Modelling Blood Flow and Metabolism in the Preclinical Neonatal Brain during and Following Hypoxic-Ischaemia

Hypoxia-ischaemia (HI) is a major cause of neonatal brain injury, often leading to long-term damage or death. In order to improve understanding and test new treatments, piglets are used as preclinical models for human neonates. We have extended an earlier computational model of piglet cerebral physiology for application to multimodal experimental data recorded during episodes of induced HI. The data include monitoring with near-infrared spectroscopy (NIRS) and magnetic resonance spectroscopy (MRS), and the model simulates the circulatory and metabolic processes that give rise to the measured signals. Model extensions include simulation of the carotid arterial occlusion used to induce HI, inclusion of cytoplasmic pH, and loss of metabolic function due to cell death. Model behaviour is compared to data from two piglets, one of which recovered following HI while the other did not. Behaviourally-important model parameters are identified via sensitivity analysis, and these are optimised to simulate the experimental data. For the non-recovering piglet, we investigate several state changes that might explain why some MRS and NIRS signals do not return to their baseline values following the HI insult. We discover that the model can explain this failure better when we include, among other factors such as mitochondrial uncoupling and poor cerebral blood flow restoration, the death of around 40% of the brain tissue. Copyright

Multiphysics simulation of a microfluidic perfusion chamber for brain slice physiology

Understanding and optimizing fluid flows through in vitro microfluidic perfusion systems is essential in mimicking in vivo conditions for biological research. In a previous study a microfluidic brain slice device (μBSD) was developed for microscale electrophysiology investigations. The device consisted of a standard perfusion chamber bonded to a polydimethylsiloxane (PDMS) microchannel substrate. Our objective in this study is to characterize the flows through the μBSD by using multiphysics simulations of injections into a pourous matrix to identify optimal spacing of ports. Three-dimensional computational fluid dynamic (CFD) simulations are performed with CFD-ACE + software to model, simulate, and assess the transport of soluble factors through the perfusion bath, the microchannels, and a material that mimics the porosity, permeability and tortuosity of brain tissue. Additionally, experimental soluble factor transport through a brain slice is predicted by and compared to simulated fluid flow in a volume that represents a porous matrix material. The computational results are validated with fluorescent dye experiments

Numerical Modeling of Fluid Flow in Solid Tumors

A mathematical model of interstitial fluid flow is developed, based on the application of the governing equations for fluid flow, i.e., the conservation laws for mass and momentum, to physiological systems containing solid tumors. The discretized form of the governing equations, with appropriate boundary conditions, is developed for a predefined tumor geometry. The interstitial fluid pressure and velocity are calculated using a numerical method, element based finite volume. Simulations of interstitial fluid transport in a homogeneous solid tumor demonstrate that, in a uniformly perfused tumor, i.e., one with no necrotic region, because of the interstitial pressure distribution, the distribution of drug particles is non-uniform. Pressure distribution for different values of necrotic radii is examined and two new parameters, the critical tumor radius and critical necrotic radius, are defined. Simulation results show that: 1) tumor radii have a critical size. Below this size, the maximum interstitial fluid pressure is less than what is generally considered to be effective pressure (a parameter determined by vascular pressure, plasma osmotic pressure, and interstitial osmotic pressure). Above this size, the maximum interstitial fluid pressure is equal to effective pressure. As a consequence, drugs transport to the center of smaller tumors is much easier than transport to the center of a tumor whose radius is greater than the critical tumor radius; 2) there is a critical necrotic radius, below which the interstitial fluid pressure at the tumor center is at its maximum value. If the tumor radius is greater than the critical tumor radius, this maximum pressure is equal to effective pressure. Above this critical necrotic radius, the interstitial fluid pressure at the tumor center is below effective pressure. In specific ranges of these critical sizes, drug amount and therefore therapeutic effects are higher because the opposing force, interstitial fluid pressure, is low in these ranges

Multiplicity of cerebrospinal fluid functions: New challenges in health and disease

This review integrates eight aspects of cerebrospinal fluid (CSF) circulatory dynamics: formation rate, pressure, flow, volume, turnover rate, composition, recycling and reabsorption. Novel ways to modulate CSF formation emanate from recent analyses of choroid plexus transcription factors (E2F5), ion transporters (NaHCO3 cotransport), transport enzymes (isoforms of carbonic anhydrase), aquaporin 1 regulation, and plasticity of receptors for fluid-regulating neuropeptides. A greater appreciation of CSF pressure (CSFP) is being generated by fresh insights on peptidergic regulatory servomechanisms, the role of dysfunctional ependyma and circumventricular organs in causing congenital hydrocephalus, and the clinical use of algorithms to delineate CSFP waveforms for diagnostic and prognostic utility. Increasing attention focuses on CSF flow: how it impacts cerebral metabolism and hemodynamics, neural stem cell progression in the subventricular zone, and catabolite/peptide clearance from the CNS. The pathophysiological significance of changes in CSF volume is assessed from the respective viewpoints of hemodynamics (choroid plexus blood flow and pulsatility), hydrodynamics (choroidal hypo- and hypersecretion) and neuroendocrine factors (i.e., coordinated regulation by atrial natriuretic peptide, arginine vasopressin and basic fibroblast growth factor). In aging, normal pressure hydrocephalus and Alzheimer's disease, the expanding CSF space reduces the CSF turnover rate, thus compromising the CSF sink action to clear harmful metabolites (e.g., amyloid) from the CNS. Dwindling CSF dynamics greatly harms the interstitial environment of neurons. Accordingly the altered CSF composition in neurodegenerative diseases and senescence, because of adverse effects on neural processes and cognition, needs more effective clinical management. CSF recycling between subarachnoid space, brain and ventricles promotes interstitial fluid (ISF) convection with both trophic and excretory benefits. Finally, CSF reabsorption via multiple pathways (olfactory and spinal arachnoidal bulk flow) is likely complemented by fluid clearance across capillary walls (aquaporin 4) and arachnoid villi when CSFP and fluid retention are markedly elevated. A model is presented that links CSF and ISF homeostasis to coordinated fluxes of water and solutes at both the blood-CSF and blood-brain transport interfaces

Symbolic numeric index analysis algorithm for differential algebraic equations

Mathematical modeling of dynamic chemical engineering systems such as flow-sheet simulation, transient analysis of reaction and separation networks, computational fluid dynamic, or control problems often leads to systems of differential-algebraic equations (DAEs). Knowing the index of a DAE is an important prerequisite for its consistent initialization and its numerical solution. For large sets of DAEs occurring in chemical engineering practice, index analysis requires computational procedures. This paper presents a new approach for automatic index analysis. Earlier index analysis algorithms were based on purely structural calculus. Unfortunately, structural methods may actually arbitrarily over- or underestimate the correct DAE index. To overcome the shortcomings of existing approaches, this paper proposes a novel algorithm expanding DAE analysis to include both symbolic and numerical information. The novel symbolic numerical analysis accounts for variable cancellation and processes linear expressions accurately. For the case of purely linear DAE, the new method is rigorous. For the general nonlinear DAE, the novel approach gives a more precise picture in most cases. The paper introduces the theory supporting the methodology and provides the proof of concept with small illustrative examples