AstrocyteAstrocytes (from Ancient Greek ἄστρον, ástron, "star" + κύτος, kútos, "cavity", "cell"), also known collectively as astroglia, are characteristic star-shaped glial cells in the brain and spinal cord. They perform many functions, including biochemical control of endothelial cells that form the blood–brain barrier, provision of nutrients to the nervous tissue, maintenance of extracellular ion balance, regulation of cerebral blood flow, and a role in the repair and scarring process of the brain and spinal cord following infection and traumatic injuries.
NeuronWithin a nervous system, a neuron, neurone, or nerve cell is an electrically excitable cell that fires electric signals called action potentials across a neural network. Neurons communicate with other cells via synapses - specialized connections that commonly use minute amounts of chemical neurotransmitters to pass the electric signal from the presynaptic neuron to the target cell through the synaptic gap. The neuron is the main component of nervous tissue in all animals except sponges and placozoa.
Ordinary differential equationIn mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .
Differential equationIn mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
AstrogliosisAstrogliosis (also known as astrocytosis or referred to as reactive astrogliosis) is an abnormal increase in the number of astrocytes due to the destruction of nearby neurons from central nervous system (CNS) trauma, infection, ischemia, stroke, autoimmune responses or neurodegenerative disease. In healthy neural tissue, astrocytes play critical roles in energy provision, regulation of blood flow, homeostasis of extracellular fluid, homeostasis of ions and transmitters, regulation of synapse function and synaptic remodeling.
Linear differential equationIn mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a0(x), ..., an(x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y′, ..., y(n) are the successive derivatives of an unknown function y of the variable x. Such an equation is an ordinary differential equation (ODE).
Rostral migratory streamThe rostral migratory stream (RMS) is a specialized migratory route found in the brain of some animals along which neuronal precursors that originated in the subventricular zone (SVZ) of the brain migrate to reach the main olfactory bulb (OB). The importance of the RMS lies in its ability to refine and even change an animal's sensitivity to smells, which explains its importance and larger size in the rodent brain as compared to the human brain, as our olfactory sense is not as developed.
Neuroimmune systemThe neuroimmune system is a system of structures and processes involving the biochemical and electrophysiological interactions between the nervous system and immune system which protect neurons from pathogens. It serves to protect neurons against disease by maintaining selectively permeable barriers (e.g., the blood–brain barrier and blood–cerebrospinal fluid barrier), mediating neuroinflammation and wound healing in damaged neurons, and mobilizing host defenses against pathogens.
GliosisGliosis is a nonspecific reactive change of glial cells in response to damage to the central nervous system (CNS). In most cases, gliosis involves the proliferation or hypertrophy of several different types of glial cells, including astrocytes, microglia, and oligodendrocytes. In its most extreme form, the proliferation associated with gliosis leads to the formation of a glial scar. The process of gliosis involves a series of cellular and molecular events that occur over several days.
Homogeneous differential equationA differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written where f and g are homogeneous functions of the same degree of x and y. In this case, the change of variable y = ux leads to an equation of the form which is easy to solve by integration of the two members. Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives.