The reservoir pressure concept: the 3-element windkessel model revisited? Application to the Asklepios population study

• Published in: Journal of engineering mathematics Vol. 64; no. 4; pp. 417 - 428
• Main Authors: Vermeersch, S. J., Rietzschel, E. R., De Buyzere, M. L., Van Bortel, L. M., Gillebert, T. C., Verdonck, P. R., Segers, P.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.08.2009
• Subjects: Applications of Mathematics; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Theoretical and Applied Mechanics; Pulse pressure; Hemodynamics; Arterial stiffness; Arterial system; Modeling; Wave reflection
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-009-9286-y

Traditionally the arterial system is either modeled as a lumped-parameter windkessel or a wave system. Recently, a hybrid model has been proposed in which the arterial system is considered to be a reservoir allowing for superimposed wave phenomena. This approach was applied to non-invasively obtained carotid pressure waveforms from 2019 subjects from the Asklepios population to investigate the contribution of reservoir pressure ( PP res,WS ) to carotid pulse pressure ( PP car ) with age and gender. Additionally, reservoir pressures were compared to the reservoir pressure ( PP res,WK ) obtained from a 3-element windkessel model. PP res,WK and PP res,WS were determined by applying a 3-element windkessel model and the wave separation model to scaled carotid artery tonometry readings. The evolution of PP car , PP res,WK and PP res,WS was examined for men and women after stratification into age quartiles. PP car increased with age regardless of sex, but was more pronounced in women, with significant ( P  < 0.001) age–gender interaction. PP res increases with age ( P  < 0.001), regardless of the model used for its determination, but more significantly for women. In men it only increases markedly in the oldest age group. Overall, the reservoir pressure concept showed large similarities to the classical 3-element windkessel model, especially in subjects characterized by a high reflection magnitude and high “windkesselness” of their arterial system. When applied to the Asklepios population, both models show the increase of pulse pressure with age to be largely due to increasing reservoir pressures.