Location: Peripheral airways matlab/CellML @ 30e6db7fb82a / PASMC_models / PASM.cellml

Author:

aram148 <42922407+aram148@users.noreply.github.com>

Date:

2022-07-26 11:49:42+12:00

Desc:

updated documentation and renamed model

Permanent Source URI:

https://models.fieldml.org/workspace/7e5/rawfile/30e6db7fb82a9bb715b0121cdfc131c19e5cb2ff/PASMC_models/PASM.cellml

<?xml version='1.0' encoding='UTF-8'?>
<model name="PASM" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
    <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="1.6e+06" name="E" units="dimensionless"/>
        <variable initial_value="0.05" 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="1e-6" name="Qout" units="dimensionless"/>
        <variable name="Pin" units="dimensionless"/>
        <variable initial_value="0.2802" name="a" units="dimensionless"/>
        <variable initial_value="-505.3" name="b" units="dimensionless"/>
        <variable initial_value="0.1324" name="c" units="dimensionless"/>
        <variable initial_value="-11.14" name="d" units="dimensionless"/>
        <variable initial_value="0.012" name="r" units="dimensionless"/>
        <variable name="h" units="dimensionless"/>
        <variable name="C" units="dimensionless"/>
        <variable name="P" units="dimensionless"/>
        <!--        var h: dimensionless {init: 0.001};-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <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>c</ci>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <ci>d</ci>
                                    <ci>r</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Pin</ci>
                <cn cellml:units="dimensionless">1</cn>
            </apply>
            <!--+1{dimensionless}*sin(5{dimensionless}*t);-->
            <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/>
                        <cn cellml:units="dimensionless">8</cn>
                        <ci>rho</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>