Equation for model intracranial aneurysm with consideration of small dissipation term

An electric circuit model of a ‘model intracranial aneurysm’ has been developed from previous experimental work showing a non linear pressure-volume relationship. This leads to a revised formulation of the following non linear differential equation which simulates the response of the model aneurysm to a pulsatile driving function

$\text{V}\text{?}\text{+?}\text{υ}\text{?}\text{+ζmυ+ξnυ}{}^2\text{=F cos(ωt + B)}$

, where V = velocity of flow within the aneurysm.Solution of this equation using the principle of harmonic balance shows that discontinuous jumps in amplitude of velocity of flow leading to turbulence or increased turbulence can occur with an increase in pulse rate or pulse pressure. It is postulated that turbulence is dangerous due to both the large increase in velocity of flow and also due to the possible stasis effect on large molecules and platelets from eddy formation.