Electrical stimulation
Living muscles are electrically excitable with contraction being activated by a Ca2+ transient.
FiberSim can create protocol files that include Ca2+ transients generated by a single two compartment model.
Model
The model has two compartments representating the sarcoplasmic reticulum (Ca2+ store) and myofilament space respectively.
The equations defining the model are as follows, where Cax is the Calcium concentration in compartment x.
\[Ca_{SR} + Ca_{myofil} = Ca_{content}\] \[\frac{\mathrm d Ca_{SR}}{\mathrm dt} = \begin{cases} t \leq stimulus\_duration\_s & k_{SERCA} Ca_{myofil} - (k_{leak} + k_{act}) * Ca_{SR} \\ t > stimulus\_duration\_s & k_{SERCA} Ca_{myofil} - k_{leak} * Ca_{SR} \end{cases}\] \[\frac{\mathrm d Ca_{myofil}}{\mathrm dt} = -\frac{\mathrm d Ca_{SR}}{\mathrm dt}\]| Parameter | Sets |
|---|---|
| Ca_content | The total Ca2+ (M) |
| stimulus_duration_s | How long Ca2+ from the sarcoplasmic reticulum after a stimulus (s) |
| k_leak | The rate at which Ca2+ leaks from the sarcoplasmic reticulum when there is no stimulus (M s-1) |
| k_act | The additive rate at which Ca2+ is released from the sarcoplasmic reticulum during a stimulus (M s-1) |
| k_serca | The rate at which Ca2+ is pumped back into the sarcoplasmic reticulum (M s-1) |