Muscle models

Currently, only variants of the Virtual Muscle Model (Brown et al., 1999) are implemented.

feedbax.mechanics.muscle.MuscleState (Module)

Type of state PyTree operated on by AbstractMuscle instances.

Note

Typically, muscle state variables are normalized. For example, muscle length is not in units of meters, but a multiple of the muscle's optimal length.

Attributes:

Name	Type	Description
activation	Array	The muscle activation.
length	Array	The muscle length.
velocity	Array	The muscle contraction velocity.
tension	Array	The tensile force generated by the muscle.

Constructors for specific variants of the Virtual Muscle Model

feedbax.mechanics.muscle.brown_1999_virtualmuscle

brown_1999_virtualmuscle(n_muscles: int = 1, noise_func: Optional[Callable] = None, params: PyTree[float] = BROWN_SLOWFAST_AVG_VIRTUALMUSCLE_PARAMS)

Returns a Virtual Muscle Model using the averaged slow/fast twitch parameters from Brown et al. 1999.

Parameters:

Name	Type	Description	Default
n_muscles	int	The number of muscles to model.	1
noise_func	Optional[Callable]	Generates noise to add to the muscle force. Has the signature noise_func(input, force, key) -> Array, where input is the input to the muscle model.	None
params	PyTree[float]	The parameters for the Virtual Muscle Model.	BROWN_SLOWFAST_AVG_VIRTUALMUSCLE_PARAMS

feedbax.mechanics.muscle.todorov_li_2004_virtualmuscle

todorov_li_2004_virtualmuscle(n_muscles: int = 1, noise_func: Optional[Callable] = None, params: PyTree[float] = TODOROV_LI_VIRTUALMUSCLE_PARAMS)

Muscle model from Todorov & Li 2004.

Simplifies the Brown et al. 1999 Virtual Muscle Model:

1. Omits the first passive element, PE1.
2. Uses averages of the fast and slow twitch parameters from Brown 1999.

Parameters:

Name	Type	Description	Default
n_muscles	int	The number of muscles to model.	1
noise_func	Optional[Callable]	Generates noise to add to the muscle force. Has the signature noise_func(input, force, key) -> Array, where input is the input to the muscle model.	None
params	PyTree[float]	The parameters for the Virtual Muscle Model.	TODOROV_LI_VIRTUALMUSCLE_PARAMS

feedbax.mechanics.muscle.lillicrap_scott_2013_virtualmuscle

lillicrap_scott_2013_virtualmuscle(n_muscles: int = 1, noise_func: Optional[Callable] = None, params: dict = LILLICRAP_SCOTT_VIRTUALMUSCLE_PARAMS)

Muscle model from Lillicrap & Scott 2013.

Simplifies the Brown et al. 1999 Virtual Muscle Model:

1. Uses the Hill approximation (removes denominator l dependency) for FV shortening.
2. Omits both passive elements, PE1 and PE2.
3. Uses the activation directly: A_f = a, thus also omits any Y and l_eff filters.
4. Uses a mixture of fast twitch and averaged slow/fast twitch parameters from Brown 1999; see LILLICRAP_SCOTT_VIRTUALMUSCLE_PARAMS.

Parameters:

Name	Type	Description	Default
n_muscles	int	The number of muscles to model.	1
noise_func	Optional[Callable]	Generates noise to add to the muscle force. Has the signature noise_func(input, force, key) -> Array, where input is the input to the muscle model.	None
params	dict	The parameters for the Virtual Muscle Model.	LILLICRAP_SCOTT_VIRTUALMUSCLE_PARAMS

Virtual Muscle Model

feedbax.mechanics.muscle.VirtualMuscle (AbstractMuscle)

Implements the Virtual Muscle Model from Brown, Cheng, & Loeb 1999.

Attributes:

Name	Type	Description
n_muscles	int	The number of muscles to model. From the perspective of this class, the muscles are modeled independently.
activation_func	AbstractActivationFunction	The muscle activation function.
force_func	AbstractFLVFunction	The muscle force-length-velocity function.
noise_func	Optional[Callable[[Array, Array, Array], Array]]	An optional function that adds noise to the muscle force.

bounds: StateBounds[MuscleState] property

Suggested bounds on the state.

__call__ (input: ModelInput,state: StateT,key: PRNGKeyArray) -> StateT

Inherited from feedbax.mechanics.muscle.AbstractMuscle

state_consistency_update (state: StateT) -> StateT

Inherited from feedbax.mechanics.muscle.AbstractMuscle

change_n_muscles (n_muscles: int) -> AbstractMuscle

Inherited from feedbax.mechanics.muscle.AbstractMuscle

init (*,key: PRNGKeyArray) -> MuscleState

Return a default state for the model.

Muscle input signal filters

feedbax.mechanics.muscle.ActivationFilter (AbstractDynamicalSystem)

First-order model of the calcium dynamics of muscle activation.

Attributes:

Name	Type	Description
tau_act	float	The activation time constant.
tau_deact	float	The deactivation time constant.

__call__ (input: PyTree[Array],state: StateT,key: PRNGKeyArray) -> StateT

Inherited from feedbax.dynamics.AbstractDynamicalSystem

vector_field (t: Scalar,state: Array,input: Array)

Return the time derivative of activation.

Abstract base classes

feedbax.mechanics.muscle.AbstractMuscle (AbstractStagedModel[MuscleState])

Base class for muscle models.

Attributes:

Name	Type	Description
n_muscles	AbstractVar[int]	The number of muscles to model. From the perspective of this class, the muscles are modeled independently.
activation_func	AbstractVar[AbstractActivationFunction]	The muscle activation function.
force_func	AbstractVar[AbstractFLVFunction]	The muscle force-length-velocity function.
noise_func	AbstractVar[Optional[Callable[[Array, Array, Array], Array]]]	An optional function that adds noise to the muscle force.

__call__ (input: ModelInput,state: StateT,key: PRNGKeyArray) -> StateT

Inherited from feedbax._staged.AbstractStagedModel

state_consistency_update (state: StateT) -> StateT

Inherited from feedbax._staged.AbstractStagedModel

init (*,key: PRNGKeyArray) -> StateT

Inherited from feedbax._staged.AbstractStagedModel

change_n_muscles (n_muscles: int) -> AbstractMuscle

Return a similar model for a different number of muscles.