Test Spheroid Tutorial
This tutorial is automatically generated from TestSpheroidTutorial at revision 98e266d4. Note that the code is given in full at the bottom of the page.
Introduction
This tutorial is an example of modelling spheroid growth with a nutrient. It covers:
- Setting up an off-lattice cell population
- Setting up a cell cycle model with oxygen dependence
- Setting up and solving an oxygen transport PDE
- Setting up a cell killer
The Test
import unittest # Python testing framework
import matplotlib.pyplot as plt # Plotting
import numpy as np # Matrix tools
import chaste # The PyChaste module
import chaste.mesh # Contains meshes
import chaste.pde # PDEs
import chaste.cell_based # Contains cell populations
import chaste.visualization # Visualization tools
chaste.init() # Set up MPI
class TestSpheroidTutorial(chaste.cell_based.AbstractCellBasedTestSuite):
Test 1 - a 2D mesh-based spheroid
In this test we set up a spheroid with a plentiful supply of oxygen on the boundary and watch it grow over time. Cells can gradually become apoptotic if the oxygen tension is too low.
def test_spheroid(self):
# JUPYTER_SETUP
This time we will use on off-lattice MeshBased
cell population. Cell centres are joined with
springs with a Delauney Triangulation used to identify neighbours. Cell area is given by the dual
(Voronoi Tesselation). We start off with a small number of cells. We use a MutableMesh
which
can change connectivity over time and a HoneycombMeshGenerator
to set it up with a simple
honeycomb pattern. Here the first and second arguments define the size of the mesh -
we have chosen a mesh that is 5 nodes (i.e. cells) wide, and 5 nodes high. The extra ‘2’ argument puts
two layers of non-cell elements around the mesh, which help to form a nicer voronoi tesselation
for area calculations.
chaste.core.OutputFileHandler("Python/TestSpheroidTutorial")
generator = chaste.mesh.HoneycombMeshGenerator(5, 5)
mesh = generator.GetMesh()
We create some cells next, with a stem-like proliferative type. This means they will continually proliferate if there is enough oxygen, similar to how a tumour spheroid may behave.
stem_type = chaste.cell_based.StemCellProliferativeType()
cell_generator = chaste.cell_based.CellsGeneratorSimpleOxygenBasedCellCycleModel_2()
cells = cell_generator.GenerateBasicRandom(mesh.GetNumNodes(), stem_type)
Define when cells become apoptotic
for eachCell in cells:
cell_cycle_model = eachCell.GetCellCycleModel()
eachCell.GetCellData().SetItem("oxygen", 30.0)
cell_cycle_model.SetDimension(2)
cell_cycle_model.SetStemCellG1Duration(4.0)
cell_cycle_model.SetHypoxicConcentration(0.1)
cell_cycle_model.SetQuiescentConcentration(0.3)
cell_cycle_model.SetCriticalHypoxicDuration(8)
g1_duration = cell_cycle_model.GetStemCellG1Duration()
sg2m_duration = cell_cycle_model.GetSG2MDuration()
rnum = chaste.core.RandomNumberGenerator.Instance().ranf()
birth_time = -rnum * (g1_duration + sg2m_duration)
eachCell.SetBirthTime(birth_time)
Now we have a mesh and a set of cells to go with it, we can create a CellPopulation
as before.
cell_population = chaste.cell_based.MeshBasedCellPopulation2_2(mesh, cells)
To view the results of this and the next test in Paraview it is necessary to explicitly generate the required .vtu files.
cell_population.AddPopulationWriterVoronoiDataWriter()
We then pass in the cell population into an OffLatticeSimulation
, and set the output directory and end time.
simulator = chaste.cell_based.OffLatticeSimulation2_2(cell_population)
simulator.SetOutputDirectory("Python/TestSpheroidTutorial")
simulator.SetEndTime(5.0)
We ask for output every 12 increments
simulator.SetSamplingTimestepMultiple(100)
We define how the springs between cells behave using a force law.
force = chaste.cell_based.GeneralisedLinearSpringForce2_2()
simulator.AddForce(force)
We set up a PDE for oxygen diffusion and consumption by cells, setting the rate of consumption to 0.1
pde = chaste.cell_based.CellwiseSourceEllipticPde2(cell_population, -0.5)
We set a constant amount of oxygen on the edge of the spheroid
bc = chaste.pde.ConstBoundaryCondition2(1.0)
is_neumann_bc = False
Set up a pde modifier to solve the PDE at each simulation time step
#pde_modifier = chaste.cell_based.EllipticGrowingDomainPdeModifier2(pde, bc, is_neumann_bc)
#pde_modifier.SetDependentVariableName("oxygen")
#simulator.AddSimulationModifier(pde_modifier)
As before, we set up a scene modifier for real-time visualization
scene = chaste.visualization.VtkScene2()
scene.SetCellPopulation(cell_population)
scene.GetCellPopulationActorGenerator().SetColorByCellData(True)
scene.GetCellPopulationActorGenerator().SetDataLabel("oxygen")
scene.GetCellPopulationActorGenerator().SetShowCellCentres(True)
scene.GetCellPopulationActorGenerator().SetShowVoronoiMeshEdges(False)
# JUPYTER_SHOW_FIRST
scene_modifier = chaste.cell_based.VtkSceneModifier2()
scene_modifier.SetVtkScene(scene)
scene_modifier.SetUpdateFrequency(100)
simulator.AddSimulationModifier(scene_modifier)
Eventually remove apoptotic cells
killer = chaste.cell_based.ApoptoticCellKiller2(cell_population)
simulator.AddCellKiller(killer)
To run the simulation, we call Solve()
. We can again do a quick rendering of the population at the end of the simulation
scene.Start()
simulator.Solve()
# JUPYTER_TEARDOWN
Full results can be visualized in Paraview from the file_handler.GetOutputDirectoryFullPath()
directory.
if __name__ == '__main__':
unittest.main(verbosity=2)
Full code
File name: TestSpheroidTutorial.py
import unittest # Python testing framework
import matplotlib.pyplot as plt # Plotting
import numpy as np # Matrix tools
import chaste # The PyChaste module
import chaste.mesh # Contains meshes
import chaste.pde # PDEs
import chaste.cell_based # Contains cell populations
import chaste.visualization # Visualization tools
chaste.init() # Set up MPI
class TestSpheroidTutorial(chaste.cell_based.AbstractCellBasedTestSuite):
def test_spheroid(self):
# JUPYTER_SETUP
chaste.core.OutputFileHandler("Python/TestSpheroidTutorial")
generator = chaste.mesh.HoneycombMeshGenerator(5, 5)
mesh = generator.GetMesh()
stem_type = chaste.cell_based.StemCellProliferativeType()
cell_generator = chaste.cell_based.CellsGeneratorSimpleOxygenBasedCellCycleModel_2()
cells = cell_generator.GenerateBasicRandom(mesh.GetNumNodes(), stem_type)
for eachCell in cells:
cell_cycle_model = eachCell.GetCellCycleModel()
eachCell.GetCellData().SetItem("oxygen", 30.0)
cell_cycle_model.SetDimension(2)
cell_cycle_model.SetStemCellG1Duration(4.0)
cell_cycle_model.SetHypoxicConcentration(0.1)
cell_cycle_model.SetQuiescentConcentration(0.3)
cell_cycle_model.SetCriticalHypoxicDuration(8)
g1_duration = cell_cycle_model.GetStemCellG1Duration()
sg2m_duration = cell_cycle_model.GetSG2MDuration()
rnum = chaste.core.RandomNumberGenerator.Instance().ranf()
birth_time = -rnum * (g1_duration + sg2m_duration)
eachCell.SetBirthTime(birth_time)
cell_population = chaste.cell_based.MeshBasedCellPopulation2_2(mesh, cells)
cell_population.AddPopulationWriterVoronoiDataWriter()
simulator = chaste.cell_based.OffLatticeSimulation2_2(cell_population)
simulator.SetOutputDirectory("Python/TestSpheroidTutorial")
simulator.SetEndTime(5.0)
simulator.SetSamplingTimestepMultiple(100)
force = chaste.cell_based.GeneralisedLinearSpringForce2_2()
simulator.AddForce(force)
pde = chaste.cell_based.CellwiseSourceEllipticPde2(cell_population, -0.5)
bc = chaste.pde.ConstBoundaryCondition2(1.0)
is_neumann_bc = False
#pde_modifier = chaste.cell_based.EllipticGrowingDomainPdeModifier2(pde, bc, is_neumann_bc)
#pde_modifier.SetDependentVariableName("oxygen")
#simulator.AddSimulationModifier(pde_modifier)
scene = chaste.visualization.VtkScene2()
scene.SetCellPopulation(cell_population)
scene.GetCellPopulationActorGenerator().SetColorByCellData(True)
scene.GetCellPopulationActorGenerator().SetDataLabel("oxygen")
scene.GetCellPopulationActorGenerator().SetShowCellCentres(True)
scene.GetCellPopulationActorGenerator().SetShowVoronoiMeshEdges(False)
# JUPYTER_SHOW_FIRST
scene_modifier = chaste.cell_based.VtkSceneModifier2()
scene_modifier.SetVtkScene(scene)
scene_modifier.SetUpdateFrequency(100)
simulator.AddSimulationModifier(scene_modifier)
killer = chaste.cell_based.ApoptoticCellKiller2(cell_population)
simulator.AddCellKiller(killer)
scene.Start()
simulator.Solve()
# JUPYTER_TEARDOWN
if __name__ == '__main__':
unittest.main(verbosity=2)