Gradient Calculations Research Articles

New parameterized quantum gates design and efficient gradient solving based on variational quantum classification algorithm

Abstract Currently, variational quantum classification algorithms (VQCAs) generally rely on traditional optimization techniques such as Powell and SLSQP in the parameter optimization session. However, the performance of these methods shows limitations in practical applications. Although the parameter-shift rule can efficiently compute the parameter gradient with quantum circuits, it needs to run the quantum circuit twice repeatedly, which significantly reduces the computation efficiency. In order to overcome this challenge, this paper innovatively integrates the principle of unitary operation in quantum mechanics with the technical characteristics of superconducting quantum chips and elaborately designs some new parameterized quantum gates (PQGs). These PQGs strictly follow the rules of unitary operation, which ensures the stability and accuracy of quantum state evolution while realizing an efficient solution to the parameter gradient. Especially for the gradient calculation of a single qubit and single-angle PQGs, the new method can be completed with only a single quantum circuit run, which greatly improves the computation efficiency. Experimental validation on benchmark datasets such as breast cancer and iris shows that the method proposed in this paper exhibits excellent performance on quantum classification tasks. Compared with the parameter-shift rule, the computation efficiency of the new method is improved by 40%. And the classification accuracy, precision, and other key performance metrics are improved by an average of 5% in comparison with traditional optimization algorithms. This work not only enriches the methodology of quantum machine learning theoretically but also demonstrates its remarkable superiority in practical applications, which indicates that the method has great potential in scientific research and industrial applications.

Surfactant-Enhanced Spreading on Solids: Roles of the Surface Tension Gradient, Spreading Contact Angle, and Viscosity.

Despite its important technological applications, surfactant-enhanced (spontaneous) spreading on a solid surface and how to optimize it on surfaces with different wettabilities are not well understood. Spontaneous spreading involves a surface tension gradient (Marangoni stresses), which enhances spreading over a large area. Experimental observations reveal that the spreading rate and surfactant concentration have an optimum substrate wettability of 60 ± 5° (Hill, R. M. Curr. Opin. Colloid Interface Sci. 1998, 3, 247).This paper discusses why the optimum for surfactant-enhanced spreading requires an initial macroscopic three-phase contact angle of 60 ± 5°. An equation based on experimental evidence allows for the calculation of the surface tension gradient over time using data on the spreading rate, spreading macroscopic contact angle, and droplet spreading radius. This novel approach for estimating the surface tension gradient and explaining the optimum substrate wettability underscores the role of the surface tension gradient, viscosity, and substrate wettability in surfactant-enhanced spreading on solids. The roles of the spreading three-phase contact angle and surface tension gradient in surfactant-enhanced spreading were analyzed, demonstrating that the surface tension gradient contributes more significantly to the spreading rate than the contact angle. Fingering instability formation, an instability at the droplet spreading edge caused by the Marangoni stresses, also serves as evidence of the role that the surface tension gradient plays in surfactant-enhanced spreading. Furthermore, applications of surfactant-enhanced spreading were demonstrated, suggesting potential uses in oil spill removal, leaf pesticide delivery, and oil spill remediation. The goal of the proposed study is to use experimental evidence to develop a model for calculating the optimum spreading rate during the first several seconds of surfactant-enhanced spreading on a solid substrate.

Reference map technique for Lagrangian exploration of coherent structures

We explore the application of the reference map technique, originally developed for Eulerian simulation of solid mechanics, in Lagrangian kinematics of turbulent flows. Unlike traditional methods based on explicit particle tracking, the reference map facilitates the calculation of flow maps and gradients without the need for particles. This is achieved through an Eulerian update of the reference map, which records the take-off positions of fluid particles. This approach is found to be mathematically equivalent to the work of Leung (J. Comput. Phys., vol. 230, issue 9, 2011, pp. 3500–3524), who computed the flow map of simple two-dimensional flows using an Eulerian approach. We discuss important modifications necessary for its first application to complex three-dimensional turbulent flows, including the conservative, low-dissipation update of the flow map and the treatment of periodic boundary conditions. We first demonstrate the accuracy of finite-time Lyapunov exponent (FTLE) calculations based on the reference map against the standard particle-based approach in a two-dimensional Taylor–Green vortex. Then we apply it to turbulent channel flow at $Re_\tau =180$ , where Lagrangian coherent structures identified as ridges of the backward-time FTLE are found to bound vortical regions of flow, consistent with Eulerian coherent structures from the $Q$ -criterion. The reference map also proves suitable for material surface tracking despite not explicitly tracking particles. This capability can provide valuable insights into the Lagrangian landscape of turbulent momentum transport, complementing Eulerian velocity field analysis. The evolution of initially wall-normal material surfaces in the viscous sublayer, buffer layer and log layer sheds light on the Reynolds stress-generating events from a Lagrangian perspective.

Highly accurate calculation of electric field for transcranial magnetic stimulation using hybridizable discontinuous galerkin method

The computation of electric field in transcranial magnetic stimulation (TMS) is essentially a problem of gradient calculation for thin layers. This paper introduces a hybrid-order hybridizable discontinuous Galerkin finite element method (HDG-FEM) and systematically demonstrates its superiority in TMS computations. The discrete format of HDG-FEM employing hybrid orders for TMS is derived and, from a fundamental numerical principle perspective, this study provides the elucidation of why HDG-FEM exhibits superior gradient computation capabilities compared to the widely used CG-FEM. Furthermore, the exceptional performance of HDG-FEM in thin layer calculation is demonstrated on both modified head models and realistic head models, focusing on three aspects: calculation errors, utilization of hybrid order, and computational cost. For the calculation of E-field in thin-layer regions with parameter mutation, the L∞ norm error of the first-order HDG-FEM with the same tetrahedral mesh is comparable to the L∞ norm error of the second-order CG-FEM. The L2 norm error of the same-order HDG-FEM is smaller than that of the same-order CG-FEM. By utilizing the hybrid order, HDG-FEM achieves a rapid reduction in errors of thin layers without a significant increase in the computational cost. This study transforms the three-dimensional TMS problem into a special two-dimensional problem for computation, reducing computational complexity from p3 in three dimensions to p2 in two dimensions, while achieving significantly higher accuracy compared to the commonly used CG-FEM. The utilization of hybrid orders in thin layers of the head demonstrates significant flexibility, making HDG-FEM a new alternative choice for TMS computations.

SENSITIVITY ASSESSMENT OF A GRADIENT-BASED LEAK LOCALIZATION PROCEDURE FOR PRESSURE SENSOR FAULTS USING A LABORATORY MODEL OF A TRANSMISSION PIPELINE

This research addresses the topic of leakage localization in liquid transmission pipelines. Particularly, it deals with the standard gradient-based procedure used for performing such a task. The procedure relies on pressure gradient calculations based on pressure data collected from measurement points distributed along the pipeline. This study aimed to verify this procedure regarding its sensitivity to typical systematic errors related to pressure transducers. The primary measure evaluated was the accuracy of the calculated coordinate of a leak spot. The uncertainty of the leak localization result was also estimated following the Guide to the Expression of Uncertainty in Measurement convention. A laboratory model of the pipeline was used to practically implement and test the procedure. During experiments, low-intensity leakages with a level of 0.25–2.00% were simulated. Regarding typical systematic errors, the bias (zero moving) type and the proportional ratio type were considered, which were numerically simulated in the measurement data. The findings reveal how sensitive the examined procedure is in relation to these errors, considering their different levels and scenarios related to used pressure transducers.

Maximization of fundamental frequency for small satellite components layout design

This paper proposes a bi-objective optimization method for the small satellite components layout optimization design, considering mass characteristics and fundamental frequency characteristics. Firstly, φ function is used to describe the geometry and position relationships between components, effectively addressing the non-overlap constraints among them. Then, the finite element method is used to calculate the stiffness and mass of the satellite load-bearing board to determine the fundamental frequency of the satellite. In addition, the paper designs a novel bi-objective optimization algorithm combined Diverse Gradient Optimization (DGO) algorithm with the Smart Normal Constraint (SNC) method, which simplifies the complex gradient calculation through semi-analytical sensitivity analysis. Finally, numerical examples validate the applicability and rationality of the proposed optimization method in solving bi-objective satellite components layout problems. The results show that the method can provide effective solutions for the layout design of small satellite components while considering both mass characteristics and fundamental frequency characteristics optimization.

Separable physics-informed DeepONet: Breaking the curse of dimensionality in physics-informed machine learning

The deep operator network (DeepONet) has shown remarkable potential in solving partial differential equations (PDEs) by mapping between infinite-dimensional function spaces using labeled datasets. However, in scenarios lacking labeled data, the physics-informed DeepONet (PI-DeepONet) approach, which utilizes the residual loss of the governing PDE to optimize the network parameters, faces significant computational challenges, particularly due to the curse of dimensionality. This limitation has hindered its application to high-dimensional problems, making even standard 3D spatial with 1D temporal problems computationally prohibitive. Additionally, the computational requirement increases exponentially with the discretization density of the domain. To address these challenges and enhance scalability for high-dimensional PDEs, we introduce the Separable physics-informed DeepONet (Sep-PI-DeepONet). This framework employs a factorization technique, utilizing sub-networks for individual one-dimensional coordinates, thereby reducing the number of forward passes and the size of the Jacobian matrix required for gradient computations. By incorporating forward-mode automatic differentiation (AD), we further optimize computational efficiency, achieving linear scaling of computational cost with discretization density and dimensionality, making our approach highly suitable for high-dimensional PDEs. We demonstrate the effectiveness of Sep-PI-DeepONet through three benchmark PDE models: the viscous Burgers’ equation, Biot’s consolidation theory, and a parametrized heat equation. Our framework maintains accuracy comparable to the conventional PI-DeepONet while reducing training time by two orders of magnitude. Notably, for the heat equation solved as a 4D problem, the conventional PI-DeepONet was computationally infeasible (estimated 289.35 h), while the Sep-PI-DeepONet completed training in just 2.5 h. These results underscore the potential of Sep-PI-DeepONet in efficiently solving complex, high-dimensional PDEs, marking a significant advancement in physics-informed machine learning.

On the adjoint state method for the gradient computation in full waveform inversion: a complete mathematical derivation for the (visco-)elastodynamics approximation

Summary High resolution seismic imaging at all scales using full waveform inversion is now routinely used in the industry and in the academy. One key element for the success of this approach is a numerical method, named adjoint state method, originally designed for optimization problems constrained by partial differential equations, a category to which full waveform inversion belongs. This method provides an efficient way to compute the gradient of the full waveform inversion misfit function, which is the most computationally demanding task in the implementation of full waveform inversion. While well known, the complete and rigorous mathematical derivation of the adjoint state method for full waveform inversion remains missing in the scientific bibliography. The aim of this study is to remedy this lack. The derivation is performed in general settings, that is in the elastodynamics approximation, with and without considering viscosity. Through the calculus, the mechanism of the adjoint state strategy makes clear the connection between the incident and adjoint fields, especially regarding their initial and boundary conditions. The impact of introducing the viscosity is carefully analyzed. The resulting gradient formulas are analyzed and shown to be consistent with already published ones. The generic approach which is adopted also makes it possible to derive misfit function gradients with respect to other quantities than the subsurface mechanical parameters, for instance with respect to the initial or the boundary conditions, which could be of interest for specific applications where the reconstructed parameters are not only volumetric mechanical parameters but boundary parameters or initial field values.

Fast and precise dose estimation for very high energy electron radiotherapy with graph neural networks

IntroductionExternal beam radiotherapy (RT) is one of the most common treatments against cancer, with photon-based RT and particle therapy being commonly employed modalities. Very high energy electrons (VHEE) have emerged as promising candidates for novel treatments, particularly in exploiting the FLASH effect, offering potential advantages over traditional modalities.MethodsThis paper introduces a Deep Learning model based on graph convolutional networks to determine dose distributions of therapeutic VHEE beams in patient tissues. The model emulates Monte Carlo (MC) simulated doses within a cylindrical volume around the beam, enabling high spatial resolution dose calculation along the beamline while managing memory constraints.ResultsTrained on diverse beam orientations and energies, the model exhibits strong generalization to unseen configurations, achieving high accuracy metrics, including a δ-index 3% passing rate of 99.8% and average relative error <1% in integrated dose profiles compared to MC simulations.DiscussionNotably, the model offers three to six orders of magnitude increased speed over full MC simulations and fast MC codes, generating dose distributions in milliseconds on a single GPU. This speed could enable direct integration into treatment planning optimization algorithms and leverage the model’s differentiability for exact gradient computation.

RLL-SWE: A Robust Linked List Steganography Without Embedding for intelligence networks in smart environments

With the rapid development of technology, smart environments utilizing the Internet of Things, artificial intelligence, and big data are improving the quality of life and work efficiency through connected devices. However, these advances present significant security challenges. The data generated by these smart devices contains many private and sensitive information. In data transmission, crime and terrorism may intercept this sensitive information and use it for secret communications and illegal activities. Steganography hides information in media files and prevents information leakage and interception by criminal and terrorist networks in an intelligent environment. It is an important technology to protect data integrity and security. Traditional steganography techniques often cause detectable distortions, whereas Steganography Without Embedding (SWE) avoids direct modification of cover media, thereby minimizing detection risks. This paper introduces an innovative and robust technique called Robust Linked List (RLL)-SWE, which improves resistance to attacks compared to traditional methods. Using multiple median downsampling and gradient calculations, this method extracts stable features. It restructures them into a multi-head unidirectional linked list, ensuring accurate message retrieval and high resistance to adversarial attacks. Comprehensive analysis and simulation experiments confirm the technique’s exceptional effectiveness and steganographic capacity.

Event-triggered approximately optimized formation control of multi-agent systems with unknown disturbances via simplified reinforcement learning

An event-triggered formation control strategy is proposed for a multi-agent system (MAS) suffered from unknown disturbances. In identifier-critic-actor neural networks (NNs), the strategy only needs to calculate the negative gradient of an approximated Hamilton-Jacobi-Bellman (HJB) equation, instead of the gradient descent method associated with Bellman residual errors. This simplified method removes the requirement for a complicated gradient calculation process of residual square of HJB equation. The weights in critic-actor NNs only update as the triggered condition is violated, and the computational burdens caused by frequent updates are thus reduced. Without dynamics information in prior, a disturbance observer is also constructed to approximate disturbances in an MAS. From stability analysis, it is proven that all signals are bounded. Two numerical examples are illustrated to verify that the proposed control strategy is effective.

Digital Twin Generalization with Meta and Geometric Deep Learning

Deep digital twins (DDTs) are deep neural networks that encode the behavior of complex physical systems. DDTs are excellent system representations due to their ability to continuously adapt to operational changes and their capability to capture complex relationships between system components and processes that cannot be explicitly modeled. For this challenge, DDTs benefit greatly from recent success in geometric deep learning (GDL) which allows the integration of information from multiple systems based on schematic representations. A major challenge in training DDTs is their dependence on the quality and representativeness of training data, especially under the dynamic conditions typical in prognostics and health management (PHM). Recent developments in differentiable simulation present new opportunities for optimizing the training data representativeness. In this thesis, we propose a novel meta-learning framework that trains DDTs using the output from differentiable simulators. This setup enables active optimization of training data sampling through gradient computation, enhancing training speed, robustness, and data representativeness. We extend this framework to address challenges in multi-system data integration in power grids and fault detection in railway traction networks. By applying our framework, we aim to tackle significant challenges in forecasting, anomaly detection and sensor-fault analysis using advanced data fusion techniques. Our approach promises substantial improvements in DDT robustness and operational efficiency, with its effectiveness to be demonstrated through empirical studies on both simple and complex case studies within the power systems domain.

Bandwidth-aware fast inverse lithography technology using Nesterov accelerated gradient

Inverse lithography technology (ILT) is a leading-edge method for improving the resolution and image fidelity of optical lithography systems in semiconductor manufacturing. However, the massive computational complexity of ILT presents the inherent runtime bottleneck, which hinders its application to the large-scale lithography layouts. This paper innovates a fast ILT method by reducing both of the inherent algorithmic complexity and the required iteration number. Based on the diffraction-limited nature of optical lithography system, a bandwidth-aware acceleration approach is applied to reduce the calculation complexities of the forward imaging model and inverse gradient computation in each ILT iteration. In addition, a carefully designed algorithm based on the Nesterov accelerated gradient (NAG) is developed to achieve nearly quadratic convergence rate, thereby reducing the total number of iterations required to obtain the optimal solution. Numerical experiments show that the proposed method can improve the speed by hundreds of times over the traditional gradient-based ILT algorithms without sacrificing accuracy.

Full waveform inversion of surface wave based on instantaneous frequency

Abstract Surface wave has many advantages, such as low attenuation, high signal-to-noise ratio, strong anti-interference ability and dispersion characteristics in layered media. It is widely used in engineering measurement and nondestructive testing. However, the applicability and reliability of surface wave processing methods are severely restricted by velocity inversion or strong heterogeneity of the medium. To overcome these shortcomings, in recent years, scholars have studied full-wave inversion methods including data preprocessing, wave field forward, gradient calculation, and inversion optimization to avoid any assumptions about underground complexity. However, the classical waveform difference mismatch function is apt to fall into a local minimum, which leads to the non-convergence of inversion. At the same time, the existence of surface waves greatly increases the non-linearity of full waveform inversion. Even small perturbations, especially in the S wave velocity structure, can cause dispersion for uniform backgrounds. To overcome this difficulty, a mismatch function based on instantaneous frequency is proposed and the adjoint wave equation is derived. Taking a layered model as an example, the effectiveness of the method is verified.

JAX-Fluids 2.0: Towards HPC for differentiable CFD of compressible two-phase flows

In our effort to facilitate machine learning-assisted computational fluid dynamics (CFD), we introduce the second iteration of JAX-Fluids. JAX-Fluids is a Python-based fully-differentiable CFD solver designed for compressible single- and two-phase flows. In this work, the first version is extended to incorporate high-performance computing (HPC) capabilities. We introduce a parallelization strategy utilizing JAX primitive operations that scales efficiently on GPU (up to 512 NVIDIA A100 graphics cards) and TPU (up to 1024 TPU v3 cores) HPC systems. We further demonstrate stable parallel computation of automatic differentiation gradients across extended integration trajectories. The new code version offers enhanced two-phase flow modeling capabilities. In particular, a five-equation diffuse-interface model is incorporated which complements the level-set sharp-interface model. Additional algorithmic improvements include positivity-preserving limiters for increased robustness, support for stretched Cartesian meshes, refactored I/O handling, comprehensive post-processing routines, and an updated list of state-of-the-art high-order numerical discretization schemes. We verify newly added numerical models by showcasing simulation results for single- and two-phase flows, including turbulent boundary layer and channel flows, air-helium shock bubble interactions, and air-water shock drop interactions.

OpenQP: A Quantum Chemical Platform Featuring MRSF-TDDFT with an Emphasis on Open-Source Ecosystem.

The OpenQP (Open Quantum Platform) is a new open-source quantum chemistry library developed to tackle sustainability and interoperability challenges in the field of computational chemistry. OpenQP provides various popular quantum chemical theories as autonomous modules such as energy and gradient calculations of HF, DFT, TDDFT, SF-TDDFT, and MRSF-TDDFT, thereby allowing easy interconnection with third-party software. A scientifically notable feature is the innovative mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT) and its customized exchange-correlation functionals such as the DTCAM series of VAEE, XI, XIV, AEE, and VEE, which significantly expand the applicability scope of DFT and TDDFT. OpenQP also supports parallel execution and is optimized with BLAS and LAPACK for high performance. Future enhancements such as extended Koopman's theorem (EKT)-MRSF-TDDFT and spin-orbit coupling (SOC)-MRSF-TDDFT will further expand OpenQP's capabilities. Additionally, a Python wrapper PyOQP is provided that performs tasks such as geometry optimization, conical intersection searches, and nonadiabatic coupling calculations, among others, by prototyping the modules of the OpenQP library in combination with third-party libraries. Overall, OpenQP aligns with modern trends in high-performance scientific software development by offering flexible prototyping and operation while retaining the performance benefits of compiled languages like Fortran and C. They enhance the sustainability and interoperability of quantum chemical software, making OpenQP a crucial platform for accelerating the development of advanced quantum theories like MRSF-TDDFT.

Efficient Implementation of Interior-Point Methods for Quantum Relative Entropy

Quantum relative entropy (QRE) programming is a recently popular and challenging class of convex optimization problems with significant applications in quantum computing and quantum information theory. We are interested in modern interior-point (IP) methods based on optimal self-concordant barriers for the QRE cone. A range of theoretical and numerical challenges associated with such barrier functions and the QRE cones have hindered the scalability of IP methods. To address these challenges, we propose a series of numerical and linear algebraic techniques and heuristics aimed at enhancing the efficiency of gradient and Hessian computations for the self-concordant barrier function, solving linear systems, and performing matrix-vector products. We also introduce and deliberate about some interesting concepts related to QRE such as symmetric quantum relative entropy. We design a two-phase method for performing facial reduction that can significantly improve the performance of QRE programming. Our new techniques have been implemented in the latest version (DDS 2.2) of the software package Domain-Driven Solver (DDS). In addition to handling QRE constraints, DDS accepts any combination of several other conic and nonconic convex constraints. Our comprehensive numerical experiments encompass several parts, including (1) a comparison of DDS 2.2 with Hypatia for the nearest correlation matrix problem, (2) using DDS 2.2 for combining QRE constraints with various other constraint types, and (3) calculating the key rate for quantum key distribution (QKD) channels and presenting results for several QKD protocols. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing and Operations Research. Accepted for Special Issue. Funding: This work was supported by the National Science Foundation [Grant CMMI-2347120] and Discovery Grants from the Natural Sciences and Engineering Research Council of Canada. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0570 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0570 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Gender differences in coronary artery disease patterns

Abstract Background Gender differences in clinical presentation, natural history, and prognosis of coronary artery disease (CAD) have been reported. Fractional flow reserve (FFR) has also been shown to yield higher values in women than men. However, the gender differences in CAD patterns (focal vs diffuse) defined by coronary physiology remain to be studied. Methods This prospective study was performed at 23 sites and enrolled patients with at least one epicardial lesion with an FFR ≤ 0.80 intended to be treated by PCI. All patients underwent a standardized physiological protocol that mandated FFR pullbacks with pullback pressure gradient (PPG) calculation. The aim was to compare CAD patterns, defined by PPG, between genders. Results Overall, 1004 patients were included in the analysis, 236 females (250 vessels) and 768 males (794 vessels). Women were older (69.8 ± 10.3 vs. 67.0 ± 10.1, p <0.001), less frequently smokers (9.7% vs. 18.6%, p = 0.002), had less prior PCI in a non-target vessel (19.1% vs. 30.6%, p = 0.001) and had less prior MIs (14.4% vs. 21.5%, p = 0.021). On the baseline seven-item Seattle Angina Questionnaire (SAQ-7), females reported more physical limitation (70.9 ± 29.5 vs. 80.9 ± 25.1, p < 0.001), more frequent angina (76.7 ± 22.9 vs. 81.5 ± 20.3, p = 0.002) and a lower quality of life (51.8 ± 29.4 vs. 57.8 ± 29.1, p = 0.006) than men for the same degree of flow reduction (FFR 0.69 ± 0.12 vs. 0.67 ± 0.11, p=0.098). In women, the pattern of CAD demonstrated a more focal nature compared to men (PPG 0.65 ± 0.16 vs. 0.61 ± 0.16, p = 0.001). Also, women achieved higher post-PCI FFR (0.88 ± 0.07 vs. 0.87 ± 0.07, p = 0.02). The rate of periprocedural MI was not statistically different between genders (5.1% vs. 5.8%, p = 0.79) Conclusion Among patients with hemodynamically significant CAD, women report more symptoms and lower quality of life. Despite sharing a similar degree of flow impairment, women exhibited a more focal CAD phenotype than men, leading to superior physiological outcomes after PCI.Study flowchartPRO and Phisiology by gender

Impact of the pullback pressure gradient (PPG) on PCI planning and decision-making

Abstract Background Coronary physiology using a distal measurement of fractional flow reserve (FFR) informs about the severity of coronary artery disease (CAD) and, when used for clinical decision-making about revascularisation, is associated with improved outcomes in patients considered for PCI. A second dimension of coronary physiology is available by performing a pullback maneuver, which aids in assessing the presence and location of focal pressure gradients. Yet, the impact of intracoronary physiology guidance with FFR pullbacks on real-time physician decision-making during PCI is not fully known. Methods This prospective study was performed at 25 sites and enrolled patients with at least one epicardial lesion with FFR ≤ 0.80 planned to be treated by PCI. A standardized physiological assessment with FFR pullbacks and Pullback Pressure Gradient (PPG) calculation was performed. Treatment plans were recorded for each lesion based on angiography alone and following FFR pullbacks. The goal of this study was to assess the procedural impact of physiology guidance in stable patients scheduled for PCI. Results Overall, 993 patients (1044 vessels) underwent complete physiological assessment with FFR and PPG. Decision-making during PCI changed in 47.5% (443/1044) after FFR pullbacks. Decision-making during PCI changed in 32.4% (289/890) after FFR pullbacks. PPG use changed revascularisation decisions in 13.9% (138/993) from PCI to CABG (5%; 50/993), from PCI to CABG in 5% (50/993) and to medical management in 8.9% ( 88/993). The frequency of decision changes was significantly higher in patients with diffuse CAD compared to focal cases (24.8% vs. 44.2%, p < 0.001). Among the subset of 855 patients (involving 880 vessels) who underwent PCI, operators modified decision-making regarding stent length in 22.1% of cases (197 out of 880), with these alterations being more prevalent in patients with diffuse CAD (57.2% vs. 46.3%, p = 0.002). Suboptimal Post-PCI result (FFR < 0.88) was more frequent in cases in which PCI strategy was not adapted based on PPG (55.5% vs. 45.6%, p= 0.016) Importantly, there was no significant change in the overall number of stents per patient after FFR pullbacks. Conclusion A standardized coronary physiological assessment impacted PCI decision-making in one-third of the vessels, with a predominant effect in vessels diffusely diseased. The assessment of the distribution of pressure losses along the coronaries modifies the treatment decision and influences PCI strategy in a significant proportion of patients. These findings provide insights into mechanisms by which coronary physiology might improve PCI outcomes.PCI strategy change based on PPGCumulative change of PCI strategy

Assessing boundary conditions in CFD for transvalvular pressure gradient calculation in cardiac hemodynamics

Abstract Background Computational fluid dynamics (CFD), which has the advantages of providing detailed pressure distribution, has been widely used for cardiac function assessment and heart disease diagnosis. However, the results are usually influenced by the boundary conditions. Particularly, the transvalvular pressure gradient, which serves as a crucial indicator for mitral stenosis and the efficacy of mitral valve surgery, can easily be miscalculated. Here, we assess the effects of widely used boundary conditions on the transvalvular pressure gradient computed based on the Bernoulli equation and the line probe, respectively. Purpose This study aims to determine the effects of boundary conditions on the transvalvular pressure gradient in CFD. Methods We constructed cardiac models including left atrium, left ventricle, aorta from CT and mitral valve from transesophageal echocardiography data (Figure 1). The intraventricular flow fields were computed using CFD tool with four different boundary conditions (BC) at the same cardiac output. BC1 involved specifying the total flow rate of the aorta, with zero pressure at the entrance of the pulmonary veins. BC2 maintained equal flow rates at the entrances of the pulmonary veins. BC3 followed Murray's law, where the flow rate ratio in the pulmonary veins is proportional to the 1.5 power of the area ratio. BC4 followed Poiseuille's law, where the flow rate ratio is proportional to the square of the area ratio. The results encompassed the mean transvalvular pressure gradient and peak transvalvular pressure gradient obtained through the Bernoulli equation and the line probe methods, respectively. Results Figures 2(A-D) present the contours of transvalvular pressure under peak flow velocity conditions and the isosurfaces of vorticity within the ventricle. The results show that the pressure within the atrium is notably lower in the BC2, leading to a 63% underestimation in the mean transvalvular pressure gradient and a 22.9% deviation in the peak transvalvular pressure gradient (Figure 2 F). The transvalvular pressure gradient for BC1, BC3, and BC4 do not exceed 10%. The results reveal that the pressure distribution and vorticity within the ventricle are consistent, primarily due to the influence of the mitral valve. Conclusion When evaluating transvalvular pressure gradient using CFD, it is crucial to specify appropriate boundary conditions. Using inappropriate boundary conditions may lead to underestimation of the transvalvular pressure gradient, thereby affecting further diagnostic decisions. In research studies, it is recommended to allocate flow in different branch vessels according to Murray's law, where the flow in different branch vessels is proportional to the 1.5 power of the vessel cross-sectional area.Modelling flow chartTransvalvular pressure gradient