Effects of friction and nonlinearities on the separation of arterial waves into their forward and backward components

In this paper we examine the importance of fluid friction and nonlinearities due to the area-pressure relationship and to the convective acceleration on the separation of arterial pressure and flow waves into their forward and backward components. Experiments were run in straight uniform nonlinearly elastic tubes. Different degrees of fluid friction and nonlinearities, covering the physiological range, have been tested. We predicted the forward and backward running pressure components using two wave separation methods: the classical linear method (Westerhof et al., Cardiovasc. Res, 6,648-656, 1972) and the first order correction (FOC) method (Pythoud et al., Trans ASME J. Biomech. Engng, in press) which takes nonlinearities and fluid friction into account. We found that the two methods yield somewhat different predictions. The differences tend to increase with the degree of fluid friction and nonlinearities and are typically of the order of 4-8%. We further compared the transmission ratio of forward and backward waves predicted by both methods. The transmission ratio was found to be overestimated by 10% by the classical linear method. The nonlinear method gave more accurate estimates, consistent with theory. We conclude that, for in vivo applications, the classical linear method should be the method of choice because it is simpler to use and the erros involved (4-8%) are comparable to measurement erros.