Heart as an Inverted Octagonal Pyramid: Fluid Dynamics of Cardiac Ejection

Pradeep Kumar Radhakrishnan

doi:doi:10.11648/j.ijcts.20251103.11

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Heart as an Inverted Octagonal Pyramid: Fluid Dynamics of Cardiac Ejection

Pradeep Kumar Radhakrishnan^*

Published in International Journal of Cardiovascular and Thoracic Surgery (Volume 11, Issue 3)

Received: 24 April 2025 Accepted: 7 May 2025 Published: 25 June 2025

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Abstract

Accurate geometric modeling of the human heart is essential for understanding and simulating cardiac fluid dynamics. Traditional left ventricular (LV) models—typically ellipsoidal, cylindrical, or conical—are limited in their ability to represent the complex regional structure and dynamic flow conditions present in a functioning heart. This study proposes an advanced geometric abstraction: the inverted octagonal pyramid model of the LV. This configuration introduces eight triangular faces converging at the apex, with an anatomically inspired octagonal base representing the mitral valve annulus, offering superior segmentation, mesh compatibility, and regional mechanical analysis. Using unsteady Navier-Stokes equations under physiological boundary conditions, this model captures systolic ejection mechanics including jet formation, vortex dynamics, wall shear stress (WSS) distribution, and flow separation zones. Quantitative simulation results across three scenarios—healthy heart, aortic stenosis, and hypertrophic cardiomyopathy (HCM)—reveal that the pyramid model predicts a Reynolds number (Re) range of 1200–5100 and vortex entropy index (VEI) values up to 0.6, indicating transitional-to-turbulent flow in diseased states. WSS distribution, especially near polygonal junctions, highlights zones of potential endocardial stress and thrombotic risk that conventional models fail to capture. This geometry is not only computationally robust for fluid–structure interaction (FSI) modeling but also aligns with echocardiographic segmental views, enhancing clinical relevance. Applications include patient-specific valve and stent design, surgical planning, CRT lead placement, and AI-based cardiac flow diagnostics. By more faithfully reflecting the true structural and flow heterogeneity of the heart, the inverted octagonal pyramid model establishes a new standard for integrative, biomechanical cardiovascular simulations. It bridges clinical imaging, computational modeling, and physiological accuracy—advancing both diagnostic precision and therapeutic planning in contemporary cardiology.

Published in	International Journal of Cardiovascular and Thoracic Surgery (Volume 11, Issue 3)
DOI	10.11648/j.ijcts.20251103.11
Page(s)	23-30
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Cardiac Fluid Dynamics, Inverted Octagonal Pyramid, Left Ventricle Modeling, Wall Shear Stress, Vortex Formation, Computational Hemodynamics, Personalized Cardiology

References

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[2]	Treece, G. M. (2001). Volume measurement and surface visualization in sequential freehand 3D ultrasound. CiteseerX. https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=63cfbc342bd8584bacedc22eae05b33c1ce7a3df
[3]	Collia, D., Pedrizzetti, G., Sato, T., & Matsubara, D. (2023). Interplay between geometry, fluid dynamics, and structure in the ventricles of the human heart. Physical Review Applied, 19, 014006. https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.19.014006
[4]	McQueen, D. M., & Peskin, C. S. (2000). A three-dimensional computer model of the human heart for studying cardiac fluid dynamics. ACM SIGGRAPH Computer Graphics, 34(1), 56–60. https://dl.acm.org/doi/pdf/10.1145/563788.604453
[5]	Wang, X. (2020). Computer simulation of a nitric oxide-releasing catheter with a novel stable convection-diffusion equation solver and automatic quantification of lung ultrasound. University of Michigan. https://deepblue.lib.umich.edu/bitstream/handle/2027.42/163182/micw_1.pdf?sequence=1
[6]	Van Stralen, M., Leung, K. Y. E., Voormolen, M. M., & Bosch, J. G. (2009). Automated analysis of 3D echocardiography. PhD Thesis, Erasmus MC Rotterdam. https://www.researchgate.net/publication/269278775
[7]	Rapoport, D. L. (2013). Klein bottle logophysics: a unified principle for non-linear systems, cosmology, geophysics, biology, biomechanics and perception. Journal of Physics: Conference Series, 437, 012024. https://iopscience.iop.org/article/10.1088/1742-6596/437/1/012024/pdf
[8]	Sartori, S., Boffito, M., & Ciardelli, G. (2014). Polymeric scaffolds for cardiac tissue engineering: requirements and fabrication technologies. Polymer International, 63(4), 603–619. https://www.academia.edu/download/42426239/Polymeric_scaffolds_for_cardiac_tissue_e20160208-14055-1qhql74.pdf
[9]	Voormolen, M. M. (2007). 3D Harmonic Echocardiography. Erasmus University, PhD Dissertation. https://repub.eur.nl/pub/10598/3D%20Harmonic%20Echocardiography%20-%20Marco%20M.%20Voormolen.pdf
[10]	He, X., Sun, J., Zhuang, J., Xu, H., Liu, Y., & Wu, D. (2019). Micro needle system for transdermal drug and vaccine delivery: devices, safety, and prospects. Dose-Response, 17(3), 1–14. https://journals.sagepub.com/doi/pdf/10.1177/1559325819878585

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APA Style

Radhakrishnan, P. K. (2025). Heart as an Inverted Octagonal Pyramid: Fluid Dynamics of Cardiac Ejection. International Journal of Cardiovascular and Thoracic Surgery, 11(3), 23-30. https://doi.org/10.11648/j.ijcts.20251103.11

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ACS Style

Radhakrishnan, P. K. Heart as an Inverted Octagonal Pyramid: Fluid Dynamics of Cardiac Ejection. Int. J. Cardiovasc. Thorac. Surg. 2025, 11(3), 23-30. doi: 10.11648/j.ijcts.20251103.11

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AMA Style

Radhakrishnan PK. Heart as an Inverted Octagonal Pyramid: Fluid Dynamics of Cardiac Ejection. Int J Cardiovasc Thorac Surg. 2025;11(3):23-30. doi: 10.11648/j.ijcts.20251103.11

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@article{10.11648/j.ijcts.20251103.11,
  author = {Pradeep Kumar Radhakrishnan},
  title = {Heart as an Inverted Octagonal Pyramid: Fluid Dynamics of Cardiac Ejection
},
  journal = {International Journal of Cardiovascular and Thoracic Surgery},
  volume = {11},
  number = {3},
  pages = {23-30},
  doi = {10.11648/j.ijcts.20251103.11},
  url = {https://doi.org/10.11648/j.ijcts.20251103.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijcts.20251103.11},
  abstract = {Accurate geometric modeling of the human heart is essential for understanding and simulating cardiac fluid dynamics. Traditional left ventricular (LV) models—typically ellipsoidal, cylindrical, or conical—are limited in their ability to represent the complex regional structure and dynamic flow conditions present in a functioning heart. This study proposes an advanced geometric abstraction: the inverted octagonal pyramid model of the LV. This configuration introduces eight triangular faces converging at the apex, with an anatomically inspired octagonal base representing the mitral valve annulus, offering superior segmentation, mesh compatibility, and regional mechanical analysis. Using unsteady Navier-Stokes equations under physiological boundary conditions, this model captures systolic ejection mechanics including jet formation, vortex dynamics, wall shear stress (WSS) distribution, and flow separation zones. Quantitative simulation results across three scenarios—healthy heart, aortic stenosis, and hypertrophic cardiomyopathy (HCM)—reveal that the pyramid model predicts a Reynolds number (Re) range of 1200–5100 and vortex entropy index (VEI) values up to 0.6, indicating transitional-to-turbulent flow in diseased states. WSS distribution, especially near polygonal junctions, highlights zones of potential endocardial stress and thrombotic risk that conventional models fail to capture. This geometry is not only computationally robust for fluid–structure interaction (FSI) modeling but also aligns with echocardiographic segmental views, enhancing clinical relevance. Applications include patient-specific valve and stent design, surgical planning, CRT lead placement, and AI-based cardiac flow diagnostics. By more faithfully reflecting the true structural and flow heterogeneity of the heart, the inverted octagonal pyramid model establishes a new standard for integrative, biomechanical cardiovascular simulations. It bridges clinical imaging, computational modeling, and physiological accuracy—advancing both diagnostic precision and therapeutic planning in contemporary cardiology.
},
 year = {2025}
}

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TY  - JOUR
T1  - Heart as an Inverted Octagonal Pyramid: Fluid Dynamics of Cardiac Ejection

AU  - Pradeep Kumar Radhakrishnan
Y1  - 2025/06/25
PY  - 2025
N1  - https://doi.org/10.11648/j.ijcts.20251103.11
DO  - 10.11648/j.ijcts.20251103.11
T2  - International Journal of Cardiovascular and Thoracic Surgery
JF  - International Journal of Cardiovascular and Thoracic Surgery
JO  - International Journal of Cardiovascular and Thoracic Surgery
SP  - 23
EP  - 30
PB  - Science Publishing Group
SN  - 2575-4882
UR  - https://doi.org/10.11648/j.ijcts.20251103.11
AB  - Accurate geometric modeling of the human heart is essential for understanding and simulating cardiac fluid dynamics. Traditional left ventricular (LV) models—typically ellipsoidal, cylindrical, or conical—are limited in their ability to represent the complex regional structure and dynamic flow conditions present in a functioning heart. This study proposes an advanced geometric abstraction: the inverted octagonal pyramid model of the LV. This configuration introduces eight triangular faces converging at the apex, with an anatomically inspired octagonal base representing the mitral valve annulus, offering superior segmentation, mesh compatibility, and regional mechanical analysis. Using unsteady Navier-Stokes equations under physiological boundary conditions, this model captures systolic ejection mechanics including jet formation, vortex dynamics, wall shear stress (WSS) distribution, and flow separation zones. Quantitative simulation results across three scenarios—healthy heart, aortic stenosis, and hypertrophic cardiomyopathy (HCM)—reveal that the pyramid model predicts a Reynolds number (Re) range of 1200–5100 and vortex entropy index (VEI) values up to 0.6, indicating transitional-to-turbulent flow in diseased states. WSS distribution, especially near polygonal junctions, highlights zones of potential endocardial stress and thrombotic risk that conventional models fail to capture. This geometry is not only computationally robust for fluid–structure interaction (FSI) modeling but also aligns with echocardiographic segmental views, enhancing clinical relevance. Applications include patient-specific valve and stent design, surgical planning, CRT lead placement, and AI-based cardiac flow diagnostics. By more faithfully reflecting the true structural and flow heterogeneity of the heart, the inverted octagonal pyramid model establishes a new standard for integrative, biomechanical cardiovascular simulations. It bridges clinical imaging, computational modeling, and physiological accuracy—advancing both diagnostic precision and therapeutic planning in contemporary cardiology.

VL  - 11
IS  - 3
ER  -

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Author Information

Pradeep Kumar Radhakrishnan

Division of Cardiothoracic Surgery, Biomexia, Visakhapatnam, India

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Plain Text BibTeX RIS

APA Style

Radhakrishnan, P. K. (2025). Heart as an Inverted Octagonal Pyramid: Fluid Dynamics of Cardiac Ejection. International Journal of Cardiovascular and Thoracic Surgery, 11(3), 23-30. https://doi.org/10.11648/j.ijcts.20251103.11

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ACS Style

Radhakrishnan, P. K. Heart as an Inverted Octagonal Pyramid: Fluid Dynamics of Cardiac Ejection. Int. J. Cardiovasc. Thorac. Surg. 2025, 11(3), 23-30. doi: 10.11648/j.ijcts.20251103.11

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AMA Style

Radhakrishnan PK. Heart as an Inverted Octagonal Pyramid: Fluid Dynamics of Cardiac Ejection. Int J Cardiovasc Thorac Surg. 2025;11(3):23-30. doi: 10.11648/j.ijcts.20251103.11

Copy | Download

@article{10.11648/j.ijcts.20251103.11,
  author = {Pradeep Kumar Radhakrishnan},
  title = {Heart as an Inverted Octagonal Pyramid: Fluid Dynamics of Cardiac Ejection
},
  journal = {International Journal of Cardiovascular and Thoracic Surgery},
  volume = {11},
  number = {3},
  pages = {23-30},
  doi = {10.11648/j.ijcts.20251103.11},
  url = {https://doi.org/10.11648/j.ijcts.20251103.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijcts.20251103.11},
  abstract = {Accurate geometric modeling of the human heart is essential for understanding and simulating cardiac fluid dynamics. Traditional left ventricular (LV) models—typically ellipsoidal, cylindrical, or conical—are limited in their ability to represent the complex regional structure and dynamic flow conditions present in a functioning heart. This study proposes an advanced geometric abstraction: the inverted octagonal pyramid model of the LV. This configuration introduces eight triangular faces converging at the apex, with an anatomically inspired octagonal base representing the mitral valve annulus, offering superior segmentation, mesh compatibility, and regional mechanical analysis. Using unsteady Navier-Stokes equations under physiological boundary conditions, this model captures systolic ejection mechanics including jet formation, vortex dynamics, wall shear stress (WSS) distribution, and flow separation zones. Quantitative simulation results across three scenarios—healthy heart, aortic stenosis, and hypertrophic cardiomyopathy (HCM)—reveal that the pyramid model predicts a Reynolds number (Re) range of 1200–5100 and vortex entropy index (VEI) values up to 0.6, indicating transitional-to-turbulent flow in diseased states. WSS distribution, especially near polygonal junctions, highlights zones of potential endocardial stress and thrombotic risk that conventional models fail to capture. This geometry is not only computationally robust for fluid–structure interaction (FSI) modeling but also aligns with echocardiographic segmental views, enhancing clinical relevance. Applications include patient-specific valve and stent design, surgical planning, CRT lead placement, and AI-based cardiac flow diagnostics. By more faithfully reflecting the true structural and flow heterogeneity of the heart, the inverted octagonal pyramid model establishes a new standard for integrative, biomechanical cardiovascular simulations. It bridges clinical imaging, computational modeling, and physiological accuracy—advancing both diagnostic precision and therapeutic planning in contemporary cardiology.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Heart as an Inverted Octagonal Pyramid: Fluid Dynamics of Cardiac Ejection

AU  - Pradeep Kumar Radhakrishnan
Y1  - 2025/06/25
PY  - 2025
N1  - https://doi.org/10.11648/j.ijcts.20251103.11
DO  - 10.11648/j.ijcts.20251103.11
T2  - International Journal of Cardiovascular and Thoracic Surgery
JF  - International Journal of Cardiovascular and Thoracic Surgery
JO  - International Journal of Cardiovascular and Thoracic Surgery
SP  - 23
EP  - 30
PB  - Science Publishing Group
SN  - 2575-4882
UR  - https://doi.org/10.11648/j.ijcts.20251103.11
AB  - Accurate geometric modeling of the human heart is essential for understanding and simulating cardiac fluid dynamics. Traditional left ventricular (LV) models—typically ellipsoidal, cylindrical, or conical—are limited in their ability to represent the complex regional structure and dynamic flow conditions present in a functioning heart. This study proposes an advanced geometric abstraction: the inverted octagonal pyramid model of the LV. This configuration introduces eight triangular faces converging at the apex, with an anatomically inspired octagonal base representing the mitral valve annulus, offering superior segmentation, mesh compatibility, and regional mechanical analysis. Using unsteady Navier-Stokes equations under physiological boundary conditions, this model captures systolic ejection mechanics including jet formation, vortex dynamics, wall shear stress (WSS) distribution, and flow separation zones. Quantitative simulation results across three scenarios—healthy heart, aortic stenosis, and hypertrophic cardiomyopathy (HCM)—reveal that the pyramid model predicts a Reynolds number (Re) range of 1200–5100 and vortex entropy index (VEI) values up to 0.6, indicating transitional-to-turbulent flow in diseased states. WSS distribution, especially near polygonal junctions, highlights zones of potential endocardial stress and thrombotic risk that conventional models fail to capture. This geometry is not only computationally robust for fluid–structure interaction (FSI) modeling but also aligns with echocardiographic segmental views, enhancing clinical relevance. Applications include patient-specific valve and stent design, surgical planning, CRT lead placement, and AI-based cardiac flow diagnostics. By more faithfully reflecting the true structural and flow heterogeneity of the heart, the inverted octagonal pyramid model establishes a new standard for integrative, biomechanical cardiovascular simulations. It bridges clinical imaging, computational modeling, and physiological accuracy—advancing both diagnostic precision and therapeutic planning in contemporary cardiology.

VL  - 11
IS  - 3
ER  -

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