Abstract
The aim of this study is to evaluate the relative importance of elastic non-linearities, viscoelasticity and resistance vessel modelling on arterial pressure and flow wave contours computed with distributed arterial network models. The computational results of a non-linear (time-domain) and a linear (frequency-domain) mode were compared using the same geometrical configuration and identical upstream and downstream boundary conditions and mechanical properties. Pressures were computed at the ascending aorta, brachial and femoral artery. In spite of the identical problem definition, computational differences were found in input impedance modulus (max. 15–20%), systolic pressure (max. 5%) and pulse pressure (max. 10%). For the brachial artery, the ratio of pulse pressure to aortic pulse pressure was practically identical for both models (3%), whereas for the femoral artery higher values are found for the linear model (+10%). The aortic/brachial pressure transfer function indicates that pressure harmonic amplification is somewhat higher in the linear model for frequencies lower than 6 Hz while the opposite is true for higher frequencies. These computational disparities were attributed to conceptual model differences, such as the treatment of geometric tapering, rather than to elastic or convective non-linearities. Compared to the effect of viscoelasticity, the discrepancy between the linear and non-linear model is of the same importance. At peripheral locations, the correct representation of terminal impedance outweights the computational differences between the linear and non-linear models.
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References
Avolio, A. P. (1980): ‘Multi-branched model of the human arterial system,’Med. Biol. Eng. Comput.,18, pp. 709–718
Bergel, D. H. (1969): ‘The viscoelastic properties of the arterial walls. PhD thesis, University of London
Hardung, V. (1953): ber eine Methode zur Messung der dynamischen Elasticitt und Viskositt von Blutgefssen, Kautchuk und synthetischen Elastomeren,’Helv. Physiol. Acta,11, pp. 194–211
Holenstein, R., Niederer, P., Anliker, M. (1980) ‘A viscoelastic model for use in predicting arterial pulse waves,’J. Biomech. Eng.,102, pp. 318–325
Karamanoglu, M., Gallagher, D. E., Avolio, A. P., O’Rourke, M. F. (1994): ‘Functional origin of reflected pressure waves in a multibranched model of the human arterial system,’Am. I. Physiol.,267, pp. H1681-H1688
Krus, P., Karlsson, M., Engval, J. ‘Modelling and simulation of the human arterial tree, using transmission line elements with viscoelastic walls,’ BED 1991Adv. Bioeng.,20, pp. 115–118
Langewouters, G. J., Wesseling, K. H., Goedhard, W. J. A. (1984): ‘The static elastic properties of 45 human thoracic and 20 abdominal aortas and the parameters of a new model,’J. Biomech.,17, pp. 425–435
Langewouters, G. J., Wesseling, K. H., Geodhard, W. J. A. (1985): ‘The pressure dependent dynamic elasticity of 35 thoracic and 16 abdmonal human aortasin vitro described by a five component model,’J. Biomech.,18, pp. 613–620
Latham, R. D., Maj, M. C., Westerhof, N., Sipkema, P., Rubal, B. J., Reuderink, P., Murgo, J. P. (1985): ‘Regional wave travel and reflections along the human aorta: a study with six simultaneous micromanometric pressures,’Circulation,72, pp. 1257–1269
Learoyd, B. M., Taylor, M. G. (1966): ‘Alterations with age in the viscoelastic properties of human arterial walls,’Cir. Res. 18, pp. 278–291
Mills, C. J., Gabe, T., Gault, J. H., Mason, D. T., Ross, J., Braunwald, E., Shillingford, J. P. (1970): ‘Pressure-flow relationships and vascular impedance in man,’Cardiovasc. Res.,4, 405–417
Milnor, W. R. (1989): ‘Hemodynamics.’ Second ed. (Williams & Wilins, Baltimore).
Murgo, J. P., Westerhof, N., Giolma, J. P., Altobelli, S. A. (1980): ‘Aortic input impedance in normal man: relationship to pressure wave forms,’Circulation,62 (1), pp. 105–116
Reuderink, P. J., Hoogstraten, H. W., Sipkema, P., Hillen, B., Westerhof, N. (1989): ‘Linear and nonlinear one-dimensional models of pulse wave transmission at high Womersley numbers,’J. Biomech.,22, pp. 819–827
Reuderink, P. J., van de Vosse, F. N., van Steenhoven, A. A., van Dongen, M. E. H., Janssen, J. D. (1993): ‘Incompressible low-speed-ratio in non-uniform distensible tubes,’Int. J. Num. Meth. Fluids,16, pp. 597–612
Schaaf, B. W., Abbrecht, P. H. (1972): ‘Digital computer simulation of human systemic arterial pulse wave transmission: a nonlinear model,’J. Biomech.,5, 345–364
Sheng, G., Sarwal, S. N., Watts, K. C., Mable, A. E. (1995): ‘Computational simulation of blood flow in human systemic circulation incorporating an external force field,’Med. Biol. Eng. Comput.,33, pp. 8–17
Snyder, M. F., Rideout, V. C., Hillest, R. J. (1968): ‘Computer modelling of the human systemic arterial tree,’J. Biomech.,1, pp. 341–353
Stergiopulos, N., Young, D. F., Rogge, T. R. (1992): ‘Computer simulation of arterial flow with applications to arterial and aortic stenoses,’J. Biomech.,25 (12), pp. 1477–1488
Stergiopulos, N., Meister, H., Westerhof, N. (1995): ‘Evaluation of methods for the estimation of total arterial compliance,’Am. J. Physiol.,268, pp. H1540-H1548
Wemple, R. R., Mockros, I. F., ‘Pressure and flow in the systemic arterial system,’J. Biomech.,5, pp. 629–641
Westerhof, N., Bosman, E., de Vries, C. J., Noordergraaf, A. (1969): ‘Analog studies of the human systemic arterial tree,’J. Biomech.,2, pp. 121–143
Westerhof, N., Noordergraaf, A., (1970): ‘Arterial viscoelasticity: a generalised model. Effect on impedance and wave travel in the systemic tree,’J. Biomech.,3, pp. 357–379
Wesseling, K. H., Weber, H., de Wit, B. (1973): ‘Estimated five component viscoleastic model parameters for human arterial walls,’J. Biomech.,6, pp. 13–24
Womersley, J. R. (1957): ‘An elastic tube theory of pulse transmission and oscillatory flow in mammalian arteries.’ Wright Air Development Centre, Technical Report WADC-TR 56-614
Young, D. F., Tsai, F. (1973): ‘Flow characteristics in models of arteriol stenoses-II. Unsteady flow,’J. Biomech.,6, 547–559
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Segers, P., Stergiopulos, N., Verdonck, P. et al. Assessment of distributed arterial network models. Med. Biol. Eng. Comput. 35, 729–736 (1997). https://doi.org/10.1007/BF02510985
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DOI: https://doi.org/10.1007/BF02510985