Proton 3D dose measurement with a multi-layer strip ionization chamber (MLSIC) device

Objective. In current clinical practice for quality assurance (QA), intensity modulated proton therapy (IMPT) fields are verified by measuring planar dose distributions at one or a few selected depths in a phantom. A QA device that measures full 3D dose distributions at high spatiotemporal resolution would be highly beneficial for existing as well as emerging proton therapy techniques such as FLASH radiotherapy. Our objective is to demonstrate feasibility of 3D dose measurement for IMPT fields using a dedicated multi-layer strip ionization chamber (MLSIC) device. Approach. Our developed MLSIC comprises a total of 66 layers of strip ion chamber (IC) plates arranged, alternatively, in the x and y direction. The first two layers each has 128 channels in 2 mm spacing, and the following 64 layers each has 32/33 IC strips in 8 mm spacing which are interconnected every eight channels. A total of 768-channel IC signals are integrated and sampled at a speed of 6 kfps. The MLSIC has a total of 19.2 cm water equivalent thickness and is capable of measurement over a 25 × 25 cm2 field size. A reconstruction algorithm is developed to reconstruct 3D dose distribution for each spot at all depths by considering a double-Gaussian–Cauchy–Lorentz model. The 3D dose distribution of each beam is obtained by summing all spots. The performance of our MLSIC is evaluated for a clinical pencil beam scanning (PBS) plan. Main results. The dose distributions for each proton spot can be successfully reconstructed from the ionization current measurement of the strip ICs at different depths, which can be further summed up to a 3D dose distribution for the beam. 3D Gamma Index analysis indicates acceptable agreement between the measured and expected dose distributions from simulation, Zebra and MatriXX. Significance. The dedicated MLSIC is the first pseudo-3D QA device that can measure 3D dose distribution in PBS proton fields spot-by-spot.


Introduction
Proton therapy has shown great advantage over external beam photon therapy in terms of reducing the integral dose to the healthy tissues, particularly dose located beyond the target volume (Kassaee 2021).Intensity-modulated proton therapy (IMPT) by pencil beam scanning (PBS) has largely replaced double scattering proton therapy due to its ability to spatially modulate proton fluence and generate an optimal dose distribution via inverse treatment plan optimization (Oelfke and Bortfeld 2003, Muzik et al 2008, Kassaee 2021).Field-specific quality assurance (QA) of the IMPT beams prior to treatment delivery is essential for the safety of proton therapy (Arjomandy et al 2019).In current clinical practice, a two-dimensional (2D) dosimetry device is used to measure the planar dose at one to three selected depths in a phantom (Trnkova et al 2016), which is not only a time-consuming process, but also insensitive to certain failures (Bizzocchi et al 2017, Chan et al 2017); for example, beam energy variation cannot be easily identified from the plane perpendicular to the beam axis and the possibility of undetected failure in areas that were not measured remains.A 3D dose measurement would be a more comprehensive solution for PBS field-specific QA.Besides patient field QA, daily and monthly treatment machine QA also prefer a device that can perform 3D dose measurement.In current practice, multiple devices are used to measure different characteristics of pencil beams.A 3D QA device that can measure all aspects of the beams with a single beam delivery can reduce the time and labor needed in these clinical tasks.
Polymer gels, radiochromic gels, and radiochromic plastics can be employed for 3D dosimetry of radiation therapy (RT) fields (De Deene 2022); however, their time-consuming fabrication and readout process, as well as possible quenching effects manifested as decreased sensitivity of dose response due to radical recombination at high LET regions of the field, make such dosimeters less appealing for routine clinical use in proton therapy clinics (Mihailidis 2020).Scintillation imaging and Cherenkov radiation imaging (Beddar andBeaulieu 2016, Darafsheh 2021) have shown great promise in 3D dosimetry in RT.However, their deployment for proton therapy 3D dosimetry is not straightforward; in the former, conventional scintillators require non-trivial correction factors for ionization quenching in high LET fields manifested as an under-response to dose as a result of non-radiative de-excitation modes.In the latter, Cherenkov radiation is extremely weak and does not directly follow the dose in proton therapy fields, particularly at larger depths (Darafsheh et al 2016(Darafsheh et al , 2017)).
In this context, ionization chamber (IC)-based technology looks appealing for development of 3D dosimeters due to the well-established use of ICs for 1D and 2D dosimetry in RT.IC array-based devices such as MatriXX and Zebra (IBA dosimetry GmbH, Germany) are commonly used in RT for 2D proton lateral profile and depth-dose measurement, respectively; however, neither of these devices can provide a 3D dose map of the beam.Previously, we developed a multi-layer strip ionization chamber (MLSIC) device that can measure the characteristics of proton beams spot-by-spot (Zhou et al 2022).In this study, we further improved the MLSIC and developed 3D dose reconstruction method that enables measurement of 3D dose distribution for MLSIC.

Dedicated multi-layer strip ionization chamber (MLSIC) design
Figure 1 illustrates the schematic and a prototype MLSIC device set up to perform measurement at a proton therapy machine (ProBeam TM , Varian Medical Systems, Palo Alto, CA, USA).In contrast to the previous MLSIC prototype (Zhou et al 2022), in which only the top two layers are strip IC plates, all layers in our novel MLSIC device are made of strip IC plates.The widths of IC strips are 2 mm in the first two layers (proximal to the beam) and 8 mm in the remaining 64 layers.The 8 mm IC strip plates are offset by 4 mm to increase spatial resolution.The additional ionization current measurements in the x and y directions at different depths provide necessary data to reconstruct the 3D dose distributions.
The first two layers have 128 channels of 2 mm wide IC strips, thus can measure a field size as large as 25 cm × 25 cm.The physical thickness of the printed circuit board (PCB) was 1.6 mm corresponding to a measured water-equivalent thickness (WET) of 2.9 mm.By introducing 1.3 mm airgap in between consecutive layers along the beam direction, the MLSIC is water-equivalent with a total WET of about 19.2 cm (i.e.2.9 mm WET of each layer × 66 layers = 191.4mm).Additional solid water buildup material can be used to measure beams with a range greater than 19 cm.
The IC plates were made from standard fiberglass PCB material.The charge collecting signal electrodes were etched on the front and back sides of the PCB.Additional high voltage electrode plates were placed between the charge collecting plates.In order to reduce the total number of channels, for layers 2-65 (start form 0), the channels on the same layer were combined and share the same ADC (analogic to digital converter) in increments of 8.The MLSIC device therefore is comprised of 768 ADC channels in total, which sample ionization current at a frame rate as high as 6k fps.FPGA firmware and computer software were developed to acquire and display the data in real-time.

Detector relative sensitivity and water equivalent thickness (WET) calibration
Each electrode plate was made of 1.6 mm thick FR4 type PCB.Due to manufacturing variation, there are slight variations in sensitivity between the different channels.A high energy PBS beam was used to scan across the maximum field size to calibrate the relative sensitivity of the all channels.The WET values of the electrode plates were calibrated using proton beams with different energies.The positions of Bragg peaks in the IDD curve were measured, and the WET of each board was determined by fitting the positions of the Bragg peaks with a linear function.

Absolute MU calibration
PBS beams of different energies and known monitor unit (MU) per spots were delivered to the MLSIC.The charges of all electrodes plates per spot were obtained by dividing the accumulated charges by the number of spots.MU calibration curves were obtained by fitting the data of a few measured energies.The MU of a proton spot beam of any energy can be interpolated from the MU calibration curve.

Absolute dose calibration
Absolute dose is proportional to the charge measured by the ADC.The MLSIC is calibrated with a monthly QA field with a known uniform dose level.A QA beam with a uniform dose across a cubic volume was administered to the MLSIC.The dose at the central point of this region served as the calibration reference for the MLSIC.

Spot dose distribution model
The strip ICs measure the line integral of two-dimensional (2D) dose distributions.Unlike computed tomography (CT) that reconstructs anatomic features from line integrals measured at hundreds of projection angles, MLSIC reconstructs 3D dose distributions from projections in x and y directions.To recover the 2D dose distribution from line integral data along x and y axes at varying depths, the dose distribution of a proton spot is modeled with a double Gaussian-Cauchy model (Yang et al 2022), terming this as the lateral profile function (LPF) where σ 1−3 are the variance of Gaussian-Cauchy distribution, w 1−3 are weights of corresponding distribution and µ is the beam center.They are determined by fitting the measurement data.

Detector geometry model
As with CT image reconstruction, it is imperative to establish the detector geometry model for spot dose reconstruction.The detector comprises two distinct board types: The strip IC plates of the first board type can measure spot dose profile with 2 mm spatial resolution at the front surface; The strip IC plates of the second board type have 8 mm physical spacing between IC channels and facilitate the reconstruction of the 3D dose distribution inside the detector.In order to increase sampling resolution, the strip IC plates of the second board type and third board type are shifted 4 mm laterally from layer to layer so that effective strip resolution is doubled.The maximum measurable spot size can be estimated by this formula: FWHM ∼ 2.355σ = 8 channels × 8 mm.The maximum beam sigam is about 27.2 mm.
The type 1 board has a total of 128 independent ADC channels and captures most information of the proton spot position; In contrast, the IC channels of type 2 board connect to only eight independent ADC channels per layer to reduce the total number of ADC channels, allowing them to record only a down-sampled profile.For example, strip ICs with channel number equal to 1 mod 8 (1, 9, 17, 25) are linked to the same ADC channel #1.As a result, signals collected by these strips are aggregated into this single channel.The accompanying figure 2(c) elucidates the mechanism of this signal accumulation across all channels where the blue curve depicts the full-scale high-resolution x profile, while the star markers represent the accumulated signal within the 8 z-channels (type 2/3 IC boards).These markers are periodically repeated (four times) to align with the original board design.The high-resolution profile to low-resolution profile conversion can be analogous to an average pooling, therefore the low-resolution peak could be slightly deviate from the high-resolution peak.

Spot dose reconstruction
Ionization currents of all channels are sampled continuously at a frame rate of 6 kfps.The dose distributions of each spot are reconstructed from the raw data.The detailed spot dose reconstruction algorithm is described in appendix.The dose distributions of all the spots are summed together to get the composite dose distribution.

QA analysis
The measurement was performed using a clinical isochronous PBS proton therapy machine (ProBeam TM , Varian Medical System, Palo Alto, California, USA).After calibration fields were measured, a clinical IMPT field for prostate cancer treatment was measured for QA analysis.Calibration and an IMPT test field was measured at the same time so that temperature and pressure correction was unnecessary.

Spot-by-spot QA analysis
An IMPT PBS beam can be compared to the treatment plan spot-by-spot.The profile, position, energy and weight of each spot can be measured and compared to the treatment plan.

2D and 3D dose distribution analysis
The dose distributions of the spots are reconstructed independently, and the 3D dose distribution of the field is obtained by adding up all the spot doses.The measured dose distributions are compared to the treatment plan using traditional metrics.2D and 3D gamma indices are calculated.

MU calibration
The top panel of figure 3 shows the measurements of proton beams with ten different energies (70,80,90,110,130,150,170,190,210,230 MeV).Since it is a relative measurement to correct for slight differences in between strips, it is machine-agnostic.All beams were delivered in a 20 × 20 cm 2 field size with 5 mm spot spacing.The beams with energies  were measured with 0, 10, and 15 cm solid water buildup.Each beam configuration encompassed a grid of 41 × 41 spots, amounting to 1681 spots in total, 10 MU per spot, the entire setup delivered 16 810 MU.The area under the fitted integral depth charge curve is proportional to the monitor unit (MU) for a given energy.Consequently, any proton beam MU conversion ratio can be deduced from the above figure.It is worth noting that the 150 MeV curves, both with and without the 10 cm buildup, exhibit a slight range offset of 1.5 mm.Several factors could contribute to this, including potential imperfections in the setup or variations in the Water Equivalent Thickness (WET) of the solid water material, which may not precisely match the intended 10.0 cm thickness.Additionally, the MLSIC's limited depth resolution of 2.9 mm or imperfect calibration could play a role.However, this offset has negligible impact on MU calibration.
Among the 768 ADC channels in this device, some of them are 'bad' channels.It is difficult to fix all of them physically.These 'bad' channels are shown up as outliers in figure 3(a), like 70 MeV curve.The 'bad' channels have unpredictable behavior, and they only affect layers at fixed location.In a scanning pencil beam, not all spots are affected by these fixed location 'bad' channels.Outliers in figure 3(a) were interpolated from their neighbors.

Spot-by-spot QA analysis
The ProBeam system delivers proton spots in quasi-continuous mode (∼72 MHz frequency).The 'raster mode' scanning leads to ambiguous separation between individual spots (beam stays on between planned spots) (Huang et al 2023).As a result, the spot 'spills' between the discrete spots in the clinical plan.We identified cluster points from the measured data.Any events within a 0.5 mm radius circle around these cluster points were considered as belonging to that particular cluster.Dose values in the same cluster were attributed to its center point, whereas non-clustered events were designated as 'out of spot' doses.
The prostate treatment field comprises 12 distinct energy layers.Black circles in the visualization represent the average locations of clustered proton events.We set the radius of these circles to 0.5 mm.Events inside these circles are referred to as 'In spot' events, while those outsides are termed 'Out spot' events.All 'In spot' MUs were aggregated and compared against the DICOM plan.However, during the dose reconstruction procedure, the dose was reconstructed from each proton event rather than from every individual spot.This distinction could be crucial for calculating the instantaneous dose rate.

Reconstruction of spot doses
The MLSIC device incorporates a total of 768 ADC channels to capture signals throughout the 3D space.Figure 5(a) shows the x and y profile measured by the first two layers (x 0 and y 0 ) that comprises 128 individual ADC channels each.The layer x 1−32 and y 1−32 not only have wider IC strips, but also all channels share eight ADCs.The measured signals in these layers exhibit a sawtooth pattern as the boards are installed with 4 mm offset from layer to layer in order to improve sample resolution.Leveraging the introduced reconstruction algorithm, the measured data were fit using the LPF based on the system matrix model of the MLSIC.Subsequently, this enables us to translate the LPF into a high-resolution 2D dose distribution of each spot as demonstrated in figure 5.

Measurement of charge to dose conversion parameter
The MLSIC device measures charge directly.The charge-to-dose conversion parameter is obtained by matching the measured depth dose with the planned depth dose of a QA field as shown in figure 6, assuming the QA field is delivered with accurate dose level.This QA field encompasses 35 energy layers, collectively contributing to a cubic region with a uniform dose of 0.92 Gy.Additionally, Zebra was employed to measure the depth dose curve at the field center, with the measurement subsequently rescaled to match the actual dose.Notably, Zebra's charge collection occurs within a circular electrode with a diameter of 2.5 cm, potentially resulting in slight differences between the depth dose curve and the dose distribution at the field center.
We reconstructed the 3D dose distribution for every proton event, like yellow dots in figure 4, across all energy levels.There are also some small artifacts in the reconstructed dose distribution, not all proton spots have the same 'good quality' , the reconstructed dose sometimes looks zig-zag between layers or have some strips.From this, we selected a central flat dose region measuring 10 mm × 10 mm × 82 mm to align the reconstructed dose with the planned dose.This determined charge-to-dose conversion ratio was subsequently employed in other proton plans for absolute dose calculation.

Measurement of 3D dose distribution of a clinical IMPT treatment field
A randomly selected clinical IMPT treatment field was measured by MLSIC.3D dose distributions were reconstructed spot by spot and the voxel size was 2 mm × 2 mm × 2.9 mm. Figure 7 qualitatively compares the plan and measured 3D dose distributions of the same treatment field.Figure 8 plots the profiles and depth dose curves of the plan and measured dose distributions.Both dose profiles and depth dose curves show excellent agreement between the planned and measured dose distributions.
In figure 9, a comparison is made between the measured and planned 3D dose distributions across three different perspectives.The initial row juxtaposes the dose distribution within the X/Y plane against both the calculated dose and the dose distribution measured using MatriXX at a depth of 156 mm (comprising 150 mm of solid water and 6 mm of internal build-up material within MatriXX).With a pixel size of approximately 7.6 mm, MatriXX cannot provide dose details.However, its measurement can serve as supplemental evidence of the accuracy of the reconstructed dose.Consequently, the reconstructed dose exhibits a high level of consistency with both the simulation and the results obtained from MatriXX.The 3D Gamma passing rate stands at 88.89%, based on a 3 mm/3% criteria, 10% threshold using plan dose set as the reference.This illustrates the measured locations of proton events.Black circles represent the mean locations of clustered proton events, each with a 0.5 mm radius.Yellow dots denote 'out of spot' events, signifying proton events occurring between planned spots, while red crosses mark 'in spot' events, located within a 0.5 mm radius of their corresponding cluster points.(b) Comparison of MU between measured and planned spots.The size of each circle is proportional to the MU value.The MUs from 'in spot' events have been aggregated to their respective cluster points.

Discussion
In this study, feasibility of 3D dosimetry was demonstrated by delivering a clinical IMPT plan to a dedicated MLSIC device and reconstructing the 3D dose distribution from the measurement.A 3D gamma passing rate of 89% (3 mm/3%) was achieved when the 3D dose measured by the MLSIC was compared to that calculated    A comparative analysis of the planned dose, reconstructed dose and the signed 3D gamma index using a 3 mm/3% criterion.The first row visualizes the dose distribution on the x/y plane, specifically at a depth of 156.3 mm, with red lines marking the slice locations for the images in the second and third rows.The second row presents the dose distribution on the x/z plane where y is set to 1 mm.The third row illustrates the dose distribution on the y/z plane with x set to −7 mm. by the TPS.Besides the real delivery variation, we speculate that one source of discrepancy can stem from partially capturing the scattered dose surrounding the primary beam.The MLSIC was engineered to accommodate the largest spot sizes of most proton machines as one of the design constraints.In the context of a prostate treatment field with ProBeam machine, the beam sigma of the lowest energy,149.2MeV, is approximately 4.8 mm, while the strip width in layer x1-32 and y1-32 as wide as 8 mm which makes it difficult to distinguish between the primary dose and the scattered dose in the measured results.In principle, by using narrower strip ICs the resolution can be improved.However, it would result in a reduction of the strip width available for the eight independent ADC channels, making it challenging to accurately reconstruct beams with a larger sigma.Adding more ADC channels can improve the accuracy with an increased engineering difficulty.Another source of discrepancy may stem from a slight misalignment of the detector, for example a small offset at the edge can leads to a large difference in the reconstructed dose.Further studies on various IMPT fields are needed to further quantify the accuracy and limitations of MLSIC.
The MLSIC device is, to the best of our knowledge, the first 3D dosimeter that can measure 3D dose distribution in an IMPT field spot-by-spot.Compared with 3D gel dosimetry, MSLIC does not require an additional readout step after irradiation which makes it convenient to use in the clinic.Compared to scintillation imaging 3D dosimetry, MLSIC can faithfully reconstruct proton depth dose profiles without being impacted by quenching effects.It can perform overall 3D dose comparison as well as spot-by-spot evaluation of the IMPT beam delivery.With a sampling rate as high as 6k fps, MLISIC can reconstruct 3D dose distribution spot-by-spot.The temporal information is very useful for the dose rate measurement, which is very important for future FLASH-RT treatments.

Conclusion
A dose reconstruction method was developed for the MLSIC.MLSIC was able to measure and reconstruct proton PBS beams spot-by-spot.The measured 3D dose distribution showed acceptable agreement with the expected dose distribution from simulation and other commercial devices.The MLSIC is the first device that can measure 3D dose distributions of PBS proton beams at such a high speed, which makes it a suitable candidate for future FLASH-RT dosimetry.
The first branch is: The second branch in depth dose function is: The PCF D a (x) was used in above formula.We can approximate it in terms of f a (x) which is a simple function that can be calculated without iteration ) .
The PCF term e − (R 0 −z) 2 { D a (0) e g(x, p−(a),q−(a)) when x < 0 D a (0) e g(x,p+(a),q+(a))− x 2 2 when x >= 0 g (x, p, q) = p 0 x 5 + p 1 x 4 + p 2 x 3 + p 3 x 2 + p 4 x x 4 + q 0 x 3 + q 1 x 2 + q 2 x + q 3 e − x 2 4 term was cancelled when x < 0, this could avoid numerical instability when x is small.The relative error of our approximation function in x ∈ [−10, 5] is less than 0.03%.The MATLAB code of the depth dose function can be found in the supplyment materials.The parameters are given below:

Technical specifications
1. Assuming the dose profile follows a Gaussian distribution, we can estimate the maximum spot size that can be recovered using its Full Width Half Maximum (FWHM).If the FWHM is smaller than the width of 8 strips, it indicates that the Gaussian shape can potentially be accurately reconstructed.The beam sigma can be given by: σ < 8 × 8 mm 2 √ 2ln2 ≈ 27.13 mm 2. The system operates at a rate of 6 kfps, with each frame lasting 160 microseconds.Within each frame, the FPGA sends data of 768 channels to the ethernet, each channel represented by 16 bits.The data latency is also 160 microseconds.Notably, the data is not buffered in the FPGA, allowing for continuous acquisition as long as the hard drive has available space.

Figure 1 .
Figure 1.(a) Schematic of the modified MLSIC device; and (b) The MLSIC device and the measurement setup.The MLSIC device is composed of 66 layers of strip ionization chamber plates that can measure an IMPT beam over a maximum 25 cm × 25 cm field size and a maximum range of 19.2 cm WET.

Figure 2 .
Figure 2. (a) The second board type with 8 mm IC strips with shared ADC every eighth channel; (b) The third board type with 4 and 8 mm IC strips with shared ADC every eighth channel; (c) The measured profiles by the first board type (blue line) and second board types (star markers).Because the ADC channels of the second board type are interconnected, the spot position is differentiated with the help of information from the first board type.

Figure 3 .
Figure 3. (a) Integral depth charge of proton beam with 10 various energies with known MU measured with MLSIC, 10 and 15 cm solid water were used as buildup for high energy beams.The dots are raw data, the solid lines and dash lines are fitted curves; and (b) MU calibration curve derived from the depth charge curves.The MU of a proton beam with an arbitrary energy can be looked up from the calibration curve.Suitable buildup was used in the measurement to stop the beams in the MLISC.

Figure 4 .
Figure 4.(a)  This illustrates the measured locations of proton events.Black circles represent the mean locations of clustered proton events, each with a 0.5 mm radius.Yellow dots denote 'out of spot' events, signifying proton events occurring between planned spots, while red crosses mark 'in spot' events, located within a 0.5 mm radius of their corresponding cluster points.(b) Comparison of MU between measured and planned spots.The size of each circle is proportional to the MU value.The MUs from 'in spot' events have been aggregated to their respective cluster points.

Figure 6 .
Figure 6.(a) The reconstructed dose distributions in x/y plane at a depth of 209 mm of a clinical QA field with a known dose level; (b) Reconstructed dose distributions in x/z plane through central axis; (c) Matching of plan, Zebra and measured depth dose curves at the field center.Depth dose curves at different energy layers are also plotted.(d) Volume rendering of reconstructed 3D dose distribution.

Figure 7 .
Figure 7. (a) Volume rendering of 3D plan dose, red means higher dose.(b) Volume rendering of 3D reconstructed dose, red means higher dose.

Figure 8 .
Figure 8. Dose profile comparisons in the x, y, and z directions with 10% mask, respectively.The red vertical dot lines pinpoints the precise x, y, z coordinates of the chosen dose profile positions, the yellow curves are the relative dose difference normalized by the dose at the chosen position.Planned dose distribution is used as reference in the plots.

Figure 9 .
Figure9.A comparative analysis of the planned dose, reconstructed dose and the signed 3D gamma index using a 3 mm/3% criterion.The first row visualizes the dose distribution on the x/y plane, specifically at a depth of 156.3 mm, with red lines marking the slice locations for the images in the second and third rows.The second row presents the dose distribution on the x/z plane where y is set to 1 mm.The third row illustrates the dose distribution on the y/z plane with x set to −7 mm.