Spherical heart chamber model. More...

#include <ChamberSphere.h>

Inheritance diagram for ChamberSphere:

Public Types
enum	ParamId { rho = 0 , thick0 = 1 , radius0 = 2 , W1 = 3 , W2 = 4 , eta = 5 , sigma_max = 6 , alpha_max = 7 , alpha_min = 8 , tsys = 9 , tdias = 10 , steepness = 11 }
	Local IDs of the parameters. More...

Public Member Functions
	ChamberSphere (int id, Model *model)
	Construct a new ChamberSphere object.

void	setup_dofs (DOFHandler &dofhandler)
	Set up the degrees of freedom (DOF) of the block.

void	update_constant (SparseSystem &system, std::vector< double > &parameters)
	Update the constant contributions of the element in a sparse system.

void	update_time (SparseSystem &system, std::vector< double > &parameters)
	Update the time-dependent contributions of the element in a sparse system.

void	update_solution (SparseSystem &system, std::vector< double > &parameters, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &y, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &dy)
	Update the solution-dependent contributions of the element in a sparse system.

void	get_elastance_values (std::vector< double > &parameters)
	Update the elastance functions which depend on time.

Public Member Functions inherited from Block
	Block (int id, Model *model, BlockType block_type, BlockClass block_class, std::vector< std::pair< std::string, InputParameter > > input_params)
	Construct a new Block object.

	~Block ()
	Destroy the Block object.

	Block (const Block &)=delete
	Copy the Block object.

std::string	get_name ()
	Get the name of the block.

void	update_vessel_type (VesselType type)
	Update vessel type of the block.

void	setup_params_ (const std::vector< int > &param_ids)
	Setup parameter IDs for the block.

void	setup_dofs_ (DOFHandler &dofhandler, int num_equations, const std::list< std::string > &internal_var_names)
	Set up the degrees of freedom (DOF) of the block.

virtual void	setup_model_dependent_params ()
	Setup parameters that depend on the model.

virtual void	setup_initial_state_dependent_params (State initial_state, std::vector< double > &parameters)
	Setup parameters that depend on the initial state.

virtual void	post_solve (Eigen::Matrix< double, Eigen::Dynamic, 1 > &y)
	Modify the solution after solving it.

virtual void	update_gradient (Eigen::SparseMatrix< double > &jacobian, Eigen::Matrix< double, Eigen::Dynamic, 1 > &residual, Eigen::Matrix< double, Eigen::Dynamic, 1 > &alpha, std::vector< double > &y, std::vector< double > &dy)
	Set the gradient of the block contributions with respect to the parameters.

virtual TripletsContributions	get_num_triplets ()
	Get number of triplets of element.

Additional Inherited Members
Public Attributes inherited from Block
const int	id
	Global ID of the block.

const Model *	model
	The model to which the block belongs.

const BlockType	block_type
	Type of this block.

const BlockClass	block_class
	Class of this block.

VesselType	vessel_type = VesselType::neither
	Vessel type of this block.

const std::vector< std::pair< std::string, InputParameter > >	input_params
	Map from name to input parameter.

std::vector< Node * >	inlet_nodes
	Inlet nodes.

std::vector< Node * >	outlet_nodes
	Outlet nodes.

bool	steady = false
	Toggle steady behavior.

bool	input_params_list = false
	Are input parameters given as a list?

std::vector< int >	global_param_ids
	Global IDs for the block parameters.

std::vector< int >	global_var_ids
	Global variable indices of the local element contributions.

std::vector< int >	global_eqn_ids
	Global equation indices of the local element contributions.

TripletsContributions	num_triplets
	Number of triplets of element.

Detailed Description

Spherical heart chamber model.

Models the mechanical behavior of a spherical heart chamber with active contraction. For reference, see [1] Equations (13a-b) for continuum mechanics (without length-dependent contraction valves, vessels) and [6] Equations (12-16) for the simplified active contraction model.

Helper Functions

Cauchy-Green deformation tensor and time derivative:

$C = \left(1 + \frac{r}{r_0} \right)^2$

$\dot{C} = 2 \left(1 + \frac{r}{r_0} \right) \frac{\dot{r}}{r_0}$

Governing equations

Balance of linear momentum:
$\rho d_0 \dot{v} + \frac{d_0}{r_0} \left(1 + \frac{r}{r_0} \right) S - P_\text{out} C = 0$
Spherical stress:
$-S + \tau + 4 (1 - C^{-3}) (W_1 + C W_2) + 2 \eta \dot{C} (1 - 2 C^{-6}) = 0$
Volume change:
$4 \pi r_0^2 Cv - \dot{V} = 0$
Active stress:
$\dot{\tau} + a \tau - \sigma_\text{max} a_+ = 0, \quad a_+ = \max(a, 0), \quad a = f\alpha_\text{max} + (1 - f)\alpha_\text{min}$
with indicator function
$f = S_+ \cdot S_-, \quad S_\pm = \frac{1}{2} \left(1.0 \pm \text{tanh}\left( \frac{t - t_\text{sys/dias}} {\gamma} \right) \right)$
Acceleration:
$\dot{r} - v = 0$
Conservation of mass:
$Q_\text{in} - Q_\text{out} - \dot{V} = 0$
Pressure equality:
$P_\text{in} - P_\text{out} = 0$

Parameters

Parameter sequence for constructing this block:

rho - Density $\rho$
thick0 - Wall thickness
radius0 - Reference radius
W1 - Material constant
W2 - Material constant
eta - Viscosity parameter $\eta$
sigma_max - Maximum active stress $\sigma_\text{max}$
alpha_max - Maximum activation parameter $\alpha_\text{max}$
alpha_min - Minimum activation parameter $\alpha_\text{min}$
tsys - Systole timing parameter $t_\text{sys}$
tdias - Diastole timing parameter $t_\text{dias}$
steepness - Activation steepness parameter $\gamma$

Usage in json configuration file

"vessels": [
   {
       "boundary_conditions": {},
       "vessel_id": 1,
       "vessel_length": 1.0,
       "vessel_name": "ventricle",
       "zero_d_element_type": "ChamberSphere",
       "zero_d_element_values": {
           "rho" : 1e3,
           "thick0" : 0.01,
           "radius0" : 0.05,
           "W1" : 10e3,
           "W2" : 40,
           "eta" : 10.0,
           "sigma_max" : 185e3,
           "alpha_max": 30.0,
           "alpha_min": -30.0,
           "tsys": 0.170,
           "tdias": 0.484,
           "steepness": 0.005
       }
   }
]

Internal variables

Names of internal variables in this block's output:

radius - Chamber radius
velo - Chamber velocity $\dot{r}$
stress - Spherical stress
tau - Active stress $\tau$
volume - Chamber volume

Member Enumeration Documentation

◆ ParamId

enum ChamberSphere::ParamId

Local IDs of the parameters.

Constructor & Destructor Documentation

◆ ChamberSphere()

ChamberSphere::ChamberSphere	(	int	id,
		Model *	model )

inline

Construct a new ChamberSphere object.

Parameters

id	Global ID of the block
model	The model to which the block belongs

Member Function Documentation

◆ get_elastance_values()

void ChamberSphere::get_elastance_values ( std::vector< double > & parameters )

Update the elastance functions which depend on time.

Parameters

parameters Parameters of the model

◆ setup_dofs()

void ChamberSphere::setup_dofs ( DOFHandler & dofhandler )

virtual

Set up the degrees of freedom (DOF) of the block.

Set global_var_ids and global_eqn_ids of the element based on the number of equations and the number of internal variables of the element.

Parameters

dofhandler Degree-of-freedom handler to register variables and equations at

Reimplemented from Block.

◆ update_constant()

void ChamberSphere::update_constant	(	SparseSystem &	system,
		std::vector< double > &	parameters )

virtual

Update the constant contributions of the element in a sparse system.

Parameters

system	System to update contributions at
parameters	Parameters of the model

Reimplemented from Block.

◆ update_solution()

void ChamberSphere::update_solution	(	SparseSystem &	system,
		std::vector< double > &	parameters,
		const Eigen::Matrix< double, Eigen::Dynamic, 1 > &	y,
		const Eigen::Matrix< double, Eigen::Dynamic, 1 > &	dy )

virtual

Update the solution-dependent contributions of the element in a sparse system.

Parameters

system	System to update contributions at
parameters	Parameters of the model
y	Current solution
dy	Current derivate of the solution

Reimplemented from Block.

◆ update_time()

void ChamberSphere::update_time	(	SparseSystem &	system,
		std::vector< double > &	parameters )

virtual

Update the time-dependent contributions of the element in a sparse system.

Parameters

system	System to update contributions at
parameters	Parameters of the model

Reimplemented from Block.

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

model/ChamberSphere.h
model/ChamberSphere.cpp

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

Helper Functions

Governing equations

Parameters

Usage in json configuration file

Internal variables

Member Enumeration Documentation

◆ ParamId

Constructor & Destructor Documentation

◆ ChamberSphere()

Member Function Documentation

◆ get_elastance_values()

◆ setup_dofs()

◆ update_constant()

◆ update_solution()

◆ update_time()