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 both therapeutic strategies and their complications. AVM hemodynamics are 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 information 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 replicated more faithfully. The technique of electrical network analysis was used to construct the biomathematical AVM model to provide an accurate rendering of transnidal and intranidal hemodynamics. The model represented a complex, noncompartmentalized AVM with 4 arterial feeders (with simulated pial and transdural supply), 2 draining veins, and a nidus consisting of 28 interconnecting plexiform and fistulous components. Simulated vessel radii were defined as observed in human AVMs. Common values were assigned for normal systemic arterial pressure, arterial feeder pressures, draining vein pressures, and central venous pressure. Using 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 the conservation of flow and voltage revealed the flow rate through each vessel in the AVM network. Once the flow rate was established, the velocity, the intravascular pressure gradient, and the wall shear stress were determined. Total volumetric flow through the AVM was 814 ml/min. Hemodynamic analysis of the AVM showed increased flow rate, flow velocity, and wall shear stress through the fistulous component. The intranidal flow rate varied from 5.5 to 57.0 ml/min with and average of 31.3 ml/min for the plexiform vessels and from 595.1 to 640.1 ml/min with an average of 617.6 ml/min for the fistulous component. The blood flow 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 480 dyne/cm2 with an average of 463.5 dyne/cm2 for the fistulous component. The wall shear stress ranged in magnitude from 33.2 to 342.1 dyne/cm2 with an average of 187.7 dyne/cm2 for the plexiform vessels and from 315.9 to 339.7 cm/s with an average of 327.8 cm/s for the fistulous component. The described novel biomathematical model characterizes the transnidal and intranidal hemodynamics of an intracranial AVM more accurately than was possible previously. This model should serve as a useful research tool for further theoretical investigations of intracranial AVMs and their hemodynamic sequelae.