Bidomain.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: Bidomain.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: Bidomain cardiac electrophysiology homogenised model.
//
///////////////////////////////////////////////////////////////////////////////
 
#include <iostream>
 
#include <CardiacEPSolver/EquationSystems/Bidomain.h>
#include <CardiacEPSolver/Filters/FilterCheckpointCellModel.h>
 
using namespace std;
 
namespace Nektar
{
/**
 * @class Bidomain
 *
 * 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 Bidomain::className = GetEquationSystemFactory().RegisterCreatorFunction(
    "Bidomain", Bidomain::create,
    "Bidomain model of cardiac electrophysiology with 3D diffusion.");
 
/**
 *
 */
Bidomain::Bidomain(const LibUtilities::SessionReaderSharedPtr &pSession,
                   const SpatialDomains::MeshGraphSharedPtr &pGraph)
    : UnsteadySystem(pSession, pGraph)
{
}
 
void Bidomain::v_InitObject(bool DeclareField)
{
    UnsteadySystem::v_InitObject(DeclareField);
    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);
    m_intVariables.push_back(1);
 
    // Load variable coefficients
    StdRegions::VarCoeffType varCoeffEnum[3] = {StdRegions::eVarCoeffD00,
                                                StdRegions::eVarCoeffD11,
                                                StdRegions::eVarCoeffD22};
    std::string varName[3]                   = {"AnisotropicConductivityX",
                                                "AnisotropicConductivityY",
                                                "AnisotropicConductivityZ"};
 
    if (m_session->DefinesFunction("IntracellularConductivity") &&
        m_session->DefinesFunction("ExtracellularConductivity"))
    {
        for (int i = 0; i < m_spacedim; ++i)
        {
            int nq = m_fields[0]->GetNpoints();
            Array<OneD, NekDouble> x0(nq);
            Array<OneD, NekDouble> x1(nq);
            Array<OneD, NekDouble> x2(nq);
 
            // get the coordinates
            m_fields[0]->GetCoords(x0, x1, x2);
            tmp1    = Array<OneD, const Array<OneD, NekDouble>>(nq);
            tmp2    = Array<OneD, const Array<OneD, NekDouble>>(nq);
            tmp3    = Array<OneD, const Array<OneD, NekDouble>>(nq);
            tmp1[i] = Array<OneD, NekDouble>(nq);
            tmp2[i] = Array<OneD, NekDouble>(nq);
            tmp3[i] = Array<OneD, NekDouble>(nq);
 
            LibUtilities::EquationSharedPtr ifunc1 =
                m_session->GetFunction("IntracellularConductivity", varName[i]);
            LibUtilities::EquationSharedPtr ifunc2 =
                m_session->GetFunction("ExtracellularConductivity", varName[i]);
            for (int j = 0; j < nq; j++)
            {
                tmp1[i][j] = ifunc1->Evaluate(x0[j], x1[j], x2[j], 0.0);
                tmp2[i][j] = ifunc2->Evaluate(x0[j], x1[j], x2[j], 0.0);
            }
            Vmath::Vadd(nq, tmp1[i], 1, tmp2[i], 1, tmp3[i], 1);
            m_vardiffi[varCoeffEnum[i]]  = tmp1[i];
            m_vardiffie[varCoeffEnum[i]] = tmp3[i];
        }
    }
 
    if (m_session->DefinesParameter("StimulusDuration"))
    {
        ASSERTL0(m_session->DefinesFunction("Stimulus", "u"),
                 "Stimulus function not defined.");
        m_session->LoadParameter("StimulusDuration", m_stimDuration);
    }
    else
    {
        m_stimDuration = 0;
    }
 
    // 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 (!m_explicitDiffusion)
    {
        m_ode.DefineImplicitSolve(&Bidomain::DoImplicitSolve, this);
    }
    m_ode.DefineOdeRhs(&Bidomain::DoOdeRhs, this);
    m_ode.DefineProjection(&Bidomain::DoDummyProjection, this);
}
 
/**
 *
 */
Bidomain::~Bidomain()
{
}
 
/**
 * @param   inarray         Input array.
 * @param   outarray        Output array.
 * @param   time            Current simulation time.
 * @param   lambda          Timestep.
 */
void Bidomain::DoImplicitSolve(
    const Array<OneD, const Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray,
    [[maybe_unused]] const NekDouble time, const NekDouble lambda)
{
    int nvariables = inarray.size();
    int nq         = m_fields[0]->GetNpoints();
 
    Array<OneD, NekDouble> grad0(nq), grad1(nq), grad2(nq), grad(nq);
    Array<OneD, NekDouble> ggrad0(nq), ggrad1(nq), ggrad2(nq), ggrad(nq),
        temp(nq);
 
    // We solve ( \sigma\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)
    {
        // Only apply diffusion to first variable.
        if (i > 1)
        {
            Vmath::Vcopy(nq, &inarray[i][0], 1, &outarray[i][0], 1);
            continue;
        }
        if (i == 0)
        {
            StdRegions::ConstFactorMap factors;
            factors[StdRegions::eFactorLambda] =
                (1.0 / lambda) * (m_capMembrane * m_chi);
            if (m_spacedim == 1)
            {
                // Take first partial derivative
                m_fields[i]->PhysDeriv(inarray[1], ggrad0);
                // Take second partial derivative
                m_fields[i]->PhysDeriv(0, ggrad0, ggrad0);
                // Multiply by Intracellular-Conductivity
                if (m_session->DefinesFunction("IntracellularConductivity") &&
                    m_session->DefinesFunction("ExtracellularConductivity"))
                {
                    Vmath::Smul(nq, m_session->GetParameter("sigmaix"), ggrad0,
                                1, ggrad0, 1);
                }
                // Add partial derivatives together
                Vmath::Vcopy(nq, ggrad0, 1, ggrad, 1);
                Vmath::Smul(nq, -1.0, ggrad, 1, ggrad, 1);
                // Multiply 1.0/timestep/lambda
                Vmath::Smul(nq, -factors[StdRegions::eFactorLambda], inarray[i],
                            1, temp, 1);
                Vmath::Vadd(nq, ggrad, 1, temp, 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_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();
            }
 
            if (m_spacedim == 2)
            {
                // Take first partial derivative
                m_fields[i]->PhysDeriv(inarray[1], ggrad0, ggrad1);
                // Take second partial derivative
                m_fields[i]->PhysDeriv(0, ggrad0, ggrad0);
                m_fields[i]->PhysDeriv(1, ggrad1, ggrad1);
                // Multiply by Intracellular-Conductivity
                if (m_session->DefinesFunction("IntracellularConductivity") &&
                    m_session->DefinesFunction("ExtracellularConductivity"))
                {
                    Vmath::Smul(nq, m_session->GetParameter("sigmaix"), ggrad0,
                                1, ggrad0, 1);
                    Vmath::Smul(nq, m_session->GetParameter("sigmaiy"), ggrad1,
                                1, ggrad1, 1);
                }
                // Add partial derivatives together
                Vmath::Vadd(nq, ggrad0, 1, ggrad1, 1, ggrad, 1);
                Vmath::Smul(nq, -1.0, ggrad, 1, ggrad, 1);
                // Multiply 1.0/timestep/lambda
                Vmath::Smul(nq, -factors[StdRegions::eFactorLambda], inarray[i],
                            1, temp, 1);
                Vmath::Vadd(nq, ggrad, 1, temp, 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_vardiffi);
                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();
            }
 
            if (m_spacedim == 3)
            {
                // Take first partial derivative
                m_fields[i]->PhysDeriv(inarray[1], ggrad0, ggrad1, ggrad2);
                // Take second partial derivative
                m_fields[i]->PhysDeriv(0, ggrad0, ggrad0);
                m_fields[i]->PhysDeriv(1, ggrad1, ggrad1);
                m_fields[i]->PhysDeriv(2, ggrad2, ggrad2);
                // Multiply by Intracellular-Conductivity
                if (m_session->DefinesFunction("IntracellularConductivity") &&
                    m_session->DefinesFunction("ExtracellularConductivity"))
                {
                    Vmath::Smul(nq, m_session->GetParameter("sigmaix"), ggrad0,
                                1, ggrad0, 1);
                    Vmath::Smul(nq, m_session->GetParameter("sigmaiy"), ggrad1,
                                1, ggrad1, 1);
                    Vmath::Smul(nq, m_session->GetParameter("sigmaiz"), ggrad2,
                                1, ggrad2, 1);
                }
                // Add partial derivatives together
                Vmath::Vadd(nq, ggrad0, 1, ggrad1, 1, ggrad, 1);
                Vmath::Vadd(nq, ggrad2, 1, ggrad, 1, ggrad, 1);
                Vmath::Smul(nq, -1.0, ggrad, 1, ggrad, 1);
                // Multiply 1.0/timestep/lambda
                Vmath::Smul(nq, -factors[StdRegions::eFactorLambda], inarray[i],
                            1, temp, 1);
                Vmath::Vadd(nq, ggrad, 1, temp, 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_vardiffi);
                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();
            }
        }
        if (i == 1)
        {
            StdRegions::ConstFactorMap factors;
            factors[StdRegions::eFactorLambda] = 0.0;
            if (m_spacedim == 1)
            {
                // Take first partial derivative
                m_fields[i]->PhysDeriv(m_fields[0]->UpdatePhys(), grad0);
                // Take second derivative
                m_fields[i]->PhysDeriv(0, grad0, grad0);
                // Multiply by Intracellular-Conductivity
                if (m_session->DefinesFunction("IntracellularConductivity") &&
                    m_session->DefinesFunction("ExtracellularConductivity"))
                {
                    Vmath::Smul(nq, m_session->GetParameter("sigmaix"), grad0,
                                1, grad0, 1);
                }
                // and sum terms
                Vmath::Vcopy(nq, grad0, 1, grad, 1);
                Vmath::Smul(nq,
                            (-1.0 * m_session->GetParameter("sigmaix")) /
                                (m_session->GetParameter("sigmaix") +
                                 m_session->GetParameter("sigmaix")),
                            grad, 1, grad, 1);
                // Now solve Poisson problem for \phi_e
                m_fields[i]->SetPhys(grad);
                m_fields[i]->HelmSolve(m_fields[i]->GetPhys(),
                                       m_fields[i]->UpdateCoeffs(), factors);
                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();
            }
 
            if (m_spacedim == 2)
            {
                // Take first partial derivative
                m_fields[i]->PhysDeriv(m_fields[0]->UpdatePhys(), grad0, grad1);
                // Take second derivative
                m_fields[i]->PhysDeriv(0, grad0, grad0);
                m_fields[i]->PhysDeriv(1, grad1, grad1);
                // Multiply by Intracellular-Conductivity
                if (m_session->DefinesFunction("IntracellularConductivity") &&
                    m_session->DefinesFunction("ExtracellularConductivity"))
                {
                    Vmath::Smul(nq, m_session->GetParameter("sigmaix"), grad0,
                                1, grad0, 1);
                    Vmath::Smul(nq, m_session->GetParameter("sigmaiy"), grad1,
                                1, grad1, 1);
                }
                // and sum terms
                Vmath::Vadd(nq, grad0, 1, grad1, 1, grad, 1);
                Vmath::Smul(nq, -1.0, grad, 1, grad, 1);
                // Now solve Poisson problem for \phi_e
                m_fields[i]->SetPhys(grad);
                m_fields[i]->HelmSolve(m_fields[i]->GetPhys(),
                                       m_fields[i]->UpdateCoeffs(), factors,
                                       m_vardiffie);
                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();
            }
 
            if (m_spacedim == 3)
            {
                // Take first partial derivative
                m_fields[i]->PhysDeriv(m_fields[0]->UpdatePhys(), grad0, grad1,
                                       grad2);
                // Take second derivative
                m_fields[i]->PhysDeriv(0, grad0, grad0);
                m_fields[i]->PhysDeriv(1, grad1, grad1);
                m_fields[i]->PhysDeriv(2, grad2, grad2);
                // Multiply by Intracellular-Conductivity
                if (m_session->DefinesFunction("IntracellularConductivity") &&
                    m_session->DefinesFunction("ExtracellularConductivity"))
                {
                    Vmath::Smul(nq, m_session->GetParameter("sigmaix"), grad0,
                                1, grad0, 1);
                    Vmath::Smul(nq, m_session->GetParameter("sigmaiy"), grad1,
                                1, grad1, 1);
                    Vmath::Smul(nq, m_session->GetParameter("sigmaiz"), grad2,
                                1, grad2, 1);
                }
                // and sum terms
                Vmath::Vadd(nq, grad0, 1, grad1, 1, grad, 1);
                Vmath::Vadd(nq, grad2, 1, grad, 1, grad, 1);
                Vmath::Smul(nq, -1.0, grad, 1, grad, 1);
                // Now solve Poisson problem for \phi_e
                m_fields[i]->SetPhys(grad);
                m_fields[i]->HelmSolve(m_fields[i]->GetPhys(),
                                       m_fields[i]->UpdateCoeffs(), factors,
                                       m_vardiffie);
                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 Bidomain::DoOdeRhs(
    const Array<OneD, const Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray, const NekDouble time)
{
    int nq = m_fields[0]->GetNpoints();
    m_cell->TimeIntegrate(inarray, outarray, time);
    if (m_stimDuration > 0 && time < m_stimDuration)
    {
        Array<OneD, NekDouble> x0(nq);
        Array<OneD, NekDouble> x1(nq);
        Array<OneD, NekDouble> x2(nq);
        Array<OneD, NekDouble> result(nq);
 
        // get the coordinates
        m_fields[0]->GetCoords(x0, x1, x2);
 
        LibUtilities::EquationSharedPtr ifunc =
            m_session->GetFunction("Stimulus", "u");
        ifunc->Evaluate(x0, x1, x2, time, result);
 
        Vmath::Vadd(nq, outarray[0], 1, result, 1, outarray[0], 1);
    }
    Vmath::Smul(nq, 1.0 / m_capMembrane, outarray[0], 1, outarray[0], 1);
}
 
void Bidomain::v_SetInitialConditions(NekDouble initialtime,
                                      bool dumpInitialConditions,
                                      const int domain)
{
    EquationSystem::v_SetInitialConditions(initialtime, dumpInitialConditions,
                                           domain);
    m_cell->Initialise();
}
 
/**
 *
 */
void Bidomain::v_GenerateSummary(SummaryList &s)
{
    UnsteadySystem::v_GenerateSummary(s);
 
    /// @TODO Update summary
    ASSERTL0(false, "Update the generate summary");
    //
    //        out << "\tChi         : " << m_chi << endl;
    //        out << "\tCm          : " << m_capMembrane << endl;
    //        if (m_session->DefinesFunction("IntracellularConductivity",
    //        "AnisotropicConductivityX") &&
    //            m_session->GetFunctionType("IntracellularConductivity",
    //            "AnisotropicConductivityX") ==
    //            LibUtilities::eFunctionTypeExpression)
    //        {
    //            out << "\tIntra-Diffusivity-x   : "
    //                << m_session->GetFunction("IntracellularConductivity",
    //                "AnisotropicConductivityX")->GetExpression()
    //                << endl;
    //        }
    //        if (m_session->DefinesFunction("IntracellularConductivity",
    //        "AnisotropicConductivityY") &&
    //            m_session->GetFunctionType("IntracellularConductivity",
    //            "AnisotropicConductivityY") ==
    //            LibUtilities::eFunctionTypeExpression)
    //        {
    //            out << "\tIntra-Diffusivity-y   : "
    //                << m_session->GetFunction("IntracellularConductivity",
    //                "AnisotropicConductivityY")->GetExpression()
    //                << endl;
    //        }
    //        if (m_session->DefinesFunction("IntracellularConductivity",
    //        "AnisotropicConductivityZ") &&
    //            m_session->GetFunctionType("IntracellularConductivity",
    //            "AnisotropicConductivityZ") ==
    //            LibUtilities::eFunctionTypeExpression)
    //        {
    //            out << "\tIntra-Diffusivity-z   : "
    //                << m_session->GetFunction("IntracellularConductivity",
    //                "AnisotropicConductivityZ")->GetExpression()
    //                << endl;
    //        }
    //        if (m_session->DefinesFunction("ExtracellularConductivity",
    //        "AnisotropicConductivityX") &&
    //            m_session->GetFunctionType("ExtracellularConductivity",
    //            "AnisotropicConductivityX") ==
    //            LibUtilities::eFunctionTypeExpression)
    //        {
    //            out << "\tExtra-Diffusivity-x   : "
    //                << m_session->GetFunction("ExtracellularConductivity",
    //                "AnisotropicConductivityX")->GetExpression()
    //                << endl;
    //        }
    //        if (m_session->DefinesFunction("ExtracellularConductivity",
    //        "AnisotropicConductivityY") &&
    //            m_session->GetFunctionType("ExtracellularConductivity",
    //            "AnisotropicConductivityY") ==
    //            LibUtilities::eFunctionTypeExpression)
    //        {
    //            out << "\tExtra-Diffusivity-y   : "
    //                << m_session->GetFunction("ExtracellularConductivity",
    //                "AnisotropicConductivityY")->GetExpression()
    //                << endl;
    //        }
    //        if (m_session->DefinesFunction("ExtracellularConductivity",
    //        "AnisotropicConductivityZ") &&
    //            m_session->GetFunctionType("ExtracellularConductivity",
    //            "AnisotropicConductivityZ") ==
    //            LibUtilities::eFunctionTypeExpression)
    //        {
    //            out << "\tExtra-Diffusivity-z   : "
    //                << m_session->GetFunction("ExtracellularConductivity",
    //                "AnisotropicConductivityZ")->GetExpression()
    //                << endl;
    //        }
    m_cell->GenerateSummary(s);
}
 
} // namespace Nektar