Does the principle of minimum work apply at the carotid bifurcation: a retrospective cohort study

Abstract

BackgroundThere is recent interest in the role of carotid bifurcation anatomy, geometry and hemodynamic factors in the pathogenesis of carotid artery atherosclerosis. Certain anatomical and geometric configurations at the carotid bifurcation have been linked to disturbed flow. It has been proposed that vascular dimensions are selected to minimize energy required to maintain blood flow, and that this occurs when an exponent of 3 relates the radii of parent and daughter arteries. We evaluate whether the dimensions of bifurcation of the extracranial carotid artery follow this principle of minimum work.MethodsThis study involved subjects who had computed tomographic angiography (CTA) at our institution between 2006 and 2007. Radii of the common, internal and external carotid arteries were determined. The exponent was determined for individual bifurcations using numerical methods and for the sample using nonlinear regression.ResultsMean age for 45 participants was 56.9 ± 16.5 years with 26 males. Prevalence of vascular risk factors was: hypertension-48%, smoking-23%, diabetes-16.7%, hyperlipidemia-51%, ischemic heart disease-18.7%.The value of the exponent ranged from 1.3 to 1.6, depending on estimation methodology.ConclusionsThe principle of minimum work (defined by an exponent of 3) may not apply at the carotid bifurcation. Additional factors may play a role in the relationship between the radii of the parent and daughter vessels.

Carotid Artery Anatomy and Geometry as Risk Factors for Carotid Atherosclerotic Disease

“…9 This software requires identifications of points within the ICA, external carotid artery (ECA), and common carotid artery (CCA). The user-defined points were automatically connected using a path of lowest cost to form a "sketch" of the artery tree.…”

“…9 The measures of carotid artery geometry were defined according to methods described previously. 8 The bifurcation angle was the angle between the ICA and ECA.…”

Vessel calibre and flow splitting relationships at the internal carotid artery terminal bifurcation

“…Others have shown that the exponent might be between 2.42 and 3 when the non--Newtonian behaviour of the blood is accounted for (Revellin et al, 2009). Besides these theoretical studies, experimental measurements have reported values ranging between 2 and 3 on diverse cardiovascular territories, and using diverse methodologies (Beare et al, 2011;Finet et al, 2008;Ingebrigtsen et al, 2004;Mittal et al, 2005;Rossitti and Lofgren, 1993b;van der Giessen et al, 2011). With rare exceptions (e.g.…”

Branching Pattern of the Cerebral Arterial Tree

“…Based on the principle of minimum work the AR would range between 1.10 for turbulent flow in larger arteries and 1.26 for laminar flow in smaller arteries (Uylings, ). From literature we know that in the human vasculature the range of AR is much larger than this theoretical range (Hutchins et al, ; Hardy‐Stashin et al, ; Fanucci et al, ; Papageorgiou et al, ; Aharinejad et al, ; Beare et al, ).…”

“…In the past, data of branching patterns of an arterial tree were gathered using manual measurements on ex vivo and in vivo specimens (Koike et al, ; Horsfield and Woldenberg, ; Papageorgiou et al, ; MacLean et al, ; Wang et al, ; Rossitti and Löfgren, ; Zamir, ; Mittal et al, ; Cassot et al, ). More modern techniques utilize newer three dimensional (3D) imaging techniques such as computed tomography angiography (CTA) and magnetic resonance imaging (MRI) for in vivo capturing of larger arteries and micro‐computed tomography (micro‐CT) and confocal laser microscopy for capturing highly detailed in vivo and ex vivo vascular networks (Cassot et al, ; Nordsletten et al, ; Beare et al, ).…”