Bidomain
Encyclopedia
The bidomain model is a mathematical model
of the electrical properties of cardiac muscle
that takes into account the anisotropy
of both the intracellular
and extracellular
spaces.
The bidomain model was developed in the late 1970s.
It is a generalization of one-dimensional cable theory
. The bidomain model is a continuum model, meaning that it represents the average properties of many cells, rather than describing each cell individually.
Many of the interesting properties of the bidomain model arise from the condition of unequal anisotropy ratios. The electrical conductivity in anisotropic tissue is different parallel and perpendicular to the fiber direction. In a tissue with unequal anisotropy ratios, the ratio of conductivities parallel and perpendicular to the fibers is different in the intracellular and extracellular spaces. For instance, in cardiac tissue, the anisotropy ratio in the intracellular space is about 10:1, while in the extracellular space it is about 5:2.
Mathematically, unequal anisotropy ratios means that the effect of anisotropy cannot be removed by a change in the distance scale in one direction.
Instead, the anisotropy has a more profound influence on the electrical behavior.
Three examples of the impact of unequal anisotropy ratios are
The bidomain model is now widely used to model defibrilation of the heart.
Mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...
of the electrical properties of cardiac muscle
Cardiac muscle
Cardiac muscle is a type of involuntary striated muscle found in the walls and histologic foundation of the heart, specifically the myocardium. Cardiac muscle is one of three major types of muscle, the others being skeletal and smooth muscle...
that takes into account the anisotropy
Anisotropy
Anisotropy is the property of being directionally dependent, as opposed to isotropy, which implies identical properties in all directions. It can be defined as a difference, when measured along different axes, in a material's physical or mechanical properties An example of anisotropy is the light...
of both the intracellular
Intracellular
Not to be confused with intercellular, meaning "between cells".In cell biology, molecular biology and related fields, the word intracellular means "inside the cell".It is used in contrast to extracellular...
and extracellular
Extracellular
In cell biology, molecular biology and related fields, the word extracellular means "outside the cell". This space is usually taken to be outside the plasma membranes, and occupied by fluid...
spaces.
The bidomain model was developed in the late 1970s.
It is a generalization of one-dimensional cable theory
Cable theory
Classical cable theory uses mathematical models to calculate the flow of electric current along passive neuronal fibers particularly dendrites that receive synaptic inputs at different sites and times...
. The bidomain model is a continuum model, meaning that it represents the average properties of many cells, rather than describing each cell individually.
Many of the interesting properties of the bidomain model arise from the condition of unequal anisotropy ratios. The electrical conductivity in anisotropic tissue is different parallel and perpendicular to the fiber direction. In a tissue with unequal anisotropy ratios, the ratio of conductivities parallel and perpendicular to the fibers is different in the intracellular and extracellular spaces. For instance, in cardiac tissue, the anisotropy ratio in the intracellular space is about 10:1, while in the extracellular space it is about 5:2.
Mathematically, unequal anisotropy ratios means that the effect of anisotropy cannot be removed by a change in the distance scale in one direction.
Instead, the anisotropy has a more profound influence on the electrical behavior.
Three examples of the impact of unequal anisotropy ratios are
- the distribution of transmembrane potential during unipolar stimulation of a sheet of cardiac tissue,
- the magnetic fieldMagnetic fieldA magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
produced by an action potential wave front propagating through cardiac tissue, - the effect of fiber curvature on the transmembrane potential distribution during a electric shock.
The bidomain model is now widely used to model defibrilation of the heart.