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Cortical spreading depression and spreading depolarization (CSD) are waves of neuronal depolarization that spread across the cortex, leading to a temporary saturation of brain activity. They are associated to various brain disorders such as…
Spreading depression (SD) is a wave phenomenon in gray matter tissue. Locally, it is characterized by massive re-distribution of ions across cell membranes. As a consequence, there is a sustained membrane depolarization and tissue…
Ionic electrodiffusion and osmotic water flow are central processes in many physiological systems. We formulate a system of partial differential equations that governs ion movement and water flow in biological tissue. A salient feature of…
Mathematical modelling of ionic electrodiffusion and water movement is emerging as a powerful avenue of investigation to provide new physiological insight into brain homeostasis. However, in order to provide solid answers and resolve…
The stability of cortical function depends critically on proper regulation. Under conditions of migraine and stroke a breakdown of transmembrane chemical gradients can spread through cortical tissue. A concomitant component of this emergent…
It is essential to understand the complex structure of the human brain to develop new treatment approaches for neurodegenerative disorders (NDDs). This review paper comprehensively discusses the challenges associated with modelling the…
Coronary Microvascular Dysfunction (CMD) is characterized by impaired vasodilation and can lead to insufficient blood flow to the myocardium during stress or exertion, affecting millions of people globally. Despite their diagnostic value,…
In these companion papers, we study how the interrelated dynamics of sodium and potassium affect the excitability of neurons, the occurrence of seizures, and the stability of persistent states of activity. In this first paper, we construct…
Modeling and simulating how oxygen supply shapes neuronal excitability is crucial for advancing the understanding of brain function in pathological scenarios, such as ischemia. This condition is caused by a reduced blood supply, leading to…
A novel approach is adopted to model cerebrospinal fluid (CSF) flow in human perivascular spaces (PVSs) surrounding brain-penetrating arteries. It is proposed that the outer PVS boundary oscillates due to brain pulsations and the arterial…
Intrathecal (IT) injection is an effective way to deliver drugs to the brain bypassing the blood-brain barrier. To evaluate and optimize IT drug delivery, it is necessary to understand the cerebrospinal fluid (CSF) dynamics in the central…
Alzheimer's disease (AD) is a complex neurodegenerative disorder characterized by the progressive accumulation of misfolded proteins, leading to cognitive decline. This study presents a novel stochastic modelling approach to simulate the…
Determining brain hemodynamics plays a critical role in the diagnosis and treatment of various cerebrovascular diseases. In this work, we put forth a physics-informed deep learning framework that augments sparse clinical measurements with…
The theoretical basis of neuronal coding, associated with short term degradation in synaptic transmission, is a matter of debate in the literature. In fact, electrophysiological signals are commonly characterized as inversely proportional…
Alzheimer's Disease (AD) is a neurodegenerative condition characterized by diverse progression rates among individuals, with changes in cortical thickness (CTh) closely linked to its progression. Accurately forecasting CTh trajectories can…
Diffuse Correlation Spectroscopy (DCS) allows the label-free investigation of microvascular dynamics deep within living tissue. However, common implementations of DCS are currently limited to measurement depths of $\sim 1-1.5cm$, which can…
Spreading depolarization (SD) is a self-propagating wave of near-complete neuronal depolarization that is abundant in a wide range of neurological conditions, including stroke. SD was only recently documented in humans and is now considered…
Cerebral aneurysms are pathological dilations of intracranial arteries that can rupture with devastating consequences, including subarachnoid hemorrhage, stroke, and death. Accumulating evidence indicates that local hemodynamic forces play…
The neuronal circuit that controls obsessive and compulsive behaviors involves a complex network of brain regions (some with known involvement in reward processing). Among these are cortical regions, the striatum and the thalamus (which…
Diffusion models are important in tissue engineering as they enable an understanding of molecular delivery to cells in tissue constructs. As three-dimensional (3D) tissue constructs become larger, more intricate, and more clinically…