Javascript is required
1.
Migliavacca, F., Pennati, G., Dubini, G., Fumero, R., Pietrabissa, R., Urcelay, G., Bove,E. L., Hsia, T-Y. & de Leval, M.R., Modeling of the Norwood circulation: effects of shunt size, vascular resistances, and heart rate. American Journal of Physiology - Heart and Circulatory Physiology, 280(5), pp. H2076–H2086, 2001.
2.
Migliavacca, F., Balossino, R., Pennati, G., Dubini, G., Hsia, T-Y., de Leval, M.R. & Bove, E.L., Multiscale modelling in biofluidynamics: application to reconstructive paediatric cardiac surgery. Journal of Biomechanics, 39(6), pp. 1010–1020, 2006. [Crossref]
3.
DeCampli, W.M., Argueta-Morales, I.R., Divo, E. & Kassab, A.J., Computational fluid dynamics in congenital heart disease. Cardiology in the Young, 22(06), pp. 800–808, 2012. [Crossref]
4.
Hsia, T-Y., Cosentino, D., Corsini, C., Pennati, G., Dubini, G., Migliavacca, F. & Mod-eling of Congenital Hearts Alliance (MOCHA) Investigators. Use of mathematical modeling to compare and predict hemodynamic effects between hybrid and surgical Norwood palliations for hypoplastic left heart syndrome. Circulation, 124(11 Suppl), pp. S204–S210, 2011. [Crossref]
5.
Ceballos, A., A Coupled CFD-Lumped Parameter Model of the Human Circulation: Elucidating the Hemodynamics of the Hybrid Norwood Palliative Treatment and Effects of the Reverse Blalock-Taussic Shunt Placement and Diameter. UCF, Orlando, Florida, 2015.
6.
Ceballos, A., Argueta-Morales, I.R., Divo, E., Osorio, R., Caldarone, C.A., Kassab, A.J. & DeCampli, W.M., Computational analysis of hybrid norwood circulation with dis-tal aortic arch obstruction and reverse Blalock-Taussig Shunt. The Annals of Thoracic Surgery, 94(5), pp. 1540–1550, 2012. [Crossref]
7.
Prather, R., A Multi-Scale CFD Analysis of Patient-Specific Geometries to Tailor LVAD Cannula Implantation Under Pulsatile Flow Conditions: an investigation aimed at reducing stroke incidence in LVADs. University of Central Florida, Orlando, 2015.
8.
Prather, R.O., Kassab, A., Ni, M.W., Divo, E., Argueta, I.R. & DeCampli, W.M., Multi-scale pulsatile CFD modeling of thrombus transport in a patient-specific LVAD implantation. International Journal of Numerical Methods for Heat & Fluid Flow, 27(5), pp. 1022–1039, 2017. [Crossref]
9.
Quarteroni, A., Ragni, S. & Veneziani, A., Coupling between lumped and distrib-uted models for blood flow problems. Computing and Visualization in Science, 4(2), pp. 111–124, 2001. [Crossref]
10.
Pepper, D.W., Kassab, A. & Divo, E., An Introduction to Finite Element, Boundary Element, and Meshless Methods with Applications to Heat Transfer and Fluid Flow, ASME Press, New York, 2014.
11.
Divo, E. & Kassab, A.J., Localized meshless modeling of natural-convective viscous flows. Numerical Heat Transfer, Part B: Fundamentals, 53(6), pp. 487–509, 2008. [Crossref]
12.
Divo, E. & Kassab, A.J., An efficient localized radial basis function meshless method for fluid flow and conjugate heat transfer. Journal of Heat Transfer, 129(2), pp. 124–136, 2006. [Crossref]
13.
Wrobel, L.C. & Brebbia, C.A., The dual reciprocity boundary element formulation for nonlinear diffusion problems. Computer Methods in Applied Mechanics and Engineer-ing, 65(2), pp. 147–164, 1987. [Crossref]
14.
Divo, E. & Kassab, A.J., Transient non-linear heat conduction solution by a dual rec-iprocity boundary element method with an effective posteriori error estimator. Heat Transfer, 1, pp. 77–86, 2004.https://doi.org/IMECE2004-59262
15.
Bueno, L.A., Divo, E.A. & Kassab, A.J., A coupled localized Rbf Meshless/DRBEM formulation for accurate modeling of incompressible fluid flows. International Journal of Computational Methods and Experimental Measurements, 5(3), pp. 359–368, 2017. [Crossref]
16.
Kind, T., Faes, T.J.C., Lankhaar, J.W., Vonk-Noordegraaf, A. & Verhaegen, M., Estima-tion of three- and four-element windkessel parameters using subspace model identifica-tion. IEEE Transactions on Biomedical Engineering, 57(7), pp. 1531–1538, 2010. [Crossref]
17.
Kokalari, I., Karaja, T. & Guerrisi, M., Review on lumped parameter method for model-ing the blood flow in systemic arteries. Journal of Biomedical Science and Engineering, 06(01), pp. 92–99, 2013. [Crossref]
18.
Faragallah, G., Wang, Y., Divo, E. & Simaan, M., A new control system for left ventric-ular assist devices based on patient-specific physiological demand. Inverse Problems in Science and Engineering, 20(5), pp. 721–734, 2012. [Crossref]
19.
Formaggia, L. & Veneziani, A., Reduced and multiscale models for the human cardio-vascular system. Lecture Notes VKI Lecture Series, 7, 2003.
20.
Creigen, V., Ferracina, L., Hlod, A., van Mourik, S., Sjauw, K., Rottschäfer, V., Vellekoop, M. & Zegeling, P., Modeling a heart pump. European Study Group Mathematics with Industry, Utrecht, p. 7, 2007.
21.
Simaan, M.A., Ferreira, A., Chen, S., Antaki, J.F. & Galati, D.G., A dynamical state space representation and performance analysis of a feedback-controlled rotary left ventricular assist device. IEEE Transactions on Control Systems Technology, 17(1), pp. 15–28, 2009. [Crossref]
22.
Yu, Y-C., Boston, J.R., Simaan, M.A. & Antaki, J.F., Minimally invasive estimation of systemic vascular parameters. Annals of Biomedical Engineering, 29(7), pp. 595–606, 2001. [Crossref]
23.
Yu, Y-C., Boston, J.R., Simaan, M.A. & Antaki, J.F., Estimation of systemic vascular bed parameters for artificial heart control. IEEE Transactions on Automatic Control, 43(6), pp. 765–778, 1998. [Crossref]
Search

Acadlore takes over the publication of IJCMEM from 2025 Vol. 13, No. 3. The preceding volumes were published under a CC BY 4.0 license by the previous owner, and displayed here as agreed between Acadlore and the previous owner. ✯ : This issue/volume is not published by Acadlore.

Open Access
Research article

Multi-Scale Cardiovascular Flow Analysis by an Integrated Meshless-Lumped Parameter Model

leonardo a. bueno1,
eduardo a. divo1,
alain j. kassab2
1
Department of Mechanical Engineering, Embry-Riddle Aeronautical University, Daytona Beach, FL, United States
2
Department of Mechanical and Aerospace Engineering University of Central Florida, Orlando, FL, United States
International Journal of Computational Methods and Experimental Measurements
|
Volume 6, Issue 6, 2018
|
Pages 1138-1148
Received: N/A,
Revised: N/A,
Accepted: N/A,
Available online: N/A
View Full Article|Download PDF

Abstract:

A computational tool that integrates a Radial basis function (RBF)-based Meshless solver with a Lumped Parameter model (LPM) is developed to analyze the multi-scale and multi-physics interaction between the cardiovascular flow hemodynamics, the cardiac function, and the peripheral circulation. The Meshless solver is based on localized RBF collocations at scattered data points which allows for automation of the model generation via CAD integration. The time-accurate incompressible flow hemodynamics are addressed via a pressure-velocity correction scheme where the ensuing Poisson equations are accurately and efficiently solved at each time step by a Dual-Reciprocity Boundary Element method (DRBEM) formulation that takes advantage of the integrated surface discretization and automated point distribution used for the Meshless collocation. The local hemodynamics are integrated with the peripheral circulation via compartments that account for branch viscous resistance (R), flow inertia (L), and vessel compliance (C), namely RLC electric circuit analogies. The cardiac function is modeled via time-varying capacitors simulating the ventricles and constant capacitors simulating the atria, connected by diodes and resistors simulating the atrioventricular and ventricular-arterial valves. This multi-scale integration in an in-house developed computational tool opens the possibility for model automation of patient-specific anatomies from medical imaging, elastodynamics analysis of vessel wall deformation for fluid-structure interaction, automated model refinement, and inverse analysis for parameter estimation.

Keywords: Lumped-parameter model, Multi-scale CFD, Meshless methods, DRBEM
References
1.
Migliavacca, F., Pennati, G., Dubini, G., Fumero, R., Pietrabissa, R., Urcelay, G., Bove,E. L., Hsia, T-Y. & de Leval, M.R., Modeling of the Norwood circulation: effects of shunt size, vascular resistances, and heart rate. American Journal of Physiology - Heart and Circulatory Physiology, 280(5), pp. H2076–H2086, 2001.
2.
Migliavacca, F., Balossino, R., Pennati, G., Dubini, G., Hsia, T-Y., de Leval, M.R. & Bove, E.L., Multiscale modelling in biofluidynamics: application to reconstructive paediatric cardiac surgery. Journal of Biomechanics, 39(6), pp. 1010–1020, 2006. [Crossref]
3.
DeCampli, W.M., Argueta-Morales, I.R., Divo, E. & Kassab, A.J., Computational fluid dynamics in congenital heart disease. Cardiology in the Young, 22(06), pp. 800–808, 2012. [Crossref]
4.
Hsia, T-Y., Cosentino, D., Corsini, C., Pennati, G., Dubini, G., Migliavacca, F. & Mod-eling of Congenital Hearts Alliance (MOCHA) Investigators. Use of mathematical modeling to compare and predict hemodynamic effects between hybrid and surgical Norwood palliations for hypoplastic left heart syndrome. Circulation, 124(11 Suppl), pp. S204–S210, 2011. [Crossref]
5.
Ceballos, A., A Coupled CFD-Lumped Parameter Model of the Human Circulation: Elucidating the Hemodynamics of the Hybrid Norwood Palliative Treatment and Effects of the Reverse Blalock-Taussic Shunt Placement and Diameter. UCF, Orlando, Florida, 2015.
6.
Ceballos, A., Argueta-Morales, I.R., Divo, E., Osorio, R., Caldarone, C.A., Kassab, A.J. & DeCampli, W.M., Computational analysis of hybrid norwood circulation with dis-tal aortic arch obstruction and reverse Blalock-Taussig Shunt. The Annals of Thoracic Surgery, 94(5), pp. 1540–1550, 2012. [Crossref]
7.
Prather, R., A Multi-Scale CFD Analysis of Patient-Specific Geometries to Tailor LVAD Cannula Implantation Under Pulsatile Flow Conditions: an investigation aimed at reducing stroke incidence in LVADs. University of Central Florida, Orlando, 2015.
8.
Prather, R.O., Kassab, A., Ni, M.W., Divo, E., Argueta, I.R. & DeCampli, W.M., Multi-scale pulsatile CFD modeling of thrombus transport in a patient-specific LVAD implantation. International Journal of Numerical Methods for Heat & Fluid Flow, 27(5), pp. 1022–1039, 2017. [Crossref]
9.
Quarteroni, A., Ragni, S. & Veneziani, A., Coupling between lumped and distrib-uted models for blood flow problems. Computing and Visualization in Science, 4(2), pp. 111–124, 2001. [Crossref]
10.
Pepper, D.W., Kassab, A. & Divo, E., An Introduction to Finite Element, Boundary Element, and Meshless Methods with Applications to Heat Transfer and Fluid Flow, ASME Press, New York, 2014.
11.
Divo, E. & Kassab, A.J., Localized meshless modeling of natural-convective viscous flows. Numerical Heat Transfer, Part B: Fundamentals, 53(6), pp. 487–509, 2008. [Crossref]
12.
Divo, E. & Kassab, A.J., An efficient localized radial basis function meshless method for fluid flow and conjugate heat transfer. Journal of Heat Transfer, 129(2), pp. 124–136, 2006. [Crossref]
13.
Wrobel, L.C. & Brebbia, C.A., The dual reciprocity boundary element formulation for nonlinear diffusion problems. Computer Methods in Applied Mechanics and Engineer-ing, 65(2), pp. 147–164, 1987. [Crossref]
14.
Divo, E. & Kassab, A.J., Transient non-linear heat conduction solution by a dual rec-iprocity boundary element method with an effective posteriori error estimator. Heat Transfer, 1, pp. 77–86, 2004.https://doi.org/IMECE2004-59262
15.
Bueno, L.A., Divo, E.A. & Kassab, A.J., A coupled localized Rbf Meshless/DRBEM formulation for accurate modeling of incompressible fluid flows. International Journal of Computational Methods and Experimental Measurements, 5(3), pp. 359–368, 2017. [Crossref]
16.
Kind, T., Faes, T.J.C., Lankhaar, J.W., Vonk-Noordegraaf, A. & Verhaegen, M., Estima-tion of three- and four-element windkessel parameters using subspace model identifica-tion. IEEE Transactions on Biomedical Engineering, 57(7), pp. 1531–1538, 2010. [Crossref]
17.
Kokalari, I., Karaja, T. & Guerrisi, M., Review on lumped parameter method for model-ing the blood flow in systemic arteries. Journal of Biomedical Science and Engineering, 06(01), pp. 92–99, 2013. [Crossref]
18.
Faragallah, G., Wang, Y., Divo, E. & Simaan, M., A new control system for left ventric-ular assist devices based on patient-specific physiological demand. Inverse Problems in Science and Engineering, 20(5), pp. 721–734, 2012. [Crossref]
19.
Formaggia, L. & Veneziani, A., Reduced and multiscale models for the human cardio-vascular system. Lecture Notes VKI Lecture Series, 7, 2003.
20.
Creigen, V., Ferracina, L., Hlod, A., van Mourik, S., Sjauw, K., Rottschäfer, V., Vellekoop, M. & Zegeling, P., Modeling a heart pump. European Study Group Mathematics with Industry, Utrecht, p. 7, 2007.
21.
Simaan, M.A., Ferreira, A., Chen, S., Antaki, J.F. & Galati, D.G., A dynamical state space representation and performance analysis of a feedback-controlled rotary left ventricular assist device. IEEE Transactions on Control Systems Technology, 17(1), pp. 15–28, 2009. [Crossref]
22.
Yu, Y-C., Boston, J.R., Simaan, M.A. & Antaki, J.F., Minimally invasive estimation of systemic vascular parameters. Annals of Biomedical Engineering, 29(7), pp. 595–606, 2001. [Crossref]
23.
Yu, Y-C., Boston, J.R., Simaan, M.A. & Antaki, J.F., Estimation of systemic vascular bed parameters for artificial heart control. IEEE Transactions on Automatic Control, 43(6), pp. 765–778, 1998. [Crossref]
Cite this:
APA Style
IEEE Style
BibTex Style
MLA Style
Chicago Style
GB-T-7714-2015
Bueno, L. A., Divo, E. A., & Kassab, A. J. (2018). Multi-Scale Cardiovascular Flow Analysis by an Integrated Meshless-Lumped Parameter Model. Int. J. Comput. Methods Exp. Meas., 6(6), 1138-1148. https://doi.org/10.2495/CMEM-V6-N6-1138-1148
L. A. Bueno, E. A. Divo, and A. J. Kassab, "Multi-Scale Cardiovascular Flow Analysis by an Integrated Meshless-Lumped Parameter Model," Int. J. Comput. Methods Exp. Meas., vol. 6, no. 6, pp. 1138-1148, 2018. https://doi.org/10.2495/CMEM-V6-N6-1138-1148
@research-article{Bueno2018Multi-ScaleCF,
title={Multi-Scale Cardiovascular Flow Analysis by an Integrated Meshless-Lumped Parameter Model},
author={Leonardo A. Bueno and Eduardo A. Divo and Alain J. Kassab},
journal={International Journal of Computational Methods and Experimental Measurements},
year={2018},
page={1138-1148},
doi={https://doi.org/10.2495/CMEM-V6-N6-1138-1148}
}
Leonardo A. Bueno, et al. "Multi-Scale Cardiovascular Flow Analysis by an Integrated Meshless-Lumped Parameter Model." International Journal of Computational Methods and Experimental Measurements, v 6, pp 1138-1148. doi: https://doi.org/10.2495/CMEM-V6-N6-1138-1148
Leonardo A. Bueno, Eduardo A. Divo and Alain J. Kassab. "Multi-Scale Cardiovascular Flow Analysis by an Integrated Meshless-Lumped Parameter Model." International Journal of Computational Methods and Experimental Measurements, 6, (2018): 1138-1148. doi: https://doi.org/10.2495/CMEM-V6-N6-1138-1148
Bueno L. A.， Divo E. A.， Kassab A. J.. Multi-Scale Cardiovascular Flow Analysis by an Integrated Meshless-Lumped Parameter Model[J]. International Journal of Computational Methods and Experimental Measurements， 2018， 6(6)： 1138-1148. https://doi.org/10.2495/CMEM-V6-N6-1138-1148