GreensFunctionSolver.cpp

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#define _BACKWARD_BACKWARD_WARNING_H 1 //Cut out the vtk deprecated warning for now (gcc4.3)
#include <vtkDoubleArray.h>
#include <vtkPointData.h>
#include <vtkSmartPointer.h>
#include "Vessel.hpp"
#include "VesselSegment.hpp"
#include "ChastePoint.hpp"
#include "LinearSystem.hpp"
#include "ReplicatableVector.hpp"
#include "UblasMatrixInclude.hpp"
#include "UnitCollection.hpp"
#include "RegularGridWriter.hpp"
#include "GeometryWriter.hpp"
#include "GreensFunctionSolver.hpp"
#include "BaseUnits.hpp"

template<unsigned DIM>
GreensFunctionSolver<DIM>::GreensFunctionSolver()
    : AbstractRegularGridDiscreteContinuumSolver<DIM>(),
      mpDomain(),
      mSinkCoordinates(),
      mSinkPointMap(),
      mSubSegmentCoordinates(),
      mSubSegmentLengths(),
      mSinkRates(),
      mSourceRates(),
      mSegmentConcentration(),
      mSegmentPointMap(),
      mGtt(),
      mGvv(),
      mGvt(),
      mGtv(),
      mSubsegmentCutoff(1.0*unit::microns)
{

}

template<unsigned DIM>
GreensFunctionSolver<DIM>::~GreensFunctionSolver()
{

}

template<unsigned DIM>
void GreensFunctionSolver<DIM>::SetSubSegmentCutoff(units::quantity<unit::length> value)
{
    mSubsegmentCutoff = value;
}

template<unsigned DIM>
void GreensFunctionSolver<DIM>::Solve()
{
    // Set up the sub-segment and tissue point co-ordinates
    GenerateSubSegments();
    GenerateTissuePoints();

    // Generate the greens function matrices
    UpdateGreensFunctionMatrices(1, 1, 1, 1);

    // Get the sink rates
    unsigned number_of_sinks = mSinkCoordinates.size();
    units::quantity<unit::concentration_flow_rate> sink_rate = this->mpPde->ComputeConstantInUSourceTerm();
    units::quantity<unit::volume> sink_volume = units::pow<3>(this->mpRegularGrid->GetSpacing());
    mSinkRates = std::vector<units::quantity<unit::molar_flow_rate> >(number_of_sinks, sink_rate * sink_volume);
    units::quantity<unit::molar_flow_rate> total_sink_rate = std::accumulate(mSinkRates.begin(), mSinkRates.end(), 0.0*unit::mole_per_second);

    // Get the sink substance demand on each vessel subsegment
    unsigned number_of_subsegments = mSubSegmentCoordinates.size();
    units::quantity<unit::diffusivity> diffusivity = this->mpPde->ComputeIsotropicDiffusionTerm();
    std::vector<units::quantity<unit::concentration> > sink_demand_per_subsegment(number_of_subsegments, 0.0*this->mReferenceConcentration);
    for (unsigned idx = 0; idx < number_of_subsegments; idx++)
    {
        for (unsigned jdx = 0; jdx < number_of_sinks; jdx++)
        {
            sink_demand_per_subsegment[idx] += ((*mGvt)[idx][jdx] / diffusivity) * mSinkRates[jdx];
        }
    }

    mSegmentConcentration = std::vector<units::quantity<unit::concentration> >(number_of_subsegments, 1.0*this->mReferenceConcentration);
    this->mConcentrations = std::vector<units::quantity<unit::concentration> >(number_of_sinks, 0.0*this->mReferenceConcentration);

    // Solve for the subsegment source rates required to meet the sink substance demand
    double tolerance = 1.e-10;
    units::quantity<unit::concentration> g0 = 0.0 * this->mReferenceConcentration;
    mSourceRates = std::vector<units::quantity<unit::molar_flow_rate> >(number_of_subsegments, 0.0*unit::mole_per_second);

    units::quantity<unit::time> reference_time = BaseUnits::Instance()->GetReferenceTimeScale();
    units::quantity<unit::concentration> reference_concentration = this->mReferenceConcentration;
    units::quantity<unit::amount> reference_amount(1.0*unit::moles);
    LinearSystem linear_system(number_of_subsegments + 1, number_of_subsegments + 1);
    linear_system.SetKspType("bcgs");

    for (unsigned iteration = 0; iteration < 10; iteration++)
    {
        linear_system.AssembleIntermediateLinearSystem();
        for (unsigned i = 0; i < number_of_subsegments; i++)
        {
            linear_system.SetRhsVectorElement(i, (mSegmentConcentration[i] - sink_demand_per_subsegment[i])/reference_concentration);
        }

        linear_system.SetRhsVectorElement(number_of_subsegments, -total_sink_rate*(reference_time/reference_amount));

        // Set up Linear system matrix
        for (unsigned iter = 0; iter < number_of_subsegments; iter++)
        {
            for (unsigned jter = 0; jter < number_of_subsegments; jter++)
            {
                linear_system.SetMatrixElement(iter, jter, ((*mGvv)[iter][jter] / diffusivity)*(reference_amount/(reference_time*reference_concentration)));
            }
            linear_system.SetMatrixElement(number_of_subsegments, iter, 1.0);
            linear_system.SetMatrixElement(iter, number_of_subsegments, 1.0);
        }
        linear_system.SetMatrixElement(number_of_subsegments, number_of_subsegments, 0.0);

        // Solve the linear system
        linear_system.AssembleFinalLinearSystem();
        ReplicatableVector soln_repl(linear_system.Solve());

        // Populate the solution vector
        std::vector<units::quantity<unit::molar_flow_rate> > solution_vector(number_of_subsegments + 1);
        for (unsigned row = 0; row < number_of_subsegments + 1; row++)
        {
            (solution_vector)[row] = soln_repl[row]*(reference_amount/reference_time);
        }

        // Check convergence
        bool all_in_tolerance = true;
        for (unsigned i = 0; i < number_of_subsegments; i++)
        {
            units::quantity<unit::molar_flow_rate> diff = units::abs(mSourceRates[i] - solution_vector[i]);
            if (diff > tolerance*unit::mole_per_second)
            {
                all_in_tolerance = false;
                break;
            }
        }
        // Retrieve the solution
        for (unsigned i = 0; i < number_of_subsegments; i++)
        {
            mSourceRates[i] = solution_vector[i];
        }
        g0 = solution_vector[number_of_subsegments]*reference_concentration*(reference_time/reference_amount);

        if (all_in_tolerance)
        {
            break;
        }
        else
        {
            if (iteration == 9)
            {
                std::cout << "Did not converge\n";
            }
        }
    }

    // Get the tissue concentration and write the solution
    for (unsigned i = 0; i < number_of_sinks; i++)
    {
        this->mConcentrations[i] = 0.0 * this->mReferenceConcentration;
        for (unsigned j = 0; j < number_of_sinks; j++)
        {
            this->mConcentrations[i] += (*mGtt)[i][j] * mSinkRates[j] / diffusivity;
        }

        for (unsigned j = 0; j < number_of_subsegments; j++)
        {
            this->mConcentrations[i] += (*mGtv)[i][j] * mSourceRates[j] / diffusivity;
        }
        this->mConcentrations[i] += g0;
    }

    std::map<std::string, std::vector<units::quantity<unit::concentration> > > segmentPointData;
    segmentPointData[this->mLabel] = mSegmentConcentration;

    this->UpdateSolution(this->mConcentrations);
    if(this->mWriteSolution)
    {
        this->WriteSolution(segmentPointData);
    }
}

template<unsigned DIM>
void GreensFunctionSolver<DIM>::GenerateSubSegments()
{
    // Set up the sub-segment points and map to original segments
    units::quantity<unit::length> max_subsegment_length = mSubsegmentCutoff;

    std::vector<boost::shared_ptr<Vessel<DIM> > > vessels = this->mpNetwork->GetVessels();
    typename std::vector<boost::shared_ptr<Vessel<DIM> > >::iterator vessel_iter;
    typename std::vector<boost::shared_ptr<VesselSegment<DIM> > >::iterator segment_iter;

    // Iterate over all segments and store midpoints and lengths of subsegment regions for
    // the greens functions calculation. Create a map of subsegment index to the parent segment
    // for later use.
    for (vessel_iter = vessels.begin(); vessel_iter != vessels.end(); vessel_iter++)
    {
        std::vector<boost::shared_ptr<VesselSegment<DIM> > > segments = (*vessel_iter)->GetSegments();
        for (segment_iter = segments.begin(); segment_iter != segments.end(); segment_iter++)
        {
            units::quantity<unit::length> segment_length = (*segment_iter)->GetLength();

            // If the segment is shorter than the max length just use its mid-point
            if (segment_length < 1.01 * max_subsegment_length)
            {
                mSubSegmentCoordinates.push_back((*segment_iter)->GetMidPoint());
                mSubSegmentLengths.push_back(segment_length);
                mSegmentPointMap[mSubSegmentCoordinates.size() - 1] = (*segment_iter);
            }
            // Otherwise generate subsegment points along its length
            else
            {
                DimensionalChastePoint<DIM> start_point = (*segment_iter)->GetNode(0)->rGetLocation();
                DimensionalChastePoint<DIM> end_point = (*segment_iter)->GetNode(1)->rGetLocation();

                double subsegment_length_factor = segment_length / max_subsegment_length;
                unsigned num_subsegments = std::floor(subsegment_length_factor) + 1;
                units::quantity<unit::length> subsegment_length = segment_length / double(num_subsegments);
                DimensionalChastePoint<DIM> increment = (end_point - start_point);
                for (unsigned i = 0; i < num_subsegments; i++)
                {
                    mSubSegmentCoordinates.push_back(start_point +  (increment*(double(i) + 0.5)));
                    mSubSegmentLengths.push_back(subsegment_length);
                    mSegmentPointMap[mSubSegmentCoordinates.size() - 1] = (*segment_iter);
                }
            }
        }
    }
}

template<unsigned DIM>
void GreensFunctionSolver<DIM>::GenerateTissuePoints()
{
    unsigned num_points = this->mpRegularGrid->GetNumberOfPoints();
    mSinkCoordinates = std::vector<DimensionalChastePoint<DIM> >(num_points);
    mSinkPointMap = std::vector<unsigned>(num_points);
    for(unsigned idx=0; idx<num_points; idx++)
    {
        mSinkCoordinates[idx] = this->mpRegularGrid->GetLocationOf1dIndex(idx);
        mSinkPointMap[idx] = idx;
    }
}

template<unsigned DIM>
void GreensFunctionSolver<DIM>::UpdateGreensFunctionMatrices(bool updateGtt, bool updateGvv, bool updateGtv,
                                                                 bool updateGvt)
{
    // Get the Greens Function coefficient matrices
    if (updateGtt)
    {
        mGtt = GetTissueTissueInteractionMatrix();
    }
    if (updateGvv)
    {
        mGvv = GetVesselVesselInteractionMatrix();
    }
    if (updateGtv)
    {
        mGtv = GetTissueVesselInteractionMatrix();
    }
    if (updateGvt)
    {
        mGvt = GetVesselTissueInteractionMatrix();
    }
}

template<unsigned DIM>
boost::shared_ptr<boost::multi_array<units::quantity<unit::per_length>, 2> > GreensFunctionSolver<DIM>::GetVesselVesselInteractionMatrix()
{
    typedef boost::multi_array<units::quantity<unit::per_length>, 2>::index index;
    unsigned num_sub_segments = mSubSegmentCoordinates.size();
    double coefficient = 1.0 / (4.0 * M_PI);

    boost::shared_ptr<boost::multi_array<units::quantity<unit::per_length>, 2> > p_interaction_matrix(new boost::multi_array<units::quantity<unit::per_length>, 2>(boost::extents[num_sub_segments][num_sub_segments]));
    for (index iter = 0; iter < num_sub_segments; iter++)
    {
        for (index iter2 = 0; iter2 < num_sub_segments; iter2++)
        {
            if (iter <= iter2)
            {
                units::quantity<unit::length> distance = mSubSegmentCoordinates[iter2].GetDistance(mSubSegmentCoordinates[iter]);
                units::quantity<unit::per_length> term;
                if (distance < mSegmentPointMap[iter]->GetRadius())
                {
                    units::quantity<unit::length> radius = mSegmentPointMap[iter]->GetRadius();
                    units::quantity<unit::length> max_segment_length = std::max(mSubSegmentLengths[iter], mSubSegmentLengths[iter2]);
                    double green_correction = 0.6 * std::exp(-0.45 * max_segment_length /radius);
                    if (iter != iter2)
                    {
                        distance = radius;
                    }
                    term = (1.298 / (1.0 + 0.297 * pow(max_segment_length /radius, 0.838))- green_correction * pow(distance / radius, 2))*coefficient/radius;
                }
                else
                {
                    term = coefficient / distance;
                }
                (*p_interaction_matrix)[iter][iter2] = term;
                (*p_interaction_matrix)[iter2][iter] = term;
            }
        }
    }
    return p_interaction_matrix;
}

template<unsigned DIM>
boost::shared_ptr<boost::multi_array<units::quantity<unit::per_length>, 2> > GreensFunctionSolver<DIM>::GetTissueTissueInteractionMatrix()
{
    typedef boost::multi_array<units::quantity<unit::per_length>, 2>::index index;
    unsigned num_points = mSinkCoordinates.size();
    double coefficient = 1.0 / (4.0 * M_PI);
    units::quantity<unit::volume> tissue_point_volume = units::pow<3>(this->mpRegularGrid->GetSpacing());
    units::quantity<unit::length> equivalent_tissue_point_radius = units::root<3>(tissue_point_volume * 0.75 / M_PI);
    boost::shared_ptr<boost::multi_array<units::quantity<unit::per_length>, 2 > > p_interaction_matrix(new boost::multi_array<units::quantity<unit::per_length>, 2>(boost::extents[num_points][num_points]));
    for (index iter = 0; iter < num_points; iter++)
    {
        for (index iter2 = 0; iter2 < num_points; iter2++)
        {
            if (iter < iter2)
            {
                units::quantity<unit::length> distance = mSinkCoordinates[iter2].GetDistance(mSinkCoordinates[iter]);
                (*p_interaction_matrix)[iter][iter2] = coefficient / distance;
                (*p_interaction_matrix)[iter2][iter] = coefficient / distance;
            }
            else if (iter == iter2)
            {
                (*p_interaction_matrix)[iter][iter2] = 1.2 * coefficient / equivalent_tissue_point_radius;
            }
        }
    }
    return p_interaction_matrix;
}

template<unsigned DIM>
boost::shared_ptr<boost::multi_array<units::quantity<unit::per_length>, 2> > GreensFunctionSolver<DIM>::GetTissueVesselInteractionMatrix()
{
    typedef boost::multi_array<units::quantity<unit::per_length>, 2>::index index;
    unsigned num_sinks = mSinkCoordinates.size();
    unsigned num_subsegments = mSubSegmentCoordinates.size();

    units::quantity<unit::volume> tissue_point_volume = units::pow<3>(this->mpRegularGrid->GetSpacing());
    units::quantity<unit::length> equivalent_tissue_point_radius = units::root<3>(tissue_point_volume * 0.75 / M_PI);
    double coefficient = 1.0 / (4.0 * M_PI);

    boost::shared_ptr<boost::multi_array<units::quantity<unit::per_length>, 2> > p_interaction_matrix(new boost::multi_array<units::quantity<unit::per_length>, 2>(boost::extents[num_sinks][num_subsegments]));
    for (index iter = 0; iter < num_sinks; iter++)
    {
        for (index iter2 = 0; iter2 < num_subsegments; iter2++)
        {
            units::quantity<unit::length> distance = mSinkCoordinates[iter2].GetDistance(mSinkCoordinates[iter]);
            units::quantity<unit::per_length> term;
            if (distance <= equivalent_tissue_point_radius)
            {
                term = coefficient * (1.5 - 0.5 * (pow(distance / equivalent_tissue_point_radius, 2))) / equivalent_tissue_point_radius;
            }
            else
            {
                term = coefficient / distance;
            }
            (*p_interaction_matrix)[iter][iter2] = term;
        }
    }
    return p_interaction_matrix;
}

template<unsigned DIM>
boost::shared_ptr<boost::multi_array<units::quantity<unit::per_length>, 2> > GreensFunctionSolver<DIM>::GetVesselTissueInteractionMatrix()
{
    typedef boost::multi_array<units::quantity<unit::per_length>, 2>::index index;
    unsigned num_subsegments = mSubSegmentCoordinates.size();
    unsigned num_sinks = mSinkCoordinates.size();
    double coefficient = 1.0 / (4.0 * M_PI);

    units::quantity<unit::volume> tissue_point_volume = units::pow<3>(this->mpRegularGrid->GetSpacing());
    units::quantity<unit::length> equivalent_tissue_point_radius = units::root<3>(tissue_point_volume * 0.75 / M_PI);

    boost::shared_ptr<boost::multi_array<units::quantity<unit::per_length>, 2> > p_interaction_matrix(new boost::multi_array<units::quantity<unit::per_length>, 2>(boost::extents[num_subsegments][num_sinks]));
    for (index iter = 0; iter < num_subsegments; iter++)
    {
        for (index iter2 = 0; iter2 < num_sinks; iter2++)
        {
            units::quantity<unit::length> distance = mSinkCoordinates[iter2].GetDistance(mSinkCoordinates[iter]);
            units::quantity<unit::per_length> term;
            if (distance <= equivalent_tissue_point_radius)
            {
                term = coefficient * (1.5 - 0.5 * (pow(distance / equivalent_tissue_point_radius, 2)))/ equivalent_tissue_point_radius;
            }
            else
            {
                term = coefficient / distance;
            }
            (*p_interaction_matrix)[iter][iter2] = term;
        }
    }
    return p_interaction_matrix;
}

template<unsigned DIM>
void GreensFunctionSolver<DIM>::WriteSolution(std::map<std::string, std::vector<units::quantity<unit::concentration> > >& segmentPointData)
{
    // Write the tissue point data
    RegularGridWriter writer;
    writer.SetFilename(this->mpOutputFileHandler->GetOutputDirectoryFullPath() + "/solution.vti");
    writer.SetImage(this->mpVtkSolution);
    writer.Write();

    // Add the segment points
    vtkSmartPointer<vtkPolyData> pPolyData = vtkSmartPointer<vtkPolyData>::New();
    vtkSmartPointer<vtkPoints> pPoints = vtkSmartPointer<vtkPoints>::New();
    for (unsigned i = 0; i < mSubSegmentCoordinates.size(); i++)
    {
        c_vector<double, DIM> location = mSubSegmentCoordinates[i].GetLocation(this->mpRegularGrid->GetReferenceLengthScale());
        pPoints->InsertNextPoint(location[0], location[1], location[2]);
    }
    pPolyData->SetPoints(pPoints);

    // Add the segment point data
    std::map<std::string, std::vector<units::quantity<unit::concentration> > >::iterator segment_iter;
    for (segment_iter = segmentPointData.begin(); segment_iter != segmentPointData.end(); ++segment_iter)
    {
        vtkSmartPointer<vtkDoubleArray> pInfo = vtkSmartPointer<vtkDoubleArray>::New();
        pInfo->SetNumberOfComponents(1);
        pInfo->SetNumberOfTuples(mSubSegmentCoordinates.size());
        pInfo->SetName(segment_iter->first.c_str());

        for (unsigned i = 0; i < mSubSegmentCoordinates.size(); i++)
        {
            pInfo->SetValue(i, segmentPointData[segment_iter->first][i]/this->mReferenceConcentration);
        }
        pPolyData->GetPointData()->AddArray(pInfo);
    }

    GeometryWriter geometry_writer;
    geometry_writer.SetFileName(this->mpOutputFileHandler->GetOutputDirectoryFullPath() + "/segments.vtp");
    geometry_writer.SetInput(pPolyData);
    geometry_writer.Write();
}

// Explicit instantiation
template class GreensFunctionSolver<2>;
template class GreensFunctionSolver<3>;