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.
Keywords
Cardiac Fluid Dynamics, Inverted Octagonal Pyramid, Left Ventricle Modeling, Wall Shear Stress, Vortex Formation, Computational Hemodynamics, Personalized Cardiology
1. Introduction
Understanding the heart’s biomechanical behavior and its complex fluid dynamics remains central to biomedical engineering, especially in computational cardiology. Traditionally modeled as ellipsoidal or conical chambers, the left ventricle’s dynamic geometry poses challenges in simulating realistic flow paths and wall motion. A refined abstraction—viewing the heart as an inverted octagonal pyramid—offers improved segmentation of the ventricular volume and enables high-resolution modeling of fluid-wall interactions. This geometric formalism provides clearer insights into regional ejection patterns, vortex structures, and wall strain gradients, making it ideal for advanced simulations in cardiac electrophysiology and hemodynamics.
2. Method
Modeling the human heart as an inverted octagonal pyramid introduces a novel geometric abstraction to understand and simulate cardiac ejection dynamics. This approach bridges the anatomical intricacy of the ventricular chamber with mathematically tractable models used in computational fluid dynamics (CFD-2). The octagonal-pyramidal approximation allows clearer insights into flow divergence, wall strain orientation, vortex formations, and valvular boundary flow regulation during systole.
This concept plays a critical role in hemodynamic simulation, ejection fraction prediction, and biomechanical tissue modeling, especially in personalized medicine and cardiac device design.
3. Results
Geometric Foundation
The inverted octagonal pyramid geometry models the left ventricle with a pointed apex at the bottom and an octagonal base aligned with the mitral valve annulus. Each triangular face represents a myocardial segment, allowing discrete simulation of contraction dynamics. This structure accommodates asymmetry across walls (septal vs. lateral) and supports hybrid modeling approaches combining finite-element analysis with image-based boundary conditions. The octagonal shape better approximates the cross-sectional anatomy seen in cardiac magnetic resonance imaging (MRI-6), capturing localized bulging or thinning, which influences flow dynamics.
In this model:
The apex of the pyramid represents the ventricular apex.
The base represents the atrioventricular (AV-1) plane, modeled as an octagon to approximate muscular ring geometry.
The sloping sides resemble myocardial walls, each forming a triangular face with variable thickness.
Each face enables finite-element meshing and stress-distribution simulations more precisely than a conical or ellipsoidal model.
Fluid Dynamics of Cardiac Ejection Core Equations
The unsteady Navier-Stokes equations in cylindrical or curvilinear coordinates are adapted:
Key Flow Phenomena in the Model
Governing Equations of Flow
The fluid dynamics of blood within this structure are governed by the incompressible Navier-Stokes equations, capturing the interaction between myocardial wall motion and intracavitary blood flow. These equations describe momentum conservation under pressure gradients and viscous forces, enabling simulation of systolic ejection from the apex toward the outflow tract. The continuity equation ensures mass conservation. Integrating myocardial velocity boundary conditions at pyramid faces allows time-resolved modeling of stroke volume, vortex ring formation, and endocardial shear stress—critical parameters in predicting cardiac efficiency.
Vortex Formation and Wall Flow
Vortex formation in the ventricle is heavily influenced by the pyramid's angular transitions between faces. During early systole, wall motion generates circular and elliptical vortex structures near the apex and along the mid-ventricle. The angularity of the octagonal base facilitates vortex anchoring and redirection of flow, reducing stagnation and supporting efficient ejection. These vortices also influence the behavior of mitral regurgitant jets and are integral to energy-efficient flow redirection toward the aortic valve.
Jet Stream and Pressure Gradients
As systole progresses, the apex-to-base contraction generates a high-velocity jet through the left ventricular outflow tract (LVOT-5). The geometric tapering of the inverted pyramid magnifies local flow velocity as per Bernoulli’s principle, while pressure gradients drive directional flow. The octagonal base allows more nuanced simulation of flow bifurcations or eccentric jets. These jets are essential in quantifying peak ejection velocity and assessing aortic valve performance, often used in Doppler echocardiography.
Wall Shear Stress (WSS-8) Distribution
Wall shear stress reflects the tangential force exerted by flowing blood on myocardial surfaces, critical for endothelial health and remodeling. In the pyramid model, WSS varies significantly across the triangular faces, peaking at the transitions between base segments and apex. Computational studies reveal that WSS gradients are higher near angular junctions, contributing to localized strain and potential arrhythmic risk. This modeling is useful in evaluating regions prone to fibrosis or thrombus formation, especially under pathological conditions like dilated cardiomyopathy.
Reynolds Number and Flow Transition
Flow characteristics within the ventricular cavity depend on the Reynolds number (Re-7), which helps distinguish laminar from turbulent flow. In healthy adults, Re during peak systole typically ranges between 1,000 and 6,000, indicating transitional or mildly turbulent regimes. The polygonal shape introduces additional flow instability, promoting earlier vortex shedding. This complexity enhances the realism of simulations and is vital in assessing flow disturbances seen in prosthetic valve dysfunctions or ventricular septal defects.
4. Discussion
Practical Applications
Applications in Medical Engineering
The octagonal pyramid model informs several areas of cardiac engineering—from stent and prosthesis design to surgical planning. It enables localized prediction of flow velocities and WSS, crucial for designing anti-thrombotic valve geometries or personalized pacing strategies. Additionally, this geometric framework integrates well with machine learning models for real-time patient-specific simulations using echocardiographic input, enabling predictive modeling in clinics.
Ventricle-Specific Modeling Advantages
Unlike generic ellipsoid models, the octagonal pyramid allows segmental modeling of different ventricles (LV-4 vs. RV) and pathologies like left bundle branch block or hypertrophy. Each face can be assigned unique material properties and contractility parameters. This adaptability improves diagnostic specificity and provides a scaffold for multi-modal simulation combining electrical activation, mechanical deformation, and fluid motion, central to whole-heart modeling.
1. Heart valve prosthesis design (using boundary layer theory at polygon corners).
2. Patient-specific modeling in MRI-driven Computational Fluid Dynamics (CFD-2) simulations.
3. Optimization of pacemaker electrode placement by understanding regional wall motion.
4. Implications and Future Applications of the Inverted Octagonal Pyramid Heart Model
The modeling of the human heart as an inverted octagonal pyramid offers an innovative structural basis for analyzing the biomechanics and fluid dynamics of cardiac function. While initially proposed as a geometrical abstraction, this model reveals deep utility in medical imaging, hemodynamic simulations, device engineering, and clinical diagnostics, pointing to a diverse landscape of future applications. Below, we explore these possibilities, indexing the supporting evidence from the previous references.
Enhanced Computational Hemodynamics
The structured faces of the octagonal pyramid enable more accurate meshing in finite element and computational fluid dynamics (CFD) simulations. This facilitates high-fidelity modeling of intracardiac vortices, jet velocities, and shear stresses—especially at geometric discontinuities
| [1] | Schröder-Schetelig, J. (2021). Multimodal high-resolution mapping of contracting intact Langendorff-perfused hearts. University of Göttingen, PhD Dissertation. https://ediss.uni-goettingen.de/bitstream/handle/21.11130/00-1735-0000-0005-1551-8/schroederschetelig_phdthesis_multimodal_mapping_contracting_hearts.pdf?sequence=1 |
| [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 |
[1, 3, 4]
. Future software platforms for cardiology could integrate this geometry into real-time MRI/CT-based modeling for diagnostics and therapy planning.
Personalized Heart Valve and Stent Design
The segmentation of myocardial walls into triangular faces allows localized assessment of flow disturbances and wall shear stress (WSS). This could significantly enhance the design of prosthetic valves and intracardiac stents by simulating localized flow dynamics in patient-specific geometries
. The approach could also help in optimizing the positioning of transcatheter heart valves in patients with complex or asymmetric anatomy.
Predictive Modeling in Heart Failure and Remodeling
This model supports the simulation of asymmetric ventricular dilation, wall thinning, or hypertrophy across discrete segments. As a result, it is well-suited for modeling progressive diseases like dilated cardiomyopathy or left bundle branch block, enabling predictive simulations of remodeling, ejection fraction loss, and therapeutic impact
| [1] | Schröder-Schetelig, J. (2021). Multimodal high-resolution mapping of contracting intact Langendorff-perfused hearts. University of Göttingen, PhD Dissertation. https://ediss.uni-goettingen.de/bitstream/handle/21.11130/00-1735-0000-0005-1551-8/schroederschetelig_phdthesis_multimodal_mapping_contracting_hearts.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 |
[1, 6, 7]
.
Advanced Echocardiography Interpretation
Modern echocardiographic platforms can incorporate octagonal segmentation to provide more precise regional functional analysis, such as regional strain, wall thickening, and local WSS distribution
| [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 |
| [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 |
[6, 9]
. Machine learning models trained on such segmentations could revolutionize early detection of regional dysfunction or ischemia.
Implantable Devices and Pacing Optimization
The model allows for spatially resolved analysis of myocardial strain and electrical activation patterns, informing optimal pacing locations for devices such as CRT (Cardiac Resynchronization Therapy) implants. A pyramid-based model could simulate the exact mechanical-electrical dyssynchrony patterns, allowing targeted electrode placements
.
Drug Delivery in Cardiovascular Therapy
The geometry enables microfluidic modeling that may inspire drug delivery systems matching the spatial stress fields in myocardial tissue. Octagonal micro needle arrays or polymer scaffolds with corresponding geometry could ensure uniform distribution of anti-inflammatory or regenerative agents during cardiac repair
| [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 |
| [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 |
[8, 10]
.
CFD Mesh suitability
The triangular planar faces of octagonal pyramid geometry area inherently mesh friendly, facilitating higher resolution CFD analysis with fewer numerical instabilities, Unlike the curved surface models that often require interpolation, the planar segmentation supports more accurate volume measurement and mesh conformity-especially when derived from 3 D imaging modalities such as ultrasound or MRI
. This structure significantly improves solver convergence and accuracy in simulating complex intra ventricular flow patterns.
Educational and Surgical Training Tools
3D-printed or virtual models of the heart using this geometry can become powerful tools for medical education and surgical simulation. The clearly defined planes and regions help students understand spatial relationships between heart structures, flow trajectories, and device placement sites
.
AI-Based Risk Prediction Systems
When integrated into AI platforms, the model could offer a superior feature space for risk prediction in diseases such as atrial fibrillation, heart failure, or post-infarct remodeling. Metrics like region-wise pressure gradients, localized vortex energy, and segmental wall motion indices can be fed into predictive models
.
Biomimetic Robotic Hearts and Artificial Organs
Future bio-inspired mechanical hearts could adopt this geometry to reproduce real-life flow trajectories and contraction mechanics. The pyramid-like structure allows for modular actuation in robotic chambers, more accurately mimicking human heart ejection patterns
| [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 |
| [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 |
[3, 8]
.
Interdisciplinary Exploration: Topological and Mathematical Physics
This heart model can also intersect with research in topology, non-Euclidean geometry, and mathematical physics. For example, vortex modeling on polyhedral surfaces or time-evolving geometrical manifolds may find applications beyond biology—in fields such as material science, soft robotics, or fluid-topological systems
| [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 |
| [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 |
[4, 7]
.
5. Conclusion
The inverted octagonal pyramid abstraction of the heart marks a significant departure from classical models by introducing a structured, mathematically rich, and clinically versatile paradigm. Its capacity to unify geometry with physiology makes it a compelling foundation for next-generation cardiac simulations, medical devices, and AI-assisted cardiology platforms. Continued research in this direction, supported by high-resolution imaging and real-time simulation technologies, could profoundly reshape both cardiac care and biomedical research.
6. Recommendations
These results affirm that inverted pyramid modeling reveals localized instabilities, vortex shedding, and hemodynamic inefficiencies far more clearly than ellipsoidal or cylindrical models, especially under pathological conditions.
Abbreviations
AV | Atrioventricular Computational Fluid Dynamics |
CRT | Cardiac Resynchronization Therapy |
LV | Left Ventricle |
LVOT | Left Ventricular Outflow Tract |
MRI | Magnetic Resonance Imaging |
Re | Reynolds Number |
WSS | Wall Shear Stress |
Author Contributions
Pradeep Kumar Radhakrishnan is the sole author. The author read and approved the final manuscript.
Conflicts of Interest
The author declares no conflicts of interest.
Appendix
Appendix I: Comparative Analysis Between the Inverted Octagonal Pyramid Model of the Heart and Existing Conventional Heart Models
.Comparative analysis between the inverted octagonal pyramid model of the heart and existing conventional heart models used in fluid dynamics, such as spherical, ellipsoidal, and cylindrical models. The comparison focuses on geometry, simulation precision, flow modeling, and biomechanical relevance, explaining why the inverted octagonal pyramid offers a superior framework for cardiac ejection and fluid flow simulation.
Table 1. Comparison: Inverted Octagonal Pyramid Model vs. Existing Heart Models.
Feature | Inverted Octagonal Pyramid Model | Conventional Models (Sphere/Ellipsoid/Cylinder) |
1. Geometric Fit | Mimics the ventricular conical shape with base detail, especially the mitral ring as an octagon | Oversimplifies with smooth curves; misses angular boundaries of real heart |
2. Anatomical Accuracy | Captures regional differences via triangular planar faces, reflecting segmental contraction | Lacks regional differentiation; treats LV as homogeneous |
3. Flow Behavior | Enables simulation of directional jets, vortex rings, and shear patterns at edges | Flow tends to be smoothed out; vortex behavior less realistic |
4. Valve Ring Modelling | Octagonal base allows realistic modelling of mitral and aortic ring deformations | Spherical/cylindrical bases do not model valve orifice dynamics precisely |
5. Wall Shear Stress (WSS) Detection | Clear edge angles generate WSS concentration zones, useful for device testing | Smooth walls miss critical shear peaks, losing diagnostic power |
6. CFD Mesh Suitability | Triangular planar faces are mesh-optimized, improving convergence and solver stability | Ellipsoids require complex meshing; can create solver instability |
7. Jet Ejection Geometry | Base-to-apex inverted geometry reflects real systolic ejection patterns into LVOT | Conventional models poorly represent LVOT directionality and jet formation |
8. Scalability to AI/ML Training | Region-defined faces support localized feature extraction for machine learning | Smooth models lack localized anatomical features |
9. Clinical Surgical Planning | Geometric facets match echocardiographic views (segments AHA-17 model) | Cannot correlate clearly with surgical segmental mapping |
10. Adaptability to Disease Models | Easily modified to simulate hypertrophy, aneurysm, or valve | Rigid symmetry limits disease morphing fidelity |
Why This Model Is Superior
The inverted octagonal pyramid model reflects both the gross anatomy and fluid dynamics of the human heart more accurately than conventional geometries. It provides:
1. Higher fidelity simulations of intra-ventricular flow.
2. A framework that aligns with clinical imaging segments.
3. Greater diagnostic and surgical value.
4. Better compatibility with CFD solvers and AI-based models.
This makes it breakthrough geometry for cardiovascular modeling, combining biomechanical realism with engineering applicability.
Appendix II: Boundary Conditions and Assumptions in the Inverted Octagonal Pyramid Heart Model
To simulate the left ventricle (LV) as an inverted octagonal pyramid, a number of precise boundary conditions and modeling assumptions are made to ensure computational fluid dynamics (CFD) simulations replicate physiological cardiac ejection. These include:
1. Geometry:
a. The LV is modeled as an inverted pyramid with 8 triangular faces.
b. The octagonal base represents the mitral valve annulus, while the apex corresponds to the ventricular tip.
2. Boundary Conditions:
a. Inlet boundary (base): Pulsatile pressure waveform or velocity profile at the mitral valve using a time-varying function, e.g.,
b. Outlet boundary (apex-LVOT): Zero-pressure or Windkessel-type outflow resistance to represent aortic impedance.
c. Wall boundary: No-slip condition at myocardial walls; optionally modeled with moving boundaries or elastic deformation using ALE (Arbitrary Lagrangian-Eulerian) formulation.
d. Initial condition: Blood at rest or previous cardiac cycle velocity profile.
3. Assumptions:
a. Incompressible Newtonian fluid
b. Quasi-steady or unsteady flow regime depending on simulation phase (systole/diastole).
c. Rigid vs deformable walls: Simplified models assume rigid walls; advanced models use FSI (Fluid-Structure Interaction) to capture myocardial motion.
d. Turbulence modeling: Depending on Reynolds number, either laminar or transitional (LES, k-ω SST) turbulence models are used.
Appendix III: Immediate Clinical Applications of the Pyramid Model
The inverted octagonal pyramid model translates directly into multiple clinical contexts, owing to its regional fidelity and ability to reproduce critical flow dynamics:
a. Valve Device Optimization: Edge-specific shear stress maps allow for precise deployment of mitral or aortic prostheses.
b. Heart Failure Analysis: Segmental geometry allows modeling of dyssynchronous contraction or apical ballooning as in Takotsubo syndrome.
c. Surgical Planning: The model overlays naturally with AHA 17-segment model, aiding decisions in ventricular reconstruction and aneurysmectomy.
d. CFD-based Diagnostic Tools: Quantification of vortex retention time and energetic efficiency supports heart failure grading.
e. Personalized Therapy: AI-enhanced simulations with pyramid-based templates enable non-invasive assessments of flow pathology before and after interventions.
Reynolds Number, Flow Transitions, and Simulation Results
The Reynolds number (Re) is a crucial non-dimensional quantity indicating the regime of blood flow, defined by:
Typical Reynolds Number Range:
Appendix IV: Quantitative Simulation Findings
Appendix V: CFD Pressure Contour Visuals of 3 Modelled States
Figure 1. Comparitive visualization of three cardiac states modelled with inverted octagonal pyramid geometry.
References
| [1] |
Schröder-Schetelig, J. (2021). Multimodal high-resolution mapping of contracting intact Langendorff-perfused hearts. University of Göttingen, PhD Dissertation.
https://ediss.uni-goettingen.de/bitstream/handle/21.11130/00-1735-0000-0005-1551-8/schroederschetelig_phdthesis_multimodal_mapping_contracting_hearts.pdf?sequence=1
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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
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| [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
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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
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| [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
|
Cite This Article
-
-
@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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