5.1.6.2. Usecase: Stimulus current with offset

Description: Many electrophysiology models contain statements such as: I_stim = stim_amplitude if (time % 1000 < 2) else 0. These statements encode discontinuities directly into the mathematics (at t=0, t=1000, t=2000,… and at t=2, t=1002, t=2002, …), and so can be replaced by reset statements.

component: StimulusCurrentWithOffset
  ├─ math:
  │   └─ x = t % 1000
  │
  ├─ variable: x
  │
  └─ variable: y, initially 0
      ├─ reset: rule 1
      │   ├─ when x == 100
      │   └─ then y = 1
      │
      └─ reset: rule 2
          ├─ when x == 101
          └─ then y = 0

See CellML syntax

<variable name="t" units="dimensionless" />
<variable name="x" units="dimensionless" />
<variable name="y" units="dimensionless" initial_value="0" />

<!-- Reset rule 1: -->
<reset variable="y" test_variable="x">
    <test_value>
        <cn units="cellml:dimensionless">100</cn>
    </test_value>
    <reset_value>
        <cn units="cellml:dimensionless">1</cn>
    </reset_value>
</reset>

<!-- Reset rule 2: -->
<reset variable="y" test_variable="x">
    <test_value>
        <cn units="cellml:dimensionless">101</cn>
    </test_value>
    <reset_value>
        <cn units="cellml:dimensionless">0</cn>
    </reset_value>
</reset>

t	0.0	…	99.9	100	…	100.9	101
x	0	…	99.9	100	…	100.9	101
y	0	…	0	0 → 1	…	1	1 → 0

Processing steps

• Cycle

  1. At t = 100 we detect that x == 100, so rule 1 becomes active.

  2. The reset value for rule 1 is calculated to be 1.

  3. The reset value for rule 1 is applied to y.

  4. The system is now in a new state: \((x^\prime, t, p) \neq (x, t, p)\) (note that \(y\) is included in \(x\)), we restart at step 1.

• Cycle

  1. Since it is still true that x == 100, rule 1 is still active.

  2. The reset value is calculated,

  3. And applied.

  4. The state hasn’t changed: \((x^\prime, t, p) = (x, t, p)\), so reset rule 1 processing halts.

• Cycle

  1. At t = 101 we detect that x == 101, so rule 2 becomes active.

  2. The reset value for rule 2 is calculated to be 0.

  3. The reset value for rule 2 is applied to y.

  4. The system is now in a new state: \((x^\prime, t, p) \neq (x, t, p)\), so restart.

• Cycle

  1. Since it is still true that x == 101, rule 2 is still active.

  2. The reset value is calculated,

  3. And applied.

  4. The state hasn’t changed: \((x^\prime, t, p) = (x, t, p)\), so reset rule 2 processing halts.