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

This 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.Mean 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.The 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.There has been recent interest in the role of carotid artery anatomy, geometry and hemodynamic factors in the pathogenesis of carotid artery atherosclerosis [1-6]. The anatomy and geometry at the carotid bifurcation within the same individuals [1,7] and between the sexes [3] vary greatly. The anatomy [7,8] and geometry [5] of the carotid bifurcation have large influence on vortex flow at the carotid sinus. These studies support observations that plaques form preferentially at such sites as carotid artery bifurcation (extracranial site) and the carotid artery siphon (intracranial site), rather than randomly in the carotid artery. This may provide an explanation for the asymmetrical nature of carotid artery stenosis [9] within the same individual despite exposure to the same factors [10]. In addition to this, there may be a role for interplay between anatomy, hemodynamic shear forces and traditional risk factors.This work on carotid artery geometry has been inspired by the writings of Murray in 1926 [11] and Rossitti and Lofgren in 1993 [12,13]. A law on harmonisation of the vascular dimensions to minimize total energy cost by balancing energy lost to shear stress