A mathematical model of the mechanical deformation of the carotid artery wall and its application to clinical data

The study of arterial wall mechanics, including the study of stresses and strains experienced by the vascular wall, is pivotal in our understanding of arterial physiology. In this paper, a mathematical model is provided describing the deformation of the arterial wall in terms of 6 parameters. Actual deformation waveforms were also obtained from the analysis of B-mode ultrasound image sequences of the carotid artery using block-matching. The mathematical model was fitted to the clinical data using nonlinear least squares to determine the 6 parameters for 6 different locations along the posterior and 6 along the anterior walls, on the interface between the lumen and the intima-media complex (L-IM). On the posterior wall, 6 locations were also investigated at the interface between the intima-media complex and the adventitia (IM-A) as well as at the adventitia-surrounding tissue (A-T) boundary. The root mean square error was low for all locations indicating a good fit of the proposed model to the clinical data. The amplitude of the deformation, expressed through parameter alpha, was significantly lower in the A-T interface compared to the other two interfaces. The time when the systolic peak occurs, expressed through parameter t
₁
, was significantly lower in the L-IM interface compared to the other two interfaces. Preliminary findings from a small group of diseased wall locations suggested that the parameters a, b and t1 were significantly different than healthy cases. This probably reflects alterations of arterial wall mechanics due to disease. This study showed that the proposed mathematical model is a satisfactory representation of the mechanical deformation of the carotid artery wall in the radial direction and can provide valuable information in the understanding of the mechanical behavior of the arterial wall.