Computational forecasting of arterial blockages in a virtual patient has the potential to provide the next generation of advanced clinical monitoring aids for stroke prevention. As a first step towards a physiologically realistic virtual patient, we have created a computer model investigating the effects of emboli (particles or gas bubbles) as they become lodged in the brain. Our model provides a framework for predicting the severity of microvascular obstruction by simulating fundamental interactions between emboli and the fractal geometry of the arterial tree through which they travel. The model vasculature consisted of a bifurcating fractal tree comprising over a million branches ranging between 1 mm and 12 µm in diameter. Motion of emboli through the tree was investigated using a Monte Carlo simulation to evaluate the effects of the embolus size, clearance time and embolization rate on the number and persistence of blocked arterioles. Our simulations reveal with striking clarity that the relationship between embolus properties and vascular obstruction is nonlinear. We observe a rapid change between free-flowing and severely blocked arteries at specific combinations of the embolus size and embolization rate. The model predicts distinct patterns of cerebral injury for solid and gaseous emboli which are consistent with clinical observations. Solid emboli are predicted to be responsible for focal persistent injuries, while fast-clearing gas emboli produce diffuse transient blockages similar to global hypoperfusion. The impact of solid emboli was found to be dramatically reduced by embolus fragmentation. Computer simulations of embolization provide a novel means of investigating the role of emboli in producing neurological injury and assessing effective strategies for stroke prevention.