# Inflation of a Passive Left Ventricular Model With Infarct

### Description

- This example guides you through setting up and running a physical and material nonlinear problem of the passive inflation of a left ventricular model using pressure (natural) boundary conditions.
- The mesh consists of 48 tri-cubic (cubic-cubic-cubic) elements. The material chosen is a transversely isotropic exponential strain energy function. The material is stiffer in the fiber direction than perpendicular to them. The fibers whose orientation is defined by fiber angles in the node form with respect to the circumferential direction vary linearly in radial direction across the wall from -60 degrees on the epicardium to +60 degrees on the endocardium. The boundary conditions assure that all rigid body motions are suppressed. Pressure is prescribed on the endocardium to simulate the passive filling of a ventricle (diastole).
- The model has an apical infarct. The myocardium is stiffer in the infarct region.

### Start Continuity

- Launch the Continuity 6.4 Client
On the About Continuity 6.4 startup screen

leave the

**mesh**checkbox checked under`Use Modules:`check the

**biomechanics**checkbox under`Use Modules:`

Click

**OK**to bring up the main window

### Load File From Database

#### Load Model

- Right click on the entry Pat7_Unloaded_Inflation.
Click

**Load.**Choose

**Reset**or not based on if you already have a model open.

#### Edit Model

Mesh→Edit→Material Coordinates...

Under

**Parameters**change the the**Fiber angle**from a set`value`of zero getting the fiber angle from a`field`.Select the

`Fiber Angle`field to use the predefined fiber angles.

In the nodes form, select a

`Linear-Linear-Linear`basis function for`Field Variable 2`

If the Dimensions Form appears, simply click

**Apply Marked Recommendations**and then**OK**

#### List Volume

Select

**undeformed**or**deformed**under`Select a Mesh`Click

**OK**to submit`List Volume Form`

#### Render Elements

Click the

**lines**radio buttonClick

**Render**to display mesh linesClick the

**surfaces**or**texture**radio buttonFor 3D elements, chose an

`Xi`plane (**1**,**2**or**3**) to renderEnter an

`Xi Location`between**0.0**and**1.0**for rendering the surfaceClick

**Render**to display mesh surfaces

#### Render Fibers

Specify a list of

**Elements**to render or leave the default`all`Specify a list of

**Xi3 Locations**Specify a vector

**Length**normalized by the element dimension or click**Auto**- Specify the number of material vectors to render per element in each direction
Click

**OK**to render material axes

### Biomechanics Menu

#### Edit Constitutive Model

Use the

**Edit equations**tab to create and name intermediate symbolic or evaluated variables and write the equations that define the`Dependent variable`for this model, which is**Stress**in terms of the`Independent variables`which include hydrostatic**pressure**, the`material coordinate transformation`**dY_dMatl**, the deformation gradient of deformed curvilinear coordinate with respect to undeformed material coordinates**dX_dMatl**, and the curvilinear world coordinate transformation**dy_dx**.**Stress**is a square matrix containing the components of the`Lagrangian Second Piola-Kirchhoff Stress tensor`with respect to`material coordinates`.Equations are entered using Sympy

Use the

**Parameters**list to set adjustable material parametersThe model

`Parameters list`is generated from the equations. Quantities delimited by <anglebrackets> in the equations are parametersSelect a

`parameter`in the listYou can edit its

`Description`, specify its default value to be defined by a constant`value`or a`field variable`or a`field variable derivative`.You can also add exceptions using the

**Add exception in...**popup menu that allows alternative parameter values or fields to be specified according to a prescribed`element list`or a prescribed`field range`for a specified field variable.

The

**View equations**displays a complete listing of the Sympy equations defining the model.The

**Compile**button is where C code is generated from the Sympy model and compiledClick the

**Compile**button to compile the model on the default serverClick

**View code**to generate and view a C code listing of the model

Click the

**Submit**button in the**Submit**tab to submit the`Constitutive Model`.

#### Edit Boundary Conditions

Biomechanics→Edit→Boundary Conditions...

The

**Initial Conditions**tab looks like the**Coordinates**tab of the Mesh→Edit→Nodes... form.You can use the Biomechanics→Update→Initial conditions with undeformed nodes command to initialize the

`Deformed Coordinates`with the undeformed nodal coordinates.Use the tabs

**Deformed Coordinate 1**,**Deformed Coordinate 2**,**Deformed Coordinate 3**,**Hydrostatic Pressure**to specify nodal boundary conditionsClick

**Insert Nodes**to create a boundary condition for one or more nodes.Insert a

**node number**, list of**node numbers**or**node number**label in the`Node(s)`fieldUse the pop-up menu to choose a nodal

**Derivative**parameter to constrain or apply force toUse the pop-up menu to select

**displacement**,**force**,**coupled**or**spring**`Boundary Condition Type`Enter a

**value**where 0.0 would mean no displacement or forceIf

**coupled**`Boundary Condition Type`is selected, the second row of options is enabledYou can couple the specified constrained nodal degrees of freedom to a selected

`Derivative`of one or more`Coupled Node(s)`of a selected`Dependent variable`via a coupling`Coefficient`. Enter one or more**Coupled Node(s)**, select**Derivative**and**Dependent Variable**from the appropriate pop-pu menus and enter the coupling**Coefficient**

Click the

**OK**button to submit`Boundary Conditions Form`

#### Update Initial conditions with undeformed nodes

Biomechanics→Update→Initial conditions with undeformed nodes

This command copies the nodal geometric coordinates and derivatives from the

`Node Form`to the`Initial Conditions`tab of the`Boundary Conditions Form`

#### Solve Nonlinear

Biomechanics→Solve Nonlinear...

Specify the

**Time Step**as 0.0,**Initial Time**as 1.0, and**Number of Steps**as 10Click the

**Solve**button, and wait for the solver to finish. While the solution is being computed the window will remain open. There will also be output listed to the console window and the Python shell.

#### List Stress and Strain

Biomechanics→List Stress and Strain...

In the

`Variables`tab, use checkboxes to deselect any variables you do not wish to listNote that the

`Output Variables`are calculated using the equations entered in the`Output Variable`folder of the submitted`Constitutive model`In the

`Locations`tab, you can selected the element list and points which which solutions will be listedClick

**OK**to display a listing of the selected`Output Variables`in the Table Manager

#### Render Surface

Biomechanics→Render Surface...

Enter

**Element List**or leave default value or**all**Select an unused

**Field Variable**that will hold nodal values of the solution to be interpolated and renderedCheck the

**undeformed**or**deformed**radio button to indicate whether you want to the solution rendered on the undeformed or deformed geometrySelect the output variable form the menu. For vector and tensor variables, a choice of components will be presented. Output will be referred to coordinate frames as determined by equations in the

`Output Variables`folder of the`Constitutive Model Editor`Click

**OK**to create a color-coded surface rendering of the chosen output variable