Effect of heart rate on aortic pulse wave velocity is modulated by wall viscoelasticity: a modelling study

Objective: Acute controlled increase in heart rate (HR) as obtained by cardiac pacing have been shown to be associated with increase in aortic PWV as measured between the carotid and femoral sites [1]. In the absence of any active neurogenic influence on smooth muscle tone, the dependency of PWV on HR has been suggested to be due to the passive dynamic and viscoelastic properties of the artery wall. This study investigates this phenomenon by simulating pulse wave propagation in a model of the aortic trunk where wall viscoelasticity is described by a complex elastic modulus and where both the real and imaginary parts are frequency dependent. Methods: The model of the aortic trunk consisted of 5 segments simulating the effective path length over which aortic PWV is conventionally measured. The input flow is determined by a cardiac pump simulated by a time varying elastance. Each segment is described in terms of transmission line components with non-linear frequency ([omega]) dependent capacitance and resistance which simulate the complex elastic modulus (E*([omega])) in terms of a dynamic elastic modulus (Ed([omega])) and a viscous dissipation term ([eta]([omega])) (E*([omega]) = Ed([omega]) + j[omega][eta]([omega])). Initial values for Ed([omega]) and [eta]([omega]) were obtained from early studies of Leroyd and Taylor [2] and model parameters were optimized by using the pacing data of Lentelme et al [1] for HR values of 60, 70, 80, 90 and 100 b/min. Results: An increase in PWV of 10.9% between HR of 60 and 100 b/min as found in the pacing studies, was simulated by an average increase of 5.9% increase in Ed([omega]) and 20.2% increase in [eta]([omega]) over the physiological frequency range (0-15Hz). No HR dependency of PWV was found when a real and frequency independent value of elastic modulus was used for the aortic segments. Conclusions: Simulation studies show that HR dependency of PWV is regulated by both the frequency dependency of the dynamic elastic modulus as well as the viscoelastic dissipative constant. For given change in HR, the wall viscoelasticity has a 3 fold contribution to the change in PWV compared to the wall elastic modulus. [1] Lantelme P et al. Hypertension. 2002; 39: 1083-1087. [2]. Learoyd BM, Taylor MG. Circulation Research. 1966; 18(3): 278-292