Mathematical modelling of haemorrhagic transformation within a multiscale microvasculature network.

Objective.Haemorrhagic transformation (HT) is one of the most common complications after ischaemic stroke, caused by damage to the blood-brain barrier (BBB) that could be the result of stroke progression or a complication of stroke treatment with reperfusion therapy. The aim of this study is to develop further a previous simple HT mathematical model into an enlarged multiscale microvasculature model in order to investigate the effects of HT on the surrounding tissue and vasculature. In addition, this study investigates the relationship between tissue displacement and vascular geometry.Approach.By modelling tissue displacement, capillary compression, hydraulic conductivity in tissue and vascular permeability, we establish a mathematical model to describe the change of intracranial pressure (ICP) surrounding the damaged vascular bed after HT onset, applied to a 3D multiscale microvasculature. The use of a voxel-scale model then enables us to compare our HT simulation with available clinical imaging data for perfusion and cerebral blood volume (CBV) in the multiscale microvasculature network.Main results. We showed that the haematoma diameter and the maximum tissue displacement are approximately proportional to the diameter of the breakdown vessel. Based on the voxel-scale model, we found that perfusion reduces by approximately13-17%andCBVreduces by around20-25%after HT onset due to the effect of capillary compression caused by increased interstitial pressure. The results are in good agreement with the limited experimental data.Significance. This model, by enabling us to bridge the gap between the microvascular scale and clinically measurable parameters, providing a foundation for more detailed validation and understanding of HT in patients.