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:

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

	MuscleSecondOrderActivationDynamicModel ()
	Default constructor. More...

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

double	getTwitchTimeConstant () const

double	getMinimumActivation () const

double	getMaximumActivation () const

double	clampActivation (double activation) const

bool	setTwitchTimeConstant (double activationTimeConstant)

bool	setMinimumActivation (double minimumActivation)

void	ensureModelUpToDate ()

Property declarations
These are the serializable properties associated with this class.
	OpenSim_DECLARE_PROPERTY (twitch_time_constant, double,"time-to-peak after an impulse (s)")

	OpenSim_DECLARE_PROPERTY (minimum_activation, double,"activation lower bound")

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

virtual Object *	clone () const =0
	Create a new heap-allocated copy of the concrete object to which this Object refers. More...

virtual const std::string &	getConcreteClassName () const =0
	Returns the class name of the concrete Object-derived class of the actual object referenced by this Object, as a string. More...

virtual const VisibleObject *	getDisplayer () const
	Methods to support making the object displayable in the GUI or Visualizer Implemented only in few objects. More...

virtual VisibleObject *	updDisplayer ()
	get Non const pointer to VisibleObject 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, call this method in your constructor if needed. 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...

void	setObjectIsUpToDateWithProperties ()
	When an object is initialized using the current values of its properties, it can set a flag indicating that it is up to date. 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...

virtual void	updateXMLNode (SimTK::Xml::Element &parent)
	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...

void	setAllPropertiesUseDefault (bool aUseDefault)

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

std::string	dump (bool dumpName=false)
	dump the XML representation of this Object into an std::string and return it. More...

void	clearObjectIsUpToDateWithProperties ()
	For testing or debugging purposes, manually clear the "object is up to date with respect to properties" flag. 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

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

static void	PrintPropertyInfo (std::ostream &os, const std::string &className, const std::string &propertyName)
	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 debug level to get verbose output. More...

static int	getDebugLevel ()
	Get 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...

Static Public Attributes inherited from OpenSim::Object
static const std::string	DEFAULT_NAME
	Name used for default objects when they are serialized. More...

Protected Member Functions inherited from OpenSim::Object
	Object ()
	The default constructor is only for use by constructors of derived types. More...

	Object (const std::string &fileName, bool aUpdateFromXMLNode=true) SWIG_DECLARE_EXCEPTION
	Constructor from a file, to be called from other constructors that take a file as input. More...

	Object (const Object &source)
	Copy constructor is invoked automatically by derived classes with default copy constructors; otherwise it must be invoked explicitly. More...

	Object (SimTK::Xml::Element &aElement)
	Construct the base class portion of an Object from a given Xml element that describes this Object. More...

template<class T >
PropertyIndex	addProperty (const std::string &name, const std::string &comment, const T &value)
	Define a new single-value property of known type T, with the given name, associated comment, and initial value. More...

template<class T >
PropertyIndex	addOptionalProperty (const std::string &name, const std::string &comment)
	Add an optional property, meaning it can contain either no value or a single value. More...

template<class T >
PropertyIndex	addOptionalProperty (const std::string &name, const std::string &comment, const T &value)
	Add an optional property, meaning it can contain either no value or a single value. More...

template<class T >
PropertyIndex	addListProperty (const std::string &name, const std::string &comment, int minSize, int maxSize)
	Define a new list-valued property of known type T, with the given name, associated comment, minimum (==0) and maximum (>0) allowable list lengths, and a zero-length initial value. More...

template<class T , template< class > class Container>
PropertyIndex	addListProperty (const std::string &name, const std::string &comment, int minSize, int maxSize, const Container< T > &valueList)
	Define a new list-valued property as above, but assigning an initial value via some templatized container class that supports size() and indexing. More...

PropertyIndex	getPropertyIndex (const std::string &name) const
	Look up a property by name and return its PropertyIndex if it is found. More...

template<class T >
PropertyIndex	getPropertyIndex () const
	Look up an unnamed property by the type of object it contains, and return its PropertyIndex if it is found. More...

void	updateFromXMLDocument ()
	Use this method only if you're deserializing from a file and the object is at the top level; that is, primarily in constructors that take a file name as input. More...

void	setDocument (XMLDocument *doc)
	Unconditionally set the XMLDocument associated with this object. More...

const XMLDocument *	getDocument () const
	Get a const pointer to the document (if any) associated with this object. More...

XMLDocument *	updDocument ()
	Get a writable pointer to the document (if any) associated with this object. More...

Protected Attributes inherited from OpenSim::Object
PropertySet	_propertySet
	OBSOLETE: Property_Deprecated set for serializable member variables of this and derived classes. More...

Related Functions inherited from OpenSim::Object
#define	OpenSim_DECLARE_CONCRETE_OBJECT(ConcreteClass, SuperClass)
	Macro to be included as the first line of the class declaration for any non-templatized, concrete class that derives from OpenSim::Object. More...

#define	OpenSim_DECLARE_ABSTRACT_OBJECT(ConcreteClass, SuperClass)
	Macro to be included as the first line of the class declaration for any still-abstract class that derives from OpenSim::Object. More...

#define	OpenSim_DECLARE_CONCRETE_OBJECT_T(ConcreteClass, TArg, SuperClass)
	Macro to be included as the first line of the class declaration for any templatized, concrete class that derives from OpenSim::Object, like Set<T>. More...

#define	OpenSim_DECLARE_ABSTRACT_OBJECT_T(ConcreteClass, TArg, SuperClass)
	Macro to be included as the first line of the class declaration for any templatized, still-abstract class that derives from OpenSim::Object. 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 grey area), and Bellmare et al.'s experimental data (thick grey 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 encorporated 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:

$\hat{a} = \frac{a}{1-a_{min}}$

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

Subsituting 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. Bellare et al. reported values of 0.0657, 0.071 and 0.116 for the biceps brachaii, adductor pollicus, and the solues 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 Bimedical 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

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

OpenSim::MuscleSecondOrderActivationDynamicModel::MuscleSecondOrderActivationDynamicModel ( )

Default constructor.

Sets data members to NAN and other error causing values

Member Function Documentation

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

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

void OpenSim::MuscleSecondOrderActivationDynamicModel::ensureModelUpToDate ( )

double OpenSim::MuscleSecondOrderActivationDynamicModel::getMaximumActivation ( ) const

Returns: The maximum activation level

Computational Cost

    ~1 flops

double OpenSim::MuscleSecondOrderActivationDynamicModel::getMinimumActivation ( ) const

Returns: The minimum activation level

Computational Cost

    ~1 flops

double OpenSim::MuscleSecondOrderActivationDynamicModel::getTwitchTimeConstant ( ) const

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

Computational Cost

    ~1 flops

OpenSim::MuscleSecondOrderActivationDynamicModel::OpenSim_DECLARE_PROPERTY	(	twitch_time_constant	,
		double	,
		"time-to-peak after an impulse (s)"
	)

OpenSim::MuscleSecondOrderActivationDynamicModel::OpenSim_DECLARE_PROPERTY	(	minimum_activation	,
		double	,
		"activation lower bound"
	)

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

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

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

OpenSim/Actuators/MuscleSecondOrderActivationDynamicModel.h

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation