TY  - JOUR
AU  - Farias, Matheus dos Santos
PY  - 2026
DA  - 2026/04/01
TI  - Analysis of the Cardiovascular System and an Aorta with Abdominal Aneurysm Using Lattice Boltzmann
JO  - ICCK Journal of Applied Mathematics
T2  - ICCK Journal of Applied Mathematics
JF  - ICCK Journal of Applied Mathematics
VL  - 2
IS  - 2
SP  - 120
EP  - 136
DO  - 10.62762/JAM.2026.170486
UR  - https://www.icck.org/article/abs/JAM.2026.170486
KW  - abdominal aortic aneurysm
KW  - Lattice Boltzmann method
KW  - hemodynamics
KW  - Newtonian fluid
KW  - computational bioengineering
AB  - This study presents a mathematical and computational analysis of blood flow in the abdominal aorta under healthy, aneurysmal, and rupture-related conditions. The proposed framework combines a Newtonian fluid approximation with a Lattice Boltzmann formulation to simulate the hemodynamic behavior of the aorta in three-dimensional geometry. The governing equations were implemented in Python, allowing the generation of numerical simulations and corresponding three-dimensional visualizations of aneurysm progression. The analysis considered clinically inspired stages ranging from the healthy vessel to advanced aneurysmal dilation and rupture. The results showed that aneurysm growth significantly alters the internal flow field, producing changes in velocity distribution, pressure loading, and wall shear stress. As the aneurysmal sac enlarges, the simulations indicate greater hemodynamic disturbance, more pronounced local stress concentration, and reduced structural stability of the aortic wall. In the rupture-related stage, the numerical model captured the transition from confined flow to loss of wall integrity, highlighting the biomechanical severity of advanced aneurysmal disease. From a physical and clinical perspective, the findings reinforce the importance of combining geometry, fluid mechanics, and wall response in the study of abdominal aortic aneurysms. The proposed approach contributes to the interpretation of aneurysm development and rupture risk by linking mathematical modeling to clinically meaningful scenarios. In addition, the work demonstrates the potential of computational methods as support tools for cardiovascular analysis, with relevant applications in bioengineering, biomathematics, and medical modeling. Thus, this study offers an interpretable and innovative framework for investigating the progression of abdominal aortic aneurysms and their hemodynamic consequences.
SN  - 3068-5656
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  - 

@article{Farias2026Analysis,
  author = {Matheus dos Santos Farias},
  title = {Analysis of the Cardiovascular System and an Aorta with Abdominal Aneurysm Using Lattice Boltzmann},
  journal = {ICCK Journal of Applied Mathematics},
  year = {2026},
  volume = {2},
  number = {2},
  pages = {120-136},
  doi = {10.62762/JAM.2026.170486},
  url = {https://www.icck.org/article/abs/JAM.2026.170486},
  abstract = {This study presents a mathematical and computational analysis of blood flow in the abdominal aorta under healthy, aneurysmal, and rupture-related conditions. The proposed framework combines a Newtonian fluid approximation with a Lattice Boltzmann formulation to simulate the hemodynamic behavior of the aorta in three-dimensional geometry. The governing equations were implemented in Python, allowing the generation of numerical simulations and corresponding three-dimensional visualizations of aneurysm progression. The analysis considered clinically inspired stages ranging from the healthy vessel to advanced aneurysmal dilation and rupture. The results showed that aneurysm growth significantly alters the internal flow field, producing changes in velocity distribution, pressure loading, and wall shear stress. As the aneurysmal sac enlarges, the simulations indicate greater hemodynamic disturbance, more pronounced local stress concentration, and reduced structural stability of the aortic wall. In the rupture-related stage, the numerical model captured the transition from confined flow to loss of wall integrity, highlighting the biomechanical severity of advanced aneurysmal disease. From a physical and clinical perspective, the findings reinforce the importance of combining geometry, fluid mechanics, and wall response in the study of abdominal aortic aneurysms. The proposed approach contributes to the interpretation of aneurysm development and rupture risk by linking mathematical modeling to clinically meaningful scenarios. In addition, the work demonstrates the potential of computational methods as support tools for cardiovascular analysis, with relevant applications in bioengineering, biomathematics, and medical modeling. Thus, this study offers an interpretable and innovative framework for investigating the progression of abdominal aortic aneurysms and their hemodynamic consequences.},
  keywords = {abdominal aortic aneurysm, Lattice Boltzmann method, hemodynamics, Newtonian fluid, computational bioengineering},
  issn = {3068-5656},
  publisher = {Institute of Central Computation and Knowledge}
}