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Mathematical and Numerical Modeling of Healthy and Unhealthy Cerebral Arterial Tissues

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Computational fluid dynamics

Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid (liquids and gases) with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems.

Numerical weather prediction

Numerical weather prediction (NWP) uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of computer simulation in the 1950s that numerical weather predictions produced realistic results. A number of global and regional forecast models are run in different countries worldwide, using current weather observations relayed from radiosondes, weather satellites and other observing systems as inputs.

Endovascular coiling

Endovascular coiling is an endovascular treatment for intracranial aneurysms and bleeding throughout the body. The procedure reduces blood circulation to the aneurysm through the use of microsurgical detachable platinum wires, with the clinician inserting one or more into the aneurysm until it is determined that blood flow is no longer occurring within the space. It is one of two main treatments for cerebral aneurysms, the other being surgical clipping. Clipping is an alternative to stenting for bleeding.

Arterial blood gas test

An arterial blood gas (ABG) test, or arterial blood gas analysis (ABGA) measures the amounts of arterial gases, such as oxygen and carbon dioxide. An ABG test requires that a small volume of blood be drawn from the radial artery with a syringe and a thin needle, but sometimes the femoral artery in the groin or another site is used. The blood can also be drawn from an arterial catheter. An ABG test measures the blood gas tension values of the arterial partial pressure of oxygen (PaO2), and the arterial partial pressure of carbon dioxide (PaCO2), and the blood's pH.

Cerebral hypoxia

Cerebral hypoxia is a form of hypoxia (reduced supply of oxygen), specifically involving the brain; when the brain is completely deprived of oxygen, it is called cerebral anoxia. There are four categories of cerebral hypoxia; they are, in order of increasing severity: diffuse cerebral hypoxia (DCH), focal cerebral ischemia, cerebral infarction, and global cerebral ischemia. Prolonged hypoxia induces neuronal cell death via apoptosis, resulting in a hypoxic brain injury.

Numerical methods for partial differential equations

Numerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.

Circulatory system

The blood circulatory system is a system of organs that includes the heart, blood vessels, and blood which is circulated throughout the entire body of a human or other vertebrate. It includes the cardiovascular system, or vascular system, that consists of the heart and blood vessels (from Greek kardia meaning heart, and from Latin vascula meaning vessels). The circulatory system has two divisions, a systemic circulation or circuit, and a pulmonary circulation or circuit.

Child development stages

Child development stages are the theoretical milestones of child development, some of which are asserted in nativist theories. This article discusses the most widely accepted developmental stages in children. There exists a wide variation in terms of what is considered "normal", caused by variations in genetic, cognitive, physical, family, cultural, nutritional, educational, and environmental factors. Many children reach some or most of these milestones at different times from the norm.

Mathematical model

A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).

Intracranial aneurysm

An intracranial aneurysm, also known as a cerebral aneurysm, is a cerebrovascular disorder in which weakness in the wall of a cerebral artery or vein causes a localized dilation or ballooning of the blood vessel. Aneurysms in the posterior circulation (basilar artery, vertebral arteries and posterior communicating artery) have a higher risk of rupture. Basilar artery aneurysms represent only 3–5% of all intracranial aneurysms but are the most common aneurysms in the posterior circulation.