Efficient Cardiovascular Parameters Estimation for Fluid-Structure Simulations Using Gappy Proper Orthogonal Decomposition.

Cardiovascular simulation Fluid structure interaction Parameter estimation Proper orthogonal decomposition Windkessel model

Journal

Annals of biomedical engineering
ISSN: 1573-9686
Titre abrégé: Ann Biomed Eng
Pays: United States
ID NLM: 0361512

Informations de publication

Date de publication:
05 Jul 2024
Historique:
received: 22 12 2023
accepted: 21 06 2024
medline: 6 7 2024
pubmed: 6 7 2024
entrez: 5 7 2024
Statut: aheadofprint

Résumé

As full-scale detailed hemodynamic simulations of the entire vasculature are not feasible, numerical analysis should be focused on specific regions of the cardiovascular system, which requires the identification of lumped parameters to represent the patient behavior outside the simulated computational domain. We present a novel technique for estimating cardiovascular model parameters using gappy Proper Orthogonal Decomposition (g-POD). A POD basis is constructed with FSI simulations for different values of the lumped model parameters, and a linear operator is applied to retain information that can be compared to the available patient measurements. Then, the POD coefficients of the reconstructed solution are computed either by projecting patient measurements or by solving a minimization problem with constraints. The POD reconstruction is then used to estimate the model parameters. In the first test case, the parameter values of a 3-element Windkessel model are approximated using artificial patient measurements, obtaining a relative error of less than 4.2%. In the second case, 4 sets of 3-element Windkessel are approximated in a patient's aorta geometry, resulting in an error of less than 8% for the flow and less than 5% for the pressure. The method shows accurate results even with noisy patient data. It automatically calculates the delay between measurements and simulations and has flexibility in the types of patient measurements that can handle (at specific points, spatial or time averaged). The method is easy to implement and can be used in simulations performed in general-purpose FSI software.

Identifiants

pubmed: 38969956
doi: 10.1007/s10439-024-03568-z
pii: 10.1007/s10439-024-03568-z
doi:

Types de publication

Journal Article

Langues

eng

Sous-ensembles de citation

IM

Informations de copyright

© 2024. The Author(s).

Références

Ritchie, H., and M. Roser. Causes of death. Our World in Data. 2018. https://ourworldindata.org/causes-of-death . February 13, 2022.
Pantos, I., and D. Katritsis. Fractional flow reserve derived from coronary imaging and computational fluid dynamics. Interventional Cardiology Review. 2014. https://doi.org/10.15420/icr.2014.9.3.145 .
doi: 10.15420/icr.2014.9.3.145 pubmed: 29588793 pmcid: 5808464
van Bakel, T. M. J., K. D. Lau, J. Hirsch-Romano, S. Trimarchi, A. L. Dorfman, and C. A. Figueroa. Patient-specific modeling of hemodynamics: supporting surgical planning in a Fontan circulation correction. Journal of Cardiovascular Translational Research. 2018. https://doi.org/10.1007/s12265-017-9781-x .
doi: 10.1007/s12265-017-9781-x pubmed: 29713934
Salleh, N. M., M. S. Zakaria, and M. J. Abd Latif. CFD simulation for reduction thrombosis in bileaflet mechanical heart valve using vortex generators. Journal of Engineering Science and Technology. 16(3):2736–2747, 2021.
Campo-Deaño, L., M. S. N. Oliveira, and F. T. Pinho. A review of computational hemodynamics in middle cerebral aneurysms and rheological models for blood flow. Applied Mechanics Reviews. 2015. https://doi.org/10.1115/1.4028946 .
doi: 10.1115/1.4028946
Hirschhorn, M., V. Tchantchaleishvili, R. Stevens, J. Rossano, and A. Throckmorton. Fluid–structure interaction modeling in cardiovascular medicine—a systematic review 2017–2019. Medical Engineering & Physics. 2020. https://doi.org/10.1016/j.medengphy.2020.01.008 .
doi: 10.1016/j.medengphy.2020.01.008
Kim, H. J., I. Vignon-Clementel, C. Figueroa, K. Jansen, and C. Taylor. Developing computational methods for three-dimensional finite element simulations of coronary blood flow. Finite Elements in Analysis and Design. 2010. https://doi.org/10.1016/j.finel.2010.01.007 .
doi: 10.1016/j.finel.2010.01.007
Sankaran, S., M. Esmaily Moghadam, A. M. Kahn, E. E. Tseng, J. M. Guccione, and A. L. Marsden. Patient-specific multiscale modeling of blood flow for coronary artery bypass graft surgery. Annals of Biomedical Engineering. 2012. https://doi.org/10.1007/s10439-012-0579-3 .
doi: 10.1007/s10439-012-0579-3 pubmed: 22539149 pmcid: 3570226
Pennati, G., C. Corsini, D. Cosentino, T.-Y. Hsia, V. S. Luisi, G. Dubini, and F. Migliavacca. Boundary conditions of patient-specific fluid dynamics modelling of cavopulmonary connections: possible adaptation of pulmonary resistances results in a critical issue for a virtual surgical planning. Interface Focus. 2011. https://doi.org/10.1098/rsfs.2010.0021 .
doi: 10.1098/rsfs.2010.0021 pubmed: 22670204 pmcid: 3262449
Duprez, D. A., D. R. Jacobs Jr., P. L. Lutsey, D. Herrington, D. Prime, P. Ouyang, R. G. Barr, and D. A. Bluemke. Race/ethnic and sex differences in large and small artery elasticity–results of the multi-ethnic study of atherosclerosis (MESA). Ethnicity & Disease. 19:243–250, 2009.
Bia, D., Cymberknop, L., Zócalo, Y., Farro, I., Torrado, J., Farro, F., Pessana, F., and Armentano, R. L. Age-related changes in reservoir and excess components of central aortic pressure in asymptomatic adults. In: 2011 annual international conference of the IEEE engineering in medicine and biology society, 2011, pp. 6454–6457.
McVeigh, G. E., C. W. Bratteli, D. J. Morgan, C. M. Alinder, S. P. Glasser, S. M. Finkelstein, and J. N. Cohn. Age-related abnormalities in arterial compliance identified by pressure pulse contour analysis. Hypertension. 1999. https://doi.org/10.1161/01.HYP.33.6.1392 .
doi: 10.1161/01.HYP.33.6.1392 pubmed: 10373222
Spilker, R. L., and C. A. Taylor. Tuning multidomain hemodynamic simulations to match physiological measurements. Annals of Biomedical Engieering. 2010. https://doi.org/10.1007/s10439-010-0011-9 .
doi: 10.1007/s10439-010-0011-9
Itu, L., P. Sharma, T. Passerini, A. Kamen, and C. Suciu. A parameter estimation framework for patient-specific assessment of aortic coarctation. In: Patient-specific hemodynamic computations: application to personalized diagnosis of cardiovascular pathologies, edited by L. M. Itu, P. Sharma, and C. Suciu. Cham: Springer International Publishing, 2017, pp. 89–109.
doi: 10.1007/978-3-319-56853-9_4
Pant, S., B. Fabrèges, J.-F. Gerbeau, and I. E. Vignon-Clementel. A methodological paradigm for patient-specific multi-scale CFD simulations: from clinical measurements to parameter estimates for individual analysis. International Journal for Numerical Methods in Biomedical Engineering. 2014. https://doi.org/10.1002/cnm.2692 .
doi: 10.1002/cnm.2692 pubmed: 25345820
Jonášová, A., and J. Vimmr. Noninvasive assessment of carotid artery stenoses by the principle of multiscale modelling of non-Newtonian blood flow in patient-specific models. Applied Mathematics and Computation. 2018. https://doi.org/10.1016/j.amc.2017.07.032 .
doi: 10.1016/j.amc.2017.07.032
Lombardi, D. Inverse problems in 1D hemodynamics on systemic networks: a sequential approach. International Journal for Numerical Methods in Biomedical Engineering. 2014. https://doi.org/10.1002/cnm.2596 .
doi: 10.1002/cnm.2596 pubmed: 24039152
Caiazzo, A., F. Caforio, G. Montecinos, L. O. Muller, P. J. Blanco, and E. F. Toro. Assessment of reduced-order unscented Kalman filter for parameter identification in 1-dimensional blood flow models using experimental data. International Journal for Numerical Methods in Biomedical Engineering. 2017. https://doi.org/10.1002/cnm.2843 .
doi: 10.1002/cnm.2843 pubmed: 28744968
Muller, L. O., A. Caiazzo, and P. J. Blanco. Reduced-order unscented kalman filter with observations in the frequency domain: application to computational hemodynamics. IEEE Transactions on Biomedical Engineering. 2019. https://doi.org/10.1109/TBME.2018.2872323 .
doi: 10.1109/TBME.2018.2872323 pubmed: 31150329
Xiao, N., J. Alastruey, and C. Alberto Figureroa. A systematic comparison between 1-D and 3-D hemodynamics in compliant arterial models. International Journal for Numerical Methods in Biomedical Engineering. 2014. https://doi.org/10.1002/cnm.2598 .
doi: 10.1002/cnm.2598 pubmed: 24115509
Arthurs, C. J., N. Xiao, P. Moireau, T. Schaeffter, and C. A. Figueroa. A flexible framework for sequential estimation of model parameters in computational hemodynamics. Advanced Modeling and Simulation in Engineering Sciences. 2020. https://doi.org/10.1186/s40323-020-00186-x .
doi: 10.1186/s40323-020-00186-x pubmed: 33282681 pmcid: 7717067
Bertoglio, C., P. Moireau, and J.-F. Gerbeau. Sequential parameter estimation for fluid-structure problems: application to hemodynamics. International Journal for Numerical Methods in Biomedical Engineering. 2012. https://doi.org/10.1002/cnm.1476 .
doi: 10.1002/cnm.1476 pubmed: 25365657
Alimohammadi, M., O. Agu, S. Balabani, and V. Díaz-Zuccarini. Development of a patient-specific simulation tool to analyse aortic dissections: assessment of mixed patient-specific flow and pressure boundary conditions. Medical Engineering & Physics. 2014. https://doi.org/10.1016/j.medengphy.2013.11.003 .
doi: 10.1016/j.medengphy.2013.11.003
Nolte, D., and C. Bertoglio. Inverse problems in blood flow modeling: a review. International Journal for Numerical Methods in Biomedical Engineering. 2022. https://doi.org/10.1002/cnm.3613 .
doi: 10.1002/cnm.3613 pubmed: 35526113 pmcid: 9541505
Figueroa, C.A., T. Mansi, P. Sharma, and N. Wilson. 2nd CFD challenge predicting patient-specific hemodynamics at rest and stress through an aortic Coarctation 2013. 2013.
Kim, H. J., I. E. Vignon-Clementel, C. A. Figueroa, J. F. LaDisa, K. E. Jansen, J. A. Feinstein, and C. A. Taylor. On coupling a lumped parameter heart model and a three-dimensional finite element aorta model. Annals of Biomedical Engineering. 2009. https://doi.org/10.1007/s10439-009-9760-8 .
doi: 10.1007/s10439-009-9760-8 pubmed: 20012558 pmcid: 2855966
Santarpia, G., G. Scognamiglio, G. Di Salvo, M. D’Alto, B. Sarubbi, E. Romeo, C. Indolfi, M. Cotrufo, and R. Calabrò. Aortic and left ventricular remodeling in patients with bicuspid aortic valve without significant valvular dysfunction: a prospective study. International Journal of Cardiology. 2012. https://doi.org/10.1016/j.ijcard.2011.01.046 .
doi: 10.1016/j.ijcard.2011.01.046 pubmed: 21315467
Vlachopoulos, C., M. O’Rourke, and W. W. Nichols. McDonald’s blood flow in arteries, theoretical, experimental and clinical principles, 6th ed. CRC Press, 2011.
doi: 10.1201/b13568
Xiao, N. Simulation of 3-D blood flow in the full systemic arterial tree and computational frameworks for efficient parameter estimation. Stanford: Stanford University, 2013.
Everson, R., and L. Sirovich. Karhunen-Loève procedure for gappy data. JOSA A. 1995. https://doi.org/10.1364/JOSAA.12.001657 .
doi: 10.1364/JOSAA.12.001657
Bui-Thanh, T., M. Damodaran, and K. Willcox. Aerodynamic data reconstruction and inverse design using proper orthogonal decomposition. AIAA Journal. 2004. https://doi.org/10.2514/1.2159 .
doi: 10.2514/1.2159
Wang, M., D. Dutta, K. Kim, and J. C. Brigham. A computationally efficient approach for inverse material characterization combining Gappy POD with direct inversion. Computer Methods in Applied Mechanics and Engineering. 286:373–393, 2015.
doi: 10.1016/j.cma.2015.01.001
Luo, J., Y. Zhu, X. Tang, and F. Liu. Flow reconstructions and aerodynamic shape optimization of turbomachinery blades by POD-based hybrid models. Science China Technological Sciences. 60:1658–1673, 2017.
doi: 10.1007/s11431-016-9093-y
Tong, Z., and Y. Li. Real-time reconstruction of contaminant dispersion from sparse sensor observations with gappy POD method. Energies. 13:1956, 2020.
doi: 10.3390/en13081956
Yakhot, A., T. Anor, and G. E. Karniadakis. A reconstruction method for gappy and noisy arterial flow data. IEEE Transactions on Medical imaging. 26:1681–1697, 2007.
doi: 10.1109/TMI.2007.901991 pubmed: 18092738
Virtanen, P., R. Gommers, T. E. Oliphant, et al. SciPy 1.0: fundamental algorithms for scientific computing in python. Nature Methods. 2020. https://doi.org/10.1038/s41592-019-0686-2 .
doi: 10.1038/s41592-019-0686-2 pubmed: 32094914 pmcid: 7056641
Willcox, K. Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition. Computers & Fluids. 2006. https://doi.org/10.1016/j.compfluid.2004.11.006 .
doi: 10.1016/j.compfluid.2004.11.006
Astrid, P. Reduction of process simulation models: a proper orthogonal decomposition approach. Eindhoven: Technische Universiteit Eindhoven, 2004.
Baumgartner H, De Backer J, Babu-Narayan SV, et al. 2020 ESC guidelines for the management of adult congenital heart disease: The Task Force for the management of adult congenital heart disease of the European Society of Cardiology (ESC). Endorsed by: Association for European Paediatric and Congenital Cardiology (AEPC), International Society for Adult Congenital Heart Disease (ISACHD). European Heart Journal. 2021. https://doi.org/10.1093/eurheartj/ehaa554 .

Auteurs

J Deus (J)

Departamento de Ingeniería Mecánica, Máquinas y Motores Térmicos y Fluidos, Universidade de Vigo, Campus Marcosende, 36310, Vigo, Spain.

E Martin (E)

Departamento de Ingeniería Mecánica, Máquinas y Motores Térmicos y Fluidos, Universidade de Vigo, Campus Marcosende, 36310, Vigo, Spain. emortega@uvigo.es.
Instituto de Física y Ciencias Aeroespaciales (IFCAE), Universidade de Vigo, Campus de As Lagoas, 32004, Ourense, Spain. emortega@uvigo.es.

Classifications MeSH