A BIOMATHEMATICAL MODEL OF INTRACRANIAL ARTERIOVENOUS-MALFORMATIONS BASED ON ELECTRICAL NETWORK ANALYSIS - THEORY AND HEMODYNAMICS

HEMODYNAMICS PLAY A significant role in the propensity of intracranial arteriovenous malformations (AVMs) to hemorrhage and in influencing b oth therapeutic strategies and their complications. AVM hemodynamics a re difficult to quantitate, particularly within or in close proximity to the nidus. Biomathematical models represent a theoretical method of investigating AVM hemodynamics but currently provide limited informat ion because of the simplicity of simulated anatomic and physiological characteristics in available models. Our purpose was to develop a new detailed biomathematical model in which the morphological, biophysical , and hemodynamic characteristics of an intracranial AVM are replicate d more faithfully. The technique of electrical network analysis was us ed to construct the biomathematical AVM model to provide an accurate r endering of transnidal and intranidal hemodynamics. The model represen ted a complex, noncompartmentalized AVM with 4 arterial feeders (with simulated pial and transdural supply), 2 draining veins, and a nidus c onsisting of 28 interconnecting plexiform and fistulous components. Si mulated vessel radii were defined as observed in human AVMs. Common va lues were assigned for normal systemic arterial pressure, arterial fee der pressures, draining vein pressures, and central venous pressure. U sing an electrical analogy of Ohm's law, flow was determined based on Poiseuille's law given the aforementioned pressures and resistances of each nidus vessel. Circuit analysis of the AVM vasculature based on t he conservation of flow and voltage revealed the flow rate through eac h vessel in the AVM network. Once the flow rate was established, the v elocity, the intravascular pressure gradient, and the wall shear stres s were determined. Total volumetric flow through the AVM was 814 ml/mi n. Hemodynamic analysis of the AVM showed increased flow rate, flow ve locity, and wall shear stress through the fistulous component. The int ranidal flow rate varied from 5.5 to 57.0 ml/min with an average of 31 .3 ml/min for the plexiform vessels and from 595.1 to 640.1 ml/min wit h an average of 617.6 ml/min for the fistulous component. The blood fl ow velocity through the AVM nidus ranged from 11.7 to 121.1 cm/s with an average of 66.4 cm/s for the plexiform vessels and from 446.9 to 48 0 dyne/cm(2) with an average of 463.5 dyne/cm(2) for the fistulous com ponent. The wall shear stress ranged in magnitude from 33.2 to 342.1 d yne/cm(2) with an average of 187.7 dyne/cm(2) for the plexiform vessel s and from 315.9 to 339.7 cm/s with an average of 327.8 cm/s for the f istulous component. The described novel biomathematical model characte rizes the transnidal and intranidal hemodynamics of an intracranial AV M more accurately than was possible previously. This model should serv e as a useful research tool for further theoretical investigations of intracranial AVMs and their hemodynamic sequelae.