**5. Conclusion**

212 Viscoelasticity – From Theory to Biological Applications

generalized viscoelastic model in GVM(2).

agreed well with the experimental results.

deformation compliance.

PP below 5%.

*Effect of the viscoelastic parameter* 

**4.3. Conclusion of this section** 

we can reach the following conclusions.

effect by viscoelasticity change.

PWV using the elastic model approximately agreed with the theoretical elastic tube velocity, since the viscosity of the tube was not included. Using the Voigt model, the small effect by the viscoelasticity on the increase in PWV and PWV was slightly larger than the theoretical elastic tube velocity; however, the calculated and experimental results agreed well with the

PP in the calculated results of the elastic model and the Voigt model was 90% of that in the experimental results. In the generalized viscoelastic model, the calculated results of GVM(2)

This results show that, with the influence of viscoelastic change shown in Fig. 18, PWV increased by around 20-30% more than theoretical elastic tube velocity and PP increased by approximately 10% because increasing the elastic modulus by the effect of the low frequency component of viscoelasticity is more effective than the energy dissipation effect by the high frequency component of viscoelasticity. Furthermore, it can be said that the increase of viscoelasticity compensated for the influence caused by the change in tube

The effect of the viscoelastic parameter was examined from the difference in the calculated results between GVM(2) and GVM(1) for the baseline internal pressure of 11.2 kPa. The dynamic modulus elasticity ratio of GVM(1) was nearly 10.1% lower than that of GVM(2) within 1–10 Hz, as shown in Fig. 18. By this effect, PWV using GVM(1) was 6.6% lower than that using GVM(2), as shown in Fig. 19, and PP with GVM(1) was 6.4% lower than that with GVM(2). Considering the results with a baseline internal pressure of 8.4kPa, the difference of PWV and PP caused by the viscoelastic parameters was almost proportional to the change of baseline internal pressure; therefore, it might be necessary to determine the dynamic modulus elasticity ratio with accuracy below 4% in order to keep the accuracy of PWV and

As described above, it was clarified that tube viscoelasticity played an important role in pulse wave propagation under periodic pulsatile conditions and had a significant effect on

Using the one-dimensional numerical simulation model of a viscoelastic tube, the effect of tube viscoelasticity on periodic pulse wave propagation was examined by comparing the experimental results with the calculated results with a viscoelastic silicone tube. As a result,

1. Numerical simulation using the generalized viscoelastic model can accurately express

2. When the dynamic modulus elasticity ratio increases, both PWV and PP increase, because increasing the elastic modulus is more effective than the energy dissipation

the experimental results with periodic pulsation of pressure waves.

clinical arterial stiffness indexes, including PWV and PP.

In this chapter, a nonlinear one-dimensional numerical model was constructed by including the effect of tube wall viscoelasticity and unsteady viscous resistance for numerical analysis of the viscoelastic tubes. This model can analyze the effect of viscoelasticity on intravascular flow that few previous papers have considered. Using a one-dimensional numerical simulation model of a viscoelastic tube, the effect of tube viscoelasticity on a pulsatile wave and periodic pulse wave propagation were examined by comparing the experimental results with the calculated results using a viscoelastic silicone tube.

Clinical blood vessel stiffness indexes vary with viscoelasticity change, because the elastic modulus is more effective than the energy dissipation effect by viscoelasticity change. This result showed that the viscoelasticity of the vessel wall plays an important role in the form of a pulsatile wave; therefore, it is important to consider the viscoelastic effect accurately in quantitative investigations using intravascular flow analysis.
