Spheroid

This tutorial is automatically generated from TestPySpheroidTutorial.py at revision 86da82f2455f.

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 chaste  # The PyChaste module
import chaste.cell_based  # Contains cell populations
import chaste.mesh  # Contains meshes
import chaste.pde  # PDEs
import chaste.visualization  # Visualization tools
import matplotlib.pyplot as plt  # Plotting
import numpy as np  # Matrix tools

class TestPySpheroidTutorial(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.CellsGenerator["SimpleOxygenBasedCellCycleModel", 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.MeshBasedCellPopulation[2, 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.OffLatticeSimulation[2, 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.GeneralisedLinearSpringForce[2, 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.pde.CellwiseSourceEllipticPde[2](cell_population, -0.5)

We set a constant amount of oxygen on the edge of the spheroid

        bc = chaste.pde.ConstBoundaryCondition[2](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.EllipticGrowingDomainPdeModifier[2](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.VtkScene[2]()
        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.VtkSceneModifier[2]()
        scene_modifier.SetVtkScene(scene)
        scene_modifier.SetUpdateFrequency(100)
        simulator.AddSimulationModifier(scene_modifier)

Eventually remove apoptotic cells

        killer = chaste.cell_based.ApoptoticCellKiller[2](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

import unittest  # Python testing framework

import chaste  # The PyChaste module
import chaste.cell_based  # Contains cell populations
import chaste.mesh  # Contains meshes
import chaste.pde  # PDEs
import chaste.visualization  # Visualization tools
import matplotlib.pyplot as plt  # Plotting
import numpy as np  # Matrix tools

class TestPySpheroidTutorial(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.CellsGenerator["SimpleOxygenBasedCellCycleModel", 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.MeshBasedCellPopulation[2, 2](mesh, cells)

        cell_population.AddPopulationWriterVoronoiDataWriter()

        simulator = chaste.cell_based.OffLatticeSimulation[2, 2](cell_population)
        simulator.SetOutputDirectory("Python/TestSpheroidTutorial")
        simulator.SetEndTime(5.0)

        simulator.SetSamplingTimestepMultiple(100)

        force = chaste.cell_based.GeneralisedLinearSpringForce[2, 2]()
        simulator.AddForce(force)

        pde = chaste.pde.CellwiseSourceEllipticPde[2](cell_population, -0.5)

        bc = chaste.pde.ConstBoundaryCondition[2](1.0)
        is_neumann_bc = False

        # pde_modifier = chaste.cell_based.EllipticGrowingDomainPdeModifier[2](pde, bc, is_neumann_bc)
        # pde_modifier.SetDependentVariableName("oxygen")
        # simulator.AddSimulationModifier(pde_modifier)

        scene = chaste.visualization.VtkScene[2]()
        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.VtkSceneModifier[2]()
        scene_modifier.SetVtkScene(scene)
        scene_modifier.SetUpdateFrequency(100)
        simulator.AddSimulationModifier(scene_modifier)

        killer = chaste.cell_based.ApoptoticCellKiller[2](cell_population)
        simulator.AddCellKiller(killer)

        scene.Start()
        simulator.Solve()

        # JUPYTER_TEARDOWN

if __name__ == "__main__":
    unittest.main(verbosity=2)

Scratch Assay

Tensile Test

Spheroid

Introduction#

The Test#

Test 1 - a 2D mesh-based spheroid#

Full code#

Introduction

The Test

Test 1 - a 2D mesh-based spheroid

Full code