Location: semantic-annotation @ dcab0d9157ad / Nima / chang_fujita_b_1999.cellml

Author:
Dewan Sarwar <sarwarcse@gmail.com>
Date:
2019-03-11 12:09:49+13:00
Desc:
added blood capillary flux model
Permanent Source URI:
https://models.physiomeproject.org/workspace/584/rawfile/dcab0d9157ad4fb602c5084666c323fb3e30323a/Nima/chang_fujita_b_1999.cellml

<?xml version='1.0'?>
<model cmeta:id="chang_1999" name="chang_1999" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
    <units name="millivolt">
        <unit prefix="milli" units="volt"/>
    </units>
    <units name="cm_per_s">
        <unit prefix="centi" units="metre"/>
        <unit exponent="-1" units="second"/>
    </units>
    <units name="mmol_per_cm3">
        <unit prefix="milli" units="mole"/>
        <unit exponent="-3" prefix="centi" units="metre"/>
    </units>
    <units name="flux">
        <unit prefix="milli" units="mole"/>
        <unit exponent="-3" prefix="centi" units="metre"/>
        <unit exponent="-1" units="second"/>
    </units>
    <units name="C_per_mmol">
        <unit units="coulomb"/>
        <unit exponent="-1" prefix="milli" units="mole"/>
    </units>
    <units name="J_per_mmol">
        <unit units="joule"/>
        <unit exponent="-1" prefix="milli" units="mole"/>
        <unit exponent="-1" units="kelvin"/>
    </units>
    <units base_units="yes" name="mmHg"/>
    <units name="cm_per_s_mmHg">
        <unit prefix="centi" units="metre"/>
        <unit exponent="-1" units="second"/>
        <unit exponent="-1" units="mmHg"/>
    </units>
    <component name="environment">
        <variable name="time" public_interface="out" units="second"/>
    </component>
    <component name="imported_variables">
        <variable initial_value="0.1033" name="C_m_Imp" private_interface="out" units="mmol_per_cm3"/>
        <variable initial_value="0.1124" name="C_c_Imp" private_interface="out" units="mmol_per_cm3"/>
        <variable initial_value="-28.0" name="psi_m" private_interface="out" public_interface="out" units="millivolt"/>
        <variable initial_value="-86.4" name="psi_c" private_interface="out" public_interface="out" units="millivolt"/>
    </component>
    <component name="solute_concentrations">
        <variable initial_value="0.05" name="C_m_Na" public_interface="out" units="mmol_per_cm3"/>
        <variable initial_value="0.002" name="C_m_K" public_interface="out" units="mmol_per_cm3"/>
        <variable initial_value="0.03" name="C_m_Cl" public_interface="out" units="mmol_per_cm3"/>
        <variable initial_value="0.0164" name="C_c_Na" public_interface="out" units="mmol_per_cm3"/>
        <variable initial_value="0.1637" name="C_c_K" public_interface="out" units="mmol_per_cm3"/>
        <variable initial_value="0.0203" name="C_c_Cl" public_interface="out" units="mmol_per_cm3"/>
        <variable initial_value="1.438E-1" name="C_s_Na" public_interface="out" units="mmol_per_cm3"/>
        <variable initial_value="4.25E-3" name="C_s_K" public_interface="out" units="mmol_per_cm3"/>
        <variable initial_value="1.12E-1" name="C_s_Cl" public_interface="out" units="mmol_per_cm3"/>
        <variable name="J_mc_Na" public_interface="in" units="flux"/>
        <variable name="J_ms_Na" public_interface="in" units="flux"/>
        <variable name="J_sc_Na" public_interface="in" units="flux"/>
        <variable name="J_mc_K" public_interface="in" units="flux"/>
        <variable name="J_ms_K" public_interface="in" units="flux"/>
        <variable name="J_sc_K" public_interface="in" units="flux"/>
        <variable name="J_mc_Cl" public_interface="in" units="flux"/>
        <variable name="J_ms_Cl" public_interface="in" units="flux"/>
        <variable name="J_sc_Cl" public_interface="in" units="flux"/>
        <variable name="time" public_interface="in" units="second"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="C_m_Na_diff_eq">
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>C_m_Na</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <plus/>
                        <ci>J_mc_Na</ci>
                        <ci>J_ms_Na</ci>
                    </apply>
                </apply>
            </apply>
            <apply id="C_s_Na_diff_eq">
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>C_s_Na</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>J_ms_Na</ci>
                    <ci>J_sc_Na</ci>
                </apply>
            </apply>
            <apply id="C_c_Na_diff_eq">
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>C_c_Na</ci>
                </apply>
                <apply>
                    <plus/>
                    <ci>J_mc_Na</ci>
                    <ci>J_sc_Na</ci>
                </apply>
            </apply>
            <apply id="C_m_K_diff_eq">
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>C_m_K</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <plus/>
                        <ci>J_mc_K</ci>
                        <ci>J_ms_K</ci>
                    </apply>
                </apply>
            </apply>
            <apply id="C_s_K_diff_eq">
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>C_s_K</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>J_ms_K</ci>
                    <ci>J_sc_K</ci>
                </apply>
            </apply>
            <apply id="C_c_K_diff_eq">
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>C_c_K</ci>
                </apply>
                <apply>
                    <plus/>
                    <ci>J_mc_K</ci>
                    <ci>J_sc_K</ci>
                </apply>
            </apply>
            <apply id="C_m_Cl_diff_eq">
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>C_m_Cl</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <plus/>
                        <ci>J_mc_Cl</ci>
                        <ci>J_ms_Cl</ci>
                    </apply>
                </apply>
            </apply>
            <apply id="C_s_Cl_diff_eq">
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>C_s_Cl</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>J_ms_Cl</ci>
                    <ci>J_sc_Cl</ci>
                </apply>
            </apply>
            <apply id="C_c_Cl_diff_eq">
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>C_c_Cl</ci>
                </apply>
                <apply>
                    <plus/>
                    <ci>J_mc_Cl</ci>
                    <ci>J_sc_Cl</ci>
                </apply>
            </apply>
        </math>
    </component>
    <component name="constants">
        <variable initial_value="2.579" name="RT" public_interface="out" units="J_per_mmol"/>
        <variable initial_value="96.48" name="F" public_interface="out" units="C_per_mmol"/>
        <variable initial_value="4.525E-2" name="C_s_Imp" public_interface="out" units="mmol_per_cm3"/>
        <variable initial_value="0.0" name="psi_s" public_interface="out" units="millivolt"/>
    </component>
    <component name="mc_sodium_flux">
        <variable name="J_mc_Na" public_interface="out" units="flux"/>
        <variable name="J_mc_NaCl" public_interface="out" units="flux"/>
        <variable name="G_mc_Na" units="flux"/>
        <variable initial_value="3.27E-6" name="P_mc_Na" units="cm_per_s"/>
        <variable initial_value="3.21E-5" name="J_mc_NaCl_max" units="flux"/>
        <variable initial_value="5.11E-2" name="K_mc_Na_NaCl" units="mmol_per_cm3"/>
        <variable initial_value="1.92E-2" name="K_mc_Cl_NaCl" units="mmol_per_cm3"/>
        <variable name="time" public_interface="in" units="second"/>
        <variable name="RT" public_interface="in" units="J_per_mmol"/>
        <variable name="F" public_interface="in" units="C_per_mmol"/>
        <variable name="C_m_Na" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_c_Na" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_m_Cl" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_c_Cl" public_interface="in" units="mmol_per_cm3"/>
        <variable name="psi_m" public_interface="in" units="millivolt"/>
        <variable name="psi_c" public_interface="in" units="millivolt"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="J_mc_Na_calculation">
                <eq/>
                <ci>J_mc_Na</ci>
                <apply>
                    <plus/>
                    <ci>J_mc_NaCl</ci>
                    <ci>G_mc_Na</ci>
                </apply>
            </apply>
            <apply id="G_mc_Na_calculation">
                <eq/>
                <ci>G_mc_Na</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>P_mc_Na</ci>
                                <ci>F</ci>
                                <apply>
                                    <minus/>
                                    <ci>psi_m</ci>
                                    <ci>psi_c</ci>
                                </apply>
                            </apply>
                            <ci>RT</ci>
                        </apply>
                        <apply>
                            <minus/>
                            <ci>C_m_Na</ci>
                            <apply>
                                <times/>
                                <ci>C_c_Na</ci>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <times/>
                                        <apply>
                                            <divide/>
                                            <apply>
                                                <minus/>
                                                <ci>F</ci>
                                            </apply>
                                            <ci>RT</ci>
                                        </apply>
                                        <apply>
                                            <minus/>
                                            <ci>psi_m</ci>
                                            <ci>psi_c</ci>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1.0</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <times/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <minus/>
                                        <ci>F</ci>
                                    </apply>
                                    <ci>RT</ci>
                                </apply>
                                <apply>
                                    <minus/>
                                    <ci>psi_m</ci>
                                    <ci>psi_c</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply id="J_mc_NaCl_calculation">
                <eq/>
                <ci>J_mc_NaCl</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>J_mc_NaCl_max</ci>
                        <apply>
                            <minus/>
                            <apply>
                                <divide/>
                                <apply>
                                    <times/>
                                    <apply>
                                        <divide/>
                                        <ci>C_m_Na</ci>
                                        <ci>K_mc_Na_NaCl</ci>
                                    </apply>
                                    <ci>C_m_Cl</ci>
                                </apply>
                                <ci>K_mc_Cl_NaCl</ci>
                            </apply>
                            <apply>
                                <divide/>
                                <apply>
                                    <times/>
                                    <apply>
                                        <divide/>
                                        <ci>C_c_Na</ci>
                                        <ci>K_mc_Na_NaCl</ci>
                                    </apply>
                                    <ci>C_c_Cl</ci>
                                </apply>
                                <ci>K_mc_Cl_NaCl</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <apply>
                                <plus/>
                                <cn cellml:units="dimensionless">1.0</cn>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <apply>
                                            <divide/>
                                            <ci>C_m_Na</ci>
                                            <ci>K_mc_Na_NaCl</ci>
                                        </apply>
                                        <ci>C_m_Cl</ci>
                                    </apply>
                                    <ci>K_mc_Cl_NaCl</ci>
                                </apply>
                            </apply>
                            <apply>
                                <plus/>
                                <cn cellml:units="dimensionless">1.0</cn>
                                <apply>
                                    <divide/>
                                    <ci>C_c_Na</ci>
                                    <ci>K_mc_Na_NaCl</ci>
                                </apply>
                            </apply>
                            <apply>
                                <plus/>
                                <cn cellml:units="dimensionless">1.0</cn>
                                <apply>
                                    <divide/>
                                    <ci>C_c_Cl</ci>
                                    <ci>K_mc_Cl_NaCl</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <apply>
                                <plus/>
                                <cn cellml:units="dimensionless">1.0</cn>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <apply>
                                            <divide/>
                                            <ci>C_c_Na</ci>
                                            <ci>K_mc_Na_NaCl</ci>
                                        </apply>
                                        <ci>C_c_Cl</ci>
                                    </apply>
                                    <ci>K_mc_Cl_NaCl</ci>
                                </apply>
                            </apply>
                            <apply>
                                <plus/>
                                <cn cellml:units="dimensionless">1.0</cn>
                                <apply>
                                    <divide/>
                                    <ci>C_m_Na</ci>
                                    <ci>K_mc_Na_NaCl</ci>
                                </apply>
                            </apply>
                            <apply>
                                <plus/>
                                <cn cellml:units="dimensionless">1.0</cn>
                                <apply>
                                    <divide/>
                                    <ci>C_m_Cl</ci>
                                    <ci>K_mc_Cl_NaCl</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="mc_potassium_flux">
        <variable name="J_mc_K" public_interface="out" units="flux"/>
        <variable name="J_mc_KCl" public_interface="out" units="flux"/>
        <variable name="G_mc_K" units="flux"/>
        <variable initial_value="6.31E-8" name="J_mc_KCl_max" units="flux"/>
        <variable initial_value="5.30E-2" name="K_mc_K_KCl" units="mmol_per_cm3"/>
        <variable initial_value="2.13E-2" name="K_mc_Cl_KCl" units="mmol_per_cm3"/>
        <variable initial_value="4.90E-7" name="P_mc_K" units="cm_per_s"/>
        <variable name="time" public_interface="in" units="second"/>
        <variable name="RT" public_interface="in" units="J_per_mmol"/>
        <variable name="F" public_interface="in" units="C_per_mmol"/>
        <variable name="C_m_K" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_c_K" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_m_Cl" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_c_Cl" public_interface="in" units="mmol_per_cm3"/>
        <variable name="psi_m" public_interface="in" units="millivolt"/>
        <variable name="psi_c" public_interface="in" units="millivolt"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="J_mc_K_calculation">
                <eq/>
                <ci>J_mc_K</ci>
                <apply>
                    <plus/>
                    <ci>J_mc_KCl</ci>
                    <ci>G_mc_K</ci>
                </apply>
            </apply>
            <apply id="G_mc_K_calculation">
                <eq/>
                <ci>G_mc_K</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>P_mc_K</ci>
                                <ci>F</ci>
                                <apply>
                                    <minus/>
                                    <ci>psi_m</ci>
                                    <ci>psi_c</ci>
                                </apply>
                            </apply>
                            <ci>RT</ci>
                        </apply>
                        <apply>
                            <minus/>
                            <ci>C_m_K</ci>
                            <apply>
                                <times/>
                                <ci>C_c_K</ci>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <times/>
                                        <apply>
                                            <divide/>
                                            <apply>
                                                <minus/>
                                                <ci>F</ci>
                                            </apply>
                                            <ci>RT</ci>
                                        </apply>
                                        <apply>
                                            <minus/>
                                            <ci>psi_m</ci>
                                            <ci>psi_c</ci>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1.0</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <times/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <minus/>
                                        <ci>F</ci>
                                    </apply>
                                    <ci>RT</ci>
                                </apply>
                                <apply>
                                    <minus/>
                                    <ci>psi_m</ci>
                                    <ci>psi_c</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply id="J_mc_KCl_calculation">
                <eq/>
                <ci>J_mc_KCl</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>J_mc_KCl_max</ci>
                        <apply>
                            <minus/>
                            <apply>
                                <divide/>
                                <apply>
                                    <times/>
                                    <apply>
                                        <divide/>
                                        <ci>C_m_K</ci>
                                        <ci>K_mc_K_KCl</ci>
                                    </apply>
                                    <ci>C_m_Cl</ci>
                                </apply>
                                <ci>K_mc_Cl_KCl</ci>
                            </apply>
                            <apply>
                                <divide/>
                                <apply>
                                    <times/>
                                    <apply>
                                        <divide/>
                                        <ci>C_c_K</ci>
                                        <ci>K_mc_K_KCl</ci>
                                    </apply>
                                    <ci>C_c_Cl</ci>
                                </apply>
                                <ci>K_mc_Cl_KCl</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <apply>
                                <plus/>
                                <cn cellml:units="dimensionless">1.0</cn>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <apply>
                                            <divide/>
                                            <ci>C_m_K</ci>
                                            <ci>K_mc_K_KCl</ci>
                                        </apply>
                                        <ci>C_m_Cl</ci>
                                    </apply>
                                    <ci>K_mc_Cl_KCl</ci>
                                </apply>
                            </apply>
                            <apply>
                                <plus/>
                                <cn cellml:units="dimensionless">1.0</cn>
                                <apply>
                                    <divide/>
                                    <ci>C_c_K</ci>
                                    <ci>K_mc_K_KCl</ci>
                                </apply>
                            </apply>
                            <apply>
                                <plus/>
                                <cn cellml:units="dimensionless">1.0</cn>
                                <apply>
                                    <divide/>
                                    <ci>C_c_Cl</ci>
                                    <ci>K_mc_Cl_KCl</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <apply>
                                <plus/>
                                <cn cellml:units="dimensionless">1.0</cn>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <apply>
                                            <divide/>
                                            <ci>C_c_K</ci>
                                            <ci>K_mc_K_KCl</ci>
                                        </apply>
                                        <ci>C_c_Cl</ci>
                                    </apply>
                                    <ci>K_mc_Cl_KCl</ci>
                                </apply>
                            </apply>
                            <apply>
                                <plus/>
                                <cn cellml:units="dimensionless">1.0</cn>
                                <apply>
                                    <divide/>
                                    <ci>C_m_K</ci>
                                    <ci>K_mc_K_KCl</ci>
                                </apply>
                            </apply>
                            <apply>
                                <plus/>
                                <cn cellml:units="dimensionless">1.0</cn>
                                <apply>
                                    <divide/>
                                    <ci>C_m_Cl</ci>
                                    <ci>K_mc_Cl_KCl</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="mc_chloride_flux">
        <variable name="J_mc_Cl" public_interface="out" units="flux"/>
        <variable name="G_mc_Cl" units="flux"/>
        <variable initial_value="1.43E-6" name="P_mc_Cl" units="cm_per_s"/>
        <variable name="time" public_interface="in" units="second"/>
        <variable name="J_mc_NaCl" public_interface="in" units="flux"/>
        <variable name="J_mc_KCl" public_interface="in" units="flux"/>
        <variable name="RT" public_interface="in" units="J_per_mmol"/>
        <variable name="F" public_interface="in" units="C_per_mmol"/>
        <variable name="C_m_Cl" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_c_Cl" public_interface="in" units="mmol_per_cm3"/>
        <variable name="psi_m" public_interface="in" units="millivolt"/>
        <variable name="psi_c" public_interface="in" units="millivolt"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="J_mc_Cl_calculation">
                <eq/>
                <ci>J_mc_Cl</ci>
                <apply>
                    <plus/>
                    <ci>J_mc_NaCl</ci>
                    <ci>J_mc_KCl</ci>
                    <ci>G_mc_Cl</ci>
                </apply>
            </apply>
            <apply id="G_mc_Cl_calculation">
                <eq/>
                <ci>G_mc_Cl</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>P_mc_Cl</ci>
                                <apply>
                                    <minus/>
                                    <cn cellml:units="dimensionless">1.0</cn>
                                </apply>
                                <ci>F</ci>
                                <apply>
                                    <minus/>
                                    <ci>psi_m</ci>
                                    <ci>psi_c</ci>
                                </apply>
                            </apply>
                            <ci>RT</ci>
                        </apply>
                        <apply>
                            <minus/>
                            <ci>C_m_Cl</ci>
                            <apply>
                                <times/>
                                <ci>C_c_Cl</ci>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <times/>
                                        <apply>
                                            <divide/>
                                            <apply>
                                                <times/>
                                                <apply>
                                                    <minus/>
                                                    <apply>
                                                        <minus/>
                                                        <cn cellml:units="dimensionless">1.0</cn>
                                                    </apply>
                                                </apply>
                                                <ci>F</ci>
                                            </apply>
                                            <ci>RT</ci>
                                        </apply>
                                        <apply>
                                            <minus/>
                                            <ci>psi_m</ci>
                                            <ci>psi_c</ci>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1.0</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <times/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <apply>
                                            <minus/>
                                            <apply>
                                                <minus/>
                                                <cn cellml:units="dimensionless">1.0</cn>
                                            </apply>
                                        </apply>
                                        <ci>F</ci>
                                    </apply>
                                    <ci>RT</ci>
                                </apply>
                                <apply>
                                    <minus/>
                                    <ci>psi_m</ci>
                                    <ci>psi_c</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="sc_sodium_flux">
        <variable name="J_a" public_interface="out" units="flux"/>
        <variable name="J_sc_Na" public_interface="out" units="flux"/>
        <variable initial_value="2.69E-6" name="J_a_max" units="flux"/>
        <variable initial_value="1.20E-2" name="K_Na_ATPase" units="mmol_per_cm3"/>
        <variable name="time" public_interface="in" units="second"/>
        <variable name="C_c_Na" public_interface="in" units="mmol_per_cm3"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="J_sc_Na_calculation">
                <eq/>
                <ci>J_sc_Na</ci>
                <apply>
                    <times/>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">3.0</cn>
                    </apply>
                    <ci>J_a</ci>
                </apply>
            </apply>
            <apply id="J_a_calculation">
                <eq/>
                <ci>J_a</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>J_a_max</ci>
                        <cn cellml:units="dimensionless">1.0</cn>
                    </apply>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1.0</cn>
                        <apply>
                            <power/>
                            <apply>
                                <divide/>
                                <ci>K_Na_ATPase</ci>
                                <ci>C_c_Na</ci>
                            </apply>
                            <cn cellml:units="dimensionless">3.0</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="sc_potassium_flux">
        <variable name="J_sc_K" public_interface="out" units="flux"/>
        <variable name="G_sc_K" units="flux"/>
        <variable initial_value="4.74E-4" name="P_sc_K" units="cm_per_s"/>
        <variable name="J_a" public_interface="in" units="flux"/>
        <variable name="time" public_interface="in" units="second"/>
        <variable name="RT" public_interface="in" units="J_per_mmol"/>
        <variable name="F" public_interface="in" units="C_per_mmol"/>
        <variable name="C_s_K" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_c_K" public_interface="in" units="mmol_per_cm3"/>
        <variable name="psi_s" public_interface="in" units="millivolt"/>
        <variable name="psi_c" public_interface="in" units="millivolt"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="J_sc_K_calculation">
                <eq/>
                <ci>J_sc_K</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2.0</cn>
                        <ci>J_a</ci>
                    </apply>
                    <ci>G_sc_K</ci>
                </apply>
            </apply>
            <apply id="G_sc_K_calculation">
                <eq/>
                <ci>G_sc_K</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>P_sc_K</ci>
                                <ci>F</ci>
                                <apply>
                                    <minus/>
                                    <ci>psi_s</ci>
                                    <ci>psi_c</ci>
                                </apply>
                            </apply>
                            <ci>RT</ci>
                        </apply>
                        <apply>
                            <minus/>
                            <ci>C_s_K</ci>
                            <apply>
                                <times/>
                                <ci>C_c_K</ci>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <times/>
                                        <apply>
                                            <divide/>
                                            <apply>
                                                <minus/>
                                                <ci>F</ci>
                                            </apply>
                                            <ci>RT</ci>
                                        </apply>
                                        <apply>
                                            <minus/>
                                            <ci>psi_s</ci>
                                            <ci>psi_c</ci>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1.0</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <times/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <minus/>
                                        <ci>F</ci>
                                    </apply>
                                    <ci>RT</ci>
                                </apply>
                                <apply>
                                    <minus/>
                                    <ci>psi_s</ci>
                                    <ci>psi_c</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="sc_chloride_flux">
        <variable name="J_sc_Cl" public_interface="out" units="flux"/>
        <variable name="G_sc_Cl" units="flux"/>
        <variable initial_value="9.16E-5" name="P_sc_Cl" units="cm_per_s"/>
        <variable name="time" public_interface="in" units="second"/>
        <variable name="RT" public_interface="in" units="J_per_mmol"/>
        <variable name="F" public_interface="in" units="C_per_mmol"/>
        <variable name="C_s_Cl" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_c_Cl" public_interface="in" units="mmol_per_cm3"/>
        <variable name="psi_s" public_interface="in" units="millivolt"/>
        <variable name="psi_c" public_interface="in" units="millivolt"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="J_sc_Cl_calculation">
                <eq/>
                <ci>J_sc_Cl</ci>
                <ci>G_sc_Cl</ci>
            </apply>
            <apply id="G_sc_Cl_calculation">
                <eq/>
                <ci>G_sc_Cl</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>P_sc_Cl</ci>
                                <apply>
                                    <minus/>
                                    <cn cellml:units="dimensionless">1.0</cn>
                                </apply>
                                <ci>F</ci>
                                <apply>
                                    <minus/>
                                    <ci>psi_s</ci>
                                    <ci>psi_c</ci>
                                </apply>
                            </apply>
                            <ci>RT</ci>
                        </apply>
                        <apply>
                            <minus/>
                            <ci>C_s_Cl</ci>
                            <apply>
                                <times/>
                                <ci>C_c_Cl</ci>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <times/>
                                        <apply>
                                            <divide/>
                                            <apply>
                                                <times/>
                                                <apply>
                                                    <minus/>
                                                    <apply>
                                                        <minus/>
                                                        <cn cellml:units="dimensionless">1.0</cn>
                                                    </apply>
                                                </apply>
                                                <ci>F</ci>
                                            </apply>
                                            <ci>RT</ci>
                                        </apply>
                                        <apply>
                                            <minus/>
                                            <ci>psi_s</ci>
                                            <ci>psi_c</ci>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1.0</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <times/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <apply>
                                            <minus/>
                                            <apply>
                                                <minus/>
                                                <cn cellml:units="dimensionless">1.0</cn>
                                            </apply>
                                        </apply>
                                        <ci>F</ci>
                                    </apply>
                                    <ci>RT</ci>
                                </apply>
                                <apply>
                                    <minus/>
                                    <ci>psi_s</ci>
                                    <ci>psi_c</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="ms_sodium_flux">
        <variable name="J_ms_Na" public_interface="out" units="flux"/>
        <variable name="G_ms_Na" units="flux"/>
        <variable initial_value="4.80E-6" name="P_ms_Na" units="cm_per_s"/>
        <variable name="time" public_interface="in" units="second"/>
        <variable name="RT" public_interface="in" units="J_per_mmol"/>
        <variable name="F" public_interface="in" units="C_per_mmol"/>
        <variable name="C_m_Na" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_s_Na" public_interface="in" units="mmol_per_cm3"/>
        <variable name="psi_m" public_interface="in" units="millivolt"/>
        <variable name="psi_s" public_interface="in" units="millivolt"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="J_ms_Na_calculation">
                <eq/>
                <ci>J_ms_Na</ci>
                <ci>G_ms_Na</ci>
            </apply>
            <apply id="G_ms_Na_calculation">
                <eq/>
                <ci>G_ms_Na</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>P_ms_Na</ci>
                                <ci>F</ci>
                                <apply>
                                    <minus/>
                                    <ci>psi_m</ci>
                                    <ci>psi_s</ci>
                                </apply>
                            </apply>
                            <ci>RT</ci>
                        </apply>
                        <apply>
                            <minus/>
                            <ci>C_m_Na</ci>
                            <apply>
                                <times/>
                                <ci>C_s_Na</ci>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <times/>
                                        <apply>
                                            <divide/>
                                            <apply>
                                                <minus/>
                                                <ci>F</ci>
                                            </apply>
                                            <ci>RT</ci>
                                        </apply>
                                        <apply>
                                            <minus/>
                                            <ci>psi_m</ci>
                                            <ci>psi_s</ci>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1.0</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <times/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <minus/>
                                        <ci>F</ci>
                                    </apply>
                                    <ci>RT</ci>
                                </apply>
                                <apply>
                                    <minus/>
                                    <ci>psi_m</ci>
                                    <ci>psi_s</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="ms_potassium_flux">
        <variable name="J_ms_K" public_interface="out" units="flux"/>
        <variable name="G_ms_K" units="flux"/>
        <variable initial_value="4.80E-6" name="P_ms_K" units="cm_per_s"/>
        <variable name="time" public_interface="in" units="second"/>
        <variable name="RT" public_interface="in" units="J_per_mmol"/>
        <variable name="F" public_interface="in" units="C_per_mmol"/>
        <variable name="C_m_K" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_s_K" public_interface="in" units="mmol_per_cm3"/>
        <variable name="psi_m" public_interface="in" units="millivolt"/>
        <variable name="psi_s" public_interface="in" units="millivolt"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="J_ms_K_calculation">
                <eq/>
                <ci>J_ms_K</ci>
                <ci>G_ms_K</ci>
            </apply>
            <apply id="G_ms_K_calculation">
                <eq/>
                <ci>G_ms_K</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>P_ms_K</ci>
                                <ci>F</ci>
                                <apply>
                                    <minus/>
                                    <ci>psi_m</ci>
                                    <ci>psi_s</ci>
                                </apply>
                            </apply>
                            <ci>RT</ci>
                        </apply>
                        <apply>
                            <minus/>
                            <ci>C_m_K</ci>
                            <apply>
                                <times/>
                                <ci>C_s_K</ci>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <times/>
                                        <apply>
                                            <divide/>
                                            <apply>
                                                <minus/>
                                                <ci>F</ci>
                                            </apply>
                                            <ci>RT</ci>
                                        </apply>
                                        <apply>
                                            <minus/>
                                            <ci>psi_m</ci>
                                            <ci>psi_s</ci>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1.0</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <times/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <minus/>
                                        <ci>F</ci>
                                    </apply>
                                    <ci>RT</ci>
                                </apply>
                                <apply>
                                    <minus/>
                                    <ci>psi_m</ci>
                                    <ci>psi_s</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="ms_chloride_flux">
        <variable name="J_ms_Cl" public_interface="out" units="flux"/>
        <variable name="G_ms_Cl" units="flux"/>
        <variable initial_value="2.40E-6" name="P_ms_Cl" units="cm_per_s"/>
        <variable name="time" public_interface="in" units="second"/>
        <variable name="RT" public_interface="in" units="J_per_mmol"/>
        <variable name="F" public_interface="in" units="C_per_mmol"/>
        <variable name="C_m_Cl" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_s_Cl" public_interface="in" units="mmol_per_cm3"/>
        <variable name="psi_m" public_interface="in" units="millivolt"/>
        <variable name="psi_s" public_interface="in" units="millivolt"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="J_ms_Cl_calculation">
                <eq/>
                <ci>J_ms_Cl</ci>
                <ci>G_ms_Cl</ci>
            </apply>
            <apply id="G_ms_Cl_calculation">
                <eq/>
                <ci>G_ms_Cl</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>P_ms_Cl</ci>
                                <apply>
                                    <minus/>
                                    <cn cellml:units="dimensionless">1.0</cn>
                                </apply>
                                <ci>F</ci>
                                <apply>
                                    <minus/>
                                    <ci>psi_m</ci>
                                    <ci>psi_s</ci>
                                </apply>
                            </apply>
                            <ci>RT</ci>
                        </apply>
                        <apply>
                            <minus/>
                            <ci>C_m_Cl</ci>
                            <apply>
                                <times/>
                                <ci>C_s_Cl</ci>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <times/>
                                        <apply>
                                            <divide/>
                                            <apply>
                                                <times/>
                                                <apply>
                                                    <minus/>
                                                    <apply>
                                                        <minus/>
                                                        <cn cellml:units="dimensionless">1.0</cn>
                                                    </apply>
                                                </apply>
                                                <ci>F</ci>
                                            </apply>
                                            <ci>RT</ci>
                                        </apply>
                                        <apply>
                                            <minus/>
                                            <ci>psi_m</ci>
                                            <ci>psi_s</ci>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1.0</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <times/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <apply>
                                            <minus/>
                                            <apply>
                                                <minus/>
                                                <cn cellml:units="dimensionless">1.0</cn>
                                            </apply>
                                        </apply>
                                        <ci>F</ci>
                                    </apply>
                                    <ci>RT</ci>
                                </apply>
                                <apply>
                                    <minus/>
                                    <ci>psi_m</ci>
                                    <ci>psi_s</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="total_transepithelial_sodium_flux">
        <variable name="J_Na" units="flux"/>
        <variable name="J_mc_Na" public_interface="in" units="flux"/>
        <variable name="J_ms_Na" public_interface="in" units="flux"/>
        <variable name="time" public_interface="in" units="second"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="J_Na_calculation">
                <eq/>
                <ci>J_Na</ci>
                <apply>
                    <plus/>
                    <ci>J_mc_Na</ci>
                    <ci>J_ms_Na</ci>
                </apply>
            </apply>
        </math>
    </component>
    <component name="total_transepithelial_potassium_flux">
        <variable name="J_K" units="flux"/>
        <variable name="J_mc_K" public_interface="in" units="flux"/>
        <variable name="J_ms_K" public_interface="in" units="flux"/>
        <variable name="time" public_interface="in" units="second"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="J_K_calculation">
                <eq/>
                <ci>J_K</ci>
                <apply>
                    <plus/>
                    <ci>J_mc_K</ci>
                    <ci>J_ms_K</ci>
                </apply>
            </apply>
        </math>
    </component>
    <component name="total_transepithelial_chloride_flux">
        <variable name="J_Cl" units="flux"/>
        <variable name="J_mc_Cl" public_interface="in" units="flux"/>
        <variable name="J_ms_Cl" public_interface="in" units="flux"/>
        <variable name="time" public_interface="in" units="second"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="J_Cl_calculation">
                <eq/>
                <ci>J_Cl</ci>
                <apply>
                    <plus/>
                    <ci>J_mc_Cl</ci>
                    <ci>J_ms_Cl</ci>
                </apply>
            </apply>
        </math>
    </component>
    <component name="osmolarities">
        <variable name="Osm_m" public_interface="out" units="mmol_per_cm3"/>
        <variable name="Osm_c" public_interface="out" units="mmol_per_cm3"/>
        <variable name="Osm_s" public_interface="out" units="mmol_per_cm3"/>
        <variable name="C_m_Na" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_m_Cl" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_m_K" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_m_Imp" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_c_Na" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_c_Cl" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_c_K" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_c_Imp" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_s_Na" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_s_Cl" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_s_K" public_interface="in" units="mmol_per_cm3"/>
        <variable name="C_s_Imp" public_interface="in" units="mmol_per_cm3"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="Osm_m_calculation">
                <eq/>
                <ci>Osm_m</ci>
                <apply>
                    <plus/>
                    <ci>C_m_Na</ci>
                    <ci>C_m_K</ci>
                    <ci>C_m_Cl</ci>
                    <ci>C_m_Imp</ci>
                </apply>
            </apply>
            <apply id="Osm_c_calculation">
                <eq/>
                <ci>Osm_c</ci>
                <apply>
                    <plus/>
                    <ci>C_c_Na</ci>
                    <ci>C_c_K</ci>
                    <ci>C_c_Cl</ci>
                    <ci>C_c_Imp</ci>
                </apply>
            </apply>
            <apply id="Osm_s_calculation">
                <eq/>
                <ci>Osm_s</ci>
                <apply>
                    <plus/>
                    <ci>C_s_Na</ci>
                    <ci>C_s_K</ci>
                    <ci>C_s_Cl</ci>
                    <ci>C_s_Imp</ci>
                </apply>
            </apply>
        </math>
    </component>
    <component name="mc_transepithelial_volume_flux">
        <variable name="J_mc_v" public_interface="out" units="cm_per_s"/>
        <variable initial_value="5.22E-9" name="L_mc_v" units="cm_per_s_mmHg"/>
        <variable name="Osm_m" public_interface="in" units="mmol_per_cm3"/>
        <variable name="Osm_c" public_interface="in" units="mmol_per_cm3"/>
        <variable name="time" public_interface="in" units="second"/>
        <variable name="RT" public_interface="in" units="J_per_mmol"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="J_mc_v_calculation">
                <eq/>
                <ci>J_mc_v</ci>
                <apply>
                    <times/>
                    <ci>L_mc_v</ci>
                    <ci>RT</ci>
                    <apply>
                        <minus/>
                        <ci>Osm_m</ci>
                        <ci>Osm_c</ci>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="ms_transepithelial_volume_flux">
        <variable name="J_ms_v" public_interface="out" units="cm_per_s"/>
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            <dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">American Journal of Physiology</dc:title>
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            <dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">&#xd;
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            <dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">A numerical model of the renal distal tubule</dc:title>
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        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#20d1b786-7957-4457-bda5-1d4df2f79cf6">
            <vCard:FN xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Catherine Lloyd</vCard:FN>
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        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#b28db5be-4a73-4d50-9675-5137f4a8235f">
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            <rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">The new version of this model has been re-coded to remove the reaction element and replace it with a simple MathML description of the model reaction kinetics.  This is thought to be truer to the original publication, and information regarding the enzyme kinetics etc will later be added to the metadata through use of an ontology. The model runs in the PCEnv simulator but gives a flat output.</rdf:value>
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        <rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#9413f374-026c-4147-b850-de6e1c16827a">
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            <rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">This is the CellML description of Chang and Fujita's 1999 numerical model of the renal distal tubule. It should be noted that the initial conditions used in this description represent those in the early distal tubule. For model representations of the late distal tublule, these initial values should be replaced with those listed in the orginal paper for the late distal tubule. The model from the original paper has been modified slightly to include differential equations defining the change in solute concentrations over time. These equations were added to facilitate the use of the CellML code in CMISS.</rdf:value>
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            <vCard:FN xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Catherine Lloyd</vCard:FN>
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