Methods for Computer Simulation

• Methods for computer simulation were illustrated following the flow chart in the next page.• Please select the user-defined mode button, and enter 6 parameters in each box (Steps 1-3). Then, click on ‘E

nter’ to start the program (Step 4). The phase response curve (PRC) will appear in the lower right panel as a blue line. In the upper right panel, the spectrum graph with the blue line shows the VPC ratio at the sinus cycle length corresponding to the mean sinus cycle length in our text. The red line in the right panel indicates the VPC-VPC interval at the same sinus cycle length.

If the model button (C1-C4 and I2) was selected, all parameters will be pre-determined according to the table in reference 1.

• ECG simulation is possible by clicking on the ‘Plot ECG’ button (Step 5).In the next panel, please select the required sinus cycle length to simulate the ECG. The parasystole cycle length is pre-set at 2,000 ms. Push ‘Enter’ to start the ECG simulation (Step 6). The corresponding PRC will appear in the upper middle panel. The phase transition plot will be displayed in the upper right panel. Click on ‘Next ECG’ to continue for a further ECG simulation (Step 7). The figures under each ECG show the R-R interval without discriminating VPCs.The limiting condition for the RIVB can be estimated by repeating the ECG simulation.

• Additional references to 6) and 7) in the text:

1.Ikeda N, Yoshizawa S, Sato T. Difference equation model of a ventricular parasystole as an interaction between cardiac pacemakers based on the phase response curve, J theor Biol, 1983: 103; 439-465,

2. Ikeda N, Takeuchi A, Hamada A, Goto H, Mamorita N, Takayanagi K: Model of bi-directional modulated parasystole as a mechanism for cyclic bursts of ventricular premature contractions. Biol Cybern 2004: 91; 37-47.

Flow chart

Step 7Continue ECG or end ECG

click on next 10 sec or Quit

Step 6: ECG simulationclick on to enter and start ECG simulation

initial 10 sec

Step 5: ECG simulationselect the sinus cycle length

(SCL <2,000 ms)

Step 4: Start simulation and check sinus cycle length dependenceAbscissa indicates sinus cycle length.

Ordinate in the left indicates VPC-VPC interval. Ordinate in the right indicates VPC ratio.

Step 3 :Select parametersfor refractory periodNormal QRS: gammaEctopic focus: delta

Step 2: Select parameterstransition point of the PRC

w(0<w<1)

Step 1; Select parametersslopes of the PRC

a,b,c

phase response curve

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0 0.2 0.4 0.6 0.8 1

b

Phase response curve approximation by a piecewise linear function with a set of parameters (a, b, c, ).

Parameters: a, b, c (0< c <999), (0< <1)

Refractory period of the normal QRS: gamma (0< gamma <1)

Refractory period of the ectopic focus: 　 delta (0< delta <1)

-c

a

Step 1: Select parameters on SIMULATOR

model

Model simulator

How to use

Parameters

enter Plot ECG (next page)

Spectrum plot delete quit

Variable model

model

Step 2 and 3. Select 6 parameters:Model simulator

How to use

Parameters

enter Plot ECG (next page)

Spectrum plot delete quit

Variable model

model

Step 4. Push enter to make VPC-VPC interval, VPC ratio map (upper panel) and PRC (lower panel). Red vertical arrow indicates the upper

limit for the RIVB at sinus cycle length of 1,176 ms.

How to use

Parameters

enter Plot ECG (next page)

Spectrum plot delete quit

Variable model

Step 5. Click on ‘Plot ECG’ (upper panel) and select SCL (=1 s) on the next page (lower new panel)

enter

ECG Plot

deleteHow to use

Next ECG

quit

SCL variation

Parameters

enter Plot ECG (next page)

Spectrum plot delete quit

Variable model

Step 6. Push ‘enter’ to reproduce ECG at selected SCL (=1.159 s). Note the location of vertical red arrow on the PRC.

enter

ECG Plot

deleteHow to use

Next ECG

quit

SCL variation

Step 6. SCL=0.745 s. Compensatory bigeminy was followed by interpolated trigeminy.

enter

ECG Plot

deleteHow to use

Next ECG

quit

SCL variation

Step 6. RIVB at SCL=1.176 s. This is the limiting condition for RIV

B, which can be estimated by comparing the next ECG.

enter

ECG Plot

deleteHow to use

Next ECG

quit

SCL variation

Step 6. No RIVB at 1,177ms.

enter

ECG Plot

deleteHow to use

Next ECG

quit

SCL variation

Statistical analysis. Figure 4: regression lines