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MacRaild M, Sarrami-Foroushani A, Lassila T, Frangi AF. Reduced order modelling of intracranial aneurysm flow using proper orthogonal decomposition and neural networks. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2024; 40:e3848. [PMID: 39155149 DOI: 10.1002/cnm.3848] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2024] [Revised: 06/03/2024] [Accepted: 06/30/2024] [Indexed: 08/20/2024]
Abstract
Reduced order modelling (ROMs) methods, such as proper orthogonal decomposition (POD), systematically reduce the dimensionality of high-fidelity computational models and potentially achieve large gains in execution speed. Machine learning (ML) using neural networks has been used to overcome limitations of traditional ROM techniques when applied to nonlinear problems, which has led to the recent development of reduced order models augmented by machine learning (ML-ROMs). However, the performance of ML-ROMs is yet to be widely evaluated in realistic applications and questions remain regarding the optimal design of ML-ROMs. In this study, we investigate the application of a non-intrusive parametric ML-ROM to a nonlinear, time-dependent fluid dynamics problem in a complex 3D geometry. We construct the ML-ROM using POD for dimensionality reduction and neural networks for interpolation of the ROM coefficients. We compare three different network designs in terms of approximation accuracy and performance. We test our ML-ROM on a flow problem in intracranial aneurysms, where flow variability effects are important when evaluating rupture risk and simulating treatment outcomes. The best-performing network design in our comparison used a two-stage POD reduction, a technique rarely used in previous studies. The best-performing ROM achieved mean test accuracies of 98.6% and 97.6% in the parent vessel and the aneurysm, respectively, while providing speed-up factors of the order10 5 .
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Affiliation(s)
- Michael MacRaild
- Centre for Computational Imaging and Modelling in Medicine (CIMIM), University of Manchester, Manchester, UK
- EPSRC Centre for Doctoral Training in Fluid Dynamics, University of Leeds, Leeds, UK
- Department of Computer Science, School of Engineering, University of Manchester, Manchester, UK
| | - Ali Sarrami-Foroushani
- Centre for Computational Imaging and Modelling in Medicine (CIMIM), University of Manchester, Manchester, UK
- School of Health Science, University of Manchester, Manchester, UK
| | - Toni Lassila
- School of Computing, University of Leeds, Leeds, UK
| | - Alejandro F Frangi
- Centre for Computational Imaging and Modelling in Medicine (CIMIM), University of Manchester, Manchester, UK
- Department of Computer Science, School of Engineering, University of Manchester, Manchester, UK
- School of Health Science, University of Manchester, Manchester, UK
- Department of Cardiovascular Sciences, KU Leuven, Leuven, Belgium
- Department of Electrical Engineering (ESAT), KU Leuven, Leuven, Belgium
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Yi H, Yang Z, Bramlage L, Ludwig B. Using DFT on ultrasound measurements to determine patient-specific blood flow boundary conditions for computational hemodynamics of intracranial aneurysms. Comput Biol Med 2024; 176:108563. [PMID: 38761498 DOI: 10.1016/j.compbiomed.2024.108563] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2024] [Revised: 04/01/2024] [Accepted: 05/05/2024] [Indexed: 05/20/2024]
Abstract
Boundary conditions (BCs) is one pivotal factor influencing the accuracy of hemodynamic predictions on intracranial aneurysms (IAs) using computational fluid dynamics (CFD) modeling. Unfortunately, a standard procedure to secure accurate BCs for hemodynamic modeling does not exist. To bridge such a knowledge gap, two representative patient-specific IA models (Case-I and Case-II) were reconstructed and their blood flow velocity waveforms in the internal carotid artery (ICA) were measured by ultrasonic techniques and modeled by discrete Fourier transform (DFT). Then, numerical investigations were conducted to explore the appropriate number of samples (N) for DFT modeling to secure the accurate BC by comparing a series of hemodynamic parameters using in-vitro validated CFD modeling. Subsequently, a comprehensive comparison in hemodynamic characteristics under patient-specific BCs and a generalized BC based on a one-dimensional (1D) model was conducted to reinforce the understanding that a patient-specific BC is pivotal for accurate hemodynamic risk evaluations on IA pathophysiology. In addition, the influence of the variance of heart rate/cardiac pulsatile period on hemodynamic characteristics in IA models was studied preliminarily. The results showed that N ≥ 16 for DFT model is a decent choice to secure the proper BC profile to calculate time-averaged hemodynamic parameters, while more data points such as N ≥ 36 can ensure the accuracy of instantaneous hemodynamic predictions. In addition, results revealed the generalized BC could overestimate or underestimate the hemodynamic risks on IAs significantly; thus, patient-specific BCs are highly recommended for hemodynamic modeling for IA risk evaluation. Furthermore, this study discovered the variance of heart rate has rare influences on hemodynamic characteristics in both instantaneous and time-averaged parameters under the assumption of an identical blood flow rate.
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Affiliation(s)
- Hang Yi
- Department of Mechanical and Materials Engineering, Wright State University, Dayton, OH, 45435, USA
| | - Zifeng Yang
- Department of Mechanical and Materials Engineering, Wright State University, Dayton, OH, 45435, USA.
| | - Luke Bramlage
- Division of NeuroInterventional Surgery, Department of Neurology, Wright State University/Premier Health-Clinical Neuroscience Institute, 30E. Apple St., Dayton, OH, 45409, USA; Boonshoft School of Medicine, Wright State University, Dayton, OH, 45435, USA
| | - Bryan Ludwig
- Division of NeuroInterventional Surgery, Department of Neurology, Wright State University/Premier Health-Clinical Neuroscience Institute, 30E. Apple St., Dayton, OH, 45409, USA; Boonshoft School of Medicine, Wright State University, Dayton, OH, 45435, USA
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Liu Q, Sarrami-Foroushani A, Wang Y, MacRaild M, Kelly C, Lin F, Xia Y, Song S, Ravikumar N, Patankar T, Taylor ZA, Lassila T, Frangi AF. Hemodynamics of thrombus formation in intracranial aneurysms: An in silico observational study. APL Bioeng 2023; 7:036102. [PMID: 37426382 PMCID: PMC10329514 DOI: 10.1063/5.0144848] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2023] [Accepted: 06/07/2023] [Indexed: 07/11/2023] Open
Abstract
How prevalent is spontaneous thrombosis in a population containing all sizes of intracranial aneurysms? How can we calibrate computational models of thrombosis based on published data? How does spontaneous thrombosis differ in normo- and hypertensive subjects? We address the first question through a thorough analysis of published datasets that provide spontaneous thrombosis rates across different aneurysm characteristics. This analysis provides data for a subgroup of the general population of aneurysms, namely, those of large and giant size (>10 mm). Based on these observed spontaneous thrombosis rates, our computational modeling platform enables the first in silico observational study of spontaneous thrombosis prevalence across a broader set of aneurysm phenotypes. We generate 109 virtual patients and use a novel approach to calibrate two trigger thresholds: residence time and shear rate, thus addressing the second question. We then address the third question by utilizing this calibrated model to provide new insight into the effects of hypertension on spontaneous thrombosis. We demonstrate how a mechanistic thrombosis model calibrated on an intracranial aneurysm cohort can help estimate spontaneous thrombosis prevalence in a broader aneurysm population. This study is enabled through a fully automatic multi-scale modeling pipeline. We use the clinical spontaneous thrombosis data as an indirect population-level validation of a complex computational modeling framework. Furthermore, our framework allows exploration of the influence of hypertension in spontaneous thrombosis. This lays the foundation for in silico clinical trials of cerebrovascular devices in high-risk populations, e.g., assessing the performance of flow diverters in aneurysms for hypertensive patients.
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Affiliation(s)
| | | | | | | | - Christopher Kelly
- Centre for Computational Imaging and Simulation Technologies in Biomedicine (CISTIB), School of Computing, University of Leeds, Leeds, United Kingdom
| | | | | | | | - Nishant Ravikumar
- Centre for Computational Imaging and Simulation Technologies in Biomedicine (CISTIB), School of Computing, University of Leeds, Leeds, United Kingdom
| | | | - Zeike A. Taylor
- School of Mechanical Engineering, University of Leeds, Leeds, United Kingdom
| | - Toni Lassila
- Centre for Computational Imaging and Simulation Technologies in Biomedicine (CISTIB), School of Computing, University of Leeds, Leeds, United Kingdom
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Römer U, Liu J, Böl M. Surrogate-based Bayesian calibration of biomechanical models with isotropic material behavior. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2022; 38:e3575. [PMID: 35094499 DOI: 10.1002/cnm.3575] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2021] [Accepted: 01/29/2022] [Indexed: 06/14/2023]
Abstract
This work introduces a computational methodology to calibrate material models in biomechanical applications under uncertainty. We adopt a Bayesian approach, which estimates the probability distributions of hyperelastic material parameters, based on force-strain measurements. We approximate the parametric biomechanical model by combining a reduced order representation of the force response with a Polynomial Chaos expansion. The surrogate model allows to employ sampling-intensive Markov chain Monte Carlo methods and provides an efficient way to estimate (generalized) Sobol coefficients. We use a Sobol sensitivity analysis to assess the influence of material parameters and present an iterative procedure to quantify the accuracy of the surrogate model as additional uncertainty during Bayesian updating. The methodology is illustrated with three cases, tensile experiments on heat-induced whey protein gel, indentation experiments for oocytes and a manufactured example. Real experimental data are used for the calibration.
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Affiliation(s)
- Ulrich Römer
- Institut für Dynamik und Schwingungen, Technische Universität Braunschweig, Braunschweig, Germany
| | - Jintian Liu
- Institut für Mechanik und Adaptronik, Technische Universität Braunschweig, Braunschweig, Germany
| | - Markus Böl
- Institut für Mechanik und Adaptronik, Technische Universität Braunschweig, Braunschweig, Germany
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In-silico trial of intracranial flow diverters replicates and expands insights from conventional clinical trials. Nat Commun 2021; 12:3861. [PMID: 34162852 PMCID: PMC8222326 DOI: 10.1038/s41467-021-23998-w] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2020] [Accepted: 05/25/2021] [Indexed: 01/18/2023] Open
Abstract
The cost of clinical trials is ever-increasing. In-silico trials rely on virtual populations and interventions simulated using patient-specific models and may offer a solution to lower these costs. We present the flow diverter performance assessment (FD-PASS) in-silico trial, which models the treatment of intracranial aneurysms in 164 virtual patients with 82 distinct anatomies with a flow-diverting stent, using computational fluid dynamics to quantify post-treatment flow reduction. The predicted FD-PASS flow-diversion success rates replicate the values previously reported in three clinical trials. The in-silico approach allows broader investigation of factors associated with insufficient flow reduction than feasible in a conventional trial. Our findings demonstrate that in-silico trials of endovascular medical devices can: (i) replicate findings of conventional clinical trials, and (ii) perform virtual experiments and sub-group analyses that are difficult or impossible in conventional trials to discover new insights on treatment failure, e.g. in the presence of side-branches or hypertension. In-silico trials rely on virtual populations and interventions simulated using patient-specific models and may offer a solution to lower costs. Here, the authors present the flow diverter performance assessment in-silico trial, which models the treatment of intracranial aneurysms with a flow-diverting stent.
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