void PopulationTestingForce<ELEMENT_DIM, SPACE_DIM>::AddForceContribution(AbstractCellPopulation<ELEMENT_DIM,SPACE_DIM>& rCellPopulation)
{
for (unsigned i=0; i<rCellPopulation.GetNumNodes(); i++)
{
c_vector<double, SPACE_DIM> force;
for (unsigned j=0; j<SPACE_DIM; j++)
{
if (mWithPositionDependence)
{
force[j] = (j+1)*i*0.01*rCellPopulation.GetNode(i)->rGetLocation()[j];
}
else
{
force[j] = (j+1)*i*0.01;
}
}
rCellPopulation.GetNode(i)->ClearAppliedForce();
rCellPopulation.GetNode(i)->AddAppliedForceContribution(force);
}
}
c_vector<double, DIM> BuskeAdhesiveForce<DIM>::CalculateForceBetweenNodes(unsigned nodeAGlobalIndex,
unsigned nodeBGlobalIndex,
AbstractCellPopulation<DIM>& rCellPopulation)
{
// This force class is defined for NodeBasedCellPopulations only
assert(dynamic_cast<NodeBasedCellPopulation<DIM>*>(&rCellPopulation) != NULL);
// We should only ever calculate the force between two distinct nodes
assert(nodeAGlobalIndex != nodeBGlobalIndex);
Node<DIM>* p_node_a = rCellPopulation.GetNode(nodeAGlobalIndex);
Node<DIM>* p_node_b = rCellPopulation.GetNode(nodeBGlobalIndex);
// Get the node locations
c_vector<double, DIM> node_a_location = p_node_a->rGetLocation();
c_vector<double, DIM> node_b_location = p_node_b->rGetLocation();
// Get the unit vector parallel to the line joining the two nodes (assuming no periodicities etc.)
c_vector<double, DIM> unit_vector = node_b_location - node_a_location;
// Calculate the distance between the two nodes
double distance_between_nodes = norm_2(unit_vector);
// Account for any cutoff in the force law
if (this->mUseCutOffLength)
{
if (distance_between_nodes >= this->GetCutOffLength())
{
return zero_vector<double>(DIM);
}
}
// Assert that the nodes are a finite, non-zero distance apart
assert(distance_between_nodes > 0);
assert(!std::isnan(distance_between_nodes));
// Normalize the unit vector
unit_vector /= distance_between_nodes;
double radius_of_cell_one = p_node_a->GetRadius();
double radius_of_cell_two = p_node_b->GetRadius();
// Compute the force vector
c_vector<double, DIM> force_between_nodes = GetMagnitudeOfForce(distance_between_nodes,radius_of_cell_one,radius_of_cell_two) * unit_vector;
return force_between_nodes;
}
void CryptProjectionForce::AddForceContribution(AbstractCellPopulation<2>& rCellPopulation)
{
// First work out the 3D location of each cell
UpdateNode3dLocationMap(rCellPopulation);
// Throw an exception message if not using a MeshBasedCellPopulation
if (dynamic_cast<MeshBasedCellPopulation<2>*>(&rCellPopulation) == NULL)
{
EXCEPTION("CryptProjectionForce is to be used with a subclass of MeshBasedCellPopulation only");
}
MeshBasedCellPopulation<2>* p_static_cast_cell_population = static_cast<MeshBasedCellPopulation<2>*>(&rCellPopulation);
for (MeshBasedCellPopulation<2>::SpringIterator spring_iterator = p_static_cast_cell_population->SpringsBegin();
spring_iterator != p_static_cast_cell_population->SpringsEnd();
++spring_iterator)
{
unsigned nodeA_global_index = spring_iterator.GetNodeA()->GetIndex();
unsigned nodeB_global_index = spring_iterator.GetNodeB()->GetIndex();
c_vector<double, 2> force = CalculateForceBetweenNodes(nodeA_global_index, nodeB_global_index, rCellPopulation);
c_vector<double, 2> negative_force = -1.0 * force;
spring_iterator.GetNodeB()->AddAppliedForceContribution(negative_force);
spring_iterator.GetNodeA()->AddAppliedForceContribution(force);
}
if (mIncludeWntChemotaxis)
{
assert(WntConcentration<2>::Instance()->IsWntSetUp());
for (AbstractCellPopulation<2>::Iterator cell_iter = rCellPopulation.Begin();
cell_iter != rCellPopulation.End();
++cell_iter)
{
if (cell_iter->GetCellProliferativeType()->IsType<StemCellProliferativeType>())
{
c_vector<double, 2> wnt_chemotactic_force = mWntChemotaxisStrength*WntConcentration<2>::Instance()->GetWntGradient(*cell_iter);
unsigned index = rCellPopulation.GetLocationIndexUsingCell(*cell_iter);
rCellPopulation.GetNode(index)->AddAppliedForceContribution(wnt_chemotactic_force);
}
}
}
}
/* The second public method overrides {{{AddForceContribution()}}}.
* This method takes in one argument, a reference to the cell population itself.
*/
void AddForceContribution(AbstractCellPopulation<2>& rCellPopulation)
{
/* Inside the method, we loop over cells, and add a vector to
* each node associated with cells with the {{{MotileCellProperty}}}, which is proportional (with constant {{{mStrength}}}) to the negative of the position. Causing
* cells to move inwards towards the origin. Note that this will currently only work with subclasses of {{{AbstractCentreBasedCellPopulation}}}s as
* we associate cells with nodes in the force calculation. However, this could easily be modified to make it work for {{{VertexBasedCellPopulation}}}s.
*/
for (AbstractCellPopulation<2>::Iterator cell_iter = rCellPopulation.Begin();
cell_iter != rCellPopulation.End();
++cell_iter)
{
if (cell_iter->HasCellProperty<MotileCellProperty>())
{
unsigned node_index = rCellPopulation.GetLocationIndexUsingCell(*cell_iter);
c_vector<double, 2> location = rCellPopulation.GetLocationOfCellCentre(*cell_iter);
c_vector<double, 2> force = -1.0 * mStrength * location;
rCellPopulation.GetNode(node_index)->AddAppliedForceContribution(force);
}
}
}
void BuskeCompressionForce<DIM>::AddForceContribution(AbstractCellPopulation<DIM>& rCellPopulation)
{
// This force class is defined for NodeBasedCellPopulations only
assert(dynamic_cast<NodeBasedCellPopulation<DIM>*>(&rCellPopulation) != NULL);
NodeBasedCellPopulation<DIM>* p_static_cast_cell_population = static_cast<NodeBasedCellPopulation<DIM>*>(&rCellPopulation);
c_vector<double, DIM> unit_vector;
// Loop over cells in the population
for (typename AbstractCellPopulation<DIM>::Iterator cell_iter = rCellPopulation.Begin();
cell_iter != rCellPopulation.End();
++cell_iter)
{
// Get the node index corresponding to this cell
unsigned node_index = rCellPopulation.GetLocationIndexUsingCell(*cell_iter);
Node<DIM>* p_node_i = rCellPopulation.GetNode(node_index);
// Get the location of this node
c_vector<double, DIM> node_i_location = p_node_i->rGetLocation();
// Get the radius of this cell
double radius_of_cell_i = p_node_i->GetRadius();
double delta_V_c = 0.0;
c_vector<double, DIM> dVAdd_vector = zero_vector<double>(DIM);
// Get the set of node indices corresponding to this cell's neighbours
std::set<unsigned> neighbouring_node_indices = p_static_cast_cell_population->GetNeighbouringNodeIndices(node_index);
// Loop over this set
for (std::set<unsigned>::iterator iter = neighbouring_node_indices.begin();
iter != neighbouring_node_indices.end();
++iter)
{
Node<DIM>* p_node_j = rCellPopulation.GetNode(*iter);
// Get the location of this node
c_vector<double, DIM> node_j_location = p_node_j->rGetLocation();
// Get the unit vector parallel to the line joining the two nodes (assuming no periodicities etc.)
unit_vector = node_j_location - node_i_location;
// Calculate the distance between the two nodes
double dij = norm_2(unit_vector);
unit_vector /= dij;
// Get the radius of the cell corresponding to this node
double radius_of_cell_j = p_node_j->GetRadius();
// If the cells are close enough to exert a force on each other...
if (dij < radius_of_cell_i + radius_of_cell_j)
{
// ...then compute the adhesion force and add it to the vector of forces...
double xij = 0.5*(radius_of_cell_i*radius_of_cell_i - radius_of_cell_j*radius_of_cell_j + dij*dij)/dij;
double dxijdd = 1.0 - xij/dij;
double dVAdd = M_PI*dxijdd*(5.0*pow(radius_of_cell_i,2.0) + 3.0*pow(xij,2.0) - 8.0*radius_of_cell_i*xij)/3.0;
dVAdd_vector += dVAdd*unit_vector;
// ...and add the contribution to the compression force acting on cell i
delta_V_c += M_PI*pow(radius_of_cell_i - xij,2.0)*(2*radius_of_cell_i - xij)/3.0;
}
}
double V_A = 4.0/3.0*M_PI*pow(radius_of_cell_i,3.0) - delta_V_c;
/**
* Target volume of the cell
* \todo Doesn't say in the Buske paper how they calculate this, so
* we need to look at this to be sure it's what we want (#1764)
*/
double V_T = 5.0;
// Note: the sign in force_magnitude is different from the one in equation (A3) in the Buske paper
c_vector<double, DIM> applied_force = -mCompressionEnergyParameter/V_T*(V_T - V_A)*dVAdd_vector;
p_node_i->AddAppliedForceContribution(applied_force);
}
}
c_vector<double,2> CryptProjectionForce::CalculateForceBetweenNodes(unsigned nodeAGlobalIndex, unsigned nodeBGlobalIndex, AbstractCellPopulation<2>& rCellPopulation)
{
MeshBasedCellPopulation<2>* p_static_cast_cell_population = static_cast<MeshBasedCellPopulation<2>*>(&rCellPopulation);
// We should only ever calculate the force between two distinct nodes
assert(nodeAGlobalIndex != nodeBGlobalIndex);
// Get the node locations in 2D
c_vector<double,2> node_a_location_2d = rCellPopulation.GetNode(nodeAGlobalIndex)->rGetLocation();
c_vector<double,2> node_b_location_2d = rCellPopulation.GetNode(nodeBGlobalIndex)->rGetLocation();
// "Get the unit vector parallel to the line joining the two nodes" [GeneralisedLinearSpringForce]
// Create a unit vector in the direction of the 3D spring
c_vector<double,3> unit_difference = mNode3dLocationMap[nodeBGlobalIndex] - mNode3dLocationMap[nodeAGlobalIndex];
// Calculate the distance between the two nodes
double distance_between_nodes = norm_2(unit_difference);
assert(distance_between_nodes > 0);
assert(!std::isnan(distance_between_nodes));
unit_difference /= distance_between_nodes;
// If mUseCutOffLength has been set, then there is zero force between
// two nodes located a distance apart greater than mUseCutOffLength
if (this->mUseCutOffLength)
{
if (distance_between_nodes >= mMechanicsCutOffLength)
{
// Return zero (2D projected) force
return zero_vector<double>(2);
}
}
// Calculate the rest length of the spring connecting the two nodes
double rest_length = 1.0;
CellPtr p_cell_A = rCellPopulation.GetCellUsingLocationIndex(nodeAGlobalIndex);
CellPtr p_cell_B = rCellPopulation.GetCellUsingLocationIndex(nodeBGlobalIndex);
double ageA = p_cell_A->GetAge();
double ageB = p_cell_B->GetAge();
assert(!std::isnan(ageA));
assert(!std::isnan(ageB));
/*
* If the cells are both newly divided, then the rest length of the spring
* connecting them grows linearly with time, until mMeinekeSpringGrowthDuration hour after division.
*/
if (ageA < mMeinekeSpringGrowthDuration && ageB < mMeinekeSpringGrowthDuration)
{
/*
* The spring rest length increases from a predefined small parameter
* to a normal rest length of 1.0, over a period of one hour.
*/
std::pair<CellPtr,CellPtr> cell_pair = p_static_cast_cell_population->CreateCellPair(p_cell_A, p_cell_B);
if (p_static_cast_cell_population->IsMarkedSpring(cell_pair))
{
double lambda = mMeinekeDivisionRestingSpringLength;
rest_length = lambda + (1.0 - lambda) * ageA/mMeinekeSpringGrowthDuration;
}
if (ageA+SimulationTime::Instance()->GetTimeStep() >= mMeinekeSpringGrowthDuration)
{
// This spring is about to go out of scope
p_static_cast_cell_population->UnmarkSpring(cell_pair);
}
}
double a_rest_length = rest_length*0.5;
double b_rest_length = a_rest_length;
/*
* If either of the cells has begun apoptosis, then the length of the spring
* connecting them decreases linearly with time.
*/
if (p_cell_A->HasApoptosisBegun())
{
double time_until_death_a = p_cell_A->GetTimeUntilDeath();
a_rest_length = a_rest_length * time_until_death_a / p_cell_A->GetApoptosisTime();
}
if (p_cell_B->HasApoptosisBegun())
{
double time_until_death_b = p_cell_B->GetTimeUntilDeath();
b_rest_length = b_rest_length * time_until_death_b / p_cell_B->GetApoptosisTime();
}
rest_length = a_rest_length + b_rest_length;
// Assert that the rest length does not exceed 1
assert(rest_length <= 1.0+1e-12);
bool is_closer_than_rest_length = true;
if (distance_between_nodes - rest_length > 0)
{
is_closer_than_rest_length = false;
}
/*
* Although in this class the 'spring constant' is a constant parameter, in
* subclasses it can depend on properties of each of the cells.
*/
double multiplication_factor = 1.0;
multiplication_factor *= VariableSpringConstantMultiplicationFactor(nodeAGlobalIndex, nodeBGlobalIndex, rCellPopulation, is_closer_than_rest_length);
// Calculate the 3D force between the two points
c_vector<double,3> force_between_nodes = multiplication_factor * this->GetMeinekeSpringStiffness() * unit_difference * (distance_between_nodes - rest_length);
// Calculate an outward normal unit vector to the tangent plane of the crypt surface at the 3D point corresponding to node B
c_vector<double,3> outward_normal_unit_vector;
double dfdr = CalculateCryptSurfaceDerivativeAtPoint(node_b_location_2d);
double theta_B = atan2(node_b_location_2d[1], node_b_location_2d[0]); // use atan2 to determine the quadrant
double normalization_factor = sqrt(1 + dfdr*dfdr);
outward_normal_unit_vector[0] = dfdr*cos(theta_B)/normalization_factor;
outward_normal_unit_vector[1] = dfdr*sin(theta_B)/normalization_factor;
outward_normal_unit_vector[2] = -1.0/normalization_factor;
// Calculate the projection of the force onto the plane z=0
c_vector<double,2> projected_force_between_nodes_2d;
double force_dot_normal = inner_prod(force_between_nodes, outward_normal_unit_vector);
for (unsigned i=0; i<2; i++)
{
projected_force_between_nodes_2d[i] = force_between_nodes[i]
- force_dot_normal*outward_normal_unit_vector[i]
+ force_dot_normal*outward_normal_unit_vector[2];
}
return projected_force_between_nodes_2d;
}