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Modeling excitable systems: Reentrant tachycardia
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Image of Fig. 1.
Fig. 1.

Numerical computation (lines) and measured circuit data (dashed) for a self-exciting Fitzhugh–Nagumo system with source term . The excitatory variable has a large amplitude, and the inhibitory variable has a small amplitude. The voltages have been normalized, and the time is dimensionless (see Table I).

Image of Fig. 2.
Fig. 2.

Numerical computation of phase-space plot (line) and nullclines (- dashed and -dot-dashed) for the self-exciting Fitzhugh–Nagumo system.

Image of Fig. 3.
Fig. 3.

Schematic of the Fitzhugh–Nagumo circuit. , , and . accounts for the inductor’s intrinsic resistance and an external resistor . The function block is shown in Fig. 4.

Image of Fig. 4.
Fig. 4.

Circuit for generation of function . Only two of the MLT04’s four multipliers are used. The unused multipliers (not shown) should be grounded.

Image of Fig. 5.
Fig. 5.

Constant current source . , , and give . The transistor is a general purpose such as 2N3906.

Image of Fig. 6.
Fig. 6.

Pulse train current source . potentiometer, potentiometer, , , and potentiometer. The pulse period, width, and amplitude are controlled by , , and , respectively.

Image of Fig. 7.
Fig. 7.

(a) Three-transistor excitable circuit and (b) its simplified model in which the two transistors responsible for the fast-response positive feedback are replaced by . , , , and . controls the period of self-exciting pulses. The and transistors are 2N3904 and 2N3906, respectively.

Image of Fig. 8.
Fig. 8.

Normalized measured conductance (filled circles) of the two-transistor fast-response positive feedback part of the three-transistor excitable circuit and its calculated value (line) from Eq. (8). The conductance is normalized by , the conductance of in Fig. 7(a).

Image of Fig. 9.
Fig. 9.

Numerical calculation (solid line) and circuit measurement (dashed line) for the three-transistor excitable circuit with . The excitatory variable demonstrates threshold-triggered positive feedback rising slowly from zero to about 0.1 where it then rises rapidly. The inhibitory variable undergoes smaller variations near 0.1.

Image of Fig. 10.
Fig. 10.

Numerical calculation of the phase-space plot (line) and nullclines (-dashed, -dot-dashed) for the three-transistor circuit.

Image of Fig. 11.
Fig. 11.

Three coupled excitable cell circuits that simulate a one-dimensional excitable medium. The characteristic time for diffusion between neighboring cells is .

Image of Fig. 12.
Fig. 12.

Numerical calculation (solid line) and measurement (dashed line) of the capacitor voltage at one cell on one side of the six cell ring in which a source cell initiates pulses that propagate down both sides and meet at the cell opposite to source. The period is about 18 ms. This behavior represents normal propagation of the heartbeat signal from the sinoatrial node through multiple paths merging at the atrioventricular node.

Image of Fig. 13.
Fig. 13.

Coupling for either normal propagation (S1 and S2 closed), unidirectional block (S1 closed, S2 open), or ablation (S1 open). With S1 closed and S2 open, pulse propagation from left to right is blocked, but from right to left, it still occurs.

Image of Fig. 14.
Fig. 14.

Numerical calculation (solid line) and measurement (dashed line) of the capacitor voltage at one cell on a six cell ring with circulating excitation caused by unidirectional block. The circulation period of about 11 ms is shorter than in Fig. 12. The increased frequency due to circulating excitations is manifested as the reentrant tachycardia.


Generic image for table
Table I.

Conversions from measured voltages and currents to dimensionless quantities. For the Fitzhugh–Nagumo circuit, Fig. 3 defines , , , , and . For the three-transistor circuit, Fig. 7(a) defines , , , , , and .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Modeling excitable systems: Reentrant tachycardia