Does the principle of minimum work apply at the carotid bifurcation: a retrospective cohort study
Richard J Beare1, Gita Das, Mandy Ren
1Stroke and Aging Research Group, Department of Medicine, Monash University, Australia.
Insights
The principle of minimum work, which suggests a specific ratio for artery sizes, may not apply to the carotid bifurcation. Further research is needed to understand the factors influencing carotid artery dimensions.
Area of Science:
- Vascular anatomy and hemodynamics
- Biomechanical principles in physiology
Background:
- Carotid bifurcation anatomy and geometry are implicated in carotid artery atherosclerosis.
- Disturbed blood flow patterns are linked to specific carotid bifurcation configurations.
- The principle of minimum work proposes a relationship between parent and daughter artery radii (exponent of 3) to minimize blood flow energy.
Purpose of the Study:
- To evaluate if extracranial carotid artery bifurcation dimensions adhere to the principle of minimum work.
- To investigate the relationship between parent and daughter vessel radii at the carotid bifurcation.
Main Methods:
- Computed tomographic angiography (CTA) data from 45 participants (2006-2007) were analyzed.
- Radii of the common, internal, and external carotid arteries were measured.
- The exponent relating vessel radii was determined using numerical methods and nonlinear regression.
Main Results:
- The study included 45 participants (mean age 56.9 years, 26 males) with common vascular risk factors.
- Calculated exponents ranged from 1.3 to 1.6, varying with estimation methods.
- These values deviate significantly from the proposed exponent of 3.
Conclusions:
- The principle of minimum work (exponent of 3) may not be applicable to the carotid bifurcation.
- Other factors likely influence the relationship between parent and daughter vessel radii at this site.
- Further investigation is required to elucidate the determinants of carotid bifurcation dimensions.
Background:
There 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.
Methods:
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.
Results:
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.
Conclusions:
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.
