Computational models to study the perfusion of the brain under healthy conditions and in neurological disorders

As the energy storage capacity of the brain is limited, a robust blood and oxygen supply is
indispensable for its well-functioning. This aspect is further underlined because microvascular
alterations play an important role during pathologies. However, experimentally quantifying
the isolated impact of specific vascular alterations is challenging but well-suited for in silico
modeling. In this context, I will present three exemplary projects, including the underlying
numerical models, that show how in silico modeling goes beyond what is accessible to in vivo
experiments.
The basis for these projects is a 1D blood flow model applicable to realistic microvascular
networks. The model’s unique feature is a discrete RBC tracking algorithm, that allows us to
study the impact of the blood’s bi-phasic characteristics in a computationally efficient
manner. Within the first project, this model is employed to quantify the impact of vascular
alterations as observed during aging.
In the second project, our blood flow model is combined with an inverse model to predict
diameter changes necessary to locally up-regulate flow. The inverse model employs a
hierarchical regularization strategy to identify the most suitable from an otherwise
ambiguous solution. By constraining the vessel type that can change its diameter we generate
insights on the role of capillary dilations in regulating flow in the brain.
A slightly altered version of this inverse model has been used to align our in silico simulations
to in vivo blood velocity measurements. Additionally, the 1D blood flow model has been
extended to describe vessel diameter changes in response to changes in inflow pressure. This
process is called cerebral autoregulation and aims at maintaining cerebral blood flow constant
despite variations in inflow pressure. This framework is employed in the context of ischemic
stroke to quantify the role of vascular anastomoses, i.e., vascular loops, and to study the loss
of autoregulatory capacity