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Numerical Investigation of Physical Parameters in Cardiac Vessels as a New Medical Support Science for Complex Blood Flow Characteristics


  • Defrianto Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas Riau, Pekanbaru, Indonesia.
  • Toto Saktioto Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas Riau, Pekanbaru, Indonesia.
  • Yan Soerbakti Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas Riau, Pekanbaru, Indonesia.
  • Andika Thoibah Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas Riau, Pekanbaru, Indonesia.
  • Bunga Meyzia Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas Riau, Pekanbaru, Indonesia.
  • Romi Fadli Syahputra Department of Physics, Faculty of Mathematics and Natural Sciences and Health, Universitas Muhammadiyah Riau, Pekanbaru, Indonesia.
  • Okfalisa Department of Informatics Engineering, Faculty of Sciences and Technology, Universitas Islam Negeri Sultan Syarif Kasim, Pekanbaru, Indonesia.
  • Syamsudhuha Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Riau, Pekanbaru, Indonesia.
  • Dedi Irawan Department of Physics Education, Faculty of Teacher Training and Education, Universitas Riau, Pekanbaru, Indonesia.
  • Haryana Hairi Department of Physics, Faculty of Applied Sciences, Universiti Teknologi MARA, Shah Alam, Malaysia.



Blood flow, Finite element analysis,Heart, Navier-Stokes,Vessels.


This study proposes a mathematical approach and numerical experiment for a simple solution of cardiac blood flow to the heart's blood vessels. A mathematical model of human blood flow through arterial branches was studied and calculated using the Navier-Stokes partial differential equation with finite element analysis (FEA) approach. Furthermore, FEA is applied to the steady flow of two-dimensional viscous liquids through different geometries. The validity of the computational method is determined by comparing numerical experiments with the results of the analysis of different functions. Numerical analysis showed that the highest blood flow velocity of 1.22 cm/s occurred in the center of the vessel which tends to be laminar and is influenced by a low viscosity factor of 0.0015 Pa.s. In addition, circulation throughout the blood vessels occurs due to high pressure in the heart and the pressure becomes lower when it returns from the blood vessels at the same parameters. Finally, when the viscosity is high, the extreme magnitudes of blood flow tend toward the vessel wall at approximately the same velocity and radius of the gradient.


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Bao G, Bazilevs Y, Chung JH, Decuzzi P, Espinosa HD, Ferrari M, et al. USNCTAM perspectives on mechanics in medicine. J R Soc Interface. 2014 Aug;11(97):1-26.

Yuan HZ, Niu XD, Shu S, Li M, Yamaguchi H. A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating a flexible filament in an incompressible flow. ComputMathAppl. 2014 Mar;67(5):1039-56.

Saktioto T, Fadilla FD, Soerbakti Y, Irawan D, Okfalisa. Application of fiber Bragg grating sensor system for simulation detection of the heart rate. J PhysConf Ser. 2021 Oct;2049(1):1-8.

Gray RA, Pathmanathan P. Patient-specific cardiovascular computational modeling: Diversity of personalization and challenges. J CardiovascTransl Res. 2018 Apr;11(2):80-8.

Lin Q, Li T, Shakeel PM, Samuel RDJ. Advanced artificial intelligence in heart rate and blood pressure monitoring for stress management. J Ambient IntellHumanizComput. 2021 Mar;12(3):3329-40.

Jamshidi M, Ghazanfarian J. Blood flow effects in thermal treatment of three-dimensional non-Fourier multilayered skin structure. Heat Transfer Eng. 2021 Jun;42(11):929-46.

Arzani A, Gambaruto AM, Chen G, Shadden SC. Lagrangian wall shear stress structures and near-wall transport in high-Schmidt-number aneurysmal flows. J Fluid Mech. 2016 Mar;790:158-72.

Detmer FJ, Lückehe D, Mut F, Slawski M, Hirsch S, Bijlenga P, et al. Comparison of statistical learning approaches for cerebral aneurysm rupture assessment. Int J Comput Assist Radiol Surg. 2020 Jan;15(1):141-50.

Hassan EA, Al-Zuhairi WS, Ahmed MA. Serum cortisol and BMI in chronic diseases and increased early cardiovascular diseases. Baghdad Sci J. 2016 Jun;13(2.2NC):399-406.‎

Saifullah PH, Nida SM, Raoof IB. Levels of glucose-6-phosphate dehydrogenase in type 1 diabetes mellitus patients with nephropathy and cardiovascular disease complication. Baghdad Sci J. 2014 Jun;11(2):461-8.

Saktioto T, Ramadhan K, Soerbakti Y, Syahputra RF, Irawan D, Okfalisa. Apodization sensor performance for TOPAS fiber Bragg grating. Telkomnika. 2021 Dec;19(6):1982-91.

Chitturi KS, Murty PSR, Babu KS. Convective flow and temperature distribution in rotating inclined composite porous and fluid layers. Songklanakarin J Sci Technol. 2022 Mar;44(2):370-80.

Blanco PJ, Bulant CA, Müller LO, Talou GM, Bezerra CG, Lemos PA, et al. Comparison of 1D and 3D models for the estimation of fractional flow reserve. Sci Rep. 2018 Nov;8(1):1-12.

Čanić S, Galić M, Muha B. Analysis of a 3D nonlinear, moving boundary problem describing fluid-mesh-shell interaction. Trans Am Math Soc. 2020 Sep;373(9):6621-81.

Defrianto D, Saktioto T, Hikma N, Soerbakti Y, Irawan D, Okfalisa O, et al. External perspective of lung airflow model through diaphragm breathing sensor using fiber optic elastic belt. Indian J Pure Appl Phys. 2022 Jul; 60(7): 561-6.

Bukač M, Yotov I, Zunino P. An operator splitting approach for the interaction between a fluid and a multilayered poroelastic structure. Numer Methods Partial Differ Equ. 2015 Jul;31(4):1054-100.

Greenstein AS, Kadir SZAS, Csato V, Sugden SA, Baylie RA, Eisner DA, et al. Disruption of pressure-induced Ca2+ spark vasoregulation of resistance arteries, rather than endothelial dysfunction, underlies obesity-related hypertension. Hypertension. 2020 Feb;75(2):539-48.

Mirramezani M, Shadden SC. A distributed lumped parameter model of blood flow. Ann Biomed Eng. 2020 Dec;48(12):2870-86.

Magder S. The meaning of blood pressure. Crit Care. 2018 Dec;22(1):1-10.

Ershkov SV, Shamin RV, Giniyatullin AR. On a new type of non-stationary helical flows for incompressible 3D Navier-Stokes equations. J King Saud Univ Sci. 2020 Jan;32(1):459-67.

Ammar A, Abisset-Chavanne E, Chinesta F, Keunings R. Flow modelling of quasi-Newtonian fluids in two-scale fibrous fabrics. Int J Mater Form. 2017 Aug;10(4):547-56.

Gowthami K, Prasad PH, Mallikarjuna B, Makinde OD. Hydrodynamic flow between rotating stretchable disks in an orthotropic porous medium. Songklanakarin J Sci Technol. 2020 Mar;42:391-7.

Ershkov SV. On Existence of general solution of the Navier-Stokes equations for 3D non-stationary incompressible flow. Int J Fluid Mech Res. 2015;42(3):206-13.

Guo X, Lu Y. Convergence and efficiency of different methods to compute the diffraction integral for gravitational lensing of gravitational waves. Phys Rev D. 2020 Dec;102(12):124076.

Haq RU, Shahzad F, Al-Mdallal QM. MHD pulsatile flow of engine oil based carbon nanotubes between two concentric cylinders. Results Phys. 2017 Jan;7:57-68.

Riemer K, Rowland EM, Broughton-Venner J, Leow CH, Tang M, Weinberg PD. Contrast agent-free assessment of blood flow and wall shear stress in the rabbit aorta using ultrasound image velocimetry. Ultrasound Med Biol. 2022 Mar;48(3):437-49.

Goodwill AG, Dick GM, Kiel AM, Tune JD. Regulation of coronary blood flow. Compr Physiol. 2017 Mar;7(2):321-82.

Sempionatto JR, Lin M, Yin L, Pei K, Sonsa-ard T, de Loyola Silva AN, et al. An epidermal patch for the simultaneous monitoring of haemodynamic and metabolic biomarkers. Nat Biomed Eng. 2021 Jul;5(7):737-48.

Toghraie D, Esfahani NN, Zarringhalam M, Shirani N, Rostami S. Blood flow analysis inside different arteries using non-Newtonian Sisko model for application in biomedical engineering. Comput. Methods Programs Biomed. 2020 Jul;190:1-8.

Rukshin I, Mohrenweiser J, Yue P, Afkhami S. Modeling superparamagnetic particles in blood flow for applications in magnetic drug targeting. Fluids. 2017 Jun;2(2):29.

Liu K, Yin D, Su H. Transient transfer shape factor for fractured tight reservoirs: Effect of the dynamic threshold pressure gradient in unsteady flow. Energy Sci Eng. 2020 Jul;8(7):2566-86.

Dellavale D, Rosselló JM. Cross-frequency couplings in non-sinusoidal dynamics of interacting oscillators: Acoustic estimation of the radial position and spatial stability of nonlinear oscillating bubbles. UltrasonSonochem. 2019 Mar;51:424-38.

Wang H, Krüger T, Varnik F. Geometry and flow properties affect the phase shift between pressure and shear stress waves in blood vessels. Fluids. 2021 Nov;6(11):1-16.

Karvelas E, Sofiadis G, Papathanasiou T, Sarris I. Effect of micropolar fluid properties on the blood flow in a human carotid model. Fluids. 2020 Sep;5(3):1-16.