# Time Scales

‘How can I specify time scales?’

Specifying time scales is important, especially in multiscale models in which dynamics occur at multiple temporal scales.

In Morpheus, we distinguish three time scales:

1. Global time: defines the time frame of a simulation.
2. Monte Carlo time scale: defines updating scheme of cells.
3. System time scale: defines updating and dynamics of systems of (differential) equations.

## Global Time

Each model must specify a global time scheme under Time that runs from StartTime to StopTime. All other processes are scheduled within this time frame.

For dimensionless models, a sensible choice for the global time scheme would be from $0$ to $1$. For an example, see the cell cycle model (ExamplesMultiScaleCellCycle).

Alternatively, for dimensional models, time units can be specified (msec, sec, min, hours, days) such that one could define the global time to run from $20 \text{ hours}$ to $7 \text{ days}$. Default interpretation is $1 \text{ sec}$.

## Monte Carlo Time Scale (CPM)

The time scale of cellular Potts models can be specified using CPMMonteCarloSamplerMCSDuration. This defines the interval between Monte Carlo steps, in terms of global time scheme.

For example, if the global time is defined from $0 \rightarrow 1$, and MCSDuration is set unitless to $1.0 \cdot 10^{−2}$, a total of $100$ Monte Carlo steps will be performed during the simulation.

Alternatively, if the global time is defined with dimenions from $0 \text{ hours}$ to $1 \text{ hours}$, and MCSDuration is set to $1.0 \text{ sec}$, a total of $3600$ Monte Carlo steps will be performed during the simulation.

Note that changing the MCSDuration time scale directly affects the CPM dynamics such as cell motility and cell shape changes. In fact, it will affect all processes under CellTypesCellType, except the processes defined within Systems.

## System Time Scale (ODE/PDE)

System dynamics: setting the time scale of ODE model dynamics, relative to the global time.

To change the time scale of the dynamics of simulated ODE model, you can use the Systemtime-scaling attribute. This scales the rates of dynamics, while maintaining the accuracy (by automatically scaling the time-step). For an example, see the multi-scale cell cycle model or (ExamplesMultiscaleCellCycle).

Note that the time symbol within a scaled system thus represents system local time.

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