Running Vertex Based Simulations

This tutorial is automatically generated from TestRunningVertexBasedSimulationsTutorial.hpp at revision 409e06cb314b. Note that the code is given in full at the bottom of the page.

Examples showing how to create, run and visualize vertex-based simulations

Introduction

In this tutorial we show how Chaste can be used to create, run and visualize vertex-based simulations. Full details of the mechanical model proposed by T. Nagai and H. Honda, 2000, “A dynamic cell model for the formation of epithelial tissues”, Philosophical Magazine Part B 81:699-719, doi:10.1103/PhysRevLett.69.2013.

The test

As in previous cell-based Chaste tutorials, we begin by including the necessary header files.

#include <cxxtest/TestSuite.h>
#include "CheckpointArchiveTypes.hpp"
#include "AbstractCellBasedTestSuite.hpp"

The remaining header files define classes that will be used in the cell-based simulation. We have encountered some of these header files in previous cell-based Chaste tutorials.

#include "CellsGenerator.hpp"
#include "OffLatticeSimulation.hpp"
#include "TransitCellProliferativeType.hpp"
#include "SmartPointers.hpp"

The next header file defines the cell cycle model.

#include "UniformG1GenerationalCellCycleModel.hpp"

The next two header files define a helper class for generating suitable meshes: one planar and one periodic.

#include "HoneycombVertexMeshGenerator.hpp"
#include "CylindricalHoneycombVertexMeshGenerator.hpp"

The next header file defines a vertex-based CellPopulation class.

#include "VertexBasedCellPopulation.hpp"

The next header file defines a force law for describing the mechanical interactions between neighbouring cells in the cell population, subject to each vertex.

#include "NagaiHondaForce.hpp"

This force law assumes that cells possess a “target area” property which determines the size of each cell in the simulation. In order to assign target areas to cells and update them in each time step, we need the next header file.

#include "SimpleTargetAreaModifier.hpp"

The next header file defines a boundary condition for the cells.

#include "PlaneBoundaryCondition.hpp"

The next header file defines a cell killer, which specifies how cells are removed from the simulation.

#include "PlaneBasedCellKiller.hpp"

Finally, we include a header that enforces running this test only on one process.

#include "FakePetscSetup.hpp"

Next, we define the test class, which inherits from AbstractCellBasedTestSuite and defines some test methods.

class TestRunningVertexBasedSimulationsTutorial : public AbstractCellBasedTestSuite
{
public:

Test 1 - a basic vertex-based simulation

In the first test, we run a simple vertex-based simulation, in which we create a monolayer of cells, using a mutable vertex mesh. Each cell is assigned a stochastic cell-cycle model.

    void TestMonolayer()
    {

First, we generate a vertex mesh. To create a MutableVertexMesh, we can use the HoneycombVertexMeshGenerator. This generates a honeycomb-shaped mesh, in which all nodes are equidistant. Here the first and second arguments define the size of the mesh - we have chosen a mesh that is 2 elements (i.e. cells) wide, and 2 elements high.

        HoneycombVertexMeshGenerator generator(2, 2);    // Parameters are: cells across, cells up
        boost::shared_ptr<MutableVertexMesh<2,2> > p_mesh = generator.GetMesh();

Having created a mesh, we now create a std::vector of CellPtrs. To do this, we use the CellsGenerator helper class, which is templated over the type of cell model required (here UniformG1GenerationalCellCycleModel) and the dimension. We create an empty vector of cells and pass this into the method along with the mesh. The second argument represents the size of that the vector cells should become - one cell for each element, the third argument specifies the proliferative type of the cell.

        std::vector<CellPtr> cells;
        MAKE_PTR(TransitCellProliferativeType, p_transit_type);
        CellsGenerator<UniformG1GenerationalCellCycleModel, 2> cells_generator;
        cells_generator.GenerateBasicRandom(cells, p_mesh->GetNumElements(), p_transit_type);

Now we have a mesh and a set of cells to go with it, we can create a CellPopulation. In general, this class associates a collection of cells with a mesh. For this test, because we have a MutableVertexMesh, we use a particular type of cell population called a VertexBasedCellPopulation.

        VertexBasedCellPopulation<2> cell_population(*p_mesh, cells);

We then pass the cell population into an OffLatticeSimulation, and set the output directory and end time.

        OffLatticeSimulation<2> simulator(cell_population);
        simulator.SetOutputDirectory("VertexBasedMonolayer");
        simulator.SetEndTime(1.0);

For longer simulations, we may not want to output the results every time step. In this case we can use the following method, to print results every 50 time steps instead. As the default time step used by the simulator (for vertex based simulations), is 0.02 hours, this method will cause the simulator to print results every 6 minutes (i.e. 0.1 hours).

        simulator.SetSamplingTimestepMultiple(50);

We must now create one or more force laws, which determine the mechanics of the vertices of each cell in a cell population. For this test, we use one force law, based on the Nagai-Honda mechanics, and pass it to the OffLatticeSimulation. For a list of possible forces see subclasses of AbstractForce. These can be found in the inheritance diagram, here, AbstractForce. Note that some of these forces are not compatible with vertex-based simulations see the specific class documentation for details, if you try to use an incompatible class then you will receive a warning.

        MAKE_PTR(NagaiHondaForce<2>, p_force);
        simulator.AddForce(p_force);

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 to model growth, we add a SimpleTargetAreaModifier to the simulation, which inherits from AbstractTargetAreaModifier.

        MAKE_PTR(SimpleTargetAreaModifier<2>, p_growth_modifier);
        simulator.AddSimulationModifier(p_growth_modifier);

To run the simulation, we call Solve().

        simulator.Solve();

The next two lines are for test purposes only and are not part of this tutorial. If different simulation input parameters are being explored the lines should be removed.

        TS_ASSERT_EQUALS(cell_population.GetNumRealCells(), 4u);
        TS_ASSERT_DELTA(SimulationTime::Instance()->GetTime(), 1.0, 1e-10);
    }

To visualize the results, open a new terminal, cd to the Chaste directory, then cd to anim. Then do: java Visualize2dVertexCells $CHASTE_TEST_OUTPUT/VertexBasedMonolayer/results_from_time_0. We may have to do: javac Visualize2dVertexCells.java beforehand to create the java executable.

Test 2 - introducing periodicity, boundaries and cell killers

In the second test, we run a simple vertex-based simulation, in which we create a monolayer of cells in a periodic geometry, using a cylindrical vertex mesh. We also include a fixed boundary which cells can’t pass through and a cell killer which removes cells once they leave a region. As before each cell is assigned a stochastic cell-cycle model.

    void TestPeriodicMonolayer()
    {

First, we generate a periodic vertex mesh. To create a Cylindrical2dVertexMesh, we can use the CylindricalHoneycombVertexMeshGenerator. This generates a honeycomb-shaped mesh, in which all nodes are equidistant and the right hand side is associated with the left hand side. Here the first and second arguments define the size of the mesh - we have chosen a mesh that is 4 elements (i.e. cells) wide, and 4 elements high.

        CylindricalHoneycombVertexMeshGenerator generator(4, 4);    // Parameters are: cells across, cells up
        boost::shared_ptr<Cylindrical2dVertexMesh> p_mesh = generator.GetCylindricalMesh();

Having created a mesh, we now create a std::vector of CellPtrs. This is exactly the same as the above test.

        std::vector<CellPtr> cells;
        MAKE_PTR(TransitCellProliferativeType, p_transit_type);
        CellsGenerator<UniformG1GenerationalCellCycleModel, 2> cells_generator;
        cells_generator.GenerateBasicRandom(cells, p_mesh->GetNumElements(), p_transit_type);

Now we have a mesh and a set of cells to go with it, we can create a CellPopulation. This is also the same as in the above test.

        VertexBasedCellPopulation<2> cell_population(*p_mesh, cells);

As always we then pass the cell population into an OffLatticeSimulation, and set the output directory, output multiple and end time.

        OffLatticeSimulation<2> simulator(cell_population);
        simulator.SetOutputDirectory("VertexBasedPeriodicMonolayer");
        simulator.SetSamplingTimestepMultiple(50);
        simulator.SetEndTime(1.0);

We now make a pointer to an appropriate force and pass it to the OffLatticeSimulation.

        MAKE_PTR(NagaiHondaForce<2>, p_force);
        simulator.AddForce(p_force);

We also make a pointer to a target area modifier and add it to the simulator.

        MAKE_PTR(SimpleTargetAreaModifier<2>, p_growth_modifier);
        simulator.AddSimulationModifier(p_growth_modifier);

We now create one or more CellPopulationBoundaryConditions, which determine any conditions which each cell in a cell population must satisfy. For this test, we use a PlaneBoundaryCondition, and pass it to the OffLatticeSimulation. For a list of possible boundary condition see subclasses of AbstractCellPopulationBoundaryCondition. These can be found in the inheritance diagram, here, AbstractCellPopulationBoundaryCondition. Note that some of these boundary conditions are not compatible with vertex-based simulations see the specific class documentation for details, if you try to use an incompatible class then you will receive a warning.

The first step is to define a point on the plane boundary and a normal to the plane.

        c_vector<double,2> point = zero_vector<double>(2);
        c_vector<double,2> normal = zero_vector<double>(2);
        normal(1) = -1.0;

We can now make a pointer to a PlaneBoundaryCondition (passing the point and normal to the plane) and pass it to the OffLatticeSimulation.

        MAKE_PTR_ARGS(PlaneBoundaryCondition<2>, p_bc, (&cell_population, point, normal));
        simulator.AddCellPopulationBoundaryCondition(p_bc);

We now create one or more CellKillers, which determine how cells are removed from the simulation. For this test, we use a PlaneBasedCellKiller, and pass it to the OffLatticeSimulation. For a list of possible cell killers see subclasses of AbstractCellKiller. These can be found in the inheritance diagram, here, AbstractCellKiller.

The first step is to define a point on the plane boundary and a normal to the plane. We reuse the point and normal from the PlaneBoundaryCondition.

        point(1) = 3.0;
        normal(1) = 1.0;

Finally we now make a pointer to a PlaneBasedCellKiller (passing the point and normal to the plane) and pass it to the OffLatticeSimulation.

        MAKE_PTR_ARGS(PlaneBasedCellKiller<2>, p_killer, (&cell_population, point, normal));
        simulator.AddCellKiller(p_killer);

To run the simulation, we call Solve().

        simulator.Solve();

The next two lines are for test purposes only and are not part of this tutorial.

        TS_ASSERT_EQUALS(cell_population.GetNumRealCells(), 12u);
        TS_ASSERT_DELTA(SimulationTime::Instance()->GetTime(), 1.0, 1e-10);
    }
};

To visualize the results, open a new terminal, cd to the Chaste directory, then cd to anim. Then do: java Visualize2dVertexCells $CHASTE_TEST_OUTPUT/VertexBasedPeriodicMonolayer/results_from_time_0.

You should see that the edges of the mesh are identical on both sides; cells no longer pass through the line y=0; and cells are removed at y=3.

Full code

#include <cxxtest/TestSuite.h>
#include "CheckpointArchiveTypes.hpp"
#include "AbstractCellBasedTestSuite.hpp"

#include "CellsGenerator.hpp"
#include "OffLatticeSimulation.hpp"
#include "TransitCellProliferativeType.hpp"
#include "SmartPointers.hpp"
#include "UniformG1GenerationalCellCycleModel.hpp"
#include "HoneycombVertexMeshGenerator.hpp"
#include "CylindricalHoneycombVertexMeshGenerator.hpp"
#include "VertexBasedCellPopulation.hpp"
#include "NagaiHondaForce.hpp"
#include "SimpleTargetAreaModifier.hpp"
#include "PlaneBoundaryCondition.hpp"
#include "PlaneBasedCellKiller.hpp"

#include "FakePetscSetup.hpp"

class TestRunningVertexBasedSimulationsTutorial : public AbstractCellBasedTestSuite
{
public:
    void TestMonolayer()
    {
        HoneycombVertexMeshGenerator generator(2, 2);    // Parameters are: cells across, cells up
        boost::shared_ptr<MutableVertexMesh<2,2> > p_mesh = generator.GetMesh();

        std::vector<CellPtr> cells;
        MAKE_PTR(TransitCellProliferativeType, p_transit_type);
        CellsGenerator<UniformG1GenerationalCellCycleModel, 2> cells_generator;
        cells_generator.GenerateBasicRandom(cells, p_mesh->GetNumElements(), p_transit_type);

        VertexBasedCellPopulation<2> cell_population(*p_mesh, cells);

        OffLatticeSimulation<2> simulator(cell_population);
        simulator.SetOutputDirectory("VertexBasedMonolayer");
        simulator.SetEndTime(1.0);

        simulator.SetSamplingTimestepMultiple(50);

        MAKE_PTR(NagaiHondaForce<2>, p_force);
        simulator.AddForce(p_force);

        MAKE_PTR(SimpleTargetAreaModifier<2>, p_growth_modifier);
        simulator.AddSimulationModifier(p_growth_modifier);

        simulator.Solve();

        TS_ASSERT_EQUALS(cell_population.GetNumRealCells(), 4u);
        TS_ASSERT_DELTA(SimulationTime::Instance()->GetTime(), 1.0, 1e-10);
    }

    void TestPeriodicMonolayer()
    {
        CylindricalHoneycombVertexMeshGenerator generator(4, 4);    // Parameters are: cells across, cells up
        boost::shared_ptr<Cylindrical2dVertexMesh> p_mesh = generator.GetCylindricalMesh();

        std::vector<CellPtr> cells;
        MAKE_PTR(TransitCellProliferativeType, p_transit_type);
        CellsGenerator<UniformG1GenerationalCellCycleModel, 2> cells_generator;
        cells_generator.GenerateBasicRandom(cells, p_mesh->GetNumElements(), p_transit_type);

        VertexBasedCellPopulation<2> cell_population(*p_mesh, cells);

        OffLatticeSimulation<2> simulator(cell_population);
        simulator.SetOutputDirectory("VertexBasedPeriodicMonolayer");
        simulator.SetSamplingTimestepMultiple(50);
        simulator.SetEndTime(1.0);

        MAKE_PTR(NagaiHondaForce<2>, p_force);
        simulator.AddForce(p_force);

        MAKE_PTR(SimpleTargetAreaModifier<2>, p_growth_modifier);
        simulator.AddSimulationModifier(p_growth_modifier);

        c_vector<double,2> point = zero_vector<double>(2);
        c_vector<double,2> normal = zero_vector<double>(2);
        normal(1) = -1.0;
        MAKE_PTR_ARGS(PlaneBoundaryCondition<2>, p_bc, (&cell_population, point, normal));
        simulator.AddCellPopulationBoundaryCondition(p_bc);

        point(1) = 3.0;
        normal(1) = 1.0;
        MAKE_PTR_ARGS(PlaneBasedCellKiller<2>, p_killer, (&cell_population, point, normal));
        simulator.AddCellKiller(p_killer);

        simulator.Solve();

        TS_ASSERT_EQUALS(cell_population.GetNumRealCells(), 12u);
        TS_ASSERT_DELTA(SimulationTime::Instance()->GetTime(), 1.0, 1e-10);
    }
};

Running Vertex Based Crypt Simulations

Simple Impedance Problem

Running Vertex Based Simulations

Examples showing how to create, run and visualize vertex-based simulations#

Introduction#

The test#

Test 1 - a basic vertex-based simulation#

Test 2 - introducing periodicity, boundaries and cell killers#

Full code#