2.1. Two-dimensional ion chamber array

The IBA MatriXX PT comprises 1020 air-vented parallel plate pixel ion chambers arranged in a $32\times 32$ grid with a 7.62 mm center-to-center distance. The sensor of each ion chamber was a cylinder measuring 4.2 mm in diameter and 2 mm in height. The active field size of the MatriXX PT was 24 cm × 24 cm.

Conventional mathematical interpolation is widely used to improve the spatial resolution of the measurements. Although the sampling frequency of the MatriXX PT is sufficient for dose distributions with smooth dose gradients, for dose distributions with more high-frequency components, the interpolation values can deviate significantly from the actual values. Fig. 2a shows the measured lateral profiles of a field measuring 10 cm × 10 cm × 10 cm with a range of 20 cm for the treatment plan, and at a depth of 15 cm in the SAPT horizontal beamline. The lateral profile measured based on the EBT3 film exhibited significant dose “horns” at the high gradient edge (indicated by arrows), which is also shown in the calculated dose distribution. The dose “horns” were optimized deliberately to sharpen the lateral fall-off. However, the lateral profile of the interpolated MatriXX PT measurement indicated no “horns” in either edges [13]. Fig. 2b shows the Fourier transform of the lateral profile of the planned dose distribution. In signal processing theory, the Nyquist frequency is twice the maximum frequency of the sampled data, and the maximum frequency is defined as the frequency above which all frequency components are below 1% of the maximum amplitude of the Fourier spectrum [11]. In this example, the maximum frequency is 0.0800/mm, which results in a Nyquist frequency of 0.16/mm and a required minimum sampling distance of 6.25 mm. Hence, the minimum sampling distance required is below the sampling distance of MatriXX PT (7.6 mm).

Fig. 2.Full-screen View

(a) Lateral profiles of field (gantry angle = 270°, couch angle = 0°) of 10 cm$\times$ 10 cm$\times$ 10 cm treatment plan in 15 cm water equivalent depth measured using EBT3-film, MatriXX PT; (b) corresponding Fourier transform of calculated dose distribution

2.2. Dose delivery reconstruction toolkit

Logfile-based reconstructed dose distributions can be reconstructed using a dose delivery reconstruction toolkit with delivered spot positions, weights, and energies recorded in logfiles. Therefore, the accuracy of logfile-based dose distributions directly affects the accuracy of the reformatted dose distributions and is primarily determined by two factors: (1) the input parameters, specifically, the delivered spot positions and weights recorded by logfiles; (2) the dose computation model, which describes the dose deposition in homogeneous or heterogeneous media mathematically. The accuracy of delivered spot positions and weights in logfiles was validated in previous by Liu Ming [14] and Miao Chun Hui [15] in studies pertaining to the SAPT horizontal beamline. The feasibility of dose reconstruction using logfiles in spot scanning proton therapy has been investigated in several proton therapy centers [16, 17]. Regarding the dose computation model, the commissioning of the dose computation model was performed by measuring the integral depth doses and in-air spot size [18, 19]. The dose delivery reconstruction toolkit used was adapted from matRad, which is an open-source software for the radiation treatment planning of intensity-modulated photon, proton, and carbon ion therapy [20]. Many researchers have demonstrated the accuracy of the transportation model in matRad [20, 21], particularly in water. Hence, the main task is to verify the beam modeling.

2.3. Data Blending

2.3.1 Theory

After verifying the accuracy of the independent dose reconstruction toolkit, it can be used to obtain high-resolution reformatted dose distributions and correctly supplement dose details lost from 2D IC array measurements due to low resolution.

In image processing theory and the frequency domain, the low-frequency components of an image are related to the region of slow intensity changes and describes the main part of an image, whereas the high-frequency components of an image correspond to the part with significant intensity changes and indicate the “detailed” part of an image [22]. The proposed method regards 2D dose distributions as images, and “finer” retrospective dose details are blended in with an interpolated measurement dose base to improve the measurement of 2D IC array detectors. Regarding the logfile-based reconstructed dose distribution and the measurement of the 2D IC array detectors, the measurement results are improved by blending the high-frequency components of the logfile-based reconstructed dose images with the low-frequency components of the measured dose images. Laplacian pyramid image blending (LPIB) [23] can blend images smoothly using alpha masks at different frequencies using Laplacian images of different resolutions. Hence, LPIB is a suitable method for blending logfile-based reconstructed and measured dose distributions. The procedures to blend the measured dose and logfile-based reconstructed dose images using LPIB are presented in Fig. 3. Briefly, the procedures are as follows:

Fig. 3Full-screen View

Flow chart of LPIB method of blending logfile-based reconstructed and measured dose images

a) Build Laplacian pyramids $L{P}_p$ and $L{P}_m$from the logfile-based reconstructed dose distribution and the mathematical interpolated measured dose distribution, respectively. The sizes of $L{P}_p$ and $L{P}_m$ at the nth level are $\frac{1}{2}$ of the (n-1)th level. Different $L{P}_p$ and $L{P}_m$ levels represent dose image details for different frequency components.

b) The alpha mask (AM) is a weight matrix. For the kth level, the hybrid Laplacian pyramid $HL{P}_k$ from $L{P}_{pk}$ and $L{P}_{mk}$ using $A{M}_k$ as weights is expressed as

$HL{P}_k\left(i,j\right)= A{M}_k\left(i,j\right)\times L{P}_{pk}\left(i,j\right)+\left(1-A{M}_k\left(i,j\right)\right)\times L{P}_{mk}\left(i,j\right),$

where i and j are the pixel indices. The AM is one of the key parameters for blending logfile-based reconstructed and measured dose distributions, and it reflects the proportion of details of the logfile-based reconstructed dose distribution in the reformatted dose distribution. Furthermore, the AM is determined by the confidence of the reformatted dose distribution, which will be explained later.

c) The base dose image, i.e., the top image of the Gaussian pyramid of the measured dose distribution, contains the low-frequency information of the measurements. The base-dose image describes the main information of the final blended dose distribution. Through the superposition of a base dose image and $HL{P}_k$ followed by an upsampling, the upsampled dose image $UD{I}_{k\left(k-1\right)}$ with the blended dose details of the kth level is obtained.

d) Iterate steps b–c for level k-1 to level 1; replace the base dose image by the corresponding $UD{I}_{\left(n+1\right)n}$ during the nth iteration calculation n (1 < n < k-1).

e) Calculate $HL{P}_0$ based on step b; superimpose $HL{P}_0$ and the upsampling dose image $UD{I}_{10}$ to obtain the final blended dose image.

In addition, the reformatted dose distribution is a combination of measurements and calculations. Because some factors that can affect the actual dose distribution, such as the fluctuation of the beam spot size, was not considered in the reconstructed dose distributions, the reconstructed dose distributions and actual doses were not exactly identical. Hence, the confidence of the reformatted dose distribution must be evaluated, as it indicates the probability of the reformatted dose distribution representing the true value. The confidence coefficient of the reformatted dose distribution was estimated based on the similarity between the dose distribution of the original low-resolution MatriXX PT measurement and the downsampled logfile-based reconstructed dose distribution. The raw low-resolution measurement data of the MatriXX PT are generally reliable. The difference between the high-resolution interpolated measurement data and the true dose distribution was due to the large sampling distance and insufficient data, which resulted in the interpolation of some error data. Based on the above, for the row measurement as a reference, the more similar the reconstruction dose to the reference, the closer is the reconstruction dose is to the true value. Therefore, the reformatted dose distribution obtained by blending the measured dose with the logfile-based reconstructed dose at high frequencies is more reliable. As such, it is rational to correlate the confidence of the reformatted dose distribution with similarity. Similarity is evaluated based on gamma pass rates [24] in two dimensions with tolerances of 3 mm and 3% of the downsampled logfile-based reconstructed dose distributions and raw measurements.

2.3.2 Experiments

Experiments were performed for three different SOBP plans (SOBP plan1: range = 10 cm, width = 6 cm, measured depth = 7 cm; SOBP plan2: range = 20 cm, width = 10 cm, measured depth = 15 cm and 7 cm; SOBP plan3: range = 30 cm, width = 10 cm, measured depth = 25 cm). The 2D dose distributions at different depths of different SOBP plans were measured using the MatriXX PT with an EBT3 film attached to the front surface, and a schematic diagram of the experimental setup is shown in Fig. 4. Film measurements were used as references because of their high resolution. To prove the accuracy of the raw MatriXX PT measurement, the gamma pass rates of the original measurement data (resolution = 7.6 mm) and the downsampled film measurements (GPR_DF&OM) were calculated. The corresponding logfile-based reconstructed dose distributions were reconstructed using a dose delivery reconstruction toolkit based on logfiles. Reformatted dose distributions were obtained by blending the interpolation measurements (resolution = 1 mm) and logfile-based reconstructed dose distributions using LPIB with four levels. Furthermore, the confidence was obtained by calculating the gamma pass rates between the original MatriXX PT measurements and the downsampled logfile-based reconstructed dose distributions. To evaluate the accuracy of the reformatted dose distributions, the gamma pass rates between the interpolated MatriXX PT measurements and film dose distributions (GPR_F&IM) as well as the gamma pass rates between the reformatted dose distributions and film measurements (GPR_F&R) were calculated. The higher the gamma pass rate, the better was the agreement with the actual dose distribution.

Fig. 4Full-screen View

(Color online) Schematic diagram of experimental setups

3.1. Verification of dose computation model

Figure 5a shows the measurements and logfile-based reconstructed absolute depth doses along the central axis with three different nominal ranges and widths of SOBP plans. Because the energies used in these plans included high, middle, and low energy sections of the horizontal beamline in the SAPT, these plans were sufficient to verify whether the modeling of energies in this machine system was accurate. Figure 5a shows that the absolute depth doses reconstructed using the dose reconstruction toolkit were consistent with the measured data. As shown in Fig. 5b, the absolute value of percentage differences between the calculated doses based on logfiles and the measured doses at different depths for the three SOBP plans were within 2%, except for the depth of 40 mm in the range of 300 mm of the SOBP plan. The lateral profiles in solid water based on data measured via EBT3 films and data reconstructed by the dose reconstruction toolkit at the center of the three SOBP plans were compared, as shown in Figs. 6a–c. The relative dose lateral profiles of these two datasets demonstrated high consistency in terms of shape and width, particularly in the shoulder areas and 20%–80% of the penumbra. In quantitative analysis, 20%–80% of the penumbra calculated using the dose reconstruction toolkit were consistent with measurements within 0.1 cm, and the 50%–50% field sizes were consistent with the measurements within 0.2 cm.

Fig. 5Full-screen View

(Color online) Verification of dose reconstruction toolkit beam modelling in terms of absolute depth dose. (a) Absolute doses of reconstruction and measured doses with depths (diamond represents measured data; solid line represents reconstructed doses) (b) Deviations between reconstructed absolute dose and measured dose at different depths for three plans.

Fig. 6Full-screen View

(Color online) Verification of dose reconstruction toolkit beam modeling in relative 2D dose distribution. (a)––(c) lateral dose profiles at center of three different SOBP plans. (d) shows isodose distribution of prostate cancer between film measurement and reconstructed dose distribution. (e) shows isodose distribution of cervical cancer between film measurement and reconstructed dose distribution. (a) Range = 10 cm, SOBP width = 6 cm; (b) range = 20 cm, SOBP width = 10 cm; (c) range = 30 cm, SOBP width = 10 cm.

Figures 6d and 6e show a comparison of the logfile-based reconstructed dose distributions of the right prostate field at a depth of 20.8 cm and of the right cervical field at a depth of 20.3 cm with the film measured isodose distributions. The logfile-based reconstructed dose distribution agreed well with the film measurement. By comparing the absolute depth doses and relative 2D dose distributions with the measured data, the accuracy of the pencil beam model in this dose reconstruction toolkit can be considered reliable and acceptable.

3.2. Data Blending

Fig. 7a shows the lateral profiles of the inline of four results (film measurement, logfile-based reconstructed dose distribution, MatriXX PT measurement interpolation, and reformatted dose distribution) at a depth of 150 mm. “Horns” (indicated by arrows) that were not detected due to the low sampling resolution of MatriXX PT appeared in the reformative dose distribution, similar to the film measurement (reference). To clearly show the details of the shoulder areas, Fig. 7a was enlarged, and the start of the longitudinal coordinate was set to 0.6 instead of 0. Although the difference between the logfile-based reconstructed dose and the film dose in the middle of the lateral dose profile was evident, it remained within 3%, as supported by fact that the intensity of the pixel did not exceed 1 in the corresponding position shown in Fig. 7c. Furthermore, many spots with small monitor units (MUs) appeared in the middle of the cube because of the dosimetric superposition of other spots. When the spots with small MUs were delivered, the recorded measurements of position and dose detectors in the nozzle might exhibit some deviations owing to the sampling frequency and sensitivity of the detectors [25]. As shown in Table 1 and Fig. 7a, although the blending weight of the logfile-based reconstructed dose distribution (confidence) was 98.01%, the reformatted lateral profile did not completely coincide with the logfile-based reconstructed dose distribution. This is because the blending weight was only the weight of the detail or high-frequency component blending, and the “main” part (low frequencies) of the reformatted dose distribution was fully derived from the MatriXX PT measurement. This proves that the LPIB method fully utilized the measurement data. Fig. 7b shows the gamma index distribution of the interpolated MatriXX PT measurement and film measurement; the gamma pass rate was 84.46%. In the gamma index distribution, the closer the pixel intensity is to 0, the better is the dose deviations of the corresponding voxel of the two dose distributions. When the pixel intensity exceeds 1, the dose difference of this voxel between the two dose distributions is unacceptable. Combined with Fig. 7a, it was observed that the differences between these two dose measurements were primarily concentrated on the “horns.” Fig. 7c shows the gamma index distribution of the reformatted dose distribution and film measurements. As shown in Fig. 7c, the gamma pass rate increased to 95.19%, and the number of pixels with a gamma index greater than 1 reduced significantly. The pixel intensities of the middle position in Fig. 7c did not exceed 1, thereby proving that the difference between the logfile-based reconstructed dose and the film dose in the middle of the lateral dose profile was acceptable.

Fig. 7Full-screen View

(Color online) Comparison of reformative dose distribution and original measured dose distribution at depth of 150 mm for range = 200 mm in SOBP plan. (a) Lateral profiles of film measurement, MatriXX PT measurement interpolation, and reformative dose distribution; (b) gamma index distribution between film measurement and MatriXX PT measurement interpolation; (c) gamma index distribution between film measurement and reformative dose distribution.

A comparison of the reformatted dose distributions and interpolated 2D IC array measurements with the reference dose distribution (film measurement) at different depths for different SOBP plans are shown in Table 1. Most of the gamma pass rates from the downsampled film measurements and 2D IC array original measurements (GPR_DF&OM) exceeded 95%, indicating that the raw data measured using MatriXX PT were sufficiently accurate compared with the film measurements. As shown in the third column of Table 1, when the minimum required sampling distance was less than the sampling distance of MatriXX PT (7.6 mm), the gamma pass rates from the mathematically interpolated 2D IC array detector measurements and film measurements (GPR_F&IM) were less than 90%, e.g., numbers.1, 2, and 3, which is consistent with the results of Brodbek et al. [11]. Comparing the fifth and sixth columns of Table 1, the gamma pass rates of the reformatted dose distributions demonstrated better agreement with the film measurements than the interpolated 2D IC array measurements. Most of the gamma pass rates from the reformatted dose distributions and film measurements (GPR_F&R) exceeded 95%. Moreover, the gamma pass rates shown in the fourth and sixth columns of Table 1 were similar, indicating that the resolution of the MatriXX PT measurements improved with the same accuracy as the original low-resolution measured data. Mathematical interpolation methods cannot achieve such results in dose distributions containing more high-frequency components.

Owing to multiple Coulomb scattering, the dose distribution was more smoothed out at larger depths, as shown by number 4 in Table 1. In most clinical plans, the minimum required sampling distance at these depths is larger; therefore, MatriXX PT measurements can fully reflect the actual dose distribution, and the original GPR_F&IM is typically higher.

In addition to the performance of the monitor chambers, the variation in spot size during irradiation contributed to the deviations between the logfile-based reconstructed dose and delivered dose distributions. Kraan et al.[26] reported that the gamma pass rates of most clinical plans with ±20% variation in medium spot size cannot achieve 90% with the 2 mm/2% criterion. The threshold of the spot size variation was 15% at the horizontal beamline of the SAPT. The variation in spot size was not considered in the logfile-based reconstructed dose distribution. Furthermore, because the beam spot shape was not round, shape distortion occurred during gantry rotation; this resulted in differences between the logfile-based reconstructed dose and delivered dose distributions, and they were not considered in the logfiles. Hence, for some smooth dose distribution or area, 2D IC array measurements are relatively accurate and can be used to improve the logfile-based reconstructed dose distribution, such as the number 4 and smooth area in Fig. 7a.

The confidence of the reformatted dose distribution was generally greater than 95%, indicating that the reformatted dose distribution can represent the true dose distribution with high probability. However, number 2 was measured at a shallow depth and possessed more high-frequency components. The sampling distance of the 2D IC array was much larger than the minimum required sampling distance, and many details were lost in the 2D IC detector measurement. In general, provided that the dose computation model for the pencil beam is correct, the logfile-based reconstructed dose distribution will exhibit better consistency with the actual distribution. Hence, the gamma pass rates of the original 2D IC detector measurement and the downsampled logfile-based reconstructed dose distribution were low, thereby resulting in a low confidence coefficient.

In data blending, the AM is determined by the confidence of the reformatted dose distribution, which is the similarity between the original measurement and the downsampled logfile-based reconstructed dose distribution. Compared with treatment plans with smooth dose distributions, owing to the low sampling rate of MatriXX PT and the dose response of a single sensor, the similarities between the raw measurements and the downsampled logfile-based reconstructed dose distributions of treatment plans with more high-frequency components were lower. Therefore, the proportion of the logfile-based reconstructed dose distribution in the blended data was smaller, and the reformatted dose distribution was not consistent with the actual data, such as Number 2. By contrast, for a smooth dose distribution, the proportion of the logfile-based reconstructed dose distribution in the reformatted dose distribution was large. Therefore, the use of confidence as an AM limits the improvement of measured dose distributions with extremely steep gradient areas.

Another essential parameter in LPIB is the number of pyramid levels, which affects the proportion of measured data in the reformatted dose distribution. When the number of pyramid levels is between 1 and 3, the logfile-based reconstructed dose distribution accounts for extremely small weights, the improvement in the measurement part that is overlooked due to low resolution is less, and the reformatted effect is not significant. When the number of pyramid levels exceeds five, the measured data account for a small proportion, which violates our intention to fully utilize the data. When the number of pyramid levels is four, the proportions of the logfile-based reconstructed dose distribution and the measured data are balanced.

Regarding the experiments performed in this study, the number of plans for clinical cases is few, and these plans are not challenging. This study lacks plans based on clinical cases that involve many organs at risk such as nasopharyngeal cancer or superficial tumors such as breast cancer. However, we believe that, with subsequent clinical testing for the horizontal beamline in the SAPT, more clinical case plans will be established to support the conclusion presented herein. Furthermore, because MatriXX PT does not perform absolute dose calibration in the SAPT, all measured and reformatted dose distributions are relative values. It is believed that LPIB demonstrates greater potential for absolute dose improvement.