MonodomainPurkinjeCableAssembler.hpp

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#ifndef MONODOMAINPURKINJECABLEASSEMBLER_HPP_
#define MONODOMAINPURKINJECABLEASSEMBLER_HPP_

#include "AbstractFeCableIntegralAssembler.hpp"
#include "HeartConfig.hpp"
#include "PdeSimulationTime.hpp"


template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
class MonodomainPurkinjeCableAssembler : public AbstractFeCableIntegralAssembler<ELEMENT_DIM,SPACE_DIM,2,false,true,NORMAL>
{
private:
    static const unsigned PROBLEM_DIM=2;

    c_matrix<double,PROBLEM_DIM*2,PROBLEM_DIM*2 /*2=number of bases per cable*/> ComputeCableMatrixTerm(
        c_vector<double, 2>& rPhi,
        c_matrix<double, ELEMENT_DIM, 2>& rGradPhi,
        ChastePoint<SPACE_DIM>& rX,
        c_vector<double,PROBLEM_DIM>& rU,
        c_matrix<double,PROBLEM_DIM, SPACE_DIM>& rGradU,
        Element<1,SPACE_DIM>* pElement)
    {
        c_matrix<double,PROBLEM_DIM*2, PROBLEM_DIM*2> ret = zero_matrix<double>(PROBLEM_DIM*2, PROBLEM_DIM*2);
        double capacitance = HeartConfig::Instance()->GetPurkinjeCapacitance();
        double chi = HeartConfig::Instance()->GetPurkinjeSurfaceAreaToVolumeRatio();
        double conductivity = HeartConfig::Instance()->GetPurkinjeConductivity();

        //We have to scale the assembled matrix by the cross sectional area of the Purkinje
        //fibre to ensure conservation of current at branch points. See #1899.
        const double fibre_cross_section_area = M_PI*pElement->GetAttribute()*pElement->GetAttribute();

        for(unsigned i=0; i<2; i++) // 2 = number of basis functions per cable element
        {
            for(unsigned j=0; j<2; j++)  // 2 = number of basis functions per cable element
            {
                ret(2*i,  2*j)   = 0;  // [V,V] block
                ret(2*i+1,2*j)   = 0;  // [Vpurkinje,V] block
                ret(2*i,  2*j+1) = 0;  // [V,Vpurkinje] block
                ret(2*i+1,2*j+1) = capacitance*chi*PdeSimulationTime::GetPdeTimeStepInverse()*rPhi(i)*rPhi(j);

                for (unsigned dim=0; dim<SPACE_DIM; dim++)
                {
                    ret(2*i+1,2*j+1) += conductivity*rGradPhi(dim,i)*rGradPhi(dim,j);
                }

                ret(2*i+1,2*j+1) *= fibre_cross_section_area;
            }
        }

        return ret;
    }
public:
    MonodomainPurkinjeCableAssembler(MixedDimensionMesh<ELEMENT_DIM,SPACE_DIM>* pMesh)
        : AbstractFeCableIntegralAssembler<ELEMENT_DIM,SPACE_DIM,2,false,true,NORMAL>(pMesh)
    {
        // Check radii have been set on the purkinje elements
        for (typename MixedDimensionMesh<ELEMENT_DIM,SPACE_DIM>::CableElementIterator iter = pMesh->GetCableElementIteratorBegin();
             iter != pMesh->GetCableElementIteratorEnd();
             ++iter)
        {
            double radius = (*iter)->GetAttribute();
            if (fabs(radius)<=DBL_EPSILON)
            {
                EXCEPTION("Radii not provided for all Purkinje elements - should be present in the mesh file or defined in test");
            }
        }
    }
};

#endif // MONODOMAINPURKINJECABLEASSEMBLER_HPP_