Computational modelling of global haemodynamics and its interaction with cerebrospinal fluid and brain dynamics with application to essential hypertension

Two major medical applications have inspired this thesis: firstly, the potential link between the venous circulation and several neurological pathologies, secondly arterial hypertension. The work presented in this thesis consists of a multiscale model of the global, arterio-venous circulation in the entire human body. The present model represents an enhanced version of the original Müller-Toro mathematical model. It includes one-dimensional, nonlinear PDE systems for major blood vessels and zero-dimensional, differential-algebraic systems for the remaining components. Highlights include the viscoelastic, rather than purely elastic, models for all blood vessels, arterial and venous; total control of blood volume, including both the stressed and unstressed components; a physiological distribution of vas- cular compliance; a nonlinear representation of venous resistances and compliances; myogenic mechanism of cerebral blood regulation; baroreflex control of arterial pressure. Concerning the first medical topic, we couple the circulation to a refined description of the cerebrospinal fluid (CSF) dynamics in the craniospinal cavity. Two versions of the CSF model are presented; both versions account for deforma-tions and interaction between the cerebral vasculature, brain parenchyma and CSF compartments during the cardiac cycle. The first one includes all major CSF pathways and the brain parenchyma represented by zero-dimensional lumped-parameter models. The linear character of intracranial compliant compartments is considered together with a classical version of the Monro-Kellie hypothesis, which states that intracranial volume inside the skull is constant over time. The second version comprises zero-dimensional lumped-parameter models for the cranial CSF and a one-dimensional co-axial model for the spinal CSF and the spinal cord. The nonlinear behaviour of the pressure-volume curves of the CSF compartments is introduced at the level of the spinal subarachnoid space and into a relaxed version of the Monro-Kellie doctrine which admits almost constant intracranial volume in the cranial space; the exponential-like character of the pressure-volume relationship is tested through an injection of fluid into the cranial subarachnoid space. The coupled models are validated through comparison of computational results against published data and MRI measurements. We present two medical scenarios: (i) transverse sinus stenoses and their relation to Idiopathic Intracranial Hypertension; (ii) extra-cranial venous strictures, their impact in the inner ear circulation and its implica-tions for Ménière’s disease. We will computationally show that intracranial pressure is the result of a dynamic inter-action between the CSF production, the arterial pulsation, the venous reabsorption of CSF and the ability of the spinal subarachnoid space in accommodating the displaced CSF from the cranial spaces. This interaction is reflected in the intracranial pressure waveform with its physiological landmark peaks, both in healthy and pathological conditions. The second topic of this thesis concerns a computational study on arterial hypertension in the context of a global model. Such an approach poses the need of controlling the total amount of blood volume in the circulatory system, as well as how it is distributed between different vascular districts by means of vascular compliance and unstressed volumes. To this end, total effective vascular compliance is determined in silico in a healthy subject by performing an infusion test of 500 ml of blood in four minutes. By means of presented computational results, we will show that effective total vascular compliance is the result of the interaction between the assigned constant physical vascular com-pliance and the capacity of the cardiovascular system to adapt to new situations via regulatory mechanisms. Focusing on arterial hypertension, the global model of the entire circulation is adapted to reproduce alterations in the cardiovas-cular system that are the cause and/or consequence of the hypertensive state. Adaptation does not only affect large systemic arteries and the heart but also the microcirculation, the pulmonary circulation and the venous system. Using a global closed-loop model allows us to establish the interplay between different blood compartments and their role in the progression of the disease. We will observe that the hypertensive state is mainly determined by the combined effects of increased arterial resistance and reduced venous compliance; the last one plays an essential role in preserving cardiac output and stroke volume in case of left ventricular hypertrophy, as well as in blood volume distribution in the hypertensive subject. Addressing arterial hypertension with a global closed-loop model of such complexity poses the basis for a more comprehensive study of this pathology and opens the way to a wide range of potential applications.