Resistor-capacitor-inductor blood vessel with optional stenosis. More...

#include <BloodVessel.h>

Inheritance diagram for BloodVessel:

Public Types
enum	ParamId { RESISTANCE = 0 , CAPACITANCE = 1 , INDUCTANCE = 2 , STENOSIS_COEFFICIENT = 3 }
	Local IDs of the parameters. More...

Public Member Functions
	BloodVessel (int id, Model *model)
	Construct a new BloodVessel 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_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	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.

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

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

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

Public Attributes
TripletsContributions	num_triplets {5, 3, 2}
	Number of triplets of element.

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

Resistor-capacitor-inductor blood vessel with optional stenosis.

Models the mechanical behavior of a bloodvessel with optional stenosis.

$\begin{circuitikz} \draw node[left] {$Q_{in}$} [-latex] (0,0) -- (0.8,0); \draw (1,0) node[anchor=south]{$P_{in}$} to [R, l=$R$, *-] (3,0) to [R, l=$S$, -] (5,0) (5,0) to [L, l=$L$, -*] (7,0) node[anchor=south]{$P_{out}$} (5,0) to [C, l=$C$, -] (5,-1.5) node[ground]{}; \draw [-latex] (7.2,0) -- (8,0) node[right] {$Q_{out}$}; \end{circuitikz}$

Governing equations

$P_\text{in}-P_\text{out} - (R + S|Q_\text{in}|) Q_\text{in}-L \dot{Q}_\text{out}=0$

$Q_\text{in}-Q_\text{out} - C \dot{P}_\text{in}+C(R + 2S|Q_\text{in}|) \dot{Q}_{in}=0$

Local contributions

$\mathbf{y}^{e}=\left[\begin{array}{llll}P_{i n} & Q_{in} & P_{out} & Q_{out}\end{array}\right]^\text{T}$

$\mathbf{F}^{e}=\left[\begin{array}{cccc} 1 & -R & -1 & 0 \\ 0 & 1 & 0 & -1 \end{array}\right]$

$\mathbf{E}^{e}=\left[\begin{array}{cccc} 0 & 0 & 0 & -L \\ -C & CR & 0 & 0 \end{array}\right]$

$\mathbf{c}^{e} = S|Q_\text{in}| \left[\begin{array}{c} -Q_\text{in} \\ 2C\dot{Q}_\text{in} \end{array}\right]$

$\left(\frac{\partial\mathbf{c}}{\partial\mathbf{y}}\right)^{e} = S \text{sgn} (Q_\text{in}) \left[\begin{array}{cccc} 0 & -2Q_\text{in} & 0 & 0 \\ 0 & 2C\dot{Q}_\text{in} & 0 & 0 \end{array}\right]$

$\left(\frac{\partial\mathbf{c}}{\partial\dot{\mathbf{y}}}\right)^{e} = S|Q_\text{in}| \left[\begin{array}{cccc} 0 & 0 & 0 & 0 \\ 0 & 2C & 0 & 0 \end{array}\right]$

with the stenosis resistance $S=K_{t} \frac{\rho}{2 A_{o}^{2}}\left(\frac{A_{o}}{A_{s}}-1\right)^{2}$ . , , and refer to Poisieuille resistance, capacitance and inductance, respectively.

Gradient

Gradient of the equations with respect to the parameters:

$\mathbf{J}^{e} = \left[\begin{array}{cccc} -y_2 & 0 & -\dot{y}_4 & -|y_2|y_2 \\ C\dot{y}_2 & (-\dot{y}_1+(R+2S|Q_\text{in}|)\dot{y}_2) & 0 & 2C|y_2|\dot{y}_2 \end{array}\right]$

Parameters

Parameter sequence for constructing this block

0 Poiseuille resistance
1 Capacitance
2 Inductance
3 Stenosis coefficient

Internal variables

This block has no internal variables.

Member Enumeration Documentation

◆ ParamId

enum BloodVessel::ParamId

Local IDs of the parameters.

Constructor & Destructor Documentation

◆ BloodVessel()

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

inline

Construct a new BloodVessel object.

Parameters

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

Member Function Documentation

◆ setup_dofs()

void BloodVessel::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 BloodVessel::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_gradient()

void BloodVessel::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 )

virtual

Set the gradient of the block contributions with respect to the parameters.

Parameters

jacobian	Jacobian with respect to the parameters
alpha	Current parameter vector
residual	Residual with respect to the parameters
y	Current solution
dy	Time-derivative of the current solution

Reimplemented from Block.

◆ update_solution()

void BloodVessel::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.

Member Data Documentation

◆ num_triplets

TripletsContributions BloodVessel::num_triplets {5, 3, 2}

Number of triplets of element.

Number of triplets that the element contributes to the global system (relevant for sparse memory reservation)

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

model/BloodVessel.h
model/BloodVessel.cpp

Public Types

Public Member Functions

Public Attributes

Detailed Description

Governing equations

Local contributions

Gradient

Parameters

Internal variables

Member Enumeration Documentation

◆ ParamId

Constructor & Destructor Documentation

◆ BloodVessel()

Member Function Documentation

◆ setup_dofs()

◆ update_constant()

◆ update_gradient()

◆ update_solution()

Member Data Documentation

◆ num_triplets