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A novel methodology to estimate pileup effects and induced error in microdosimetric spectra

This paper presents a novel algorithm, validated through GEANT4 simulations and experimental data from a spherical TEPC exposed to proton beams, to estimate pileup effects and their induced errors in microdosimetric spectra, thereby enabling more accurate clinical applications of microdosimetry in particle therapy.

Original authors: E. Pierobon, M. Missiaggia, F. G. Cordoni, C. La Tessa

Published 2026-09-10

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CC BY 4.0

Original authors: E. Pierobon, M. Missiaggia, F. G. Cordoni, C. La Tessa

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of radiation therapy, doctors use beams of particles to destroy cancer cells while sparing healthy tissue. To ensure these beams are working correctly, scientists need to measure exactly how the energy is deposited as it travels through the body. One powerful way to do this is by looking at the radiation not just as a steady stream, but as a collection of individual, tiny impacts. This field, known as microdosimetry, allows researchers to see the granular details of how radiation interacts with matter on a microscopic scale, providing a much clearer picture of the radiation's quality than older methods. This level of detail is becoming increasingly important for verifying the safety and effectiveness of particle therapy treatments. However, there is a significant hurdle: in a real-world hospital setting, the beam is often so intense that the detectors used to measure it get overwhelmed. When too many particles arrive in a fraction of a second, the detector cannot distinguish between them, causing the signals to merge into a single, distorted reading. This phenomenon, called pileup, scrambles the data and can lead to inaccurate conclusions about the treatment's quality.

A team of researchers set out to solve this problem by developing a new way to understand and correct for these distortions. They focused on a specific type of detector, a spherical device filled with gas that mimics human tissue, which is considered the gold standard for these measurements. The scientists wanted to know exactly how much the pileup effect was messing up their data and whether they could still trust the results if they could mathematically account for the error. To find the answer, they conducted experiments at a proton therapy center in Italy, firing beams of protons at two different energy levels into their detector. They measured the radiation at a wide range of intensities, from very low rates where the detector worked perfectly, up to extremely high rates where the signals began to overlap and merge.

To separate the truth from the distortion, the researchers used a clever two-step approach. First, they used powerful computer simulations to create a perfect, theoretical version of the radiation data, free from any real-world errors. Then, they wrote a new computer algorithm that could intentionally introduce the same kind of signal-mixing errors into their perfect simulation, mimicking exactly what happens in the real detector. By comparing the real, messy experimental data against their simulated data with varying amounts of "fake" pileup, they could pinpoint exactly how much pileup was present in their measurements. It was like having a pristine reference photo and then digitally adding different amounts of blur to it until the blurred version matched the real, damaged photo perfectly. This allowed them to calculate the precise probability that any given signal was actually a combination of multiple particles rather than a single one.

The study revealed that the relationship between the speed of the particle beam and the amount of distortion is not a simple straight line. As the beam gets faster, the chance of signals overlapping increases, but eventually, the detector reaches a point where it is so overwhelmed that the distortion levels off. The researchers found that this behavior depends on the energy of the beam; higher energy beams caused more distortion at the same speed compared to lower energy beams. Crucially, they determined the specific limits for safe measurement. They found that if the particle rate is kept below roughly 429 particles per second, the pileup is so rare—occurring in only about one in ten thousand events—that the error in the final measurement is less than one percent, which is negligible. However, if the rate climbs higher, the error grows. To keep the error in the final energy measurement below five percent, a level generally considered acceptable for high-quality data, the pileup probability must stay below 18 percent. This corresponds to a particle rate of about 10,120 particles per second.

The team also compared their new, detailed method against older, simpler techniques that rely only on counting how many signals are lost. They found that while the old methods give a rough idea, their new approach provides a much more accurate picture of how the spectrum is actually changing shape. They discovered that the older methods sometimes fail to capture the full complexity of the problem, particularly because the way particles are delivered by medical machines does not always follow the random patterns that older theories assume. By using their new algorithm, the researchers showed that even when pileup is present, it is possible to recover the true nature of the radiation field if the level of distortion is known and corrected. This means that hospitals do not necessarily have to slow down their beams to impossibly low speeds to get good data. Instead, they can use this new tool to understand the errors in their current measurements and correct them, making microdosimetry a viable and reliable tool for quality assurance in particle therapy clinics around the world.

Technical Summary: A Novel Methodology to Estimate Pileup Effects and Induced Error in Microdosimetric Spectra

Problem Statement
Microdosimetry offers a granular characterization of radiation fields, utilizing lineal energy ( $y$ ) as a well-defined physical quantity, making it increasingly vital for quality assurance (QA) in particle therapy. However, the high particle rates inherent to clinical treatment delivery often exceed the capabilities of standard detectors, leading to "pileup." Pileup occurs when the time between consecutive events is shorter than the detector's charge collection time or the electronic acquisition chain's processing time. This results in the overlap of signals, distorting the microdosimetric spectrum by shifting it toward higher lineal energy values. Consequently, derived quantities such as the frequency-mean lineal energy ( $y_F$ ) and dose-mean lineal energy ( $y_D$ ) are overestimated, compromising the accuracy of radiobiological modeling and clinical QA. While pileup has been studied in neutron beams and limited rate ranges, there is a significant gap in understanding its impact on ion beams at therapeutic rates, particularly regarding the quantification of induced errors in microdosimetric spectra.

Methodology
The authors investigated pileup effects in a commercial spherical Tissue Equivalent Proportional Counter (TEPC) exposed to 11 MeV and 70 MeV proton beams at the Trento Proton Therapy Center. The study employed a dual approach combining experimental measurements with Monte Carlo simulations:

Experimental Setup: Microdosimetric spectra were acquired across a particle rate range of $10^3$ to $10^6$ particles per second (pps). Beam intensity was monitored using an Ionization Chamber (IC) calibrated against a plastic scintillator (SC) to establish a robust relationship between IC counts and actual particle rates. The TEPC readout chain utilized multiple gain settings to cover the dynamic range, with pileup rejection mechanisms intentionally disabled to study raw pileup effects.
Particle Rate Estimation: A linear calibration was established between the IC count rate and the particle rate measured by the SC. This allowed for the extrapolation of the true particle rate incident on the TEPC ( $TEPC_{IC-SC}$ ) across the full dynamic range, correcting for saturation effects observed in the TEPC's own readout.
Monte Carlo Simulation (Novel Algorithm): Using Geant4, the authors simulated the experimental geometry to generate pileup-free reference spectra. A stochastic algorithm was then developed to artificially induce pileup on these simulated spectra. This algorithm models pileup by assuming additional interactions follow a Poisson distribution. For a given pileup probability ( $p$ ), the algorithm samples a multiplicity ( $k$ ) for each event and sums the energy depositions of $k$ randomly selected events from the reference dataset.
Quantitative Comparison: The simulated spectra, generated at various pileup probabilities, were compared to experimental spectra using the Kolmogorov-Smirnov (K-S) test. This statistical test identified the pileup probability that best matched the experimental data, establishing a direct correlation between the corrected particle rate and the pileup probability.
Validation: The proposed methodology was cross-validated against a traditional dead-time based approach (assuming a non-paralyzable system) to estimate pileup probability and dead time ( $\tau$ ).

Key Contributions

Stochastic Pileup Simulation: Development of a novel algorithm that applies pileup effects to simulated microdosimetric spectra based on a defined probability, allowing for the generation of a comprehensive library of distorted spectra.
Experimental Pileup Estimation: A methodology to estimate the pileup contribution on experimental data by matching measured spectra against the simulated library using the K-S test.
Error Quantification: A systematic evaluation of the induced error on $y_F$ as a function of particle rate and pileup probability.
Rate Thresholds: Identification of specific particle rate thresholds where pileup effects become negligible or manageable for clinical applications.

Results

Rate-Pileup Relationship: The study established a non-linear relationship between particle rate and pileup probability, modeled by an exponential saturation function. The 70 MeV beam exhibited higher pileup susceptibility compared to the 11 MeV beam at equivalent rates.
Negligible Pileup Threshold: At a particle rate of 429 ± 21 pps, the pileup probability was found to be negligible (0.01 ± 0.01%), resulting in an error on $y_F$ of less than 1%.
Acceptable Error Threshold: To maintain an error on $y_F$ below 5%, the pileup level must be kept below 18 ± 2%. This corresponds to a particle rate of 1.012 ± 0.005 × 10⁴ pps (approx. 10.12 kpps).
Energy Dependence: The 70 MeV setup showed a higher dead time and greater pileup susceptibility than the 11 MeV setup, contrary to the expectation that lower energy protons (depositing more energy) would be more susceptible. The authors attribute this to the temporal structure of the cyclotron beam (bunching), which violates the Poissonian assumption of independent events, particularly affecting the 11 MeV setup which requires higher initial intensities to compensate for beam degradation.
Validation: The pileup probabilities derived from the novel Monte Carlo method showed reasonable agreement with those estimated via the dead-time method, particularly for the 70 MeV data, though discrepancies were noted at high rates for the 11 MeV data due to non-Poissonian beam structures.

Significance and Claims
The paper claims that while acquiring microdosimetric data at clinical rates without pileup is often impossible due to facility constraints, the proposed methodology allows for the effective use of pileup-affected data. By quantifying the pileup probability and the resulting error on key microdosimetric quantities, researchers can determine if the uncertainty is within acceptable limits for their specific application.

The authors emphasize that their approach provides a reliable tool for addressing pileup issues without requiring the modification of clinical beamlines or the reduction of particle rates to unfeasible levels. The algorithm is presented as a generalizable tool applicable to any type of microdosimetric measurement, facilitating the integration of microdosimetry into clinical settings for quality assurance. The study concludes that experimental microdosimetry can still provide valuable information for characterizing radiation quality in particle therapy, provided the associated pileup-induced uncertainties are accurately estimated and deemed acceptable.

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