Arteriovenous malformation in the brain: a theoretical study explaining the behavior of liquid embolic agents during endovascular treatment.

There is no theoretical study on blood flow in brain arteriovenous malformation (AVM). We present a numerical theory on AVM and liquid embolic agent AVM embolization. Darcy's law was used to compute flow relations for brain AVMs. Maag's formula was used to explain the diffuse patterns of N-butyl-2-cyanoacrylate (NBCA) and ethylene-vinyl alcohol copolymer (EVOH) in brain AVMs. According to Darcy's law, the instantaneous blood flow rate through an AVM is directly proportional to the pressure drop between two places in the AVM and indirectly proportional to the distance between them. The greater the pressure gradient (through the AVM), the greater the discharge rate, and the discharge rate of blood will often differ through different AVM (or even through the same AVM, in a different direction) even if the same pressure gradient exists in both cases. Subsequent to Darcy's initial discovery, Maag found that the radius of NBCA or EVOH diffusion is inversely proportional to their viscosity. Darcy's Law and Maag's formula could be used to analyze flow patterns of brain AVM and liquid embolic agent behavior in AVM near ideal.