Mathematical modeling of neurovascular coupling

Abstract: The brain is critically dependent on the continuous supply of oxygen and glucose, which is carried and delivered by blood. When a brain region is activated, metabolism of these substrates increases rapidly, but is quickly offset by a substantially higher increase in blood flow to that region, resulting in a brief oversupply of these substrates. This phenomenon is referred to as functional hyperemia, and forms the foundation of functional neuroimaging techniques such as functional Magnetic Resonance Imaging (fMRI), which captures a Blood Oxygen Level-Dependent (BOLD) signal. fMRI exploits these BOLD signals to infer brain activity, an approach that has revolutionized the research of brain function over the last 30 years. Due to the indirect nature of this measure, a deeper understanding of the connection between brain activity and hemodynamic changes — a neurovascular coupling (NVC) — is essential in order to fully interpret such functional imaging data. NVC connects the synaptic activity of neurons with local changes in cerebral blood flow, cerebral blood volume, and cerebral metabolism of oxygen, through a complex signaling network, consisting of multiple different brain cells which release a myriad of distinct vasoactive messengers with specific vascular targets. To aid with this complexity, mathematical modeling can provide vital help using methods and tools from the field of Systems Biology. Previous models of the NVC exist, conventionally describing quasi-phenomenological steps translating neuronal activity into hemodynamic changes. However, no mechanistic mathematical model that describe the known intracellular mechanisms or hypotheses underlying the NVC, and which can account for a wide variety of NVC related measurements, currently exists. Therefore, in this thesis, we apply a Systems Biology approach to develop such intracellular mechanisms based models using in vivo experimental data consisting of different NVC related measures in rodents, primates, and humans.Paper I investigates two widely discussed hypotheses describing the NVC: the metabolic feedback hypothesis, and the vasoactive feed-forward hypothesis. We illustrate through multiple model rejections that only a model describing a combination of the two hypotheses can capture the qualitative features of the BOLD signal, as measured in humans. This combined model can describe data used for training, as well as predict independent validation data not previously seen by the model before.Paper II extends this model to describe the negative BOLD response, where the blood oxygenation drops below basal levels, which is commonly observed in clinical and cognitive studies. The model explains the negative BOLD response as the result of neuronal inhibition, describing and adequately predicting experimental data from two different experiments.In Paper III, we develop a first model including the cell-specific contributions of GABAergic interneurons and pyramidal neurons to functional hyperemia, using data of optogenetic and sensory stimuli in rodents for both awake and anesthesia conditions. The model captures the effect of the anesthetic as purely acting on the neuronal level if a Michaelis-Menten expression is included, and it also correctly predicts data from experiments with different pharmacological inhibitors.Finally, in Paper IV, we extend the model in Paper III to describe and predict a majority of the relevant hemodynamic NVC measures using data from rodents, primates, and humans. The model suggests an explanation for observed bi-modal behaviors, and can be used to generate new insights regarding the underpinnings of other complicated observed behaviors. This model constitutes the most complete mechanistic model of the NVC to date.This new model-based understanding opens the door for a more integrative approach to the analysis of neuroimaging data, with potential applications in both basic science and in the clinic.