NeurostimulationNeurostimulation is the purposeful modulation of the nervous system's activity using invasive (e.g. microelectrodes) or non-invasive means (e.g. transcranial magnetic stimulation or transcranial electric stimulation, tES, such as tDCS or transcranial alternating current stimulation, tACS). Neurostimulation usually refers to the electromagnetic approaches to neuromodulation.
Deep brain stimulationDeep brain stimulation (DBS) is a neurosurgical procedure involving the placement of a medical device called a neurostimulator, which sends electrical impulses, through implanted electrodes, to specific targets in the brain (the brain nucleus) for the treatment of movement disorders, including Parkinson's disease, essential tremor, dystonia, and other conditions such as obsessive-compulsive disorder (OCD) and epilepsy. While its underlying principles and mechanisms are not fully understood, DBS directly changes brain activity in a controlled manner.
Euler methodIn mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).
Iterative methodIn computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.
Heun's methodIn mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. Both variants can be seen as extensions of the Euler method into two-stage second-order Runge–Kutta methods.
Transcranial magnetic stimulationTranscranial magnetic stimulation (TMS) is a noninvasive form of brain stimulation in which a changing magnetic field is used to induce an electric current at a specific area of the brain through electromagnetic induction. An electric pulse generator, or stimulator, is connected to a magnetic coil connected to the scalp. The stimulator generates a changing electric current within the coil which creates a varying magnetic field, inducing a current within a region in the brain itself.
Transcranial direct-current stimulationTranscranial direct current stimulation (tDCS) is a form of neuromodulation that uses constant, low direct current delivered via electrodes on the head. It was originally developed to help patients with brain injuries or neuropsychiatric conditions such as major depressive disorder. It can be contrasted with cranial electrotherapy stimulation, which generally uses alternating current the same way, as well as transcranial magnetic stimulation. Research shows increasing evidence for tDCS as a treatment for depression.
Jacobi methodIn numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.
Scientific methodThe scientific method is an empirical method for acquiring knowledge that has characterized the development of science since at least the 17th century (with notable practitioners in previous centuries; see the article history of scientific method for additional detail.) It involves careful observation, applying rigorous skepticism about what is observed, given that cognitive assumptions can distort how one interprets the observation.
Surface chargeA surface charge is an electric charge present on a two-dimensional surface. These electric charges are constrained on this 2-D surface, and surface charge density, measured in coulombs per square meter (C•m−2), is used to describe the charge distribution on the surface. The electric potential is continuous across a surface charge and the electric field is discontinuous, but not infinite; this is unless the surface charge consists of a dipole layer. In comparison, the potential and electric field both diverge at any point charge or linear charge.
