Asian Journal of Basic Science & Research Volume 4, Issue 4, Pages 47-59, October-December 2022 ISSN: 2582-5267 47 Murmurs from the Vascular Members: A Generalized Theoretical Outlook Nzerem, Francis Egenti Department of Mathematics and Statistics, University of Port Harcourt. Email: frankjournals@yahoo.com DOI: http://doi.org/10.38177/AJBSR.2022.4406 Copyright: © 2022 Nzerem, Francis Egenti. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Article Received: 14 November 2022 Article Accepted: 17 December 2022 Article Published: 26 December 2022 ░ 1. INTRODUCTION The cardiovascular system, which refers to the heart, blood vessels, and the blood is the basis of the vivacity of virtually all animated life. The heart (cardio) ensures the pumping of blood and the blood vessels (vasculature) are the appurtenances that passively maintain the integrity of flow. The flow of blood in the vessel is driven by the pressure difference between any two arbitrary points along the length of the vessel. While the latter is true, the pressure difference across an organ is described by the variation between arterial pressure ( P A ) and venous pressure (P V ). The circulatory system is, by default, marked by laminar blood flow in which concentric layers of blood flow parallel down the length of a blood vessel. However, in more or less pathological conditions, the laminar flow regime may be upset by turbulence in which the critical Reynolds number (Re) is exceeded. Turbulence is, to all intent and purposes, chaos. Both the vasculature and the cardiac chambers may experience distressed regions being implicated or exacerbated by turbulent flow. In all, pressure fluctuations and their incidences are produced by an ensemble of fluid-structure interaction-based factors. In essence, the pulsating cardio-vascular structures, distressed areas of turbulent flow, mixing of flows of varying temperatures, and their semblances produce pressure fluctuations that are transmitted through the fluid as sound. In both the vasculature and the cardiac chambers, this sound due to turbulent flow is the progression of compressions and rarefactions propagated away from the source environs. In the former, such sounds are called bruits such as can be auscultated in the carotid, renal, and visceral arteries among others. Stenosis is a culprit in diverse abnormal flow conditions in the vessel. Seo and Mittal [1] suggested that the chief source of arterial bruits is perturbation initiated by vortex flow in the near post-stenotic region. Lees and Dewey [2] proposed phono-angiography as a non-invasive diagnostic technique. In Fredberg [3] the fluctuating mechanical stress on the arterial-wall downstream of stenosis by turbulent blood flow was investigated. The work found that the distance downstream of the stenosis at which the mean-square fluctuating pressure attains its maximum intensity was dependent upon jet velocity and fluid viscosity ABSTRACT Stenosis-induced turbulence can bring many insidious effects to bear on the vasculature. The sound generated in an arterial compartment due to fluctuating turbulent pressure and the distortions in the flow characteristics around a stenotic region leave much to be desired. As vascular sounds are generated locally in the peripheral blood vessels, they require near-field auscultation. It is commonplace in clinical practice to place premium on near-field auscultation, with little attention to events in the far field. Nevertheless, retrograde waves that travel some distance away from the vicinity of the acoustic source require attention. They create an incipient murmur that pervades from a distance well before the source point on impact with the advancing anterograde wave. This paper, a theoretical study on vascular murmurs, utilized the concept of acoustic power spectrum and Lighthill’s acoustic analogy in describing vascular murmurs. Apologies for far -field acoustic auscultation are made since in-situ-generated vascular sounds may travel beyond the near field. Keywords: Auscultation; Green’s function; Lighthill’s analogy; Stenosis; Turbulence.