An electrical network model of intracranial arteriovenous malformations: analysis of variations in hemodynamic and biophysical parameters.

The propensity of intracranial arteriovenous malformations (AVMs) to hemorrhage is correlated significantly with their hemodynamic features. Biomathematical models offer a theoretical approach to analyse complex AVM hemodynamics, which otherwise are difficult to quantify, particularly within or in close proximity to the nidus. Our purpose was to investigate a newly developed biomathematical AVM model based on electrical network analysis in which morphological, biophysical, and hemodynamic characteristics of intracranial AVMs were replicated accurately. Several factors implemented into the model were altered systematically to study the effects of a possible wide range of normal variations in AVM hemodynamic and biophysical parameters on the behavior of this model and its fidelity to physiological reality. The model represented a complex, noncompartmentalized AVM with four arterial feeders, two draining veins, and a nidus consisting of 28 interconnected plexiform and fistulous components. Various clinically-determined experimentally-observed, or hypothetically-assumed values for the nidus vessel radii (plexiform: 0.01 cm-0.1 cm; fistulous: 0.1 cm-0.2 cm), mean systemic arterial pressure (71 mm Hg-125 mm Hg), mean arterial feeder pressures (21 mm Hg-80 mm Hg), mean draining vein pressures (5 mm Hg-23 mm Hg), wall thickness of nidus vessels (20 microns-70 microns), and elastic modulus of nidus vessels (1 x 10(4) dyn/cm2 to 1 x 10(5) dyn/cm2) were used as normal or realistic ranges of parameters implemented in the model. Using an electrical analogy of Ohm's law, flow was determined based on Poiseuille's law given the aforementioned pressures and resistance of each nidus vessel. Circuit analysis of the AVM vasculature based on the conservation of flow and voltage revealed the flow rate through each vessel in the AVM network. An expression for the risk of AVM nidus rupture was derived based on the functional distribution of the critical radii of component vessels. The two characteristics which were used to judge the fidelity of the theoretical performance of the AVM model against the physiological one of human AVMs were total volumetric flow through the AVM (< or = 900 ml/min), and its risk of rupture (< 100%). Applying these criteria, a series of 216 (out of 260) AVM models using different combinations of these hemodynamic and biophysical parameters resulted in a physiologically-realistic conduct of the model (yielding a total flow through the AVM model varying from 449.9 ml/min to 888.6 ml/min, and a maximum risk of rupture varying from 26.4 to 99.9%). The described novel biomathematical model characterizes the transnidal and intranidal hemodynamics of an intracranial AVM more accurately than previously possible. A wide range of hemodynamic and biophysical parameters can be implemented in this AVM model to result in simulation of human AVMs with differing characteristics (e.g. low-flow and high-flow AVMs). This experimental model should serve as a useful research tool for further theoretical investigations of a variety of intracranial AVMs and their hemodynamic sequelae.