arXiv subjects

Zoltán Perkó

Publications and source records attributed to Zoltán Perkó.

14 recordsLinked to original sources

arXiv2026

Direct probabilistic IMPT treatment planning with setup and range errors for neuro-oncological patients

To show clinical feasibility of a previously proposed probabilistic planning approach that can precisely optimize for clinical goals with patient-specific acceptance probabilities on a neuro-oncological patient group, we compared probabilistic plans with (automated) robust plans for one patient (group A) that could achieve sufficient clinical target coverage and for four patients (group B) where target coverage had to be compromised due to organ-at-risk (OAR) dose constraints. The probabilistic approach is percentile-based and uses the fact that a (dose) percentile can be approximated as a linear combination of its expected value and standard deviation. The optimization has a nested structure: the inner optimization optimizes the beam weights for a given percentile estimate, while an outer loop iteratively updates and improves the accuracy of the percentile estimate. For every outer iteration, the optimization is warm-started from the previous iteration. Percentiles are efficiently calculated by sampling a polynomial chaos expansion of the dose-influence matrix. The patient in group A achieved cumulative OAR dose reductions (of OAR-related DVH-metrics) of 19 GyRBE, for identical target coverage. Target coverage improved for all patients in group B (the 10th percentile of $D_{99.8\%}$ increased up to 0.93 GyRBE), at the same time reaching cumulative OAR dose reductions (of OAR-related DVH-metrics) up to 33 GyRBE. Probabilistic plans were optimized in 44h to 141h. For two representative patients, eliminating warm-starting (i.e., the outer loop) from the approach reduced total optimization times to below 10h (which took originally 80h and 141h). Compared to robust optimization methods, the probabilistic approach achieves improved trade-offs between probabilistic target coverage and OAR sparing, potentially leading to better treatments.

physics.med-ph↗

arXiv2026

A Deep Learning-based surrogate model for Severe Accidents in nuclear reactors using ASTEC

Integral codes like the Accident Source Term Evaluation Code (ASTEC) are powerful tools to study the physics of Severe Accidents (SAs) in nuclear reactors. Real time SA simulators can also be helpful in training operators of nuclear plants to react correctly to malfunctions. However, SA simulators can take up to several days per simulation, making their use infeasible for real time applications. In this work we show how to speed up a SA simulator with a fast, Deep Learning based (DL), surrogate model (SM). The SM is built as a combination of a dimensionality reduction stage, via an AutoEncoder, and a time-stepping stage, via a Neural Ordinary Differential Equation. The data on which the SM is trained are obtained from the ASTEC simulator, by sampling a set of operator actions for station blackout (SBO) and loss-of-coolant accidents (LOCA). The objective of the developed SM is to approximate multiple spatio-temporal fields for the thermal-hydraulic physics, core degradation, and fission product release modules in ASTEC's vessel domain. The SM predicts simultaneously around $80$ different physical variables (both scalar and fields), maintaining a stable autoregressive rollout up to $50$ thousand time steps. In addition, the AutoEncoder achieves a dimensionality reduction by a factor of over $300$, which allows the SM to predict up to $40$ hours of simulation in under a minute, both on CPU and GPU. This work is the first study of the capabilities and limits of DL based surrogate modeling in approximating the challenging, highly non-linear physics of ASTEC.

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arXiv2026

Angle dependent dose transformer algorithm for fast proton therapy dose calculations

Accurate 3D dose calculation for Pencil Beam Scanning Proton Therapy (PBSPT) is typically performed with Monte Carlo (MC) engines, but their runtimes limit adaptive workflows and repeated evaluations. Current deep-learning proton dose engines often require orthogonality between proton rays and the CT grid, forcing computationally expensive beamlet-wise 3D reinterpolation. We propose the Angle-dependent Dose Transformer Algorithm (ADoTA), which eliminates grid rotation by augmenting the model input with a fast analytical beamlet-shape projection that explicitly encodes beam direction. The model was trained on CT data from 108 patients to predict beamlet dose distributions for initial energies of $70$--$270\,\mathrm{MeV}$ over an $80\times110\,\mathrm{mm}^2$ field, and tested on an independent cohort of 50 patients. On the test set, gamma pass rates $(1\%,3\,\mathrm{mm})$ were $99.40\pm0.86\%$ (thorax) and $99.87\pm0.23\%$ (abdomen/pelvis). Single-beamlet inference took $1.72\pm0.8\,\mathrm{ms}$. By avoiding reinterpolation, end-to-end 3D dose computation was reduced by $\approx86\%$ relative to the fastest published reinterpolation-based methods. For full treatment plans, gamma pass rates $Γ(2\%,2\,\mathrm{mm})$ with a 10\% dose cut-off reached $98.4\%$ (lung) and $98.9\%$ (prostate). ADoTA provides an angle-aware deep-learning proton dose engine that preserves MC-level accuracy across heterogeneous anatomies while substantially reducing computational overhead.

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arXiv2026

An AI dose engine for fast carbon ion treatment planning

Monte Carlo (MC) simulations provide gold-standard accuracy for carbon ion therapy dose calculations but are computationally intensive. Analytical pencil beam algorithms offer speed but reduced accuracy in heterogeneous tissues. We developed the first AI-based dose engine capable of predicting absorbed dose, the alpha and beta parameters for relative biological effectiveness (RBE)- weighted optimisation in carbon ion therapy, delivering MC-level accuracy with drastically reduced computation time. We extended the transformer-based DoTA model to predict absorbed dose (C-DoTA-d), alpha (C-DoTA-alpha), and beta (C-DoTA-beta), introducing a cross-attention mechanism for alpha and beta to combine dose and energy inputs. The training dataset consisted of ~70,000 pencil beams from 187 head-and-neck patients, with ground-truth values obtained using the GPU-accelerated MC toolkit FRED. Performance was evaluated on an independent test set using gamma pass rate (1%/1 mm), depth-dose, and isodose contour Dice coefficients. MC dropout-based uncertainty analysis was performed. Median gamma pass rates exceeded 98% for all predictions (99.76% for dose, 99.14% for alpha, and 98.74% for beta), with minima above 85% in the most heterogeneous anatomies. The Dice coefficient was 0.95 for 1% isodose contours, with slightly reduced agreement in high-gradient regions. Compared to MC FRED, inference was over 400x faster (0.032 s vs. 14 s per pencil beam) while maintaining accuracy. Uncertainty analysis showed high stability, with mean standard deviations below 0.5% for all models. C-DoTA achieves MC-quality predictions of absorbed dose and RBE model parameters in ~30 milliseconds per beam. Its speed and accuracy support online adaptive planning, paving the way for more effective carbon ion therapy workflows. Future work will expand to additional anatomical sites, beam geometries, and clinical beamlines.

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arXiv2025

Probabilistic Proton Treatment Planning: a novel approach for optimizing underdosage and overdosage probabilities of target and organ structures

Treatment planning uncertainties are typically managed using margin-based or robust optimization. Margin-based methods expand the clinical target volume (CTV) to a planning target volume, generally unsuited for proton therapy. Robust optimization considers worst-case scenarios, but its quality depends on the uncertainty scenario set: excluding extremes reduces robustness, while too many make plans overly conservative. Probabilistic optimization overcomes these limits by modeling a continuous scenario distribution. We propose a novel probabilistic optimization approach that steers plans toward individualized probability levels to control CTV and organs-at-risk (OARs) under- and overdosage. Voxel-wise dose percentiles ($d$) are estimated by expected value ($E$) and standard deviation (SD) as $E[d] \pm δ\cdot SD[d]$, where $δ$ is iteratively tuned to match the target percentile given Gaussian-distributed setup (3 mm) and range (3%) uncertainties. The method involves an inner optimization of $E[d] \pm δ\cdot SD[d]$ for fixed $δ$, and an outer loop updating $δ$. Polynomial Chaos Expansion (PCE) provides accurate and efficient dose estimates during optimization. We validated the method on a spherical CTV abutted by an OAR in different directions and a horseshoe-shaped CTV surrounding a cylindrical spine. For spherical cases with similar CTV coverage, $P(D_{2\%} > 30 Gy)$ dropped by 10-15%; for matched OAR dose, $P(D_{98\%} > 57 Gy)$ increased by 67.5-71%. In spinal plans, $P(D_{98\%} > 57 Gy)$ increased by 10-15% while $P(D_{2\%} > 30 Gy)$ dropped 24-28%. Probabilistic and robust optimization times were comparable for spherical (hours) but longer for spinal cases (7.5 - 11.5 h vs. 9 - 20 min). Compared to discrete scenario-based optimization, the probabilistic method offered better OAR sparing or target coverage depending on the set priorities.

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arXiv2025

A Deep Learning approach for parametrized and time dependent Partial Differential Equations using Dimensionality Reduction and Neural ODEs

Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently increasingly Deep Learning (DL) techniques. A conclusive methodology capable of accounting both for (continuous) time and parameter dependency in such DL models however is still lacking. In this paper, we propose an autoregressive and data-driven method using the analogy with classical numerical solvers for time-dependent, parametric and (typically) nonlinear PDEs. We present how Dimensionality Reduction (DR) can be coupled with Neural Ordinary Differential Equations (NODEs) in order to learn the solution operator of arbitrary PDEs. The idea of our work is that it is possible to map the high-fidelity (i.e., high-dimensional) PDE solution space into a reduced (low-dimensional) space, which subsequently exhibits dynamics governed by a (latent) Ordinary Differential Equation (ODE). Solving this (easier) ODE in the reduced space allows avoiding solving the PDE in the high-dimensional solution space, thus decreasing the computational burden for repeated calculations for e.g., uncertainty quantification or design optimization purposes. The main outcome of this work is the importance of exploiting DR as opposed to the recent trend of building large and complex architectures: we show that by leveraging DR we can deliver not only more accurate predictions, but also a considerably lighter and faster DL model compared to existing methodologies.

cs.LG↗

arXiv2024

A deep learning model for inter-fraction head and neck anatomical changes

Objective: To assess the performance of a probabilistic deep learning based algorithm for predicting inter-fraction anatomical changes in head and neck patients. Approach: A probabilistic daily anatomy model for head and neck patients $(\mathrm{DAM}_{\mathrm{HN}})$ is built on the variational autoencoder architecture. The model approximates the generative joint conditional probability distribution of the repeat computed tomography (rCT) images and their corresponding masks on the planning CT images (pCT) and their masks. The model outputs deformation vector fields, which are used to produce possible rCTs and associated masks. The dataset is composed of 93 patients (i.e., 367 pCT - rCT pairs), 9 (i.e., 37 pairs) of which were set aside for final testing. The performance of the model is assessed based on the reconstruction accuracy and the generative performance for the set aside patients. Main results: The model achieves a DICE score of 0.92 and an image similarity score of 0.65 on the test set. The generated parotid glands volume change distributions and center of mass shift distributions were also assessed. For both, the medians of the distributions are close to the true ones, and the distributions are broad enough to encompass the real observed changes. Moreover, the generated images display anatomical changes in line with the literature reported ones, such as the medial shifts of the parotids glands. Significance: $(\mathrm{DAM}_{\mathrm{HN}})$ is capable of generating realistic anatomies observed during the course of the treatment and has applications in anatomical robust optimization, treatment planning based on plan library approaches and robustness evaluation against inter-fractional changes.

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arXiv2024

Yet anOther Dose Algorithm (YODA) for independent computations of dose and dose changes due to anatomical changes

$\textbf{Purpose:}$ To assess the viability of a physics-based, deterministic and adjoint-capable algorithm for performing treatment planning system independent dose calculations and for computing dosimetric differences caused by anatomical changes. $\textbf{Methods:}$ A semi-numerical approach is employed to solve two partial differential equations for the proton phase-space density which determines the deposited dose. Lateral hetereogeneities are accounted for by an optimized (Gaussian) beam splitting scheme. Adjoint theory is applied to approximate the change in the deposited dose caused by a new underlying patient anatomy. $\textbf{Results:}$ The quality of the dose engine was benchmarked through three-dimensional gamma index comparisons against Monte Carlo simulations done in TOPAS. The worst passing rate for the gamma index with (1 mm, 1 %, 10 % dose cut-off) criteria is 95.62 %. The effect of delivering treatment plans on repeat CTs was also tested. For a non-robustly optimized plan the adjoint component was accurate to 6.2 % while for a robustly optimized plan it was accurate to 1 %. $\textbf{Conclusions:}$ YODA is capable of accurate dose computations in both single and multi spot irradiations when compared to TOPAS. Moreover, it is able to compute dosimetric differences due to anatomical changes with small to moderate errors thereby facilitating its use for patient-specific quality assurance in online adaptive proton therapy.

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arXiv2022

A probabilistic deep learning model of inter-fraction anatomical variations in radiotherapy

In radiotherapy, the internal movement of organs between treatment sessions causes errors in the final radiation dose delivery. Motion models can be used to simulate motion patterns and assess anatomical robustness before delivery. Traditionally, such models are based on principal component analysis (PCA) and are either patient-specific (requiring several scans per patient) or population-based, applying the same deformations to all patients. We present a hybrid approach which, based on population data, allows to predict patient-specific inter-fraction variations for an individual patient. We propose a deep learning probabilistic framework that generates deformation vector fields (DVFs) warping a patient's planning computed tomography (CT) into possible patient-specific anatomies. This daily anatomy model (DAM) uses few random variables capturing groups of correlated movements. Given a new planning CT, DAM estimates the joint distribution over the variables, with each sample from the distribution corresponding to a different deformation. We train our model using dataset of 312 CT pairs from 38 prostate cancer patients. For 2 additional patients (22 CTs), we compute the contour overlap between real and generated images, and compare the sampled and ground truth distributions of volume and center of mass changes. With a DICE score of 0.86 and a distance between prostate contours of 1.09 mm, DAM matches and improves upon PCA-based models. The distribution overlap further indicates that DAM's sampled movements match the range and frequency of clinically observed daily changes on repeat CTs. Conditioned only on a planning CT and contours of a new patient without any pre-processing, DAM can accurately predict CTs seen during following treatment sessions, which can be used for anatomically robust treatment planning and robustness evaluation against inter-fraction anatomical changes.

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arXiv2022

Sub-second photon dose prediction via transformer neural networks

Fast dose calculation is critical for online and real time adaptive therapy workflows. While modern physics-based dose algorithms must compromise accuracy to achieve low computation times, deep learning models can potentially perform dose prediction tasks with both high fidelity and speed. We present a deep learning algorithm that, exploiting synergies between Transformer and convolutional layers, accurately predicts broad photon beam dose distributions in few milliseconds. The proposed improved Dose Transformer Algorithm (iDoTA) maps arbitrary patient geometries and beam information (in the form of a 3D projected shape resulting from a simple ray tracing calculation) to their corresponding 3D dose distribution. Treating the 3D CT input and dose output volumes as a sequence of 2D slices along the direction of the photon beam, iDoTA solves the dose prediction task as sequence modeling. The proposed model combines a Transformer backbone routing long-range information between all elements in the sequence, with a series of 3D convolutions extracting local features of the data. We train iDoTA on a dataset of 1700 beam dose distributions, using 11 clinical volumetric modulated arc therapy (VMAT) plans (from prostate, lung and head and neck cancer patients with 194-354 beams per plan) to assess its accuracy and speed. iDoTA predicts individual photon beams in ~50 milliseconds with a high gamma pass rate of 97.72% (2 mm, 2%). Furthermore, estimating full VMAT dose distributions in 6-12 seconds, iDoTA achieves state-of-the-art performance with a 99.51% (2 mm, 2%) pass rate. Offering the sub-second speed needed in online and real-time adaptive treatments, iDoTA represents a new state of the art in data-driven photon dose calculation. The proposed model can massively speed-up current photon workflows, reducing calculation times from few minutes to just a few seconds.

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arXiv2022

A deterministic adjoint-based semi-analytical algorithm for fast response change computations in proton therapy

In this paper we propose a solution to the need for a fast particle transport algorithm in Online Adaptive Proton Therapy capable of cheaply, but accurately computing the changes in patient dose metrics as a result of changes in the system parameters. We obtain the proton phase-space density through the product of the numerical solution to the one-dimensional Fokker-Planck equation and the analytical solution to the Fermi-Eyges equation. Moreover, a corresponding adjoint system was derived and solved for the adjoint flux. The proton phase-space density together with the adjoint flux and the metric (chosen as the energy deposited by the beam in a variable region of interest) allowed assessing the accuracy of our algorithm to different perturbation ranges in the system parameters and regions of interest. The algorithm achieved negligible errors ($1.1 \times 10^{-6}$ $\%$ to $3.6 \times 10^{-3}$ $\%$) for small perturbation ranges ($-40 \text{ HU to } 40 \text{ HU}$) and small to moderate errors ($3 \text{ $\%$ to } 17 \text{ $\%$}$) -- in line with the well-known limitation of adjoint approaches -- for large perturbation ranges ($-400 \text{ HU to } 400 \text{ HU}$) in the case of most clinical interest where the region of interest surrounds the Bragg peak. Given these results coupled with the capability of further improving the timing performance it can be concluded that our algorithm presents a viable solution for the specific purpose of Online Adaptive Proton Therapy.

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arXiv2022

Millisecond speed deep learning based proton dose calculation with Monte Carlo accuracy

Next generation online and real-time adaptive radiotherapy workflows require precise particle transport simulations in sub-second times, which is unfeasible with current analytical pencil beam algorithms (PBA) or stochastic Monte Carlo (MC) methods. We present a data-driven millisecond speed dose calculation algorithm (DoTA) accurately predicting the dose deposited by mono-energetic proton pencil beams for arbitrary energies and patient geometries. Given the forward-scattering nature of protons, we frame 3D particle transport as modeling a sequence of 2D geometries in the beam's eye view. DoTA combines convolutional neural networks extracting spatial features (e.g., tissue and density contrasts) with a transformer self-attention backbone that routes information between the sequence of geometry slices and a vector representing the beam's energy, and is trained to predict low noise MC simulations of proton beamlets using 80,000 different head and neck, lung, and prostate geometries. Predicting beamlet doses in 5 ms with a very high gamma pass rate of 99.37% (1%, 3 mm) compared to the ground truth MC calculations, DoTA significantly improves upon analytical pencil beam algorithms both in precision and speed. Offering MC accuracy 100 times faster than PBAs for pencil beams, our model calculates full treatment plan doses in 10 to 15 s depending on the number of beamlets, achieving a 99.70% (2%, 2 mm) gamma pass rate across 9 test patients. Outperforming all previous analytical pencil beam and deep learning based approaches, DoTA represents a new state of the art in data-driven dose calculation and can directly compete with the speed of even commercial GPU MC approaches. Providing the sub-second speed required for adaptive treatments, straightforward implementations could offer similar benefits to other steps of the radiotherapy workflow or other modalities such as helium or carbon treatments.

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arXiv2021

Learning the Physics of Particle Transport via Transformers

Particle physics simulations are the cornerstone of nuclear engineering applications. Among them radiotherapy (RT) is crucial for society, with 50% of cancer patients receiving radiation treatments. For the most precise targeting of tumors, next generation RT treatments aim for real-time correction during radiation delivery, necessitating particle transport algorithms that yield precise dose distributions in sub-second times even in highly heterogeneous patient geometries. This is infeasible with currently available, purely physics based simulations. In this study, we present a data-driven dose calculation algorithm predicting the dose deposited by mono-energetic proton beams for arbitrary energies and patient geometries. Our approach frames particle transport as sequence modeling, where convolutional layers extract important spatial features into tokens and the transformer self-attention mechanism routes information between such tokens in the sequence and a beam energy token. We train our network and evaluate prediction accuracy using computationally expensive but accurate Monte Carlo (MC) simulations, considered the gold standard in particle physics. Our proposed model is 33 times faster than current clinical analytic pencil beam algorithms, improving upon their accuracy in the most heterogeneous and challenging geometries. With a relative error of 0.34% and very high gamma pass rate of 99.59% (1%, 3 mm), it also greatly outperforms the only published similar data-driven proton dose algorithm, even at a finer grid resolution. Offering MC precision 400 times faster, our model could overcome a major obstacle that has so far prohibited real-time adaptive proton treatments and significantly increase cancer treatment efficacy. Its potential to model physics interactions of other particles could also boost heavy ion treatment planning procedures limited by the speed of traditional methods.

cs.LG↗

arXiv2021

A semi-supervised autoencoder framework for joint generation and classification of breathing

One of the main problems with biomedical signals is the limited amount of patient-specific data and the significant amount of time needed to record the sufficient number of samples needed for diagnostic and treatment purposes. In this study, we present a framework to simultaneously generate and classify biomedical time series based on a modified Adversarial Autoencoder (AAE) algorithm and one-dimensional convolutions. Our work is based on breathing time series, with specific motivation to capture breathing motion during radiotherapy lung cancer treatments. First, we explore the potential in using the Variational Autoencoder (VAE) and AAE algorithms to model breathing from individual patients. We extend the AAE algorithm to allow joint semi-supervised classification and generation of different types of signals. To simplify the modeling task, we introduce a pre-processing and post-processing compressing algorithm that transforms the multi-dimensional time series into vectors containing time and position values, which are transformed back into time series through an additional neural network. By incorporating few labeled samples during training, our model outperforms other purely discriminative networks in classifying breathing baseline shift irregularities from a dataset completely different from the training set. To our knowledge, the presented framework is the first approach that unifies generation and classification within a single model for this type of biomedical data, enabling both computer aided diagnosis and augmentation of labeled samples within a single framework.

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