Project: s41467-025-58566-z | Function: CustomHexagonalNagaiHondaForce::GetAdhesionParameter (cpp)

system: You are an expert C++ programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow C++ best practices and maintain consistent code style.
Return **only** the complete C++ function code.

user: Complete this C++ function:

**DESCRIPTION:** Determines adhesion energy parameters between different cell types and boundaries based on cell properties, implementing heterotypic and homotypic adhesion rules

**KEY TERMS:** {
  "Similar": "Similar to neural tube closure, palate closure, or embryonic wound healing, the sealing of a patterned tissue eventually leads to a perfectly assembled, segmented, and scar-free epithelium ^1,2,9",
  "JNK": "To maintain the contractile seam and pulling force until an epithelial segment is fully assembled, a complex machinery operates in the two tissues, involving JNK and integrin-based adhesions (Fig",
  "These": "These forces are generated by the joint action of the epidermis and the AS tissue and depend on the actomyosin cytoskeleton",
  "Although": "Although previous studies identified that epithelial adhesion depends on filopodia and lamellipodia ^17,18,19 , how zippering can be achieved and controlled remains elusive",
  "How": "How JNK activity is maintained still needs to be revealed",
  "During": "During DC, an epidermal gap on the dorsal side of the embryo is sealed due to the convergence and progressive adhesion of the two epidermal leaflets",
  "Remarkably": "Remarkably, epithelial sealing then takes place via a zippering of the two layers over several hundred microns, resulting in scar-free epidermal tissue with assembled body segments ^17,18",
  "Epithelial": "Epithelial sealing is necessary to ensure the closure of gaps, eventually leading to scar-free tissue during embryonic development or wound healing ^1,2"
}

**CONTEXT CODE:** 
template<unsigned DIM>
CustomHexagonalNagaiHondaForce<DIM>::~CustomHexagonalNagaiHondaForce()
{
}

template<unsigned DIM>
template<unsigned DIM>
void CustomHexagonalNagaiHondaForce<DIM>::AddForceContribution(AbstractCellPopulation<DIM>& rCellPopulation)
{
    if (dynamic_cast<VertexBasedCellPopulation<DIM>*>(&rCellPopulation) == nullptr)
    {
        throw std::invalid_argument("Vertex-based cell population expected.");
    }

    VertexBasedCellPopulation<DIM>& rVertexCellPopulation = static_cast<VertexBasedCellPopulation<DIM>&>(rCellPopulation);

    // Get the mesh and nodes
    typename AbstractMesh<DIM, DIM>::EdgeIterator edge_iter = rVertexCellPopulation.rGetMesh().GetEdgeIteratorBegin();
    typename AbstractMesh<DIM, DIM>::EdgeIterator edge_end = rVertexCellPopulation.rGetMesh().GetEdgeIteratorEnd();

    for (; edge_iter != edge_end; ++edge_iter)
    {
        c_vector<double, DIM> force = zero_vector<double>(DIM);

        unsigned nodeAIndex = edge_iter->GetNodeA()->GetIndex();
        unsigned nodeBIndex = edge_iter->GetNodeB()->GetIndex();
        Node<DIM>* pNodeA = rVertexCellPopulation.GetNode(nodeAIndex);
        Node<DIM>* pNodeB = rVertexCellPopulation.GetNode(nodeBIndex);

        // Calculate deformation contribution
        double elementArea = rVertexCellPopulation.GetVolumeOfElement(rVertexCellPopulation.GetContainingElementIndex(*pNodeA));
        double targetArea = rVertexCellPopulation.GetElement(nodeAIndex)->GetCell()->GetTargetArea();
        double areaDifference = elementArea - targetArea;

        double deformationContrib = mNagaiHondaDeformationEnergyParameter * areaDifference / rVertexCellPopulation.GetElement(nodeAIndex)->GetCell()->GetRadius();

        c_vector<double, DIM> edgeVector = pNodeA->rGetLocation() - pNodeB->rGetLocation();
        double edgeLength = norm_2(edgeVector);

        force += deformationContrib * (pNodeA->rGetLocation() - pNodeB->rGetLocation()) / edgeLength;

        // Calculate membrane surface tension contribution
        double perimeterDifference = edgeLength - rVertexCellPopulation.GetElement(nodeAIndex)->GetCell()->GetTargetPerimeter();

        double membraneSurfaceTensionContrib = mNagaiHondaMembraneSurfaceEnergyParameter * perimeterDifference / edgeLength;

        force -= membraneSurfaceTensionContrib * (pNodeA->rGetLocation() - pNodeB->rGetLocation()) / edgeLength;

        // Calculate adhesion contribution
        double adhesionParameter = GetAdhesionParameter(pNodeA, pNodeB, rVertexCellPopulation);

        double adhesionContrib = adhesionParameter / edgeLength;

        force -= adhesionContrib * (pNodeA->rGetLocation() - pNodeB->rGetLocation()) / edgeLength;

        // Apply forces
        c_vector<double, DIM> currentForceOnA = pNodeA->GetAppliedForce();
        c_vector<double, DIM> currentForceOnB = pNodeB->GetAppliedForce();

        pNodeA->AddAppliedForce(-force);
        pNodeB->AddAppliedForce(force);
    }
}

template<unsigned DIM>
template<unsigned DIM>
double CustomHexagonalNagaiHondaForce<DIM>::GetAdhesionParameter(Node<DIM>* pNodeA,
                                                                      Node<DIM>* pNodeB,
                                                                      VertexBasedCellPopulation<DIM>& rVertexCellPopulation)
{
    CellPtr pCellA = rVertexCellPopulation.GetCellUsingLocationIndex(pNodeA->GetNodeGlobalIndex());
    CellPtr pCellB = rVertexCellPopulation.GetCellUsingLocationIndex(pNodeB->GetNodeGlobalIndex());

    CellMutationState* pStateA = pCellA->GetMutationState();
    CellMutationState* pStateB = pCellB->GetMutationState();

    // Assuming mutation states are named as "type_A", "type_B", "type_C", and "scar"
    if (pStateA->GetName() == "type_A" && pStateB->GetName() == "type_A") {
        return GetNagaiHonda_A_A_AdhesionEnergyParameter();
    } else if (pStateA->GetName() == "type_A" && pStateB->GetName() == "type_B") {
        return GetNagaiHonda_A_B_AdhesionEnergyParameter();
    } else if (pStateA->GetName() == "type_B" && pStateB->GetName() == "type_A") {
        return GetNagaiHonda_A_B_AdhesionEnergyParameter();
    } else if (pStateA->GetName() == "type_B" && pStateB->GetName() == "type_B") {
        return GetNagaiHonda_B_B_AdhesionEnergyParameter();
    } else if (pStateA->GetName() == "type_A" && pStateB->GetName() == "type_C") {
        return GetNagaiHonda_A_C_AdhesionEnergyParameter();
    } else if (pStateA->GetName() == "type_C" && pStateB->GetName() == "type_A") {
        return GetNagaiHonda_A_C_AdhesionEnergyParameter();
    } else if (pStateA->GetName() == "type_B" && pStateB->GetName() == "type_C") {
        return GetNagaiHonda_B_C_AdhesionEnergyParameter();
    } else if (pStateA->GetName() == "type_C" && pStateB->GetName() == "type_B") {
        return GetNagaiHonda_B_C_AdhesionEnergyParameter();
    } else if (pStateA->GetName() == "type_C" && pStateB->GetName() == "type_C") {
        return GetNagaiHonda_C_C_AdhesionEnergyParameter();
    } else if (pStateA->GetName() == "scar" || pStateB->GetName() == "scar") {
        return GetNagaiHonda_Scar_AdhesionEnergyParameter();
    } else {
        throw std::invalid_argument("Unknown cell type(s) encountered.");
    }
}


template<unsigned DIM>
double CustomHexagonalNagaiHondaForce<DIM>::GetNagaiHondaDeformationEnergyParameter()
{
    return mNagaiHondaDeformationEnergyParameter;
}

template<unsigned DIM>
double CustomHexagonalNagaiHondaForce<DIM>::GetNagaiHonda_A_DeformationEnergyParameter()
{
    return mNagaiHonda_A_DeformationEnergyParameter;
}

template<unsigned DIM>
double CustomHexagonalNagaiHondaForce<DIM>::GetNagaiHondaMembraneSurfaceEnergyParameter()
{
    return mNagaiHondaMembraneSurfaceEnergyParameter;
}

template<unsigned DIM>
double CustomHexagonalNagaiHondaForce<DIM>::GetNagaiHonda_A_A_AdhesionEnergyParameter()
{
    return mNagaiHonda_A_A_AdhesionEnergyParameter;
}

template<unsigned DIM>
double CustomHexagonalNagaiHondaForce<DIM>::GetNagaiHonda_A_Boundary_AdhesionEnergyParameter()
{
    return mNagaiHonda_A_Boundary_AdhesionEnergyParameter;
}

template<unsigned DIM>
double CustomHexagonalNagaiHondaForce<DIM>::GetNagaiHonda_A_B_AdhesionEnergyParameter()
{
    return mNagaiHonda_A_B_AdhesionEnergyParameter;
}

template<unsigned DIM>
double CustomHexagonalNagaiHondaForce<DIM>::GetNagaiHonda_B_B_AdhesionEnergyParameter()
{
    return mNagaiHonda_B_B_AdhesionEnergyParameter;
}

template<unsigned DIM>
double CustomHexagonalNagaiHondaForce<DIM>::GetNagaiHonda_B_Boundary_AdhesionEnergyParameter()
{
    return mNagaiHonda_B_Boundary_AdhesionEnergyParameter;


Complete the function implementation replacing "throw std::runtime_error("Not implemented");".