# Single cell simulation¶

class myokit.Simulation(model, protocol=None, apd_var=None)

Runs single cell simulations using the CVODE solver (see [1]); CVODE uses an implicit multi-step method to achieve high accuracy and stability with adaptive step sizes.

The model passed to the simulation is cloned and stored internally, so changes to the original model object will not affect the simulation. A protocol can be passed in as protocol or set later using set_protocol().

Simulations maintain an internal state consisting of

• the current simulation time
• the current state
• the default state

When a simulation is created, the simulation time is set to 0 and both the current and the default state are copied from the model. After each call to Simulation.run() the time variable and current state are updated, so that each successive call to run continues where the previous simulation left off. A reset() method is provided that will set the time back to 0 and revert the current state to the default state. To change the time or state manually, use set_time() and set_state().

A pre-pacing method pre() is provided that doesn’t affect the simulation time but will update the current and the default state. This allows you to pre-pace, run a simulation, reset to the pre-paced state, run another simulation etc.

To get action potential duration (APD) measurements, the simulation can be run with threshold crossing detection. To enable this, the membrane potential variable must be specified when the simulation is created using the apd_var argument. This can be either a variable object or a string containing the variable’s fully qualified name. When running a simulation a threshold value can be passed in. In addition to the usual simulation log the run method will then return a list of all times at which apd_var crossed the threshold. Please note this is an APD calculated as the time between the crossing of a fixed threshold, it does not calculate dynamic thresholds like “90% of max(V) - min(V)”.

The simulation provides four inputs a model variable can be bound to:

time
This input provides the simulation time.
pace
This input provides the current value of the pacing variable. This is determined using the protocol passed into the Simulation.
evaluations
This input provides the number of rhs evaluations used at each point in time and can be used to gain some insight into the solver’s behaviour.
realtime
This input provides the elapsed system time at each logged point.

No variable labels are required for this simulation type.

[1] SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers. Hindmarsh, Brown, Woodward, et al. (2005) ACM Transactions on Mathematical Software.

default_state()

Returns the default state.

eval_derivatives(y=None)

Evaluates and returns the state derivatives.

The state to evaluate for can be given as y. If no state is given the current simulation state is used.

last_number_of_evaluations()

Returns the number of rhs evaluations performed by the solver during the last simulation.

last_number_of_steps()

Returns the number of steps taken by the solver during the last simulation.

last_state()

If the last simulation resulted in an error, this will return the last state reached during that simulation. In all other cases, this method will return None.

pre(duration, progress=None, msg='Pre-pacing Simulation')

This method can be used to perform an unlogged simulation, typically to pre-pace to a (semi-)stable orbit.

After running this method

• The simulation time is not affected
• The current state and the default state are updated to the final state reached in the simulation.

Calls to reset() after using pre() will set the current state to this new default state.

To obtain feedback on the simulation progress, an object implementing the myokit.ProgressReporter interface can be passed in. passed in as progress. An optional description of the current simulation to use in the ProgressReporter can be passed in as msg.

reset()

Resets the simulation:

• The time variable is set to 0
• The state is set to the default state
run(duration, log=None, log_interval=None, log_times=None, apd_threshold=None, progress=None, msg='Running simulation')

Runs a simulation and returns the logged results. Running a simulation has the following effects:

• The internal state is updated to the last state in the simulation.
• The simulation’s time variable is updated to reflect the time
elapsed during the simulation.

The number of time units to simulate can be set with duration.

The method returns a myokit.DataLog dictionary that maps variable names to lists of logged values. The variables to log can be indicated using the log argument. There are several options for its value:

• None (default), to log all states.
• An integer flag or a combination of flags. Options: myokit.LOG_NONE, myokit.LOG_STATE, myokit.LOG_BOUND, myokit.LOG_INTER, myokit.LOG_DERIV or myokit.LOG_ALL.
• A sequence of variable names. To log derivatives, use “dot(membrane.V)”.
• A myokit.DataLog object. In this case, the new data will be appended to the existing log.

For detailed information about the log argument, see the function myokit.prepare_log().

By default, every step the solver takes is logged. This is usually advantageous, since more points are added exactly at the times the system gets more interesting. However, if equidistant points are required a log_interval can be set. Alternatively, the log_times argument can be used to specify logging times directly.

To obtain accurate measurements of the action potential (AP) duration, the argument apd_threshold can be set to a fixed threshold level used to define the AP. This functionality is only available for simulations created with a valid apd_var argument. If apd measurements are enabled, the value returned by this method has the form (log, apds).

To obtain feedback on the simulation progress, an object implementing the myokit.ProgressReporter interface can be passed in. passed in as progress. An optional description of the current simulation to use in the ProgressReporter can be passed in as msg.

set_constant(var, value)

Changes a model constant. Only literal constants (constants not dependent on any other variable) can be changed.

The constant var can be given as a Variable or a string containing a variable qname. The value should be given as a float.

set_default_state(state)

Allows you to manually set the default state.

set_fixed_form_protocol(times=None, values=None)

Configures this simulation to run with a predetermined protocol instead of the usual event-based mechanism.

A 1D time-series should be given as input. During the simulation, the value of the pacing variable will be determined by linearly interpolating between the two nearest points in the series. If the simulation time is outside the bounds of the time-series, the first or last value in the series will be used.

Setting a predetermined protocol clears any previously set (event-based or pre-determined) protocol. To clear all protocols, call this method with times=None. When a simulation is run without any protocol, the value of any variables bound to pace will be set to 0.

Arguments:

times
A non-decreasing array of times. If any times appear more than once, only the value at the highest index will be used.
values
An array of values for the pacing variable. Must have the same size as times.
set_max_step_size(dtmax=None)

Sets a maximum step size. To let the solver pick any step size it likes use dtmax = None.

set_min_step_size(dtmin=None)

Sets a minimum step size. To let the solver pick any step size it likes use dtmin = None.

set_protocol(protocol=None)

Sets the pacing Protocol used by this simulation.

To run without pacing call this method with protocol = None. In this case, the value of any variables bound to pace will be set to 0.

set_state(state)

Sets the current state.

set_time(time=0)

Sets the current simulation time.

set_tolerance(abs_tol=1e-06, rel_tol=0.0001)

Sets the solver tolerances. Absolute tolerance is set using abs_tol, relative tolerance using rel_tol. For more information on these values, see the Sundials CVODE documentation.

state()

Returns the current state.

time()

Returns the current simulation time.

## Sundials utility classes¶

class myokit.Sundials

Tests for Sundials/Sundials support.

static version()

Returns the detected Sundials version on this system, or None if no version of Sundials was found.

static version_int()

Returns a sundials version number as an integer, or None if no version number could be detected.