NhsModelWithBackwardSolver.cpp

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#include "NhsModelWithBackwardSolver.hpp"
#include <iostream>
#include <cmath>
#include "LogFile.hpp"
#include "Exception.hpp"
#include "TimeStepper.hpp"

const double NhsModelWithBackwardSolver::mTolerance = 1e-10;

double NhsModelWithBackwardSolver::ImplicitSolveForQ()
{
    mTemporaryStateVariables[2] = (mTemporaryStateVariables[2] + mDt*mA1*mDLambdaDt)/(1 + mAlpha1*mDt);
    mTemporaryStateVariables[3] = (mTemporaryStateVariables[3] + mDt*mA2*mDLambdaDt)/(1 + mAlpha2*mDt);
    mTemporaryStateVariables[4] = (mTemporaryStateVariables[4] + mDt*mA3*mDLambdaDt)/(1 + mAlpha3*mDt);

    return mTemporaryStateVariables[2] + mTemporaryStateVariables[3] + mTemporaryStateVariables[4];
}

void NhsModelWithBackwardSolver::CalculateCaTropAndZDerivatives(double calciumTroponin, double z, double Q,
                                                                double& dCaTrop, double& dz)
{
//As in straight Nhs, we don't cover the exception code
#define COVERAGE_IGNORE
    if(calciumTroponin < 0)
    {
        EXCEPTION("CalciumTrop concentration went negative");
    }
    if(z<0)
    {
        EXCEPTION("z went negative");
    }
    if(z>1)
    {
        EXCEPTION("z became greater than 1");
    }
#undef COVERAGE_IGNORE

    double T0 = CalculateT0(z);

    double Ta;
    if(Q>0)
    {
        Ta = T0*(1+(2+mA)*Q)/(1+Q);
    }
    else
    {
        Ta = T0*(1+mA*Q)/(1-Q);
    }

    dCaTrop =   mKon * mCalciumI * ( mCalciumTroponinMax - calciumTroponin)
             - mKrefoff * (1-Ta/(mGamma*mTref)) * calciumTroponin;

    double ca_trop_to_ca_trop50_ratio_to_n = pow(calciumTroponin/mCalciumTrop50, mN);

    dz =   mAlpha0 * ca_trop_to_ca_trop50_ratio_to_n * (1-z)
         - mAlphaR1 * z
         - mAlphaR2 * pow(z,mNr) / (pow(z,mNr) + pow(mKZ,mNr));
}



void NhsModelWithBackwardSolver::CalculateBackwardEulerResidual(double calciumTroponin, double z, double Q,
                                                                double& residualComponent1, double& residualComponent2)
{
    double dcatrop;
    double dz;
    CalculateCaTropAndZDerivatives(calciumTroponin,z,Q,dcatrop,dz);

    residualComponent1 = calciumTroponin - mDt*dcatrop - mTemporaryStateVariables[0];
    residualComponent2 = z - mDt*dz - mTemporaryStateVariables[1];
}



NhsModelWithBackwardSolver::NhsModelWithBackwardSolver()
{
    mTemporaryStateVariables.resize(5);
}



void NhsModelWithBackwardSolver::RunDoNotUpdate(double startTime, double endTime, double timestep)
{
    assert(startTime < endTime);

    mDt = timestep;

    mTemporaryStateVariables = mStateVariables;

    // loop in time
    TimeStepper stepper(startTime, endTime, timestep);

    while ( !stepper.IsTimeAtEnd() )
    {
        // Q1,Q2,Q3 using backward euler can solved straightaway
        double new_Q = ImplicitSolveForQ();

        // Solve the 2D nonlinear problem for Backward Euler Ca_trop and z

        // see what the residual is
        double catrop_guess = mTemporaryStateVariables[0];
        double z_guess = mTemporaryStateVariables[1];
        double f1,f2; // f=[f1,f2]=residual

        CalculateBackwardEulerResidual(catrop_guess, z_guess, new_Q, f1, f2);
        double norm_resid = sqrt(f1*f1+f2*f2);

        // solve using Newton's method, no damping. Stop if num iterations
        // reaches 15 (very conservative)
        unsigned counter = 0;
        while ((norm_resid>mTolerance) && (counter++<15))
        {
            // numerically approximate the jacobian J
            double j11,j12,j21,j22; // J = [j11, j12; j21 j22]
            double temp1,temp2;

            double h = std::max(fabs(catrop_guess/100),1e-8);
            CalculateBackwardEulerResidual(catrop_guess+h, z_guess, new_Q, temp1, temp2);
            j11 = (temp1-f1)/h;
            j21 = (temp2-f2)/h;

            h = std::max(fabs(z_guess/100),1e-8);
            CalculateBackwardEulerResidual(catrop_guess, z_guess+h, new_Q, temp1, temp2);
            j12 = (temp1-f1)/h;
            j22 = (temp2-f2)/h;

            // compute u = J^{-1} f (exactly, as a 2D problem)
            double one_over_det = 1.0/(j11*j22-j12*j21);
            double u1 = one_over_det*(j22*f1  - j12*f2);
            double u2 = one_over_det*(-j21*f1 + j11*f2);

            catrop_guess -= u1;
            z_guess -= u2;

            CalculateBackwardEulerResidual(catrop_guess, z_guess, new_Q, f1, f2);
            norm_resid = sqrt(f1*f1+f2*f2);
        }
        assert(counter<15); // if this fails, see corresponding code in old NhsModelWithImplicitSolver

        mTemporaryStateVariables[0] = catrop_guess;
        mTemporaryStateVariables[1] = z_guess;

        stepper.AdvanceOneTimeStep();
    }
}

double NhsModelWithBackwardSolver::GetNextActiveTension()
{
    double T0 = CalculateT0(mTemporaryStateVariables[1]);
    double Q = mTemporaryStateVariables[2]+mTemporaryStateVariables[3]+mTemporaryStateVariables[4];

    if(Q>0)
    {
        return T0*(1+(2+mA)*Q)/(1+Q);
    }
    else
    {
        return T0*(1+mA*Q)/(1-Q);
    }
}

void NhsModelWithBackwardSolver::RunAndUpdate(double startTime, double endTime, double timestep)
{
    RunDoNotUpdate(startTime, endTime, timestep);
    UpdateStateVariables();
}