This function is a muscle modeling utility class that simulates dynamics of muscle force development as a function of input excitation. More...

Inheritance diagram for OpenSim::MuscleSecondOrderActivationDynamicModel:

OpenSim Properties, Sockets, Outputs, Inputs
Properties (single-value)
double	twitch_time_constant
	"time-to-peak after an impulse (s)" More...

double	minimum_activation
	"activation lower bound" More...

Public Member Functions
	MuscleSecondOrderActivationDynamicModel (double twitchTimeConstant, double minActivation, const std::string &muscleName)
	More...

	MuscleSecondOrderActivationDynamicModel ()
	Default constructor. More...

double	calcDerivative (double dactivation_dt, double activation, double excitation) const
	More...

double	getTwitchTimeConstant () const
	More...

double	getMinimumActivation () const
	More...

double	getMaximumActivation () const
	More...

double	clampActivation (double activation) const
	More...

bool	setTwitchTimeConstant (double activationTimeConstant)
	More...

bool	setMinimumActivation (double minimumActivation)
	More...

void	ensureModelUpToDate ()

Property-related functions
const double &	get_twitch_time_constant () const
	Get the value of the twitch_time_constant property. More...

double &	upd_twitch_time_constant ()
	Get a writable reference to the twitch_time_constant property. More...

void	set_twitch_time_constant (const double &value)
	Set the value of the twitch_time_constant property. More...

const double &	get_minimum_activation () const
	Get the value of the minimum_activation property. More...

double &	upd_minimum_activation ()
	Get a writable reference to the minimum_activation property. More...

void	set_minimum_activation (const double &value)
	Set the value of the minimum_activation property. More...

Public Member Functions inherited from OpenSim::Object
virtual	~Object ()
	Virtual destructor for cleanup. More...

bool	isEqualTo (const Object &aObject) const
	Equality operator wrapper for use from languages not supporting operator overloading. More...

Object &	operator= (const Object &aObject)
	Copy assignment copies he base class fields, including the properties. More...

virtual bool	operator== (const Object &aObject) const
	Determine if two objects are equal. More...

virtual bool	operator< (const Object &aObject) const
	Provide an ordering for objects so they can be put in sorted containers. More...

void	setName (const std::string &name)
	Set the name of the Object. More...

const std::string &	getName () const
	Get the name of this Object. More...

void	setDescription (const std::string &description)
	Set description, a one-liner summary. More...

const std::string &	getDescription () const
	Get description, a one-liner summary. More...

const std::string &	getAuthors () const
	Get Authors of this Object. More...

void	setAuthors (const std::string &authors)
	Set Authors of this object. More...

const std::string &	getReferences () const
	Get references or publications to cite if using this object. More...

void	setReferences (const std::string &references)
	Set references or publications to cite if using this object. More...

int	getNumProperties () const
	Determine how many properties are stored with this Object. More...

const AbstractProperty &	getPropertyByIndex (int propertyIndex) const
	Get a const reference to a property by its index number, returned as an AbstractProperty. More...

AbstractProperty &	updPropertyByIndex (int propertyIndex)
	Get a writable reference to a property by its index number, returned as an AbstractProperty. More...

bool	hasProperty (const std::string &name) const
	Return true if this Object has a property of any type with the given name, which must not be empty. More...

const AbstractProperty &	getPropertyByName (const std::string &name) const
	Get a const reference to a property by its name, returned as an AbstractProperty. More...

AbstractProperty &	updPropertyByName (const std::string &name)
	Get a writable reference to a property by its name, returned as an AbstractProperty. More...

template<class T >
bool	hasProperty () const
	Return true if this Object contains an unnamed, one-object property that contains objects of the given template type T. More...

template<class T >
const Property< T > &	getProperty (const PropertyIndex &index) const
	Get property of known type Property<T> as a const reference; the property must be present and have the right type. More...

template<class T >
Property< T > &	updProperty (const PropertyIndex &index)
	Get property of known type Property<T> as a writable reference; the property must be present and have the right type. More...

bool	isObjectUpToDateWithProperties () const
	Returns `true` if no property's value has changed since the last time setObjectIsUpToDateWithProperties() was called. More...

void	readObjectFromXMLNodeOrFile (SimTK::Xml::Element &objectElement, int versionNumber)
	We're given an XML element from which we are to populate this Object. More...

virtual void	updateFromXMLNode (SimTK::Xml::Element &objectElement, int versionNumber)
	Use this method to deserialize an object from a SimTK::Xml::Element. More...

void	updateXMLNode (SimTK::Xml::Element &parent, const AbstractProperty *prop=nullptr) const
	Serialize this object into the XML node that represents it. More...

bool	getInlined () const
	Inlined means an in-memory Object that is not associated with an XMLDocument. More...

void	setInlined (bool aInlined, const std::string &aFileName="")
	Mark this as inlined or not and optionally provide a file name to associate with the new XMLDocument for the non-inline case. More...

std::string	getDocumentFileName () const
	If there is a document associated with this object then return the file name maintained by the document. More...

int	getDocumentFileVersion () const
	If there is a document associated with this object then return its version number. More...

void	setAllPropertiesUseDefault (bool aUseDefault)

bool	print (const std::string &fileName) const
	Write this Object into an XML file of the given name; conventionally the suffix to use is ".osim". More...

std::string	dump () const
	dump the XML representation of this Object into an std::string and return it. More...

virtual bool	isA (const char *type) const
	The default implementation returns true only if the supplied string is "Object"; each Object-derived class overrides this to match its own class name. More...

const std::string &	toString () const
	Wrapper to be used on Java side to display objects in tree; this returns just the object's name. More...

PropertySet &	getPropertySet ()
	OBSOLETE: Get a reference to the PropertySet maintained by the Object. More...

const PropertySet &	getPropertySet () const

Auto-generated functions
static MuscleSecondOrderActivationDynamicModel *	safeDownCast (OpenSim::Object *obj)
	For use in MATLAB and Python to access the concrete class. More...

static const std::string &	getClassName ()
	This returns "MuscleSecondOrderActivationDynamicModel". More...

MuscleSecondOrderActivationDynamicModel *	clone () const override
	Create a new heap-allocated copy of the concrete object to which this Object refers. More...

const std::string &	getConcreteClassName () const override
	Returns the class name of the concrete Object-derived class of the actual object referenced by this Object, as a string. More...

Additional Inherited Members
Static Public Member Functions inherited from OpenSim::Object
static void	registerType (const Object &defaultObject)
	Register an instance of a class; if the class is already registered it will be replaced. More...

static void	renameType (const std::string &oldTypeName, const std::string &newTypeName)
	Support versioning by associating the current Object type with an old name. More...

static const Object *	getDefaultInstanceOfType (const std::string &concreteClassName)
	Return a pointer to the default instance of the registered (concrete) Object whose class name is given, or NULL if the type is not registered. More...

template<class T >
static bool	isObjectTypeDerivedFrom (const std::string &concreteClassName)
	Return true if the given concrete object type represents a subclass of the template object type T, and thus could be referenced with a T*. More...

static Object *	newInstanceOfType (const std::string &concreteClassName)
	Create a new instance of the concrete Object type whose class name is given as concreteClassName. More...

static void	getRegisteredTypenames (Array< std::string > &typeNames)
	Retrieve all the typenames registered so far. More...

template<class T >
static void	getRegisteredObjectsOfGivenType (ArrayPtrs< T > &rArray)
	Return an array of pointers to the default instances of all registered (concrete) Object types that derive from a given Object-derived type that does not have to be concrete. More...

static bool	PrintPropertyInfo (std::ostream &os, const std::string &classNameDotPropertyName, bool printFlagInfo=true)
	Dump formatted property information to a given output stream, useful for creating a "help" facility for registered objects. More...

static bool	PrintPropertyInfo (std::ostream &os, const std::string &className, const std::string &propertyName, bool printFlagInfo=true)
	Same as the other signature but the class name and property name are provided as two separate strings. More...

static Object *	makeObjectFromFile (const std::string &fileName)
	Create an OpenSim object whose type is based on the tag at the root node of the XML file passed in. More...

static const std::string &	getClassName ()
	Return the name of this class as a string; i.e., "Object". More...

static void	setSerializeAllDefaults (bool shouldSerializeDefaults)
	Static function to control whether all registered objects and their properties are written to the defaults section of output files rather than only those values for which the default was explicitly overwritten when read in from an input file or set programmatically. More...

static bool	getSerializeAllDefaults ()
	Report the value of the "serialize all defaults" flag. More...

static bool	isKindOf (const char *type)
	Returns true if the passed-in string is "Object"; each Object-derived class defines a method of this name for its own class name. More...

static void	setDebugLevel (int newLevel)
	Set the amount of logging output. More...

static int	getDebugLevel ()
	Get the current setting of debug level. More...

static Object *	SafeCopy (const Object *aObject)
	Use the clone() method to duplicate the given object unless the pointer is null in which case null is returned. More...

static void	RegisterType (const Object &defaultObject)
	OBSOLETE alternate name for registerType(). More...

static void	RenameType (const std::string &oldName, const std::string &newName)
	OBSOLETE alternate name for renameType(). More...

Detailed Description

This function is a muscle modeling utility class that simulates dynamics of muscle force development as a function of input excitation.

Though it has been long been assumed that a second-order, critically damped filter models the twitch response of muscle very accurately (Bellmare et al.) first order models have persisted in the literature. Zajac originally chose to use first order, rather than second order equations in an effort to reduce simulation times. First order activation dynamics were later popularized in two influential muscle modeling papers by Winters in 1995, and later by Thelen in 2003. Computing power is far greater today than it was at the time Zajac wrote his influential muscle modeling paper, and so it makes sense to include activation dynamics that more closely match the experimental literature.

The figure shows that there are very large differences in the impulse response between a first order system (filled gray area), and Bellmare et al.'s experimental data (thick gray line). The first order system has an instantaneous rise time, reaches a peak value when the impulse terminates (in 0 time). Additionally the impulse response of the second order system is orders of magnitude higher than the second order system (peaking at a value of just under 0.01), and so, its peak is not shown in the figure. The second order system peaks at the same time as Bellmare et al.'s experimental data, and then slowly decays. These plots suggest that a second order system decays far slower than the experiments indicate.

The quality of match between the second order model and the experimental data can be improved by having separate time constants for rising ( \(\dot{a} > 0\)) and falling ( \(\dot{a} < 0\)). This small change can be easily incorporated into a canonical second order ODE of a damped system with a forced input where \(a\) is activation, \(\zeta\) is damping, \(\omega\) is the natural frequency of the system, \(\mu\) is excitation (bounded by 0 and 1).

\[ \ddot{a} + 2 \zeta \omega \dot{a} + \omega^2 a = \omega^2\mu \]

For a critically damped system \(\zeta = 1\). To obtain a quicker rate of decay a the value of \(\omega\) changes depending on the sign of \(\dot{a}\):

if \(\dot{a}>0\)

\[ \omega = \frac{1}{T} \]

else if \(\dot{a}<0\)

\[ \omega = \frac{2}{T} \]

where \( T \) is the contraction time of the muscle. Values of \( T \) vary from muscle to muscle, depending mainly on their fiber composition.

Although the above second order system approximates the twitch response of muscle very well, it has a lower bound of 0. The conventional muscle model formulation requires that activation smoothly approach a lower bound that is above zero. This can be achieved by rescaling activation, and the lower bound:

\[ \hat{a} = \frac{a}{1-a_{min}} \]

\[ \hat{a}_{min} = \frac{a_{min}}{1-a_{min}} \]

Substituting in the rescaled activation and lower bound into the second order system yields

\[ \ddot{a}+2\zeta\omega\dot{a}+\omega^2(\hat{a}-\hat{a}_{min})=\omega^2\mu \]

This is the activation dynamic equation that this class implements as it matches Bellmare et al.'s experimental data quite well, and has a user-settable lower bound.

Default

The default time to peak (or twitchTimeConstant) is 0.050 seconds. This is on the faster end of skeletal muscles. Bellmare et al. reported values of 0.0657, 0.071 and 0.116 for the biceps brachii, adductor pollicis, and the soleus respectively.

References

Bellmare, F., Woods, JJ., Johansson, R., and Bigland-Ritchie, B. (1983). Motor-unit discharge rates in maximal voluntary contractions of three human muscles. J. Neurophysiology(50), pp. 1380-1392.

Thelen, DG.(2003), Adjustment of Muscle Mechanics Model Parameters to Simulate Dynamic Contractions in Older Adults. ASME Journal of Biomechanical Engineering (125).

Winters, JM. (1995). An Improved Muscle-Reflex Actuator for Use in Large-Scale Neuromusculoskeletal Models. Annals of Biomedical Engineering (25), pp. 359-374.

Zajac, FE (1989). Muscle and Tendon: Properties, Models, Scaling and Application to Biomechanics and Motor Control. Critical Reviews in Biomedical Engineering (17), pp. 359-410.

Computational Cost Details All computational costs assume the following operation costs:

Operation Type   : #flops
+,-,=,Boolean Op : 1 
               / : 10
             sqrt: 20
             trig: 40

Author: Matt Millard

Version: 0.0

Constructor & Destructor Documentation

◆ MuscleSecondOrderActivationDynamicModel() [1/2]

OpenSim::MuscleSecondOrderActivationDynamicModel::MuscleSecondOrderActivationDynamicModel	(	double	twitchTimeConstant,
		double	minActivation,
		const std::string &	muscleName
	)

Parameters

twitchTimeConstant	The time-to-peak, in seconds, in response to an impulse.
minActivation	The minimum activation allowed. Equilibrium muscle models might set this value to be between 0.01-0.1, as they have a singularity when a = 0. Muscle models that don't have a singularity at a=0 will set minActivation to be 0. (Unitless).
muscleName	The name of the muscle that this activation object belongs to. This string is used to create useful exception messages.

Conditions

    0 < twitchTime 
    0 <= minActivation < 1

Computational Cost

    ~15 flops

◆ MuscleSecondOrderActivationDynamicModel() [2/2]

OpenSim::MuscleSecondOrderActivationDynamicModel::MuscleSecondOrderActivationDynamicModel ( )

Default constructor.

Sets data members to NAN and other error causing values

Member Function Documentation

◆ calcDerivative()

double OpenSim::MuscleSecondOrderActivationDynamicModel::calcDerivative	(	double	dactivation_dt,
		double	activation,
		double	excitation
	)		const

Parameters

dactivation_dt	The derivative of activation
excitation	The excitation signal being sent to the muscle (Unitless, [0,1]). This value will be clamped between 0 and 1-minActivation.
activation	The current activation of the muscle(Unitless [0,1]) This value will be clamped to its permitted range between minActivation and 1.

Returns: the time derivative of activation

Conditions

    0 <= excitation <= 1

Computational Cost

◆ clampActivation()

double OpenSim::MuscleSecondOrderActivationDynamicModel::clampActivation ( double activation ) const

Returns

activation that has been clamped to a legal range, that is between minActivation specified in the constructor and 1.0 Computational Cost

    ~2 flops

◆ clone()

MuscleSecondOrderActivationDynamicModel* OpenSim::MuscleSecondOrderActivationDynamicModel::clone ( ) const

inlineoverridevirtual

Create a new heap-allocated copy of the concrete object to which this Object refers.

It is up to the caller to delete the returned object when no longer needed. Every concrete object deriving from Object implements this pure virtual method automatically, via the declaration macro it invokes (e.g., OpenSim_DECLARE_CONCRETE_OBJECT()). Note that the concrete class overrides modify the return type to be a pointer to the concrete object; that still overrides the base class method because the return type is covariant with (that is, derives from) Object.

Implements OpenSim::Object.

◆ ensureModelUpToDate()

void OpenSim::MuscleSecondOrderActivationDynamicModel::ensureModelUpToDate ( )

◆ get_minimum_activation()

const double& OpenSim::MuscleSecondOrderActivationDynamicModel::get_minimum_activation ( ) const

inline

Get the value of the minimum_activation property.

◆ get_twitch_time_constant()

const double& OpenSim::MuscleSecondOrderActivationDynamicModel::get_twitch_time_constant ( ) const

inline

Get the value of the twitch_time_constant property.

◆ getClassName()

static const std::string& OpenSim::MuscleSecondOrderActivationDynamicModel::getClassName ( )

inlinestatic

This returns "MuscleSecondOrderActivationDynamicModel".

See getConcreteClassName() if you want the class name of the underlying concrete object instead.

◆ getConcreteClassName()

const std::string& OpenSim::MuscleSecondOrderActivationDynamicModel::getConcreteClassName ( ) const

inlineoverridevirtual

Returns the class name of the concrete Object-derived class of the actual object referenced by this Object, as a string.

This is the string that is used as the tag for this concrete object in an XML file. Every concrete class derived from Object automatically overrides this method via the declaration macro it uses. See getClassName() to get the class name of the referencing (possibly abstract) class rather than the concrete object.

See also: getClassName()

Implements OpenSim::Object.

◆ getMaximumActivation()

double OpenSim::MuscleSecondOrderActivationDynamicModel::getMaximumActivation ( ) const

Returns: The maximum activation level

Computational Cost

    ~1 flops

◆ getMinimumActivation()

double OpenSim::MuscleSecondOrderActivationDynamicModel::getMinimumActivation ( ) const

Returns: The minimum activation level

Computational Cost

    ~1 flops

◆ getTwitchTimeConstant()

double OpenSim::MuscleSecondOrderActivationDynamicModel::getTwitchTimeConstant ( ) const

Returns: The time to peak of the impulse response of the muscle (sec).

Computational Cost

    ~1 flops

◆ safeDownCast()

static MuscleSecondOrderActivationDynamicModel* OpenSim::MuscleSecondOrderActivationDynamicModel::safeDownCast ( OpenSim::Object * obj )

inlinestatic

For use in MATLAB and Python to access the concrete class.

Example: cObj = MuscleSecondOrderActivationDynamicModel.safeDownCast(obj). This is equivalent to dynamic_cast<MuscleSecondOrderActivationDynamicModel*>(obj) in C++.

◆ set_minimum_activation()

void OpenSim::MuscleSecondOrderActivationDynamicModel::set_minimum_activation ( const double & value )

inline

Set the value of the minimum_activation property.

◆ set_twitch_time_constant()

void OpenSim::MuscleSecondOrderActivationDynamicModel::set_twitch_time_constant ( const double & value )

inline

Set the value of the twitch_time_constant property.

◆ setMinimumActivation()

bool OpenSim::MuscleSecondOrderActivationDynamicModel::setMinimumActivation ( double minimumActivation )

Returns

The minimum activation level

a bool that indicates if the value was set or not
Computational Cost

    ~1 flops

◆ setTwitchTimeConstant()

bool OpenSim::MuscleSecondOrderActivationDynamicModel::setTwitchTimeConstant ( double activationTimeConstant )

Parameters

activationTimeConstant The activation time constant in units of seconds

Returns

a bool that indicates if the value was set or not
Computational Cost

    ~1 flops

◆ upd_minimum_activation()

double& OpenSim::MuscleSecondOrderActivationDynamicModel::upd_minimum_activation ( )

inline

Get a writable reference to the minimum_activation property.

◆ upd_twitch_time_constant()

double& OpenSim::MuscleSecondOrderActivationDynamicModel::upd_twitch_time_constant ( )

inline

Get a writable reference to the twitch_time_constant property.

OpenSim Property, Socket, Output, Input Documentation

◆ minimum_activation

double OpenSim::MuscleSecondOrderActivationDynamicModel::minimum_activation

"activation lower bound"

This property appears in XML files under the tag <minimum_activation>. This property was generated with the OpenSim_DECLARE_PROPERTY macro; see Property to learn about the property system.

See also: get_minimum_activation(), upd_minimum_activation(), set_minimum_activation()

◆ twitch_time_constant

double OpenSim::MuscleSecondOrderActivationDynamicModel::twitch_time_constant

"time-to-peak after an impulse (s)"

This property appears in XML files under the tag <twitch_time_constant>. This property was generated with the OpenSim_DECLARE_PROPERTY macro; see Property to learn about the property system.

See also: get_twitch_time_constant(), upd_twitch_time_constant(), set_twitch_time_constant()

The documentation for this class was generated from the following file:

OpenSim/Actuators/MuscleSecondOrderActivationDynamicModel.h

OpenSim Properties, Sockets, Outputs, Inputs

Public Member Functions

Auto-generated functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ MuscleSecondOrderActivationDynamicModel() [1/2]

◆ MuscleSecondOrderActivationDynamicModel() [2/2]

Member Function Documentation

◆ calcDerivative()

◆ clampActivation()

◆ clone()

◆ ensureModelUpToDate()

◆ get_minimum_activation()

◆ get_twitch_time_constant()

◆ getClassName()

◆ getConcreteClassName()

◆ getMaximumActivation()

◆ getMinimumActivation()

◆ getTwitchTimeConstant()

◆ safeDownCast()

◆ set_minimum_activation()

◆ set_twitch_time_constant()

◆ setMinimumActivation()

◆ setTwitchTimeConstant()

◆ upd_minimum_activation()

◆ upd_twitch_time_constant()

OpenSim Property, Socket, Output, Input Documentation

◆ minimum_activation

◆ twitch_time_constant