The role of theoretical and physical models in scientific and engineering advancements
Four levels of modeling in electric EEG systems: quantum mechanics of semiconductors, design of current sources and amplifiers, circuit design, and use by EEG scientists
Two general types of mathematical models in EEG: volume conductor models and models of brain current source dynamics
Volume conductor models are based on Poisson's equation and relate current sources to macroscopic currents and potentials in the volume conductor
Models of brain current source dynamics are much more complex, taking into account non-linear interactions, time-varying nature, and spatial distribution of sources, using advanced mathematical tools and incorporating biophysical properties of neurons
From the point of view of Physics, the human brain is a complex system, making it challenging to develop accurate models of brain activity
Advances in computational and experimental techniques are helping to improve our understanding of brain current source dynamics.
As the field of science and engineering advances, it is essential to understand the role of both theoretical and physical models in this progress. Often, a hierarchy of models can be seen in even the simplest of systems. One such example is the design of current sources or amplifiers that contain transistors.
At the lowest level, solid-state physicists develop quantum mechanical models of semiconductor or metal properties, with little consideration for their circuit applications. The next level involves engineers and applied physicists who use these models to design current sources and amplifiers, while the third level involves engineers who design specific circuits, such as those used in EEG systems. Finally, at the fourth level, the users of these circuits, such as EEG scientists, rely on the properties provided by the previous levels.
In EEG, mathematical models are of two general types: volume conductor models and models of the dynamic behavior of brain current sources. These two types of models are vastly different in terms of complexity, assumptions, and accuracy.
Volume conductor models are far simpler than models of brain dynamics. They are based on Poisson's equation, which relates current sources to the macroscopic currents and potentials produced in the volume conductor. The equation is linear in nature and can be used to determine the potential at all locations external to the source volumes. The net potential at any location is due to a linear superposition of contributions from all brain sources, generally having different frequencies and phases.
On the other hand, models of the dynamic behavior of brain current sources are much more complex. These models typically take into account the non-linear interactions between different sources, the time-varying nature of these interactions, and the spatial distribution of the sources. To do this, we must use advanced mathematical tools such as differential equations, stochastic processes, and nonlinear dynamics to try to describe the behavior of electrical currents in the brain. They also incorporate information about the biophysical properties of neurons, including the ion channels that mediate the flow of ions into and out of the cell, and the synaptic connections between neurons.
All these models are challenging to develop because the human brain is an incredibly complex system, and it is difficult to accurately measure the underlying processes that contribute to brain activity. However, advances in computational and experimental techniques are helping to improve our understanding of the dynamic behavior of brain current sources.
Read more:
Electric Fields of the Brain: The Neurophysics of EEG by Paul L. Nunez, Ramesh Srinivasan
Comentarios