Deep learning-based surrogate models for parametrized PDEs: Handling geometric variability through graph neural networks.

Mesh-based simulations play a key role when modeling complex physical systems that, in many disciplines across science and engineering, require the solution to parametrized time-dependent nonlinear partial differential equations (PDEs). In this context, full order models (FOMs), such as those relying on the finite element method, can reach high levels of accuracy, however often yielding intensive simulations to run. For this reason, surrogate models are developed to replace computationally expensive solvers with more efficient ones, which can strike favorable trade-offs between accuracy and efficiency. This work explores the potential usage of graph neural networks (GNNs) for the simulation of time-dependent PDEs in the presence of geometrical variability. In particular, we propose a systematic strategy to build surrogate models based on a data-driven time-stepping scheme where a GNN architecture is used to efficiently evolve the system. With respect to the majority of surrogate models, the proposed approach stands out for its ability of tackling problems with parameter-dependent spatial domains, while simultaneously generalizing to different geometries and mesh resolutions. We assess the effectiveness of the proposed approach through a series of numerical experiments, involving both two- and three-dimensional problems, showing that GNNs can provide a valid alternative to traditional surrogate models in terms of computational efficiency and generalization to new scenarios.

Reduced Order Modeling of Nonlinear Vibrating Multiphysics Microstructures with Deep Learning-Based Approaches.

Micro-electro-mechanical-systems are complex structures, often involving nonlinearites of geometric and multiphysics nature, that are used as sensors and actuators in countless applications. Starting from full-order representations, we apply deep learning techniques to generate accurate, efficient, and real-time reduced order models to be used for the simulation and optimization of higher-level complex systems. We extensively test the reliability of the proposed procedures on micromirrors, arches, and gyroscopes, as well as displaying intricate dynamical evolutions such as internal resonances. In particular, we discuss the accuracy of the deep learning technique and its ability to replicate and converge to the invariant manifolds predicted using the recently developed direct parametrization approach that allows the extraction of the nonlinear normal modes of large finite element models. Finally, by addressing an electromechanical gyroscope, we show that the non-intrusive deep learning approach generalizes easily to complex multiphysics problems.

Data integration for the numerical simulation of cardiac electrophysiology.

The increasing availability of extensive and accurate clinical data is rapidly shaping cardiovascular care by improving the understanding of physiological and pathological mechanisms of the cardiovascular system and opening new frontiers in designing therapies and interventions. In this direction, mathematical and numerical models provide a complementary relevant tool, able not only to reproduce patient-specific clinical indicators but also to predict and explore unseen scenarios. With this goal, clinical data are processed and provided as inputs to the mathematical model, which quantitatively describes the physical processes that occur in the cardiac tissue. In this paper, the process of integration of clinical data and mathematical models is discussed. Some challenges and contributions in the field of cardiac electrophysiology are reported.

An Autoencoder-Based Deep Learning Approach for Load Identification in Structural Dynamics.

In civil engineering, different machine learning algorithms have been adopted to process the huge amount of data continuously acquired through sensor networks and solve inverse problems. Challenging issues linked to structural health monitoring or load identification are currently related to big data, consisting of structural vibration recordings shaped as a multivariate time series. Any algorithm should therefore allow an effective dimensionality reduction, retaining the informative content of data and inferring correlations within and across the time series. Within this framework, we propose a time series AutoEncoder (AE) employing inception modules and residual learning for the encoding and the decoding parts, and an extremely reduced latent representation specifically tailored to tackle load identification tasks. We discuss the choice of the dimensionality of this latent representation, considering the sources of variability in the recordings and the inverse-forward nature of the AE. To help setting the aforementioned dimensionality, the false nearest neighbor heuristics is also exploited. The reported numerical results, related to shear buildings excited by dynamic loadings, highlight the signal reconstruction capacity of the proposed AE, and the capability to accomplish the load identification task.

Pharmacokinetic study between a bilayer matrix fentalyl patch and a monolayer matrix fentanyl patch: single dose administration in healthy volunteers.

AIMS: Transdermal fentanyl is a well established treatment for cancer pain. The aim of the present study is to assess the relative bioavailability of fentanyl from two different transdermal systems by evaluating plasma drug concentrations after single administration of Fentalgon® (test), a novel bilayer matrix type patch, and Durogesic SMAT (reference), a monolayer matrix type patch. In the Fentalgon patch the upper 6% fentanyl reservoir layer maintains a stable concentration gradient between the lower 4% donor layer and the skin. The system provides a constant drug delivery over 72 h. METHODS: This was an open label, single centre, randomized, single dose, two period crossover clinical trial, that included 36 healthy male volunteers. The patches were applied to non-irritated and non-irradiated skin on the intraclavicular pectoral area. Blood samples were collected at different time points (from baseline to 120 h post-removal of the devices) and fentanyl concentrations were determined using a validated LC/MS/MS method. Bioequivalence was to be claimed if the 90% confidence interval of AUC(0,t) and C(max) ratios (test: reference) were within the acceptance range of 80-125% and 75-133%, respectively. RESULTS: The 90% confidence intervals of the AUC(0,t) ratio (116.3% [109.6, 123.4%]) and C(max) ratio (114.4% [105.8, 123.8%] were well included in the acceptance range and the C(max) ratio also met the narrower bounds of 80-125%. There was no relevant difference in overall safety profiles of the two preparations investigated, which were adequately tolerated, as expected for opioid-naïve subjects. CONCLUSIONS: The new bilayer matrix type patch, Fentalgon®, is bioequivalent to the monolayer matrix type Durogesic SMAT fentanyl patch with respect to the rate and extent of exposure of fentanyl (Eudra/CT no. 2005-000046-36).

Efficient approximation of cardiac mechanics through reduced-order modeling with deep learning-based operator approximation.

Reducing the computational time required by high-fidelity, full-order models (FOMs) for the solution of problems in cardiac mechanics is crucial to allow the translation of patient-specific simulations into clinical practice. Indeed, while FOMs, such as those based on the finite element method, provide valuable information on the cardiac mechanical function, accurate numerical results can be obtained at the price of very fine spatio-temporal discretizations. As a matter of fact, simulating even just a few heartbeats can require up to hours of wall time on high-performance computing architectures. In addition, cardiac models usually depend on a set of input parameters that are calibrated in order to explore multiple virtual scenarios. To compute reliable solutions at a greatly reduced computational cost, we rely on a reduced basis method empowered with a new deep learning-based operator approximation, which we refer to as Deep-HyROMnet technique. Our strategy combines a projection-based POD-Galerkin method with deep neural networks for the approximation of (reduced) nonlinear operators, overcoming the typical computational bottleneck associated with standard hyper-reduction techniques employed in reduced-order models (ROMs) for nonlinear parametrized systems. This method can provide extremely accurate approximations to parametrized cardiac mechanics problems, such as in the case of the complete cardiac cycle in a patient-specific left ventricle geometry. In this respect, a 3D model for tissue mechanics is coupled with a 0D model for external blood circulation; active force generation is provided through an adjustable parameter-dependent surrogate model as input to the tissue 3D model. The proposed strategy is shown to outperform classical projection-based ROMs, in terms of orders of magnitude of computational speed-up, and to return accurate pressure-volume loops in both physiological and pathological cases. Finally, an application to a forward uncertainty quantification analysis, unaffordable if relying on a FOM, is considered, involving output quantities of interest such as, for example, the ejection fraction or the maximal rate of change in pressure in the left ventricle.

Uncertainty quantification and sensitivity analysis of neuron models with ion concentration dynamics.

This paper provides a comprehensive and computationally efficient case study for uncertainty quantification (UQ) and global sensitivity analysis (GSA) in a neuron model incorporating ion concentration dynamics. We address how challenges with UQ and GSA in this context can be approached and solved, including challenges related to computational cost, parameters affecting the system's resting state, and the presence of both fast and slow dynamics. Specifically, we analyze the electrodiffusive neuron-extracellular-glia (edNEG) model, which captures electrical potentials, ion concentrations (Na+, K+, Ca2+, and Cl-), and volume changes across six compartments. Our methodology includes a UQ procedure assessing the model's reliability and susceptibility to input uncertainty and a variance-based GSA identifying the most influential input parameters. To mitigate computational costs, we employ surrogate modeling techniques, optimized using efficient numerical integration methods. We propose a strategy for isolating parameters affecting the resting state and analyze the edNEG model dynamics under both physiological and pathological conditions. The influence of uncertain parameters on model outputs, particularly during spiking dynamics, is systematically explored. Rapid dynamics of membrane potentials necessitate a focus on informative spiking features, while slower variations in ion concentrations allow a meaningful study at each time point. Our study offers valuable guidelines for future UQ and GSA investigations on neuron models with ion concentration dynamics, contributing to the broader application of such models in computational neuroscience.

Approximation bounds for convolutional neural networks in operator learning.

Recently, deep Convolutional Neural Networks (CNNs) have proven to be successful when employed in areas such as reduced order modeling of parametrized PDEs. Despite their accuracy and efficiency, the approaches available in the literature still lack a rigorous justification on their mathematical foundations. Motivated by this fact, in this paper we derive rigorous error bounds for the approximation of nonlinear operators by means of CNN models. More precisely, we address the case in which an operator maps a finite dimensional input µ∈Rp onto a functional output uµ:[0,1]d→R, and a neural network model is used to approximate a discretized version of the input-to-output map. The resulting error estimates provide a clear interpretation of the hyperparameters defining the neural network architecture. All the proofs are constructive, and they ultimately reveal a deep connection between CNNs and the Fourier transform. Finally, we complement the derived error bounds by numerical experiments that illustrate their application.

Learning high-order interactions for polygenic risk prediction.

Within the framework of precision medicine, the stratification of individual genetic susceptibility based on inherited DNA variation has paramount relevance. However, one of the most relevant pitfalls of traditional Polygenic Risk Scores (PRS) approaches is their inability to model complex high-order non-linear SNP-SNP interactions and their effect on the phenotype (e.g. epistasis). Indeed, they incur in a computational challenge as the number of possible interactions grows exponentially with the number of SNPs considered, affecting the statistical reliability of the model parameters as well. In this work, we address this issue by proposing a novel PRS approach, called High-order Interactions-aware Polygenic Risk Score (hiPRS), that incorporates high-order interactions in modeling polygenic risk. The latter combines an interaction search routine based on frequent itemsets mining and a novel interaction selection algorithm based on Mutual Information, to construct a simple and interpretable weighted model of user-specified dimensionality that can predict a given binary phenotype. Compared to traditional PRSs methods, hiPRS does not rely on GWAS summary statistics nor any external information. Moreover, hiPRS differs from Machine Learning-based approaches that can include complex interactions in that it provides a readable and interpretable model and it is able to control overfitting, even on small samples. In the present work we demonstrate through a comprehensive simulation study the superior performance of hiPRS w.r.t. state of the art methods, both in terms of scoring performance and interpretability of the resulting model. We also test hiPRS against small sample size, class imbalance and the presence of noise, showcasing its robustness to extreme experimental settings. Finally, we apply hiPRS to a case study on real data from DACHS cohort, defining an interaction-aware scoring model to predict mortality of stage II-III Colon-Rectal Cancer patients treated with oxaliplatin.

Stereotactic Radiosurgery with Gamma Knife in Recurrent Rathke's Cleft Cyst: Case Report and Literature Analysis.

Background: Rathke's cleft cyst is a benign expansive lesion of the sella turcica. If related to clinical disorders, the patient needs surgical treatment. Objective: To demonstrate the efficacy of radiosurgery in the treatment of relapse of Rathke's cleft cyst as an alternative to surgery. Methods and Material: The stereotactic radiosurgical treatment was performed at the Gamma Knife Center of the Niguarda Hospital in a patient with Rathke's cleft cyst subjected to two subsequent neurosurgical resections with early regrowth of the cyst. The cyst underwent radiosurgery with a prescription dose of 12 Gy at 50% (minimum dose 9.8, mean 17.3 and maximum 24.4). Results: Three years after stereotactic radiosurgical treatment the patient is asymptomatic and does not present disorders of the hypothalamic-pituitary axis or further visual alterations. The control MRI shows a reduction of the cyst's volume. Conclusions: Stereotactic radiosurgery resulted in a reduction of the cyst's volume and avoided further recourse to surgery.

Are the forearm muscles excited equally in different, professional piano players?

BACKGROUND AND OBJECTIVES: Professional pianists tend to develop playing-related musculoskeletal disorders mostly in the forearm. These injuries are often due to overuse, suggesting the existence of a common forearm region where muscles are often excited during piano playing across subjects. Here we use a grid of electrodes to test this hypothesis, assessing where EMGs with greatest amplitude are more likely to be detected when expert pianists perform different excerpts. METHODS: Tasks were separated into two groups: classical excerpts and octaves, performed by eight, healthy, professional pianists. Monopolar electromyograms (EMGs) were sampled with a grid of 96 electrodes, covering the forearm region where hand and wrist muscles reside. Regions providing consistently high EMG amplitude across subjects were assessed with a non-parametric permutation test, designed for the statistical analysis of neuroimaging experiments. Spatial consistency across trials was assessed with the Binomial test. RESULTS: Spatial consistency of muscle excitation was found across subjects but not across tasks, confining at most 20% of the electrodes in the grid. These local groups of electrodes providing high EMG amplitude were found at the ventral forearm region during classical excerpts and at the dorsal region during octaves, when performed both at preferred and at high, playing speeds. DISCUSSION: Our results revealed that professional pianists consistently load a specific forearm region, depending on whether performing octaves or classical excerpts. This spatial consistency may help furthering our understanding on the incidence of playing-related muscular disorders and provide an anatomical reference for the study of active muscle loading in piano players using surface EMG.

Slow Conduction Corridors and Pivot Sites Characterize the Electrical Remodeling in Atrial Fibrillation.

OBJECTIVES: This study aimed to evaluate the progression of electrophysiological phenomena in a cohort of patients with paroxysmal atrial fibrillation (PAF) and persistent atrial fibrillation (PsAF). BACKGROUND: Electrical remodeling has been conjectured to determine atrial fibrillation (AF) progression. METHODS: High-density electroanatomic maps during sinus rhythm of 20 patients with AF (10 PAF, 10 PsAF) were compared with 5 healthy control subjects (subjects undergoing ablation of a left-sided accessory pathway). A computational postprocessing of electroanatomic maps was performed to identify specific electrophysiological phenomena: slow conductions corridors, defined as discrete areas of conduction velocity <50 cm/s, and pivot points, defined as sites showing high wave-front curvature documented by a curl module >2.5 1/s. RESULTS: A progressive decrease of mean conduction velocity was recorded across the groups (111.6 ± 55.5 cm/s control subjects, 97.1 ± 56.3 cm/s PAF, and 84.7 ± 55.7 cm/s PsAF). The number and density of slow conduction corridors increase in parallel with the progression of AF (8.6 ± 2.2 control subjects, 13.3 ± 3.2 PAF, and 20.5 ± 4.5 PsAF). In PsAF the atrial substrate is characterized by a higher curvature of wave-front propagation (0.86 ± 0.71 1/s PsAF vs 0.74 ± 0.63 1/s PAF; P = 0.003) and higher number of pivot points (25.1 ± 13.8 PsAF vs 9.5 ± 6.7 PAF; P < 0.0001). Slow conductions: corridors were mostly associated with pivot sites tending to cluster around pulmonary veins antra. CONCLUSIONS: The electrical remodeling hinges mainly on corridors of slow conduction and higher curvature of wave-front propagation. Pivot points associated to SC corridors may be the major determinants for functional localized re-entrant circuits creating the substrate for maintenance of AF.

Enabling forward uncertainty quantification and sensitivity analysis in cardiac electrophysiology by reduced order modeling and machine learning.

We present a new, computationally efficient framework to perform forward uncertainty quantification (UQ) in cardiac electrophysiology. We consider the monodomain model to describe the electrical activity in the cardiac tissue, coupled with the Aliev-Panfilov model to characterize the ionic activity through the cell membrane. We address a complete forward UQ pipeline, including both: (i) a variance-based global sensitivity analysis for the selection of the most relevant input parameters, and (ii) a way to perform uncertainty propagation to investigate the impact of intra-subject variability on outputs of interest depending on the cardiac potential. Both tasks exploit stochastic sampling techniques, thus implying overwhelming computational costs because of the huge amount of queries to the high-fidelity, full-order computational model obtained by approximating the coupled monodomain/Aliev-Panfilov system through the finite element method. To mitigate this computational burden, we replace the full-order model with computationally inexpensive projection-based reduced-order models (ROMs) aimed at reducing the state-space dimensionality. Resulting approximation errors on the outputs of interest are finally taken into account through artificial neural network (ANN)-based models, enhancing the accuracy of the whole UQ pipeline. Numerical results show that the proposed physics-based ROMs outperform regression-based emulators relying on ANNs built with the same amount of training data, in terms of both numerical accuracy and overall computational efficiency.

POD-Enhanced Deep Learning-Based Reduced Order Models for the Real-Time Simulation of Cardiac Electrophysiology in the Left Atrium.

The numerical simulation of multiple scenarios easily becomes computationally prohibitive for cardiac electrophysiology (EP) problems if relying on usual high-fidelity, full order models (FOMs). Likewise, the use of traditional reduced order models (ROMs) for parametrized PDEs to speed up the solution of the aforementioned problems can be problematic. This is primarily due to the strong variability characterizing the solution set and to the nonlinear nature of the input-output maps that we intend to reconstruct numerically. To enhance ROM efficiency, we proposed a new generation of non-intrusive, nonlinear ROMs, based on deep learning (DL) algorithms, such as convolutional, feedforward, and autoencoder neural networks. In the proposed DL-ROM, both the nonlinear solution manifold and the nonlinear reduced dynamics used to model the system evolution on that manifold can be learnt in a non-intrusive way thanks to DL algorithms trained on a set of FOM snapshots. DL-ROMs were shown to be able to accurately capture complex front propagation processes, both in physiological and pathological cardiac EP, very rapidly once neural networks were trained, however, at the expense of huge training costs. In this study, we show that performing a prior dimensionality reduction on FOM snapshots through randomized proper orthogonal decomposition (POD) enables to speed up training times and to decrease networks complexity. Accuracy and efficiency of this strategy, which we refer to as POD-DL-ROM, are assessed in the context of cardiac EP on an idealized left atrium (LA) geometry and considering snapshots arising from a NURBS (non-uniform rational B-splines)-based isogeometric analysis (IGA) discretization. Once the ROMs have been trained, POD-DL-ROMs can efficiently solve both physiological and pathological cardiac EP problems, for any new scenario, in real-time, even in extremely challenging contexts such as those featuring circuit re-entries, that are among the factors triggering cardiac arrhythmias.

Characterization of cardiac electrogram signals in atrial arrhythmias.

Despite significant advancements in 3D cardiac mapping systems utilized in daily electrophysiology practices, the characterization of atrial substrate remains crucial for the comprehension of supraventricular arrhythmias. During mapping, intracardiac electrograms (EGM) provide specific information that the cardiac electrophysiologist is required to rapidly interpret during the course of a procedure in order to perform an effective ablation. In this review, EGM characteristics collected during sinus rhythm (SR) in patients with paroxysmal atrial fibrillation (pAF) are analyzed, focusing on amplitude, duration and fractionation. Additionally, EGMs recorded during atrial fibrillation (AF), including complex fractionated atrial EGMs (CFAE), may also provide precious information. A complete understanding of their significance remains lacking, and as such, we aimed to further explore the role of CFAE in strategies for ablation of persistent AF. Considering focal atrial tachycardias (AT), current cardiac mapping systems provide excellent tools that can guide the operator to the site of earliest activation. However, only careful analysis of the EGM, distinguishing low amplitude high frequency signals, can reliably identify the absolute best site for RF. Evaluating macro-reentrant atrial tachycardia circuits, specific EGM signatures correspond to particular electrophysiological phenomena: the careful recognition of these EGM patterns may in fact reveal the best site of ablation. In the near future, mathematical models, integrating patient-specific data, such as cardiac geometry and electrical conduction properties, may further characterize the substrate and predict future (potential) reentrant circuits.

Development of a method for generating SNP interaction-aware polygenic risk scores for radiotherapy toxicity.

AIM: To identify the effect of single nucleotide polymorphism (SNP) interactions on the risk of toxicity following radiotherapy (RT) for prostate cancer (PCa) and propose a new method for polygenic risk score incorporating SNP-SNP interactions (PRSi). MATERIALS AND METHODS: Analysis included the REQUITE PCa cohort that received external beam RT and was followed for 2 years. Late toxicity endpoints were: rectal bleeding, urinary frequency, haematuria, nocturia, decreased urinary stream. Among 43 literature-identified SNPs, the 30% most strongly associated with each toxicity were tested. SNP-SNP combinations (named SNP-allele sets) seen in ≥10% of the cohort were condensed into risk (RS) and protection (PS) scores, respectively indicating increased or decreased toxicity risk. Performance of RS and PS was evaluated by logistic regression. RS and PS were then combined into a single PRSi evaluated by area under the receiver operating characteristic curve (AUC). RESULTS: Among 1,387 analysed patients, toxicity rates were 11.7% (rectal bleeding), 4.0% (urinary frequency), 5.5% (haematuria), 7.8% (nocturia) and 17.1% (decreased urinary stream). RS and PS combined 8 to 15 different SNP-allele sets, depending on the toxicity endpoint. Distributions of PRSi differed significantly in patients with/without toxicity with AUCs ranging from 0.61 to 0.78. PRSi was better than the classical summed PRS, particularly for the urinary frequency, haematuria and decreased urinary stream endpoints. CONCLUSIONS: Our method incorporates SNP-SNP interactions when calculating PRS for radiotherapy toxicity. Our approach is better than classical summation in discriminating patients with toxicity and should enable incorporating genetic information to improve normal tissue complication probability models.

Deep learning-based reduced order models in cardiac electrophysiology.

Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential, that is the polarization/depolarization cycle occurring at every heart beat that models the time evolution of the electrical potential across the cell membrane, as well as a set of ionic variables. Multiple solutions of these systems, corresponding to different model inputs, are required to evaluate outputs of clinical interest, such as activation maps and action potential duration. More importantly, these models feature coherent structures that propagate over time, such as wavefronts. These systems can hardly be reduced to lower dimensional problems by conventional reduced order models (ROMs) such as, e.g., the reduced basis method. This is primarily due to the low regularity of the solution manifold (with respect to the problem parameters), as well as to the nonlinear nature of the input-output maps that we intend to reconstruct numerically. To overcome this difficulty, in this paper we propose a new, nonlinear approach relying on deep learning (DL) algorithms-such as deep feedforward neural networks and convolutional autoencoders-to obtain accurate and efficient ROMs, whose dimensionality matches the number of system parameters. We show that the proposed DL-ROM framework can efficiently provide solutions to parametrized electrophysiology problems, thus enabling multi-scenario analysis in pathological cases. We investigate four challenging test cases in cardiac electrophysiology, thus demonstrating that DL-ROM outperforms classical projection-based ROMs.

Outer loop and isthmus in ventricular tachycardia circuits: Characteristics and implications.

BACKGROUND: The isthmus of ventricular tachycardia (VT) circuits has been extensively characterized. Few data exist regarding the contribution of the outer loop (OL) to the VT circuit. OBJECTIVE: The purpose of this study was to characterize the electrophysiological properties of the OL. METHODS: Complete substrate activation mapping during sinus rhythm (SR) and full activation mapping of the VT circuit with high-density mapping were performed. Maps were analyzed mathematically to reconstruct conduction velocities (CVs) within the circuit. CV >100 cm/s was defined as normal and <50 cm/s as slow. Electrograms along the entire circuit were analyzed for fractionation, duration, and amplitude. RESULTS: Six postmyocardial infarction patients were enrolled. The VT circuit was a figure-of-eight reentrant circuit in 4 patients and a single-loop circuit in 2 patients. The OL exhibited a mean of 1.9 ± 0.9 and 1.6 ± 0.5 corridors of slow conduction (SC) during VT and SR, respectively. SC in the OL were longer and faster than SC in the isthmus during SR. At the OL, SC sites showed local abnormal ventricular activity in 92%, and a bipolar voltage <0.5 mV was identified in 80.7%. Of the double-loop circuits, only 1 patient had fixed lines of block as isthmus boundaries, whereas in 3 patients the circuits were at least partially functional. CONCLUSION: In ischemic reentrant VT circuits, the OL contributes significantly to reentry with multiple corridors of SC. These corridors can result from structural or functional phenomena. Isthmus boundaries may correspond to functional or fixed lines of block.

A Deep Learning Approach Validates Genetic Risk Factors for Late Toxicity After Prostate Cancer Radiotherapy in a REQUITE Multi-National Cohort.

Background: REQUITE (validating pREdictive models and biomarkers of radiotherapy toxicity to reduce side effects and improve QUalITy of lifE in cancer survivors) is an international prospective cohort study. The purpose of this project was to analyse a cohort of patients recruited into REQUITE using a deep learning algorithm to identify patient-specific features associated with the development of toxicity, and test the approach by attempting to validate previously published genetic risk factors. Methods: The study involved REQUITE prostate cancer patients treated with external beam radiotherapy who had complete 2-year follow-up. We used five separate late toxicity endpoints: ≥grade 1 late rectal bleeding, ≥grade 2 urinary frequency, ≥grade 1 haematuria, ≥ grade 2 nocturia, ≥ grade 1 decreased urinary stream. Forty-three single nucleotide polymorphisms (SNPs) already reported in the literature to be associated with the toxicity endpoints were included in the analysis. No SNP had been studied before in the REQUITE cohort. Deep Sparse AutoEncoders (DSAE) were trained to recognize features (SNPs) identifying patients with no toxicity and tested on a different independent mixed population including patients without and with toxicity. Results: One thousand, four hundred and one patients were included, and toxicity rates were: rectal bleeding 11.7%, urinary frequency 4%, haematuria 5.5%, nocturia 7.8%, decreased urinary stream 17.1%. Twenty-four of the 43 SNPs that were associated with the toxicity endpoints were validated as identifying patients with toxicity. Twenty of the 24 SNPs were associated with the same toxicity endpoint as reported in the literature: 9 SNPs for urinary symptoms and 11 SNPs for overall toxicity. The other 4 SNPs were associated with a different endpoint. Conclusion: Deep learning algorithms can validate SNPs associated with toxicity after radiotherapy for prostate cancer. The method should be studied further to identify polygenic SNP risk signatures for radiotherapy toxicity. The signatures could then be included in integrated normal tissue complication probability models and tested for their ability to personalize radiotherapy treatment planning.

Reduced-order modeling of blood flow for noninvasive functional evaluation of coronary artery disease.

We present a novel computational approach, based on a parametrized reduced-order model, for accelerating the calculation of pressure drop along blood vessels. Vessel lumina are defined by a geometric parametrization using the discrete empirical interpolation method on control points located on the surface of the vessel. Hemodynamics are then computed using a reduced-order representation of the parametrized three-dimensional unsteady Navier-Stokes and continuity equations. The reduced-order model is based on an offline-online splitting of the solution process, and on the projection of a finite volume full-order model on a low-dimensionality subspace generated by proper orthogonal decomposition of pressure and velocity fields. The algebraic operators of the hemodynamic equations are assembled efficiently during the online phase using the discrete empirical interpolation method. Our results show that with this approach calculations can be sped up by a factor of about 25 compared to the conventional full-order model, while maintaining prediction errors within the uncertainty limits of invasive clinical measurement of pressure drop. This is of importance for a clinically viable implementation of noninvasive, medical imaging-based computation of fractional flow reserve.