- Open Access
- Access by Xinjiang University
Lagrangian analysis of turbulent blood flow in the human left heart
Phys. Rev. Fluids 11, 064604 – Published 4 June, 2026
DOI: https://doi.org/10.1103/d56r-y1lm
Abstract
We present a Lagrangian analysis of turbulent blood flow in the human left heart using high-fidelity simulations based on a patient-specific anatomical model. Leveraging a fully coupled fluid-structure-electrophysiology interaction framework, we track the motion of Lagrangian (passive) tracers to investigate the multiscale statistical properties of velocity fluctuations over more than 4 orders of magnitude. Our analysis reveals strong Lagrangian intermittency throughout the left heart, reflecting the complex and unsteady nature of cardiovascular flow. The present work underscores the sensitivity of Lagrangian statistics to physiological parameters and highlights their potential for improving the understanding of pathological flow conditions in cardiovascular systems. Such Lagrangian tool provides a statistical foundation for modeling shear-induced damage in red blood cells (hemolysis), with implications for the evaluation of prosthetic valves and blood-contacting medical devices.
Physics Subject Headings (PhySH)
Article Text
References (50)
- R. Verzicco, Electro-fluid-mechanics of the heart, J. Fluid Mech. 941, P1 (2022).
- A. Santiago, J. Aguado-Sierra, M. Zavala-Aké, R. Doste-Beltran, S. Gómez, R. Arís, J. C. Cajas, E. Casoni, and M. Vázquez, Fully coupled fluid-electro-mechanical model of the human heart for supercomputers, Int. J. Numer. Methods Biomed. Eng. 34, e3140 (2018).
- M. Bucelli, A. Zingaro, P. C. Africa, I. Fumagalli, L. Dede', and A. Quarteroni, A mathematical model that integrates cardiac electrophysiology, mechanics, and fluid dynamics: Application to the human left heart, Int. J. Numer. Methods Biomed. Eng. 39, e3678 (2023).
- M. Davey, C. Puelz, S. Rossi, M. A. Smith, D. R. Wells, G. M. Sturgeon, W. P. Segars, J. P. Vavalle, C. S. Peskin, and B. E. Griffith, Simulating cardiac fluid dynamics in the human heart, PNAS nexus 3, pgae392 (2024).
- K. Cheng, S. Akhtar, K. Y. Lee, S. W. Lee, and S.-W. Lee, Characteristics of transition to turbulence in a healthy thoracic aorta using large eddy simulation, Sci. Rep. 15, 3236 (2025).
- J. Lantz, R. Gårdhagen, and M. Karlsson, Quantifying turbulent wall shear stress in a subject specific human aorta using large eddy simulation, Med. Eng. Phys. 34, 1139 (2012).
- C. Chnafa, S. Mendez, and F. Nicoud, Image-based large-eddy simulation in a realistic left heart, Comput. Fluids 94, 173 (2014).
- C. Chnafa, S. Mendez, and F. Nicoud, Image-based simulations show important flow fluctuations in a normal left ventricle: What could be the implications? Ann. Biomed. Eng. 44, 3346 (2016).
- L. Bennati, V. Giambruno, F. Renzi, V. D. Nicola, C. Maffeis, G. Puppini, G. B. Luciani, and C. Vergara, Turbulent blood dynamics in the left heart in the presence of mitral regurgitation: A computational study based on multi-series cine-MRI, Biomech. Model. Mechanobiol. 22, 1829 (2023).
- A. Nitti, G. D. Cillis, and M. D. Tullio, Numerical investigation of turbulent features past different mechanical aortic valves, J. Fluid Mech. 940, A43 (2022).
- F. Toschi and E. Bodenschatz, Lagrangian properties of particles in turbulence, Annu. Rev. Fluid Mech. 41, 375 (2009).
- L. Biferale, E. Bodenschatz, M. Cencini, A. S. Lanotte, N. T. Ouellette, F. Toschi, and H. Xu, Lagrangian structure functions in turbulence: A quantitative comparison between experiment and direct numerical simulation, Phys. Fluids 20, 065103 (2008).
- R. Benzi and F. Toschi, Lectures on turbulence, Phys. Rep. 1021, 1 (2023).
- L. Bentkamp, C. C. Lalescu, and M. Wilczek, Persistent accelerations disentangle Lagrangian turbulence, Nat. Commun. 10, 3550 (2019).
- D. Arora, M. Behr, and M. Pasquali, A tensor-based measure for estimating blood damage, Artificial Organs 28, 1002 (2004).
- M. A. Scarpolini, G. Vagnoli, F. Guglietta, R. Verzicco, and F. Viola, Hemodynamic effects of intra- and supra-deployment locations for a bioprosthetic aortic valve, Phys. Rev. Fluids 10, 090501 (2025).
- F. Guglietta, M. Behr, L. Biferale, G. Falcucci, and M. Sbragaglia, On the effects of membrane viscosity on transient red blood cell dynamics, Soft Matter 16, 6191 (2020).
- F. Guglietta, M. Behr, G. Falcucci, and M. Sbragaglia, Loading and relaxation dynamics of a red blood cell, Soft Matter 17, 5978 (2021).
- F. Guglietta, M. Behr, L. Biferale, G. Falcucci, and M. Sbragaglia, Lattice Boltzmann simulations on the tumbling to tank-treading transition: Effects of membrane viscosity, Philos. Trans. R. Soc. A 379, 20200395 (2021).
- D. Taglienti, F. Guglietta, and M. Sbragaglia, Droplet dynamics in homogeneous isotropic turbulence with the immersed boundary–lattice Boltzmann method, Phys. Rev. E 110, 015302 (2024).
- L. Biferale, C. Meneveau, and R. Verzicco, Deformation statistics of sub-Kolmogorov-scale ellipsoidal neutrally buoyant drops in isotropic turbulence, J. Fluid Mech. 754, 184 (2014).
- F. Viola, G. D. Corso, R. D. Paulis, and R. Verzicco, GPU accelerated digital twins of the human heart open new routes for cardiovascular research, Sci. Rep. 13, 8230 (2023).
- M. M. S. Reza and A. Arzani, A critical comparison of different residence time measures in aneurysms, J. Biomech. 88, 122 (2019).
- Y. Li, Y. Xi, H. Wang, A. Sun, X. Deng, Z. Chen, and Y. Fan, A new way to evaluate thrombotic risk in failure heart and ventricular assist devices, Med. Nov. Technol. Devices 16, 100135 (2022).
- F. Viola, V. Meschini, and R. Verzicco, An FSEI approach for the assessment of stenotic aortic valve effects on the left heart hemodynamics, Comput. Fluids 265, 106017 (2023).
- F. Viola, V. Spandan, V. Meschini, J. Romero, M. Fatica, M. D. de Tullio, and R. Verzicco, FSEI-GPU: GPU accelerated simulations of the fluid–structure–electrophysiology interaction in the left heart, Comput. Phys. Commun. 273, 108248 (2022).
- Helmut Baumgartner (chair), J. Hung, J. Bermejo, J. B. Chambers, T. Edvardsen, S. Goldstein, P. Lancellotti, M. LeFevre, F. Miller, Jr., C. M. Otto, et al., Recommendations on the echocardiographic assessment of aortic valve stenosis: A focused update from the European Association of Cardiovascular Imaging and the American Society of Echocardiography, Eur. Heart J. Cardiovasc. Imaging 18, 254 (2017).
- A. Fedorov, R. Beichel, J. Kalpathy-Cramer, J. Finet, J.-C. Fillion-Robin, S. Pujol, C. Bauer, D. Jennings, F. Fennessy, M. Sonka, et al., 3D Slicer as an image computing platform for the Quantitative Imaging Network, Magn. Reson. Imaging 30, 1323 (2012).
- V. Meschini, F. Viola, and R. Verzicco, Modeling mitral valve stenosis: A parametric study on the stenosis severity level, J. Biomech. 84, 218 (2019).
- F. Viola, V. Meschini, and R. Verzicco, Fluid–structure-electrophysiology interaction (FSEI) in the left-heart: A multi-way coupled computational model, Eur. J. Mech. B Fluids 79, 212 (2020).
- M. A. Scarpolini, G. Piumini, E. Gasparotti, E. Maffei, F. Cademartiri, S. Celi, and F. Viola, Guiding patient-specific cardiac simulations through data-assimilation of soft tissue kinematics from dynamic CT scan, Comput. Biol. Med. 189, 109876 (2025).
- M. D. de Tullio and G. Pascazio, A moving-least-squares immersed boundary method for simulating the fluid–structure interaction of elastic bodies with arbitrary thickness, J. Comput. Phys. 325, 201 (2016).
- P. Stradins, R. Lacis, I. Ozolanta, B. Purina, V. Ose, L. Feldmane, and V. Kasyanov, Comparison of biomechanical and structural properties between human aortic and pulmonary valve, Eur. J. Cardiothorac. Surg. 26, 634 (2004).
- A. Caballero, F. Sulejmani, C. Martin, T. Pham, and W. Sun, Evaluation of transcatheter heart valve biomaterials: Biomechanical characterization of bovine and porcine pericardium, J. Mech. Behav. Biomed. Mater. 75, 486 (2017).
- J.-P. Jehl, P. Dan, A. Voignier, N. Tran, T. Bastogne, P. Maureira, and F. Cleymand, Transverse isotropic modelling of left-ventricle passive filling: Mechanical characterization for epicardial biomaterial manufacturing, J. Mech. Behav. Biomed. Mater. 119, 104492 (2021).
- P. Moireau, D. Chapelle, and P. Le Tallec, Filtering for distributed mechanical systems using position measurements: Perspectives in medical imaging, Inverse Probl. 25, 035010 (2009).
- M. Nakamura, S. Bessho, and S. Wada, Analysis of red blood cell deformation under fast shear flow for better estimation of hemolysis, Int. J. Numer. Methods Biomed. Eng. 30, 42 (2014).
- D. A. Fedosov, B. Caswell, and G. E. Karniadakis, Systematic coarse-graining of spectrin-level red blood cell models, Comput. Methods Appl. Mech. Eng. 199, 1937 (2010).
- M. Chen and F. J. Boyle, Investigation of membrane mechanics using spring networks: Application to red-blood-cell modelling, Mater. Sci. Eng. C 43, 506 (2014).
- P. E. Hammer, M. S. Sacks, P. J. Del Nido, and R. D. Howe, Mass-spring model for simulation of heart valve tissue mechanical behavior, Ann. Biomed. Eng. 39, 1668 (2011).
- S. Kumar, M. J. McHenry, J.-H. Seo, and R. Mittal, Mechanical intelligence in propulsion via flexible caudal fins, Bioinspir. Biomim. 21, 016027 (2026).
- S. Kumar, J.-H. Seo, and R. Mittal, Computational modelling and analysis of the coupled aero-structural dynamics in bat-inspired wings, J. Fluid Mech. 1010, A53 (2025).
- J. Sundnes, G. T. Lines, X. Cai, B. F. Nielsen, K.-A. Mardal, and A. Tveito, Computing the Electrical Activity in the Heart (Springer Science and Business Media, Berlin, Heidelberg, 2007), Vol. 1.
- C. S. Peskin, The immersed boundary method, Acta Numer. 11, 479 (2002).
- R. Benzi, S. Ciliberto, R. Tripiccione, C. Baudet, F. Massaioli, and S. Succi, Extended self-similarity in turbulent flows, Phys. Rev. E 48, R29 (1993).
- N. Westerhof, J.-W. Lankhaar, and B. E. Westerhof, The arterial Windkessel, Med. Biol. Eng. Comput. 47, 131 (2009).
- A. La Porta, G. A. Voth, A. M. Crawford, J. Alexander, and E. Bodenschatz, Fluid particle accelerations in fully developed turbulence, Nature (London) 409, 1017 (2001).
- V. Meschini, F. Viola, and R. Verzicco, Heart rate effects on the ventricular hemodynamics and mitral valve kinematics, Comput. Fluids 197, 104359 (2020).
- C. C. Smid, G. A. Pappas, N. Cesarovic, V. Falk, and P. Ermanni, Novel heart valve leaflet designs with stiff polymeric materials and biomimetic kinematics, Bio-des. Manuf. 7, 1018 (2024).
- B. E. Griffith, Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions, Int. J. Numer. Methods Biomed. Eng. 28, 317 (2012).