Bidomain
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. [1] [2] [3] [4] [5] [6] [7] [8] 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. [9]
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. [10] Mathematically, unequal anisotropy ratios means that the effect of anisotropy cannot be removed by a change in the distance scale in one direction. [11] Instead, the anisotropy has a more profound influence on the electrical behavior. [12]
Three examples of the impact of unequal anisotropy ratios are
- the distribution of transmembrane potential during unipolar stimulation of a sheet of cardiac tissue,[13]
- the magnetic field produced by an action potential wave front propagating through cardiac tissue,[14]
- the effect of fiber curvature on the transmembrane potential distribution during a electric shock.[15]
The bidomain model is now widely used to model defibrilation of the heart.
References
- ^ Muler AL, Markin VS (1977). "Electrical properties of anisotropic nerve-muscle syncytia-I. Distribution of the electrotonic potential.". Biofizika 22 (2): 307–312. PMID 861269.
- ^ Muler AL, Markin VS (1977). "Electrical properties of anisotropic nerve-muscle syncytia-II. Spread of flat front of excitation.". Biofizika 22 (3): 518–522. PMID 889914.
- ^ Muler AL, Markin VS (1977). "Electrical properties of anisotropic nerve-muscle syncytia-III. Steady form of the excitation front.". Biofizika 22 (4): 671–675. PMID 901827.
- ^ Tung L (1978). "A bi-domain model for describing ischemic myocardial d-c potentials.". PhD dissertation, MIT, Cambridge, Mass..
- ^ Miller WT III, Geselowitz DB (1978). "Simulation studies of the electrocardiogram, I. The normal heart.". Circulation Research 43 (2): 301–315. PMID 668061.
- ^ Peskoff A (1979). "Electric potential in three-dimensional electrically syncytial tissues.". Bulletin of Mathematical Biology 41 (2): 163–181. PMID 760880.
- ^ Peskoff A (1979). "Electric potential in cylindrical syncytia and muscle fibers.". Bulletin of Mathematical Biology 41 (2): 183–192. PMID 760881.
- ^ Eisenberg RS, Barcilon V, Mathias RT (1979). "Electrical properties of spherical syncytia.". Biophysical Journal 48 (3): 449–460. Bibcode 1985BpJ....48..449E. doi:10.1016/S0006-3495(85)83800-5. PMC 1329358. PMID 4041538. http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=1329358.
- ^ Neu JC, Krassowska W (1993). "Homogenization of syncytial tissues.". Critical Reviews of Biomedical Engineering 21: 137–199.
- ^ Roth BJ (1997). "Electrical conductivity values used with the bidomain model of cardiac tissue.". IEEE Transactions on Biomedical Engineering 44 (4): 326–328. doi:10.1109/10.563303. PMID 9125816.
- ^ Roth BJ (1992). "How the anisotropy of the intracellular and extracellular conductivities influences stimulation of cardiac muscle.". Journal of Mathematical Biology 30 (6): 633–646. doi:10.1007/BF00948895. PMID 1640183.
- ^ Henriquez CS (1993). "Simulating the electrical behavior of cardiac tissue using the bidomain model.". Critical Reviews of Biomedical Engineering 21: 1–77.
- ^ Sepulveda NG, Roth BJ, Wikswo JP Jr (1989). "Current injection into a two-dimensional bidomain.". Biophysical Journal 55 (5): 987–999. Bibcode 1989BpJ....55..987S. doi:10.1016/S0006-3495(89)82897-8. PMC 1330535. PMID 2720084. http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=1330535.
- ^ Sepulveda NG, Wikswo JP Jr (1987). "Electric and magnetic fields from two-dimensional bisyncytia.". Biophysical Journal 51 (4): 557–568. Bibcode 1987BpJ....51..557S. doi:10.1016/S0006-3495(87)83381-7. PMC 1329928. PMID 3580484. http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=1329928.
- ^ Trayanova N, Roth BJ, Malden LJ (1993). "The response of a spherical heart to a uniform electric field: A bidomain analysis of cardiac stimulation.". IEEE Transactions on Biomedical Engineering 40 (9): 899–908. doi:10.1109/10.245611. PMID 8288281.