Monodomain.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File Monodomain.cpp
//
// For more information, please see: http://www.nektar.info
//
// The MIT License
//
// Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
// Department of Aeronautics, Imperial College London (UK), and Scientific
// Computing and Imaging Institute, University of Utah (USA).
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
//
// Description: Monodomain cardiac electrophysiology homogenised model.
//
///////////////////////////////////////////////////////////////////////////////
 
#include <iostream>
 
#include <CardiacEPSolver/EquationSystems/Monodomain.h>
#include <CardiacEPSolver/Filters/FilterCellHistoryPoints.h>
#include <CardiacEPSolver/Filters/FilterCheckpointCellModel.h>
 
using namespace std;
 
namespace Nektar
{
/**
 * @class Monodomain
 *
 * Base model of cardiac electrophysiology of the form
 * \f{align*}{
 *     \frac{\partial u}{\partial t} = \nabla^2 u + J_{ion},
 * \f}
 * where the reaction term, \f$J_{ion}\f$ is defined by a specific cell
 * model.
 *
 * This implementation, at present, treats the reaction terms explicitly
 * and the diffusive element implicitly.
 */
 
/**
 * Registers the class with the Factory.
 */
string Monodomain::className =
    GetEquationSystemFactory().RegisterCreatorFunction(
        "Monodomain", Monodomain::create,
        "Monodomain model of cardiac electrophysiology.");
 
/**
 *
 */
Monodomain::Monodomain(const LibUtilities::SessionReaderSharedPtr &pSession,
                       const SpatialDomains::MeshGraphSharedPtr &pGraph)
    : UnsteadySystem(pSession, pGraph)
{
}
 
/**
 *
 */
void Monodomain::v_InitObject()
{
    UnsteadySystem::v_InitObject();
 
    m_session->LoadParameter("Chi", m_chi);
    m_session->LoadParameter("Cm", m_capMembrane);
 
    std::string vCellModel;
    m_session->LoadSolverInfo("CELLMODEL", vCellModel, "");
 
    ASSERTL0(vCellModel != "", "Cell Model not specified.");
 
    m_cell = GetCellModelFactory().CreateInstance(vCellModel, m_session,
                                                  m_fields[0]);
 
    m_intVariables.push_back(0);
 
    // Load variable coefficients
    StdRegions::VarCoeffType varCoeffEnum[6] = {
        StdRegions::eVarCoeffD00, StdRegions::eVarCoeffD01,
        StdRegions::eVarCoeffD11, StdRegions::eVarCoeffD02,
        StdRegions::eVarCoeffD12, StdRegions::eVarCoeffD22};
    std::string varCoeffString[6] = {"xx", "xy", "yy", "xz", "yz", "zz"};
    std::string aniso_var[3]      = {"fx", "fy", "fz"};
 
    const int nq            = m_fields[0]->GetNpoints();
    const int nVarDiffCmpts = m_spacedim * (m_spacedim + 1) / 2;
 
    // Allocate storage for variable coeffs and initialize to 1.
    for (int i = 0, k = 0; i < m_spacedim; ++i)
    {
        for (int j = 0; j < i + 1; ++j)
        {
            if (i == j)
            {
                m_vardiff[varCoeffEnum[k]] = Array<OneD, NekDouble>(nq, 1.0);
            }
            else
            {
                m_vardiff[varCoeffEnum[k]] = Array<OneD, NekDouble>(nq, 0.0);
            }
            ++k;
        }
    }
 
    // Apply fibre map f \in [0,1], scale to conductivity range
    // [o_min,o_max], specified by the session parameters o_min and o_max
    if (m_session->DefinesFunction("AnisotropicConductivity"))
    {
        if (m_session->DefinesCmdLineArgument("verbose"))
        {
            cout << "Loading Anisotropic Fibre map." << endl;
        }
 
        NekDouble o_min = m_session->GetParameter("o_min");
        NekDouble o_max = m_session->GetParameter("o_max");
        int k           = 0;
 
        Array<OneD, NekDouble> vTemp_i;
        Array<OneD, NekDouble> vTemp_j;
 
        /*
         * Diffusivity matrix D is upper triangular and defined as
         *    d_00   d_01  d_02
         *           d_11  d_12
         *                 d_22
         *
         * Given a principle fibre direction _f_ the diffusivity is given
         * by
         *    d_ij = { D_2 + (D_1 - D_2) f_i f_j   if i==j
         *           {       (D_1 - D_2) f_i f_j   if i!=j
         *
         * The vector _f_ is given in terms of the variables fx,fy,fz in the
         * function AnisotropicConductivity. The values of D_1 and D_2 are
         * the parameters o_max and o_min, respectively.
         */
 
        // Loop through columns of D
        for (int j = 0; j < m_spacedim; ++j)
        {
            ASSERTL0(m_session->DefinesFunction("AnisotropicConductivity",
                                                aniso_var[j]),
                     "Function 'AnisotropicConductivity' not correctly "
                     "defined.");
            GetFunction("AnisotropicConductivity")
                ->Evaluate(aniso_var[j], vTemp_j);
 
            // Loop through rows of D
            for (int i = 0; i < j + 1; ++i)
            {
                ASSERTL0(m_session->DefinesFunction("AnisotropicConductivity",
                                                    aniso_var[i]),
                         "Function 'AnisotropicConductivity' not correctly "
                         "defined.");
                GetFunction("AnisotropicConductivity")
                    ->Evaluate(aniso_var[i], vTemp_i);
 
                Vmath::Vmul(nq, vTemp_i, 1, vTemp_j, 1,
                            m_vardiff[varCoeffEnum[k]], 1);
 
                Vmath::Smul(nq, o_max - o_min, m_vardiff[varCoeffEnum[k]], 1,
                            m_vardiff[varCoeffEnum[k]], 1);
 
                if (i == j)
                {
                    Vmath::Sadd(nq, o_min, m_vardiff[varCoeffEnum[k]], 1,
                                m_vardiff[varCoeffEnum[k]], 1);
                }
 
                ++k;
            }
        }
    }
    else
    {
        // Otherwise apply isotropic conductivity value (o_max) to
        // diagonal components of tensor
        NekDouble o_max = m_session->GetParameter("o_max");
        for (int i = 0; i < nVarDiffCmpts; ++i)
        {
            Vmath::Smul(nq, o_max, m_vardiff[varCoeffEnum[i]], 1,
                        m_vardiff[varCoeffEnum[i]], 1);
        }
    }
 
    // Scale by scar map (range 0->1) derived from intensity map
    // (range d_min -> d_max)
    if (m_session->DefinesFunction("IsotropicConductivity"))
    {
        if (m_session->DefinesCmdLineArgument("verbose"))
        {
            cout << "Loading Isotropic Conductivity map." << endl;
        }
 
        const std::string varName = "intensity";
        Array<OneD, NekDouble> vTemp;
        GetFunction("IsotropicConductivity")->Evaluate(varName, vTemp);
 
        // If the d_min and d_max parameters are defined, then we need to
        // rescale the isotropic conductivity to convert from the source
        // domain (e.g. late-gad intensity) to conductivity
        if (m_session->DefinesParameter("d_min") ||
            m_session->DefinesParameter("d_max"))
        {
            const NekDouble f_min    = m_session->GetParameter("d_min");
            const NekDouble f_max    = m_session->GetParameter("d_max");
            const NekDouble scar_min = 0.0;
            const NekDouble scar_max = 1.0;
 
            // Threshold based on d_min, d_max
            for (int j = 0; j < nq; ++j)
            {
                vTemp[j] = (vTemp[j] < f_min ? f_min : vTemp[j]);
                vTemp[j] = (vTemp[j] > f_max ? f_max : vTemp[j]);
            }
 
            // Rescale to s \in [0,1] (0 maps to d_max, 1 maps to d_min)
            Vmath::Sadd(nq, -f_min, vTemp, 1, vTemp, 1);
            Vmath::Smul(nq, -1.0 / (f_max - f_min), vTemp, 1, vTemp, 1);
            Vmath::Sadd(nq, 1.0, vTemp, 1, vTemp, 1);
            Vmath::Smul(nq, scar_max - scar_min, vTemp, 1, vTemp, 1);
            Vmath::Sadd(nq, scar_min, vTemp, 1, vTemp, 1);
        }
 
        // Scale anisotropic conductivity values
        for (int i = 0; i < nVarDiffCmpts; ++i)
        {
            Vmath::Vmul(nq, vTemp, 1, m_vardiff[varCoeffEnum[i]], 1,
                        m_vardiff[varCoeffEnum[i]], 1);
        }
    }
 
    // Write out conductivity values
    for (int j = 0, k = 0; j < m_spacedim; ++j)
    {
        // Loop through rows of D
        for (int i = 0; i < j + 1; ++i)
        {
            // Transform variable coefficient and write out to file.
            m_fields[0]->FwdTransLocalElmt(m_vardiff[varCoeffEnum[k]],
                                           m_fields[0]->UpdateCoeffs());
            std::stringstream filename;
            filename << "Conductivity_" << varCoeffString[k] << ".fld";
            WriteFld(filename.str());
 
            ++k;
        }
    }
 
    // Search through the loaded filters and pass the cell model to any
    // CheckpointCellModel filters loaded.
    for (auto &x : m_filters)
    {
        if (x.first == "CheckpointCellModel")
        {
            std::shared_ptr<FilterCheckpointCellModel> c =
                std::dynamic_pointer_cast<FilterCheckpointCellModel>(x.second);
            c->SetCellModel(m_cell);
        }
        if (x.first == "CellHistoryPoints")
        {
            std::shared_ptr<FilterCellHistoryPoints> c =
                std::dynamic_pointer_cast<FilterCellHistoryPoints>(x.second);
            c->SetCellModel(m_cell);
        }
    }
 
    // Load stimuli
    m_stimulus = Stimulus::LoadStimuli(m_session, m_fields[0]);
 
    if (!m_explicitDiffusion)
    {
        m_ode.DefineImplicitSolve(&Monodomain::DoImplicitSolve, this);
    }
    m_ode.DefineOdeRhs(&Monodomain::DoOdeRhs, this);
}
 
/**
 *
 */
Monodomain::~Monodomain()
{
}
 
/**
 * @param   inarray         Input array.
 * @param   outarray        Output array.
 * @param   time            Current simulation time.
 * @param   lambda          Timestep.
 */
void Monodomain::DoImplicitSolve(
    const Array<OneD, const Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray, const NekDouble time,
    const NekDouble lambda)
{
    int nvariables = inarray.size();
    int nq         = m_fields[0]->GetNpoints();
    StdRegions::ConstFactorMap factors;
    // lambda = \Delta t
    factors[StdRegions::eFactorLambda] = 1.0 / lambda * m_chi * m_capMembrane;
 
    // We solve ( \nabla^2 - HHlambda ) Y[i] = rhs [i]
    // inarray = input: \hat{rhs} -> output: \hat{Y}
    // outarray = output: nabla^2 \hat{Y}
    // where \hat = modal coeffs
    for (int i = 0; i < nvariables; ++i)
    {
        // Multiply 1.0/timestep
        Vmath::Smul(nq, -factors[StdRegions::eFactorLambda], inarray[i], 1,
                    m_fields[i]->UpdatePhys(), 1);
 
        // Solve a system of equations with Helmholtz solver and transform
        // back into physical space.
        m_fields[i]->HelmSolve(m_fields[i]->GetPhys(),
                               m_fields[i]->UpdateCoeffs(), factors, m_vardiff);
 
        m_fields[i]->BwdTrans(m_fields[i]->GetCoeffs(),
                              m_fields[i]->UpdatePhys());
        m_fields[i]->SetPhysState(true);
 
        // Copy the solution vector (required as m_fields must be set).
        outarray[i] = m_fields[i]->GetPhys();
    }
}
 
/**
 *
 */
void Monodomain::DoOdeRhs(
    const Array<OneD, const Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray, const NekDouble time)
{
    // Compute I_ion
    m_cell->TimeIntegrate(inarray, outarray, time);
 
    // Compute I_stim
    for (unsigned int i = 0; i < m_stimulus.size(); ++i)
    {
        m_stimulus[i]->Update(outarray, time);
    }
}
 
/**
 *
 */
void Monodomain::v_SetInitialConditions(NekDouble initialtime,
                                        bool dumpInitialConditions,
                                        const int domain)
{
    EquationSystem::v_SetInitialConditions(initialtime, dumpInitialConditions,
                                           domain);
    m_cell->Initialise();
}
 
/**
 *
 */
void Monodomain::v_GenerateSummary(SummaryList &s)
{
    UnsteadySystem::v_GenerateSummary(s);
    if (m_session->DefinesFunction("d00") &&
        m_session->GetFunctionType("d00", "intensity") ==
            LibUtilities::eFunctionTypeExpression)
    {
        AddSummaryItem(
            s, "Diffusivity-x",
            m_session->GetFunction("d00", "intensity")->GetExpression());
    }
    if (m_session->DefinesFunction("d11") &&
        m_session->GetFunctionType("d11", "intensity") ==
            LibUtilities::eFunctionTypeExpression)
    {
        AddSummaryItem(
            s, "Diffusivity-y",
            m_session->GetFunction("d11", "intensity")->GetExpression());
    }
    if (m_session->DefinesFunction("d22") &&
        m_session->GetFunctionType("d22", "intensity") ==
            LibUtilities::eFunctionTypeExpression)
    {
        AddSummaryItem(
            s, "Diffusivity-z",
            m_session->GetFunction("d22", "intensity")->GetExpression());
    }
    m_cell->GenerateSummary(s);
}
} // namespace Nektar