A theoretical analysis of hemodynamic and biomechanical alterations in intracranial AVMs after radiosurgery

Stereotactic radiosurgery is being increasingly used to treat intracranial arteriovenous malformations (AVMs). However, successful radiosurgery may involve latent periods of 1-2 years prior to AVM obliteration. This latent period include states of altered flow patterns that may or may not influence hemorrhage probabilities. The probability of hemorrhage is likely to be related to the degree of biomechanical stress across the AVM shunt walls. This paper describes a theoretical analysis of the altered hemodynamics and biomechanical stresses within AVM shunts post-radiosurgery.

The mathematical model is comprised of linked flow compartments that represent the AVM and adjacent normal vasculature. As obliteration of the irradiated shunts occur, changes in flow rates and pressure gradients are calculated based on first order fluid dynamics. Stress on the AVM shunt walls is calculated based on tangential forces due to intramural pressure. Two basic models are presented: a distribution of shunts with fixed thin walls subject to step-function obliteration (Model I), and a distribution of shunts subject to luminal obliteration from slowly thickening walls (Model II). Variations on these models are analyzed, including sequential, selective and random shunt obliteration, and uniform or Poisson distributions of shunt radii.

Model I reveals that the range of pressure alterations in the radiosurgically-treated AVM include the possibility of transient increases in the total biomechanical stress within the shunt walls prior to obliteration. Model II demonstrates that uniform luminal narrowing via thickened walls should lead to reduced transmural stresses. The precise temporal pattern of AVM flow decrease and biomechanical stress reduction depends on the selection of shunts that are obliterated.

(a) The hemodynamic and biomechanical changes appear to be relatively independent of the shunt distribution but highly dependent on the temporal pattern of the obliterative process, (b) uniformly thickened shunt walls should uniformly decrease biomechanical stresses in the latent period prior to complete obliteration, but if uniform obliteration is not achieved, (c) transient alterations in pressure versus stress relationships may lead to temporarily increased biomechanical stress prior to complete obliteration, and (d) reduction in stress may not reach significant levels until the AVM is almost completely obliterated.