StreeterFibreGenerator.cpp

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*/

#include "UblasCustomFunctions.hpp"

#include "StreeterFibreGenerator.hpp"

#include <cmath>
#include <fstream>
#include <sstream>
#include "OutputFileHandler.hpp"
#include "Exception.hpp"
//#include "HeartRegionCodes.hpp"

// Add the citation for original Streeter paper.
#include "Citations.hpp"
static PetscBool StreeterCite = PETSC_FALSE;
const char StreeterCitation[] = "@article{streeter1969fiber,\n"
"  title={Fiber orientation in the canine left ventricle during diastole and systole},\n"
"  author={Streeter, Daniel D and Spotnitz, Henry M and Patel, Dali P and Ross, John and Sonnenblick, Edmund H},\n"
"  journal={Circulation research},\n"
"  volume={24},\n"
"  number={3},\n"
"  pages={339--347},\n"
"  year={1969},\n"
"  publisher={Am Heart Assoc}\n"
"}\n";

template<unsigned SPACE_DIM>
double StreeterFibreGenerator<SPACE_DIM>::GetAveragedThicknessLocalNode(
        const unsigned nodeIndex, const std::vector<double>& wallThickness) const
{
    if (nodeIndex < this->mpMesh->GetDistributedVectorFactory()->GetLow() ||
        nodeIndex >= this->mpMesh->GetDistributedVectorFactory()->GetHigh() )
    {
        return 0.0;  //Don't calculate this for nodes which aren't local
    }

    // Initialise the average with the value corresponding to the current node
    double average = wallThickness[nodeIndex];
    unsigned nodes_visited = 1;

    // Use a set to store visited nodes
    std::set<unsigned> visited_nodes;
    visited_nodes.insert(nodeIndex);

    Node<SPACE_DIM>* p_current_node = this->mpMesh->GetNode(nodeIndex);

    // Loop over the elements containing the given node
    for(typename Node<SPACE_DIM>::ContainingElementIterator element_iterator = p_current_node->ContainingElementsBegin();
        element_iterator != p_current_node->ContainingElementsEnd();
        ++element_iterator)
    {
        // Get a pointer to the container element
        Element<SPACE_DIM,SPACE_DIM>* p_containing_element = this->mpMesh->GetElement(*element_iterator);

       // Loop over the nodes of the element
       for(unsigned node_local_index=0;
           node_local_index<p_containing_element->GetNumNodes();
           node_local_index++)
       {
            Node<SPACE_DIM>* p_neighbour_node = p_containing_element->GetNode(node_local_index);
            unsigned neighbour_node_index = p_neighbour_node->GetIndex();

            // Check if the neighbour node has already been visited
            if (visited_nodes.find(neighbour_node_index) == visited_nodes.end())
            {
                average += wallThickness[neighbour_node_index];
                visited_nodes.insert(neighbour_node_index);
                nodes_visited++;
            }
       }
    }

    return average/nodes_visited;
}




template<unsigned SPACE_DIM>
double StreeterFibreGenerator<SPACE_DIM>::GetFibreMaxAngle(
        const c_vector<HeartRegionType, SPACE_DIM+1>& nodesRegionsForElement) const
{
    unsigned lv=0, rv=0;

    for (unsigned index=0; index<SPACE_DIM+1; index++)
    {
        switch (nodesRegionsForElement[index])
        {
            case HeartGeometryInformation<SPACE_DIM>::LEFT_VENTRICLE_SURFACE:
            case HeartGeometryInformation<SPACE_DIM>::LEFT_VENTRICLE_WALL:
            case HeartGeometryInformation<SPACE_DIM>::LEFT_SEPTUM:
                lv++;
                break;

            case HeartGeometryInformation<SPACE_DIM>::RIGHT_VENTRICLE_SURFACE:
            case HeartGeometryInformation<SPACE_DIM>::RIGHT_VENTRICLE_WALL:
            case HeartGeometryInformation<SPACE_DIM>::RIGHT_SEPTUM:
                rv++;
                break;

            case HeartGeometryInformation<SPACE_DIM>::UNKNOWN:
            default:
                NEVER_REACHED;
        }
    }

    // If most of the nodes are in the right ventricle
    if (rv>lv)
    {
        return M_PI/4.0;
    }

    // Anywhere else
    return M_PI/3.0;
}

template<unsigned SPACE_DIM>
StreeterFibreGenerator<SPACE_DIM>::StreeterFibreGenerator(AbstractTetrahedralMesh<SPACE_DIM,SPACE_DIM>& rMesh)
    : AbstractPerElementWriter<SPACE_DIM,SPACE_DIM,SPACE_DIM*SPACE_DIM>(&rMesh),
      mpGeometryInfo(NULL),
      mApexToBase(zero_vector<double>(SPACE_DIM)),
      mLogInfo(false)
{
    // Record a reference for the calculations performed here, can be extracted with the '-citations' flag.
    Citations::Register(StreeterCitation, &StreeterCite);

    mWallThickness.resize(rMesh.GetNumNodes());
    mAveragedWallThickness.resize(rMesh.GetNumNodes());
}

template<unsigned SPACE_DIM>
StreeterFibreGenerator<SPACE_DIM>::~StreeterFibreGenerator()
{
    delete mpGeometryInfo;
}

template<unsigned SPACE_DIM>
void StreeterFibreGenerator<SPACE_DIM>::SetSurfaceFiles(
            const std::string& rEpicardiumFile,
            const std::string& rRightVentricleFile,
            const std::string& rLeftVentricleFile,
            bool indexFromZero)
{
    // Compute the distance map of each surface
     mpGeometryInfo = new HeartGeometryInformation<SPACE_DIM>(*(this->mpMesh), rEpicardiumFile, rLeftVentricleFile, rRightVentricleFile, indexFromZero);
}

template<unsigned SPACE_DIM>
void StreeterFibreGenerator<SPACE_DIM>::WriteHeaderOnMaster()
{
    *(this->mpMasterFile) << this->mpMesh->GetNumElements();
    *(this->mpMasterFile) << std::setprecision(16);
}

template<unsigned SPACE_DIM>
void StreeterFibreGenerator<SPACE_DIM>::PreWriteCalculations(OutputFileHandler& rOutputDirectory)
{
    assert(SPACE_DIM == 3);
    if (mpGeometryInfo == NULL)
    {
        EXCEPTION("Files defining the heart surfaces not set");
    }

    // Open files
    out_stream p_regions_file, p_thickness_file, p_ave_thickness_file;

    //Make sure that only the master process writes the log files if requested.
    bool logInfo = PetscTools::AmMaster() & mLogInfo;

    if (logInfo)
    {
        p_regions_file  = rOutputDirectory.OpenOutputFile("node_regions.data");
        p_thickness_file = rOutputDirectory.OpenOutputFile("wall_thickness.data");
        p_ave_thickness_file = rOutputDirectory.OpenOutputFile("averaged_thickness.data");
    }

    //We expect that the apex to base has been set
    if (fabs(norm_2(mApexToBase)) < DBL_EPSILON)
    {
        EXCEPTION("Apex to base vector has not been set");
    }

    // Compute wall thickness parameter
    unsigned num_nodes = this->mpMesh->GetNumNodes();
    for (unsigned node_index=0; node_index<num_nodes; node_index++)
    {
        double dist_epi, dist_endo;

        HeartRegionType node_region = mpGeometryInfo->GetHeartRegion(node_index);

        switch(node_region)
        {
            case HeartGeometryInformation<SPACE_DIM>::LEFT_VENTRICLE_SURFACE:
            case HeartGeometryInformation<SPACE_DIM>::LEFT_VENTRICLE_WALL:
                dist_epi = mpGeometryInfo->rGetDistanceMapEpicardium()[node_index];
                dist_endo = mpGeometryInfo->rGetDistanceMapLeftVentricle()[node_index];
                break;

            case HeartGeometryInformation<SPACE_DIM>::RIGHT_VENTRICLE_SURFACE:
            case HeartGeometryInformation<SPACE_DIM>::RIGHT_VENTRICLE_WALL:
                dist_epi = mpGeometryInfo->rGetDistanceMapEpicardium()[node_index];
                dist_endo = mpGeometryInfo->rGetDistanceMapRightVentricle()[node_index];
                break;

            case HeartGeometryInformation<SPACE_DIM>::LEFT_SEPTUM:
                dist_epi = mpGeometryInfo->rGetDistanceMapRightVentricle()[node_index];
                dist_endo = mpGeometryInfo->rGetDistanceMapLeftVentricle()[node_index];
                break;

            case HeartGeometryInformation<SPACE_DIM>::RIGHT_SEPTUM:
                dist_epi = mpGeometryInfo->rGetDistanceMapLeftVentricle()[node_index];
                dist_endo = mpGeometryInfo->rGetDistanceMapRightVentricle()[node_index];
                break;

            case HeartGeometryInformation<SPACE_DIM>::UNKNOWN:
                #define COVERAGE_IGNORE
                std::cerr << "Wrong distances node: " << node_index << "\t"
                          << "Epi " << mpGeometryInfo->rGetDistanceMapEpicardium()[node_index] << "\t"
                          << "RV " << mpGeometryInfo->rGetDistanceMapRightVentricle()[node_index] << "\t"
                          << "LV " << mpGeometryInfo->rGetDistanceMapLeftVentricle()[node_index]
                          << std::endl;

                // Make wall_thickness=0 as in Martin's code
                dist_epi = 1;
                dist_endo = 0;
                break;
                #undef COVERAGE_IGNORE

            default:
                NEVER_REACHED;
        }

        mWallThickness[node_index] = dist_endo / (dist_endo + dist_epi);

        if (std::isnan(mWallThickness[node_index]))
        {
            #define COVERAGE_IGNORE
            /*
             *  A node contained on both epicardium and lv (or rv) surfaces has wall thickness 0/0.
             *  By setting its value to 0 we consider it contained only on the lv (or rv) surface.
             */
            mWallThickness[node_index] = 0;
            #undef COVERAGE_IGNORE
        }

        if (logInfo)
        {
            *p_regions_file << node_region*100 << "\n";
            *p_thickness_file << mWallThickness[node_index] << "\n";
        }
    }

    /*
     *  For each node, average its value of e with the values of all the neighbours
     */
    std::vector<double> my_averaged_wall_thickness(num_nodes);
    for (unsigned node_index=0; node_index<num_nodes; node_index++)
    {
        my_averaged_wall_thickness[node_index] = GetAveragedThicknessLocalNode(node_index, mWallThickness);
    }

    // Non-local information appear as zeros in the vector
    MPI_Allreduce(&my_averaged_wall_thickness[0], &mAveragedWallThickness[0], num_nodes,
                  MPI_DOUBLE, MPI_SUM, PETSC_COMM_WORLD);

    if (logInfo)
    {
        for (unsigned node_index=0; node_index<num_nodes; node_index++)
        {
             *p_ave_thickness_file << mAveragedWallThickness[node_index] << "\n";
        }
    }

    if (logInfo)
    {
        p_regions_file->close();
        p_thickness_file->close();
        p_ave_thickness_file->close();
    }
}

template<unsigned SPACE_DIM>
void StreeterFibreGenerator<SPACE_DIM>::Visit(Element<SPACE_DIM, SPACE_DIM>* pElement,
                                              unsigned localElementIndex,
                                              c_vector<double, SPACE_DIM*SPACE_DIM>& rData)
{
    /*
     *  The gradient of the averaged thickness at the element is:
     *
     *     grad_ave_wall_thickness[element_index] = ave' * BF * inv(J)
     *
     *  being : ave, averaged thickness values of the nodes defining the element
     *          J,   the Jacobian of the element as defined in class Element.
     *                               (-1 -1 -1)
     *          BF,  basis functions ( 1  0  0)
     *                               ( 0  1  0)
     *                               ( 0  0  1)
     *
     *  Defined as u in Streeter paper.
     */
    c_vector<double, SPACE_DIM> grad_ave_wall_thickness;
    c_vector<double, SPACE_DIM+1> elem_nodes_ave_thickness;
    double element_averaged_thickness = 0.0;
    c_vector<HeartRegionType, SPACE_DIM+1> elem_nodes_region;

    for (unsigned local_node_index=0; local_node_index<SPACE_DIM+1; local_node_index++)
    {
        // Get node's global index
        unsigned global_node_index = pElement->GetNode(local_node_index)->GetIndex();

        elem_nodes_ave_thickness[local_node_index] = mAveragedWallThickness[global_node_index];
        elem_nodes_region[local_node_index] = mpGeometryInfo->GetHeartRegion(global_node_index);

        // Calculate wall thickness averaged value for the element
        element_averaged_thickness +=  mWallThickness[global_node_index];
    }

    element_averaged_thickness /= SPACE_DIM+1;

    c_matrix<double, SPACE_DIM+1, SPACE_DIM> basis_functions( zero_matrix<double>(4u,3u) );
    basis_functions(0,0) = basis_functions(0,1) = basis_functions(0,2) = -1.0;
    basis_functions(1,0) = basis_functions(2,1) = basis_functions(3,2) =  1.0;

    c_matrix<double, SPACE_DIM+1, SPACE_DIM> temp;
    c_matrix<double, SPACE_DIM, SPACE_DIM> jacobian, inverse_jacobian;
    double jacobian_det;
    unsigned element_index = pElement->GetIndex();
    this->mpMesh->GetInverseJacobianForElement(element_index, jacobian, jacobian_det, inverse_jacobian);
    noalias(temp) = prod (basis_functions, inverse_jacobian);
    noalias(grad_ave_wall_thickness) = prod(elem_nodes_ave_thickness, temp);

    grad_ave_wall_thickness /= norm_2(grad_ave_wall_thickness);

    /*
     * Normal to the gradient (v in Streeter paper) which is then the circumferential direction
     * (it will be the fibre direction after rotation)
     *
     * Computed as the cross product with the base-apex direction (originally assumed base-apex axis is x). The output vector is not normal,
     * since the angle between them may be != 90, normalise it.
     */
    c_vector<double, SPACE_DIM> fibre_direction = VectorProduct(grad_ave_wall_thickness, mApexToBase);
    fibre_direction /= norm_2(fibre_direction);

    /*
     *  Longitude direction (w in Streeter paper)
     */
    c_vector<double, SPACE_DIM> longitude_direction = VectorProduct(grad_ave_wall_thickness, fibre_direction);

    /*
     *  Compute fibre to v angle: alpha = R*(1-2e)^3
     *
     *    R is the maximum angle between the fibre and the v axis (heart region dependant)
     *    (1 - 2e)^3 scales it by a value in [-1, 1] defining the rotation of the fibre based
     *       on the position in the wall
     */
    double alpha = GetFibreMaxAngle(elem_nodes_region) * SmallPow( (1 - 2*element_averaged_thickness), 3 );

    /*
     *  Apply alpha rotation about the u axis to the orthonormal basis
     *
     *               ( u(1) v(1) w(1) )
     *   (u, v, w) = ( u(2) v(2) w(2) )
     *               ( u(3) v(3) w(3) )
     *
     *  The following matrix defines a rotation about the u axis
     *
     *                 ( 1        0           0      ) (u')
     *   R = (u, v, w) ( 0    cos(alpha) -sin(alpha) ) (v')
     *                 ( 0    sin(alpha)  cos(alpha) ) (w')
     *
     *  The rotated basis is computed like:
     *
     *                                             ( 1        0           0      )
     *  (u, v_r, w_r ) = R * (u, v, w) = (u, v, w) ( 0    cos(alpha) -sin(alpha) )
     *                                             ( 0    sin(alpha)  cos(alpha) )
     *
     *  Which simplifies to:
     *
     *   v_r =  v*cos(alpha) + w*sin(alpha)
     *   w_r = -v*sin(alpha) + w*cos(alpha)
     */
    c_vector<double, SPACE_DIM> rotated_fibre_direction = fibre_direction*cos(alpha) + longitude_direction*sin(alpha);
    c_vector<double, SPACE_DIM> rotated_longitude_direction = -fibre_direction*sin(alpha) + longitude_direction*cos(alpha);


    /*
     * Test the orthonormality of the basis
     */
    assert( fabs(norm_2(rotated_fibre_direction) - 1) < 100*DBL_EPSILON );
    assert( fabs(norm_2(grad_ave_wall_thickness) - 1) < 100*DBL_EPSILON );
    assert( fabs(norm_2(rotated_longitude_direction) - 1) < 100*DBL_EPSILON );

    assert( fabs(inner_prod(rotated_fibre_direction, grad_ave_wall_thickness)) < 100*DBL_EPSILON );
    assert( fabs(inner_prod(rotated_fibre_direction, rotated_longitude_direction)) < 100*DBL_EPSILON);
    assert( fabs(inner_prod(grad_ave_wall_thickness, rotated_longitude_direction)) < 100*DBL_EPSILON);

    /*
     *  Output the direction of the myofibre, the transverse to it in the plane
     *  of the myocite laminae and the normal to this laminae (in that order)
     *
     *  See Fig. 1 "Laminar Structure of the Heart: a mathematical model" LeGrice et al. 97
     *
     */
    rData[0] = rotated_fibre_direction[0];
    rData[1] = rotated_fibre_direction[1];
    rData[2] = rotated_fibre_direction[2];
    rData[3] = grad_ave_wall_thickness[0];
    rData[4] = grad_ave_wall_thickness[1];
    rData[5] = grad_ave_wall_thickness[2];
    rData[6] = rotated_longitude_direction[0];
    rData[7] = rotated_longitude_direction[1];
    rData[8] = rotated_longitude_direction[2];
}


template<unsigned SPACE_DIM>
void StreeterFibreGenerator<SPACE_DIM>::SetApexToBase(const c_vector<double, SPACE_DIM>& apexToBase)
{
    double norm = norm_2(apexToBase);
    if (norm < DBL_EPSILON)
    {
        EXCEPTION("Apex to base vector should be non-zero");
    }
    mApexToBase = apexToBase / norm;
}

template<unsigned SPACE_DIM>
void StreeterFibreGenerator<SPACE_DIM>::SetApexToBase(unsigned axis)
{
    if (axis >= SPACE_DIM)
    {
        EXCEPTION("Apex to base coordinate axis was out of range");
    }
    mApexToBase = zero_vector<double>(SPACE_DIM);
    mApexToBase[axis] = 1.0;
}

template<unsigned SPACE_DIM>
void StreeterFibreGenerator<SPACE_DIM>::SetLogInfo(bool logInfo)
{
    mLogInfo = logInfo;
}

// Explicit instantiation
#define COVERAGE_IGNORE
template class StreeterFibreGenerator<3>;
#undef COVERAGE_IGNORE