This tutorial is automatically generated from the file test/python/cell_based/tutorials/TestTensileTestTutorial.py.

In [2]:
# Jupyter notebook specific imports
import matplotlib as mpl
from IPython import display
%matplotlib inline


# Introduction¶

In this tutorial we will demonstrate a simulated tensile test on an epithelial sheet. This test demonstrates:

• Working with vertex based off lattice populations
• Applying boundary conditions
• Working with forces

## The Test¶

In [3]:
import matplotlib.pyplot as plt # Plotting
import numpy as np # Matrix tools
import chaste # The PyChaste module
chaste.init() # Set up MPI
import chaste.cell_based # Contains cell populations
import chaste.mesh # Contains meshes
import chaste.visualization # Visualization tools


## Test 1 - A 2d test¶

In [4]:
# Set up the test
chaste.cell_based.SetupNotebookTest()


First, we generate a vertex mesh using a HoneycombVertexMeshGenerator.

In [5]:
generator = chaste.mesh.HoneycombVertexMeshGenerator(5, 15)
mesh = generator.GetMesh()


Now set up the cells, again we want to avoid proliferation.

In [6]:
cells = chaste.cell_based.VecCellPtr()
differentiated_type = chaste.cell_based.DifferentiatedCellProliferativeType()
cell_generator = chaste.cell_based.CellsGeneratorUniformG1GenerationalCellCycleModel_2()
cell_generator.GenerateBasicRandom(cells, mesh.GetNumElements(), differentiated_type)


Next, create the cell population

In [7]:
cell_population = chaste.cell_based.VertexBasedCellPopulation2(mesh, cells)


Pass the cell population into an OffLatticeSimulation, and set the output directory, output multiple and end time

In [8]:
simulator = chaste.cell_based.OffLatticeSimulation2_2(cell_population)
simulator.SetOutputDirectory("Python/TestTensileTest")
simulator.SetEndTime(1.0)
simulator.SetSamplingTimestepMultiple(1000)


Now create a force law

In [9]:
force = chaste.cell_based.NagaiHondaForce2()


A NagaiHondaForce assumes that each cell has a target area. The target areas of cells are used to determine pressure forces on each vertex and eventually determine the size of each cell in the simulation. In order to assign target areas to cells and update them in each time step we add a SimpleTargetAreaModifier to the simulation, which inherits from AbstractTargetAreaModifier.

In [10]:
growth_modifier = chaste.cell_based.SimpleTargetAreaModifier2()


For our tensile test we will fix the bottom of the sheet and subject the top to an applied displacement. We neglect fixing lateral degress of freedom for simplicity, since we are using an over-damped mechanical model.

In [11]:
point = (0.0, 0.0)
normal = (0.0, -1.0)
bc = chaste.cell_based.AttractingPlaneBoundaryCondition2_2(cell_population, point, normal)
point = (0.0, 13.3)
normal = (0.0, 1.0)
bc2 = chaste.cell_based.AttractingPlaneBoundaryCondition2_2(cell_population, point, normal)


We want to displace our top boundary over time. We could write a custom boundary condition class to do this. A more simple alternative is to modify the the position of the point describing our boundary plane in bc2 as the simulation progresses. As per earlier tutorials we make a new SimulationModifier class to do this.

In [12]:
class BoundaryConditionModifier(chaste.cell_based.AbstractCellBasedSimulationModifier2_2):
""" Class for time varying boundary conditions
"""
def __init__(self, boundary_condition):
self.boundary_condition = boundary_condition
self.original_location = boundary_condition.rGetPointOnPlane()
self.velocity = 0.5 # cell lengths per time
super(BoundaryConditionModifier, self).__init__()
def UpdateAtEndOfTimeStep(self, cell_population):
""" Move the boundary upwards at the specified velocity
"""
total_time = chaste.cell_based.SimulationTime.Instance().GetTime()
new_location = [self.original_location[0],
self.original_location[1] + self.velocity*total_time]
self.boundary_condition.SetPointOnPlane(np.array(new_location))
def SetupSolve(self, cell_population, output_directory):
""" Make sure the cell population is in the correct state at the start of the simulation
"""
cell_population.Update()
def OutputSimulationModifierParameters(self, rParamsFile):
""" This needs to be explicitly over-ridden as the C++ method is pure virtual.
"""
pass
bc_modifier = BoundaryConditionModifier(bc2)


PyChaste can do simple 3D rendering with VTK. We set up a VtkScene so that we can see the population evovle in real time.

In [13]:
scene= chaste.visualization.VtkScene2()
scene.SetCellPopulation(cell_population)
nb_manager = chaste.visualization.JupyterNotebookManager()
scene_modifier = chaste.visualization.JupyterSceneModifier2(nb_manager)
scene_modifier.SetVtkScene(scene)
scene_modifier.SetUpdateFrequency(1000)

To run the simulation, we call Solve().
scene.Start()