Location: Peripheral airways matlab/CellML @ d5ff515c4729 / PASMC_models / PASM - Exported.cellml

Author:

aram148 <a.rampadarath@auckland.ac.nz>

Date:

2022-05-16 16:33:40+12:00

Desc:

Simple ftu for gas exchange Bental, Lambert

Permanent Source URI:

https://staging.physiomeproject.org/workspace/7e5/rawfile/d5ff515c472999f862521b53b22950b63ec44995/PASMC_models/PASM - Exported.cellml

<?xml version='1.0' encoding='UTF-8'?>
<model name="PASM" xmlns="http://www.cellml.org/cellml/1.0#">
    <component name="environment">
        <variable name="t" public_interface="out" units="second"/>
    </component>
    <component name="PASM">
        <variable name="t" public_interface="in" units="second"/>
        <variable initial_value="1.04" name="rho" units="dimensionless"/>
        <variable initial_value="0.04" name="mu" units="dimensionless"/>
        <variable initial_value="2" name="xi" units="dimensionless"/>
        <variable initial_value="25" name="E" units="dimensionless"/>
        <variable initial_value="8.6" name="l" units="dimensionless"/>
        <variable initial_value="1.032" name="h0" units="dimensionless"/>
        <variable initial_value="0.5" name="nu" units="dimensionless"/>
        <variable initial_value="1.8602" name="A0" units="dimensionless"/>
        <variable initial_value="0" name="P0" units="dimensionless"/>
        <variable name="kr" units="dimensionless"/>
        <variable name="K" units="dimensionless"/>
        <variable name="R" units="dimensionless"/>
        <variable name="Rv" units="dimensionless"/>
        <variable name="L" units="dimensionless"/>
        <variable initial_value="0" name="Pv" units="dimensionless"/>
        <variable initial_value="0" name="Q" units="dimensionless"/>
        <variable initial_value="0.001" name="Qout" units="dimensionless"/>
        <variable name="Pin" units="dimensionless"/>
        <variable name="a" units="dimensionless"/>
        <variable name="b" units="dimensionless"/>
        <variable name="c" units="dimensionless"/>
        <variable name="d" units="dimensionless"/>
        <variable initial_value="0.01" name="r" units="dimensionless"/>
        <variable name="h" units="dimensionless"/>
        <variable name="C" units="dimensionless"/>
        <variable name="P" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:cellml="http://www.cellml.org/cellml/1.0#">
            <apply>
                <eq/>
                <ci>h</ci>
                <apply>
                    <times/>
                    <ci>r</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>a</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>b</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>b</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>d</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Pin</ci>
                <apply>
                    <plus/>
                    <cn type="e-notation" cellml:units="dimensionless">1<sep/>6</cn>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <sin/>
                            <apply>
                                <times/>
                                <cn cellml:units="dimensionless">2</cn>
                                <pi/>
                                <cn cellml:units="dimensionless">0.02</cn>
                                <ci>t</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>kr</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <apply>
                            <plus/>
                            <ci>xi</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                        <pi/>
                        <ci>mu</ci>
                    </apply>
                    <ci>rho</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>K</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>h0</ci>
                        <ci>E</ci>
                        <apply>
                            <root/>
                            <pi/>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">1</cn>
                            <apply>
                                <power/>
                                <ci>nu</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                        <apply>
                            <root/>
                            <ci>A0</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>C</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>h</ci>
                        <ci>E</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>L</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>rho</ci>
                        <ci>kr</ci>
                        <ci>l</ci>
                    </apply>
                    <apply>
                        <times/>
                        <pi/>
                        <apply>
                            <power/>
                            <ci>r</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Rv</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="dimensionless">0.01</cn>
                    <ci>C</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>Q</ci>
                </apply>
                <apply>
                    <times/>
                    <apply>
                        <divide/>
                        <cn cellml:units="dimensionless">1</cn>
                        <ci>L</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>Pin</ci>
                            <apply>
                                <times/>
                                <ci>R</ci>
                                <ci>Q</ci>
                            </apply>
                        </apply>
                        <ci>P</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>Pv</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci>Q</ci>
                        <ci>Qout</ci>
                    </apply>
                    <ci>C</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>P</ci>
                <apply>
                    <plus/>
                    <ci>Pv</ci>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <ci>Q</ci>
                            <ci>Qout</ci>
                        </apply>
                        <ci>Rv</ci>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <connection>
        <map_components component_1="environment" component_2="PASM"/>
        <map_variables variable_1="t" variable_2="t"/>
    </connection>
</model>