equal to The calculated fluence reduction for any gap as contiguous leaves are shifted a distance s is represented in figure 3. The curve starts with a flat segment where there is no fluence reduction since the MLC model does not take into account the TG at the leaf tip. As the distance from the leaf tip increases, the fluence reduction increases linearly with a slope that depends on the transmission and the tongue-and-groove width. Finally, a plateau of fluence reduction is reached when leaves interdigitate.

Procedure for deriving the optimal MLC configuration parameters
In this section the procedure for the determination of the optimal MLC configuration parameters in RayStation is provided. The procedure is based on the measurements of the SG and aSG tests using a Farmer-type ionisation chamber placed at the central axis and the previously derived equations. The length of the Farmer chamber makes it notably suited for these measurements because we want to determine the average doses and this chamber spans several leaves (Hernandez et al 2017).
(a) The average transmission T is obtained as the ratio of measurements of a field with all leaves closed and an open field. (b) A set of measurements of sweeping gaps with different gap sizes is measured to obtain the constant of proportionality between the dose and the nominal gap (λ) and its y-intercept (γ). The constant k that relates fluence to dose can be obtained from λ using equation (8a) and the parameter δ can be computed using equation (8b). (c) The asynchronous sweeping gap fields are measured with different distances between neighbouring leaves. The experimental fluence reduction ∆ϕ exp TG (s) can be obtained from the sweeping gap doses and the previously obtained constant k (see equation (11)). (d) The parameters l tip and w TG are obtained by fitting the fluence reduction curve ∆ϕ TG , with the characteristics shown in figure 3, to the experimental fluence reduction ∆ϕ exp TG (s). (e) Finally, the x-offset is computed using equation (16).
In the last step we omitted the gain and curvature because dose calculations at the central axis are independent of these parameters. Gain and curvature can be set to zero as a first approximation, but very small values can be carefully used to fine tune the MLC positions. The gain parameter has no influence on the doses from the sweeping gaps because it shifts the leaf positions in the same direction for both MLC banks and it can be used to compensate for linear discrepancies in the MLC positioning calibration. The curvature parameter directly affects the sweeping gap doses because of the different sign for each MLC bank in equation (12), which for a positive curvature produces a gradual increment in the offset (and in the DLG) at increasing off-axis positions. Thus, the curvature parameter can be assessed in several ways: (a) From the dose measurement of the SG tests at different off-axis positions. If a different δ value is obtained, this will result in different x off values (see equation (16)) and these differences can be accounted for using equation (12) and an appropriate curvature parameter. (b) From a measured dose profile along the leaf movement direction (for instance with a detector array or film dosimetry) for a SG beam with a small gap size, e.g. a 2 mm or 5 mm gap. The curvature parameter can then be adjusted to fit the calculated profile to the measured profile.

Equipment and experiments
The MLC model assessed corresponds to version 9A of the RayStation TPS and the dose calculation algorithm was a collapsed cone convolution. Dose calculations were carried out with both a 1 mm and a 2 mm grid size. The measurement procedure for determining the optimal configuration parameters was carried out on two TrueBeam linear accelerators (Varian Medical Systems) equipped with a High Definition 120 MLC (HDMLC) and a Millennium120 MLC. Photons with nominal energies of 6 MV with flattening filter (6WFF) and without flattening filter (6FFF), 10 MV (10WFF) and 15 MV (15WFF) with flattening filter.
All measurements were carried out with a Farmer ionisation chamber placed in a water phantom at 10 cm depth and with a source to surface distance of 90 cm.
The following test fields were measured, with jaws set to a 10 cm x 10 cm square field: (a) Transmission fields for both leaf carriages with leaves closed behind the jaws. (b) Regular sweeping gap tests for gap sizes 2, 5, 10, 20 and 30 mm. The leaves moved from a position where the gap center was at -60 mm to a position where the gap centre was at +60 mm, travelling a total distance d = 120 mm. (c) Asynchronous sweeping gap tests for a 20 mm gap size with shifts between adjacent leaves s from 0 to 10 mm in 1 mm steps and from 10 to 30 mm in 2 mm steps. (d) Asynchronous sweeping gap tests for gaps 5, 10 and 30 mm with several shifts s. These fields were used only to validate that the fluence reduction due to the tongue-and-groove is independent of the leaf gap used and that the same curve ∆ϕ exp TG (s) is obtained regardless of the gap size.
From these measurements the optimal parameters T, l tip , w TG and x off were obtained and compared with a set of initial values obtained following the manufacturer recommended procedure (Savini et al 2016), which consisted of profile measurements for a set of static MLC defined fields containing square fields and MLC fields that abutted at the leaf side or with abutting leaf tips.
Finally, the optimal values obtained earlier were validated in a set of clinical plans. In particular, ten stereotactic clinical plans with small target volumes (ranging between 1 and 10 cc) were selected that were considered particularly challenging for the MLC model. The mean MLC gap ranged between 4 and 18 mm and the mean tongue and groove index (Vieillevigne et al 2019), defined as the ratio of the tongue and groove length exposed over the corresponding gap, ranged from 0.04 to 0.38. All plans were delivered using a 6FFF energy and the HDMLC onto a solid water plastic phantom (Phantom model 036A from CIRS Inc.) containing an EBT3 radiochromic film placed at the isocentre plane. The films were calibrated in absolute dose and handled according to a well establish protocol (Lewis et al 2012). All plans were then calculated with both the initial and optimal set of parameters. A planar dose analysis using the gamma method with a 2 %-2 mm global criteria and a dose threshold set at 10% of the maximum dose was used for comparison.

Results
We will develop this section around the results obtained for the HDMLC and the 6MV FFF beam energy. The results and the optimal configuration parameters for other energies and also for the Millennium MLC are reported in table 1. The figures for these other combinations of MLC models and energies are provided as Supplementary Material. The values for the initial parameters obtained from the recommended procedure were l tip = 3 mm, w TG = 0.5 mm and x off = 0.2 mm.

Measurements and determination of optimal parameters
No differences were found between the 2 mm and 1 mm dose calculation grid sizes. The measured average transmission was 1.03 %, which is in close agreement to values reported in other studies (Kim et al 2018).
Results for the SG tests are shown in figure 4(a). A linear regression fit (r 2 > 0.999 9) was carried out on the dose of the SG tests versus the nominal gap, with a proportionality constant λ = 0.614 Gy/(MU mm) and a y-intercept γ = 1.015 Gy/MU. Using equation (8a) a constant k = 0.248 2 Gy/(MU mm 2 ) was obtained. The offset δ was calculated from equation (8b) as 0.205 mm, which is equivalent to a DLG parameter of 0.41 mm.
The measured doses for the aSG tests for different gap sizes are represented in figure 4(b) as a function of the distance between adjacent leaves s. The figure clearly illustrates the dose reduction caused by the tongue-and-groove effect as leaf sides are increasingly exposed. The experimental fluence reduction ∆ϕ exp TG (s) can be readily computed for all the gap sizes using equation (11) and has been represented in figure 5(a). The curves obtained for different gap sizes coincide for s < gap, demonstrating that the fluence reduction caused by the tongue and groove is independent of the gap size and depends only on the amount of leaf side exposed.   To derive the optimal configuration parameters we used the ∆ϕ exp TG (s) for the 20 mm gap, depicted in figure 5(b). The experimental fluence reduction exhibits a linear segment for s values between 5 mm and 20 mm. A linear regression fit was carried out in this region and a and slope of 0.322 7 mm was obtained. Using this slope and the transmission value T = 1.03 % the tongue and groove width parameter w TG was computed with equation (18) as w TG = 0.43 mm.
The leaf tip width parameter l tip was also determined through the ∆ϕ exp TG (s) curve. We estimated it as the intersection of the extrapolated linear fit (depicted with a dashed blue line in figure 5(b)) and the abscissa axis, which yielded a value of l tip = 1.05 mm.
The obtained l tip parameter produces an intrinsic offset δ i = 0.107 mm (see equation (15)). Using equation (16) the offset parameter x off was calculated from δ and δ i as x off = 0.12 mm.
Finally, the curvature was assessed by repeating the sweeping gap test measurements at off-axis positions of -4 cm and +4 cm and recalculating the δ parameter. The values agreed with the δ value measured at the isocentre to within ± 0.03 mm, which corresponds to differences in the DLG parameter around ± 0.06 mm. These results indicate that the optimal value for gain and curvature can be considered zero within the experimental uncertainties. . Measured doses and doses calculated with both the initial and the optimal set of parameters for the aSG tests with a 6FFF beam and the HDMLC (upper plots) and dose differences between calculations and measurements (lower plots).

Validation
The agreement between measured and calculated doses for both the original and the optimal set of configuration parameters was performed in two stages. First the dose agreement for the synchronous and the asynchronous sweeping gaps was evaluated. Then, the agreement in clinical plans was investigated.

Test cases
TPS calculations were carried out for the test fields with both (i) the original set of configuration parameters and (ii) the optimal parameters obtained with the proposed procedure. For each test field the calculated dose was computed as the average dose to a Farmer-type structure in the TPS and compared to the measured dose. Both the calculated and measured doses and the differences between calculations and measurements are represented in figure 6. The original set of parameters produced dose differences of up to 10 % and 15 % for the smaller sweeping gap tests of 10 mm and 5 mm gap, respectively. When no shift was applied to adjacent leaves (s = 0), the doses obtained with the original set of parameters differed only around 2 % from the measured doses except for the smallest sweeping gap of 5 mm, which showed a 5 % difference. However, as adjacent leaves were shifted the dose difference increased and reached a maximum of around s = 3 mm. As the distance s increased the dose difference slowly decreased, indicating that the original set of parameter overestimated the dose reduction due to the tongue and groove effect.
On the other hand, the optimal set of parameters provided doses in close agreement with measurements, with differences smaller than 1 % for all gaps except for the 5 mm gap, which yielded a maximum difference of 2 %. The largest discrepancies were found for s values around the leaf tip width parameter (l tip = 1.05 mm) and also when the opposing leaves begin to interdigitate (s ≳ gap), coinciding with the regions where the fitted ∆ϕ TG (s) curve differed the most from the experimental curve (see figure 5(b)). Similar dose differences were obtained for the other combination of MLCs and energies, with the optimal parameters providing an excellent agreement with measured doses. Figure 7. Comparison of gamma analysis results for the selected stereotactic cases with a 2-2 mm criteria for both the original set of MLC configuration parameters and the optimal set of parameters derived with procedure described in the text.

Clinical cases
When the MLC configuration parameters in table 1 for the 6FFF beam and the MLCHD were used in the clinical plans the gamma passing rate improved significantly with respect to the passing rates obtained with the initial configuration parameters (see figure 7).

Discussion
We have described a novel procedure for the determination of the MLC configuration parameters based on synchronous and asynchronous sweeping gaps and measurements with a Farmer chamber. This chamber is recommended because the method is based on average doses and consequently a sufficient length to integrate the doses from different parts of several leaves is needed. Alternatively, a semiflex ion chamber could be used, but the Farmer chamber is preferred due to its greater length and active volume. The major advantage of this procedure is that it separates the effect of each dosimetric characteristic of the MLC, offering comprehensive equations for the determination of the configuration parameters used in the TPS model. Additionally, the derived equations clearly illustrate the intricate relationships between the different configuration parameters and how they intertwine. Furthermore, the method only requires prior knowledge of the nominal leaf width and is based on doses measured with a Farmer chamber, which is a very well established and robust methodology (LoSasso et al 1998, Arnfield et al 2000. Another significant advantage is the required time, since measuring the tests takes only about 30 minutes per energy as opposed to the time-consuming process of iteratively tuning the parameters for optimising the dose agreement for clinical plans. We found that a tongue and groove width of 0.44 mm is suitable for both the MLCHD and the Milllennium regardless of the beam energy. This result is consistent with the fact that both MLCs share the same tongue and groove design and physical width. Values of around 0.33 mm have been reported for the same MLC models and another TPS (Hernandez et al 2017), but this is compatible with the values obtained in the present study because the 0.33 mm value was obtained for an MLC model that assigned null transmission to this region. Interestingly, the corresponding fluence reduction is indistinguishable from the reduction in which zero transmission is assigned to the tongue and groove width provided that the dose calculation grid is larger than the tongue and groove width. Despite that, an MLC model that considers both the tongue and the groove widths can better model the regions of overlap between the tongue and the groove of adjacent leaves and provide more accurate dose calculations.
Regarding the leaf tip width, the value obtained for the MLCHD (~1.1 mm) is smaller than the value obtained for the Millennium MLC (~1.7 mm). This was expected because the radius of the rounded leaf end for the HDMLC is double that of the Millennium leaves (16 cm and 8 cm, respectively). The leaf tip width exhibits a modest energy dependence, with slightly larger values for higher energies.
We showed that the total offset can be divided into two different components. The first is the intrinsic offset, which is a direct consequence of the leaf tip model and the increased transmission across the rounded leaf end. The second is the offset due to the leaf positioning calibration. Our results show that the total offset δ (equal to half the dosimetric leaf gap) is energy dependent. On the other hand, when the intrinsic offset is removed the remaining x-offset is rather constant for the different energies, which supports this interpretation of intrinsic and calibration offsets.
Finally, the gain and curvature should be set to zero as a first approximation. These parameters can be used to account for a second order correction in the leaf positions at off-axis distances, but their use should be carefully evaluated. For instance, some investigators have reported slight variations in the DLG at off-axis positions (Kumaraswamy et al 2014, Mei et al 2011. The curvature parameter can be used to model these variations, but we recommend that a thorough validation is carried out in those cases. Our approach explicitly highlights the fact that the MLC configuration parameters intertwine in complex ways. As a consequence, when these parameters are determined by tentatively trying to maximise the agreement between calculations and measurements for clinical plans some compensations might take place, producing a reasonably good modelling for a particular set of treatment plans but not for other plans with different characteristics. This could explain why the need to configure various MLC models for plans with different characteristics (Kielar et al 2012, Yao and Farr 2015, Kim et al 2018 has been reported. An example of such entanglement was recently shown for the Eclipse TPS, in which tuning of the dosimetric leaf gap in the TPS could compensate for limitations in their tongue and groove model (Vieillevigne et al 2019).
Another important advantage of our procedure is that it reveals the limitations of the MLC model implemented in the TPS, identifying the main aspects in need of improvement. For instance, for both MLCs considered in the present study, the largest differences between the calculated and the experimental fluence reductions take place for 's' values in the first few millimetres because the current MLC model does not account for the tongue and groove at the leaf tip. A possible development to overcome this limitation might be to assign a variable tongue width or a variable transmission in the tongue and groove regions (Hernandez et al 2018). A simpler and more straightforward improvement would be to assign, as a first approximation, a certain constant transmission to the tongue and groove region at the leaf tip such as T 1/4 (i.e. the square of the transmission assigned to the leaf tip width). This transmission would produce a certain slope in the calculated ∆ϕ at the region 0 < s < l tip , improving the agreement between calculated and measured doses in the first few millimetres (< 5 mm). Note that a larger tip width would then be required to reach the intersection with the linear region of ∆ϕ exp . Hence, the intrinsic offset δ i would be larger and the x-offset parameter should be decreased to keep the total offset (and the doses for the SG beams) unaltered.
In a recent analysis (Kerns et al 2017) of the IROC-Houston anthropomorphic phantom irradiations, submitted plans were recalculated using an independent calculation system that used generic reference beam data. For a vast majority of the participating centers (68%) that failed the credentialing process, recalculations with the reference beam data had greater accuracy than the institution's TPS, which suggests a poor modelling of the TPS. The same group has recently published the reference dataset of users' photon beam modelling parameters gathered through an electronic survey with a questionnaire (Glenn et al 2019). Parameters were collected from 642 institutions for Eclipse, Pinnacle and RayStation and a large variability was found in the MLC configuration parameters. This large variability could be the reason behind the results found by Kerns et al. We believe that these variations are mainly due to the lack of standardised procedures and to the different methodologies used in the determination of these parameters rather than to real differences in the MLC characteristics and that the systematic and comprehensive methodology and tests described in this study could be adapted to other TPSs. The rationale is that each TPS has a certain calculated ∆ϕ TG (s) curve that depends on its MLC configuration parameters and fitting this curve to the experimental ∆ϕ exp TG (s) curve will therefore allow the determination of these parameters. For instance, the 'tongue and groove width' parameter in Pinnacle (Williams and Metcalfe 2006) and the 'leaf groove width' parameter in Monaco (Kinsella et al 2016) could also be determined from the slope in the linear region of the experimental ∆ϕ exp TG (s). Depending on the leaf tip model of each TPS a different expression for the intrinsic offset δ i will be obtained and the parameters related to the leaf tip model ('rounded leaf tip radius' and 'leaf offset calibration' in Pinnacle, 'leaf tip leakage' and 'leaf tip offset' in Monaco) could also be derived similarly to x-offset and l tip in RayStation. As a consequence, the proposed methodology can be helpful for standardising the configuration of MLC models in TPSs and for reducing the variability in the parameters used in different centres.
A limitation of the present study is that the expressions derived are specific to a particular TPS. However, the procedure could be applied in general to other TPSs as long as the effect of each configuration parameter is known and the total primary fluence for the sweeping gaps can be computed. Another limitation is that only Varian MLC models were evaluated, although the method is valid for any MLC. Future work will address other MLC models, as well as the variability of the MLC configuration parameters obtained with this procedure in different institutions.

Conclusions
We have presented a comprehensive and robust procedure for obtaining the optimal value for the configuration parameters of an MLC model based on measurements with a Farmer chamber for a set of modified sweeping gap tests 1 . The proposed procedure is much faster and streamlined than the typical trial-and-error methods and increases the dose calculation accuracy in clinical plans. Additionally, the procedure can be useful for standardising the MLC configuration process and it reveals the limitations of MLC models, providing guidance for their further improvement in TPSs.