Mathematical Modelling Of The Biomechancial Progression Of Ischemic Stroke And Penumbra

Stroke is a major disease that seriously threatens human health,which has a high incidence,high mortality,and high disability rate.The prevention and treatment of stroke,especially ischemic stroke,has always been a hot spot in clinical research.Ischemic stroke accounts for about 87% of all strokes,it is mainly due to the reduction of local or global cerebral perfusion.The lack of oxygen supply results in a series of ischemic cascades,leading to loss of some functions.In this process,some cells maintain a certain degree of blood perfusion due to the presence of collateral circulation,and they are in a failure of function,but the state of injury is reversible.This region is called the penumbra that is often surrounding an ischemic event such as thrombotic or embolic stroke.Penumbra is a key target to be rescued in the treatment of ischemic stroke.It is generally considered that the penumbra only exists within a short timewindow of 3 to 4.5 hours,therefore a better understanding the dynamic evolution of the penumbra is of great significance in the prevention and treatment of ischemic stroke.Based on the biomechanical modeling method,a hybrid model taking into account of brain microcirculation and ion activity is established to simulate the changes of brain tissue pathophysiological activity and the dynamic progression of penumbra following ischemic stroke as well as the response after treatments.The brain microvascular network model was based on anatomical microscopic images;the brain microcirculation model was a hemodynamic coupling model of intravascular blood flow-transmural infiltration-interstitial fluid flow and oxygen transport based on the convection-diffusion equation.The ion activity model is a reaction-diffusion model calculated by the coupling relationship between ion channel current,ion concentration,and cell volume changes.The ion activity model is related to the microcirculation model through oxygen concentration.The distribution of various parameters such as blood pressure,blood flow velocity,oxygen concentration,and ion concentration can be obtained.According to the ion concentration,the simulation region was divided into penumbra and necrotic cores,and the dynamic process of the penumbra can be visually displayed.By setting the arterial inlet pressure,the process of ischemic stroke caused by arterial inlet blockage and reperfusion therapy at different time after ischemia was also simulated.The physiological and pathological parameters and the evolution of penumbra in these two cases were simulated.The results show that in the course of ischemia,the penumbra area gradually expands,but is eventually converted to a necrotic core without treatment.The earlier the time of reperfusion therapy,the better the treatment effects,indicating that “time is the brain".The results provide a theoretical basis for a series of physiological and pathological phenomena such as the existence of collateral circulation,treatment time window,and so on,which may act as a useful tool for treatment plan and optimization in patients with ischemic stroke.