Mathematical Model and Simulation of Blood Flow Dynamics in Renal Interlobar Artery of Patients with Human immunodeficiency Virus

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International Journal of Research and Innovation in Applied Science (IJRIAS) |Volume VIII, Issue IV, April 2023|ISSN 2454-6194

Mathematical Model and Simulation of Blood Flow Dynamics in Renal Interlobar Artery of Patients with Human immunodeficiency Virus

 Abubakar, U.1, Ugwu, A. C.2, Tivde, T.3 and Mbah, GCE4
1Department of Radiography, Usmanu Danfodiyo University, Sokoto, Nigeria
2Department of Radiography and Radiological Sciences, Nnamdi Adzikiwe University, Awka, Nigeria
3Department of Mathematics, Joseph Sarwuan Tarka University, Makurdi, Nigeria
4Department of Mathematics, University of Nigeria, Nsukka, Nigeria
Received: 28 October 2022; Accepted: 17 November 2022; Published: 28 April 2023

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Abstract: Mathematical models were developed considering wall movement, blood pulsation and flow dynamics of the blood in the interlobar artery. The formulated models were based on the fact that the motion of blood vessel wall is not only influenced by pulsation, but also other physiological processes like heartbeat, breathing, and body posture. The Newton’s second Law of motion was employed in assembling the forces acting on the interlobar artery. The wall shear stress (WSS) was studied alongside, arterial walls to study the actual flow dynamics and investigate the blood flow behaviour. The results of the study were presented on both two – dimensional (2D) and three (3D) – dimensional graphs showing a more realistic interaction between the arterial wall and the blood flow in patients with HIV/AIDS. It was deduced that the blood flow velocity decreased with time across the varying frequency from 0.20Hz to 0.50Hz in the interlobar arterial channel.

Keywords: Mathematical Modelling, Blood flow, interlobar artery, blood flow dynamics, blood flow velocity, wall shear stress

Reference to this paper should be made as follows:

Biographical notes: (ABS)

I. Introduction

Human Immunodeficiency Virus (HIV) is an infection that attacks the body’s immune system and over time, if not treated, leads to acquired immunodeficiency syndrome (AIDS)[1]. Human Immunodeficiency Virus Associated Nephropathy (HIVAN) is the commonest cause of renal failure in HIV- 1- seropositive patients and the third most common end stage renal failure in African Americans between the ages of 20 to 64 [2]. Various types of renal disease were identified in the AIDS populace including those related to systemic and local renal infections, tubule interstitial disease, renal associated neoplasm and glomerular infection including collapsing glomerulopathy3. Atherosclerosis causes stenosis in the artery and is one of the most common types of cardiovascular disease.
The main cause of stenosis is the formation of plaque by the accumulation of cholesterol, lipid substances, cellular waste products, calcium, and fibrin in the endothelium of the tunica intima. The plaque may lead to stenosis or atresia in the artery, which may eventually result to heart attack and stroke [4]-[6]. Additionally, it is a proven fact that once a mild stenosis is developed, it will result to flow disorders that will consequently change the regional blood rheology, arterial deformability and influence the development of the disease7.

Consequently, many scientific researchers have made remarkable efforts to develop new velocimetry estimation, signal processing, clutter filter, and visualization techniques to obtain more accurate signals of blood flow [16]. It is imperative to evaluate these new techniques. In order to overcome the aforementioned challenges faced by diagnostic ultrasound, the computer simulation is a useful validation method because all parameters can be well defined. Hence, some researchers developed mathematical models and simulations to imitate the behaviour of pulsatile blood flow based on the assumption that the wall of the artery is rigid17-19. Recently, taking into cognizance the compromised SNR as a result of interaction between blood flow and the vessel wall, several researchers have developed more realistic and complex models with the aid of computational fluid dynamics (CFD) software20-26.
The Renal Arteries Arise from the Abdominal Aorta. The single renal artery enters the hilum and then branches to form the interlobar arteries, so-named because they pass between the lobes of the kidney. At the junction of the cortex and medulla, the interlobar arteries bend over to form incomplete arches.