- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2009-06-17 14:41:25+12:00
- Desc:
- committing version01 of itskov_ehret_mavrilas_2006
- Permanent Source URI:
- http://models.cellml.org/workspace/itskov_ehret_mavrilas_2006/rawfile/eae81aa4fe236f24bcac0996898645f8268ad161/itskov_ehret_mavrilas_2006.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : Polyconvex_law_2005.cml
CREATED : 24th January 2007
LAST MODIFIED : 7th February 2007
AUTHOR : Jesse Ashton
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/1/02 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of the Polyconvex Anisotropic (Orthotropic) constitutive material law (anisotropic strain-energy function for soft collagenous tissues), defining the relation between the nine independent strain components and the stress components.
CHANGES:
18/02/04 - CML - Completed the Metadata.
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="PoleZero" name="itskov_ehret_mavrilas_2005_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Exponential Polyconvex Anisotropic Strain-Energy Function</title>
<author>
<firstname>Jesse</firstname>
<surname>Ashton</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Polyconvexity of a strain energy function is a very important mathematical condition, especially in the context of a boundary-value problem.
In the paper presented here, the authors Itskov, Ehret and Mavrilas propose an exponential polyconvex anisotropic strain energy function.
It is represented by a series with an arbitrary number of terms and associated material constants.
Each term of this series a priori satisfies the condition of the energy- and stress free natural state so that no additional restrictions have to be imposed.
The proposed strain energy function has an exponential form and is, therefore, very suitable for the application to soft biological tissues.
Thus, a good agreement with experimental data on different types of tissues is achieved.
</para>
<para>
Histologically, soft biological tissues consist of various cell
types and the extracellular matrix. The latter is composed
of proteins such as fibrous collagen, elastin and
of the ground substance. The mechanical behavior of soft
tissues under quasi-static loading is dominated by the performance
of its fibrous components, primarily collagen and
elastin fibers.
</para>
<para>
Collagen is the main load-carrying element of tissue.
The most common form being the fiber-forming collagen I.
The variety of types, the amount and the structural organization
of collagen fibrils and fibers among different collagenous
tissues are responsible for their strong anisotropy and
influence their mechanical properties accordingly.
</para>
<para>
Elastin fibers are thin strands of a rubbery consistence.
The ensemble consisting of collagen and elastin leads to the
characteristic exponential or "J-shaped" (Holzapfel 2001)
stress strain response of soft biological tissues in tension tests.
At smaller strains, the collagen fibers remain unstretched,
wavy and crimped so that the mechanical response of the tissue
is controlled by the soft and almost isotropic elastin. With increasing load,
the collagen fibers gradually straighten and tend to align in the direction of loading,
which causes a strong increase in the stiffness of the material.
</para>
<para>
At quasi-static loading, this response can be described by a hyperelastic constitutive
model with an exponential strain energy function (Fung <emphasis>et al.</emphasis> 1979).
</para>
<para>
Soft collagenous tissues can be described more or less accurately using a model known as
the Fung-elastic model (a strain energy function model). The Fung-Model although used to
model soft-tissues, is not that accurate as it is generally not elliptic and for this reason not polyconvex
and thus exhibits non-physical behaviour. Polyconvexity represents a very important mathematical condition,
especially in the context of a boundary-value problem. In contrast, the polyconvex strain energy function
that already exists, exhibits non-physical behaviour.
</para>
<para>
To avoid such non-physical behavior, Itskov <emphasis>et al.</emphasis> have proposed an exponential polyconvex anisotropic strain energy function
that allows soft biological tissues to be more accurately modelled.
</para>
<para>
The model was implemented in a manner that could be used for peforming finite element model simulations on the CMISS software program developed at the Bioengineering Institute, University of Auckland.
</para>
<para>
For additional information on implementation of cellML files in CMISS, please refer to the following <ulink url="http://www.bioeng.auckland.ac.nz/people/nickerso/cmiss/help.html">Link</ulink>.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
A Polyconvex anisotropic strain-energy function for soft collagenous tissues, M. Itskov, A.E. Ehret and D. Mavrilas, 2006. <ulink url="http://www.springerlink.com/content/f73u218v35317864/">
<emphasis>Biomechanics and Modeling in Mechanobiology</emphasis>
</ulink>, 5(1), 17-26. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/">PubMed ID: Unknown</ulink> </para>
</sect1>
</article>
</documentation>
<!-- Global units -->
<units name="strain">
<unit units="dimensionless"/>
</units>
<units name="stress">
<unit units="dimensionless"/>
</units>
<component name="interface" cmeta:id="interface">
<!-- Variables we expect to be set/controlled externally -->
<variable units="strain" private_interface="out" name="E11"/>
<variable units="strain" private_interface="out" name="E22"/>
<variable units="strain" private_interface="out" name="E33"/>
<variable units="strain" private_interface="out" name="E12"/>
<variable units="strain" private_interface="out" name="E13"/>
<variable units="strain" private_interface="out" name="E21"/>
<variable units="strain" private_interface="out" name="E23"/>
<variable units="strain" private_interface="out" name="E31"/>
<variable units="strain" private_interface="out" name="E32"/>
<variable units="strain" private_interface="out" name="mu1" initial_value="0"/>
<variable units="strain" private_interface="out" name="a1" initial_value="0"/>
<variable units="strain" private_interface="out" name="b1" initial_value="0"/>
<variable units="strain" private_interface="out" name="x11" initial_value="0"/>
<variable units="strain" private_interface="out" name="x21" initial_value="0"/>
<variable units="strain" private_interface="out" name="mu2" initial_value="0"/>
<variable units="strain" private_interface="out" name="a2" initial_value="0"/>
<variable units="strain" private_interface="out" name="b2" initial_value="0"/>
<variable units="strain" private_interface="out" name="x12" initial_value="0"/>
<variable units="strain" private_interface="out" name="x22" initial_value="0"/>
<!-- Variables we want to make available externally -->
<variable units="stress" public_interface="out" private_interface="in" name="Tdev11"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdev22"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdev33"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdev12"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdev13"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdev21"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdev23"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdev31"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdev32"/>
</component> <!--interface-->
<component name="equations" cmeta:id="equations">
<!-- Inputs -->
<variable units="strain" public_interface="in" name="E11"/>
<variable units="strain" public_interface="in" name="E22"/>
<variable units="strain" public_interface="in" name="E33"/>
<variable units="strain" public_interface="in" name="E12"/>
<variable units="strain" public_interface="in" name="E13"/>
<variable units="strain" public_interface="in" name="E21"/>
<variable units="strain" public_interface="in" name="E23"/>
<variable units="strain" public_interface="in" name="E31"/>
<variable units="strain" public_interface="in" name="E32"/>
<variable units="strain" public_interface="in" name="mu1"/>
<variable units="strain" public_interface="in" name="a1"/>
<variable units="strain" public_interface="in" name="b1"/>
<variable units="strain" public_interface="in" name="x11"/>
<variable units="strain" public_interface="in" name="x21"/>
<variable units="strain" public_interface="in" name="mu2"/>
<variable units="strain" public_interface="in" name="a2"/>
<variable units="strain" public_interface="in" name="b2"/>
<variable units="strain" public_interface="in" name="x12"/>
<variable units="strain" public_interface="in" name="x22"/>
<!-- Outputs computed here -->
<variable units="stress" public_interface="out" name="Tdev11"/>
<variable units="stress" public_interface="out" name="Tdev22"/>
<variable units="stress" public_interface="out" name="Tdev33"/>
<variable units="stress" public_interface="out" name="Tdev12"/>
<variable units="stress" public_interface="out" name="Tdev13"/>
<variable units="stress" public_interface="out" name="Tdev21"/>
<variable units="stress" public_interface="out" name="Tdev23"/>
<variable units="stress" public_interface="out" name="Tdev31"/>
<variable units="stress" public_interface="out" name="Tdev32"/>
<!-- Temporary variables -->
<variable units="strain" public_interface="none" private_interface="none" name="i1"/>
<variable units="strain" public_interface="none" private_interface="none" name="i2"/>
<variable units="strain" public_interface="none" private_interface="none" name="i3"/>
<variable units="strain" public_interface="none" private_interface="none" name="detc"/>
<variable units="strain" public_interface="none" private_interface="none" name="k1"/>
<variable units="strain" public_interface="none" private_interface="none" name="k2"/>
<variable units="strain" public_interface="none" private_interface="none" name="k3"/>
<variable units="strain" public_interface="none" private_interface="none" name="x11denom"/>
<variable units="strain" public_interface="none" private_interface="none" name="x21denom"/>
<variable units="strain" public_interface="none" private_interface="none" name="x12denom"/>
<variable units="strain" public_interface="none" private_interface="none" name="x22denom"/>
<variable units="strain" public_interface="none" private_interface="none" name="i1tilde"/>
<variable units="strain" public_interface="none" private_interface="none" name="i2tilde"/>
<variable units="strain" public_interface="none" private_interface="none" name="k1tilde"/>
<variable units="strain" public_interface="none" private_interface="none" name="k2tilde"/>
<!-- Calculation of Temporaries -->
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i1_calculation_eq">
<apply id="i1_calculation">
<eq/>
<ci>i1</ci>
<apply>
<plus/>
<cn cellml:units="strain">1</cn>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>E11</ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i2_calculation_eq">
<apply id="i2_calculation">
<eq/>
<ci>i2</ci>
<apply>
<plus/>
<cn cellml:units="strain">1</cn>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>E22</ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i3_calculation_eq">
<apply id="i3_calculation">
<eq/>
<ci>i3</ci>
<apply>
<plus/>
<cn cellml:units="strain">1</cn>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>E33</ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="detc_calculation_eq">
<apply id="detc_calculation">
<eq/>
<ci>detc</ci>
<apply>
<plus/>
<cn cellml:units="strain">1</cn>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>E11</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="strain">4</cn>
</apply>
<ci>E12</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>E22</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">4</cn>
<ci>E11</ci>
<ci>E22</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="strain">4</cn>
</apply>
<ci>E13</ci>
<ci>E31</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="strain">-8</cn>
</apply>
<ci>E13</ci>
<ci>E22</ci>
<ci>E31</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">8</cn>
<ci>E12</ci>
<ci>E23</ci>
<ci>E31</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">8</cn>
<ci>E13</ci>
<ci>E21</ci>
<ci>E32</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="strain">4</cn>
</apply>
<ci>E23</ci>
<ci>E32</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="strain">8</cn>
</apply>
<ci>E11</ci>
<ci>E23</ci>
<ci>E31</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>E33</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">4</cn>
<ci>E11</ci>
<ci>E33</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="strain">-8</cn>
</apply>
<ci>E12</ci>
<ci>E21</ci>
<ci>E33</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">4</cn>
<ci>E22</ci>
<ci>E33</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">8</cn>
<ci>E11</ci>
<ci>E22</ci>
<ci>E33</ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="k1_calculation_eq">
<apply id="k1_calculation">
<eq/>
<ci>k1</ci>
<apply>
<divide/>
<apply>
<plus/>
<cn cellml:units="strain">1</cn>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>E22</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="strain">4</cn>
</apply>
<ci>E23</ci>
<ci>E32</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>E33</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">4</cn>
<ci>E22</ci>
<ci>E33</ci>
</apply>
</apply>
<ci>detc</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="k2_calculation_eq">
<apply id="k2_calculation">
<eq/>
<ci>k2</ci>
<apply>
<divide/>
<apply>
<plus/>
<cn cellml:units="strain">1</cn>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>E11</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="strain">4</cn>
</apply>
<ci>E13</ci>
<ci>E31</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>E33</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">4</cn>
<ci>E11</ci>
<ci>E33</ci>
</apply>
</apply>
<ci>detc</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="k3_calculation_eq">
<apply id="k3_calculation">
<eq/>
<ci>k3</ci>
<apply>
<divide/>
<apply>
<plus/>
<cn cellml:units="strain">1</cn>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>E11</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="strain">4</cn>
</apply>
<ci>E12</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>E22</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">4</cn>
<ci>E11</ci>
<ci>E22</ci>
</apply>
</apply>
<ci>detc</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="x11denom_calculation_eq">
<apply id="x11denom_calculation">
<eq/>
<ci>x11denom</ci>
<apply>
<plus/>
<cn cellml:units="strain">1</cn>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="x21denom_calculation_eq">
<apply id="x21denom_calculation">
<eq/>
<ci>x21denom</ci>
<apply>
<plus/>
<cn cellml:units="strain">1</cn>
<apply>
<power/>
<ci>x21</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="x12denom_calculation_eq">
<apply id="x12denom_calculation">
<eq/>
<ci>x12denom</ci>
<apply>
<plus/>
<cn cellml:units="strain">1</cn>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="x22denom_calculation_eq">
<apply id="x22denom_calculation">
<eq/>
<ci>x22denom</ci>
<apply>
<plus/>
<cn cellml:units="strain">1</cn>
<apply>
<power/>
<ci>x22</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i1tilde_calculation_eq">
<apply id="i1tilde_calculation">
<eq/>
<ci>i1tilde</ci>
<apply>
<plus/>
<apply>
<divide/>
<ci>i1</ci>
<ci>x11denom</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>i2</ci>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>i3</ci>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x21</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i2tilde_calculation_eq">
<apply id="i2tilde_calculation">
<eq/>
<ci>i2tilde</ci>
<apply>
<plus/>
<apply>
<divide/>
<ci>i1</ci>
<ci>x12denom</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>i2</ci>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>i3</ci>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x22</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="k1tilde_calculation_eq">
<apply id="k1tilde_calculation">
<eq/>
<ci>k1tilde</ci>
<apply>
<plus/>
<apply>
<divide/>
<ci>k1</ci>
<ci>x11denom</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k2</ci>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k3</ci>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x21</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="k2tilde_calculation_eq">
<apply id="k2tilde_calculation">
<eq/>
<ci>k2tilde</ci>
<apply>
<plus/>
<apply>
<divide/>
<ci>k1</ci>
<ci>x12denom</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k2</ci>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>k3</ci>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x22</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- Calculation of Stress -->
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev11_calculation_eq">
<apply id="Tdev11_calculation">
<eq/>
<ci>Tdev11</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<plus/>
<apply>
<times/>
<ci>mu1</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>i1tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>a1</ci>
</apply>
</apply>
<ci>x11denom</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>k1tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>b1</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<power/>
<ci>k1</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x11denom</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E21</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E23</ci>
<ci>E31</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E12</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E12</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E32</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E13</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E13</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E23</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E31</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E31</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E21</ci>
<ci>E32</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x21</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>mu2</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>i2tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>a2</ci>
</apply>
</apply>
<ci>x12denom</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>k2tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>b2</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<power/>
<ci>k1</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x12denom</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E21</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E23</ci>
<ci>E31</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E12</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E12</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E32</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E31</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E13</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E23</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E31</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E31</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E21</ci>
<ci>E32</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x22</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev12_calculation_eq">
<apply id="Tdev12_calculation">
<eq/>
<ci>Tdev12</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>mu1</ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>k1tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>b1</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E13</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E13</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E23</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E31</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E32</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E32</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x21</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E12</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E12</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E32</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>k2</ci>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E12</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E12</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E32</ci>
</apply>
</apply>
<ci>k1</ci>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x11denom</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>mu2</ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>k2tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>b2</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E13</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E13</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E23</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E31</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E32</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E32</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x22</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E12</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E12</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E32</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>k2</ci>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E12</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E12</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E32</ci>
</apply>
</apply>
<ci>k1</ci>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x12denom</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev13_calculation_eq">
<apply id="Tdev13_calculation">
<eq/>
<ci>Tdev13</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>mu1</ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>k1tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>b1</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E23</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E23</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E32</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E12</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E12</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E13</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E13</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E23</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x21</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>k3</ci>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E13</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E13</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E23</ci>
</apply>
</apply>
<ci>k1</ci>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x11denom</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>mu2</ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>k2tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>b2</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E23</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E23</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E32</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E12</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E12</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E13</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E13</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E23</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x22</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>k3</ci>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E13</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E13</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E23</ci>
</apply>
</apply>
<ci>k1</ci>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x12denom</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev21_calculation_eq">
<apply id="Tdev21_calculation">
<eq/>
<ci>Tdev21</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>mu1</ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>k1tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>b1</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E23</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E23</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E21</ci>
<ci>E32</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E31</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E31</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x21</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E21</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E23</ci>
<ci>E31</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>k2</ci>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E21</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E23</ci>
<ci>E31</ci>
</apply>
</apply>
<ci>k1</ci>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x11denom</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>mu2</ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>k2tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>b2</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E23</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E23</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E21</ci>
<ci>E32</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E31</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E31</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x22</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E21</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E23</ci>
<ci>E31</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>k2</ci>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E21</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E23</ci>
<ci>E31</ci>
</apply>
</apply>
<ci>k1</ci>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x12denom</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev22_calculation_eq">
<apply id="Tdev22_calculation">
<eq/>
<ci>Tdev22</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<plus/>
<apply>
<times/>
<ci>mu1</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>i1tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>a1</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>k1tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>b1</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<power/>
<ci>k2</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E23</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E23</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E31</ci>
<ci>E21</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E32</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E32</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E31</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x21</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E21</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E23</ci>
<ci>E31</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E12</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E12</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E32</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x11denom</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>mu2</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>i2tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>a2</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>k2tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>b2</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<power/>
<ci>k2</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E23</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E23</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E32</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E32</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E31</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x22</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E21</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E23</ci>
<ci>E31</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E12</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E12</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E32</ci>
</apply>
</apply>
</apply>
</apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x12denom</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev23_calculation_eq">
<apply id="Tdev23_calculation">
<eq/>
<ci>Tdev23</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>mu1</ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>k1tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>b1</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E23</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E23</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x21</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>k3</ci>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E23</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E23</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E21</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>k2</ci>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E13</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E13</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E23</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E21</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E23</ci>
<ci>E31</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x11denom</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>mu2</ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>k2tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>b2</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E23</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E23</ci>
</apply>
</apply>
<ci>k3</ci>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x22</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E23</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E23</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E21</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>k2</ci>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E13</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E13</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E23</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E21</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E23</ci>
<ci>E31</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x12denom</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev31_calculation_eq">
<apply id="Tdev31_calculation">
<eq/>
<ci>Tdev31</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>mu1</ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>k1tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>b1</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E21</ci>
<ci>E32</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E31</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E31</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x21</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>k3</ci>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E31</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E31</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E21</ci>
<ci>E32</ci>
</apply>
</apply>
<ci>k1</ci>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x11denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E21</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E23</ci>
<ci>E31</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E31</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E32</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E32</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>mu2</ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>k2tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>b2</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E21</ci>
<ci>E32</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E31</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E31</ci>
</apply>
</apply>
<ci>k3</ci>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x22</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E31</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E31</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E21</ci>
<ci>E32</ci>
</apply>
</apply>
<ci>k1</ci>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x12denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E21</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E23</ci>
<ci>E31</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E32</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E32</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E31</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev32_calculation_eq">
<apply id="Tdev32_calculation">
<eq/>
<ci>Tdev32</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>mu1</ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>k1tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>b1</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E31</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E32</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E32</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x21</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>k3</ci>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn> </apply>
<ci>E11</ci>
<ci>E32</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E32</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E31</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>k2</ci>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E12</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E12</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E32</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn> </apply>
<ci>E22</ci>
<ci>E31</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E31</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E21</ci>
<ci>E32</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x11denom</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>mu2</ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>k2tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>b2</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E31</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E32</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E32</ci>
</apply>
</apply>
<ci>k2</ci>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E32</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E32</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E31</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x22</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>k3</ci>
</apply>
<apply>
<times/>
<ci>detc</ci>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E33</ci>
<ci>E12</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E12</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E32</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E31</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E31</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E21</ci>
<ci>E32</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x12denom</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev33_calculation_eq">
<apply id="Tdev33_calculation">
<eq/>
<ci>Tdev33</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<plus/>
<apply>
<times/>
<ci>mu1</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>i1tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>a1</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x21</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>k1tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>b1</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<power/>
<ci>k3</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x21</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E23</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E23</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E21</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E32</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E32</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E31</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x11</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x11denom</ci>
<ci>x21denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E13</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E13</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E23</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E31</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E31</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E21</ci>
<ci>E32</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x11denom</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>mu2</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>i2tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>a2</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x22</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>k2tilde</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>b2</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<power/>
<ci>k3</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>x22</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E13</ci>
<ci>E21</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E23</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E23</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E11</ci>
<ci>E32</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E32</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E31</ci>
</apply>
</apply>
<apply>
<power/>
<ci>x12</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x12denom</ci>
<ci>x22denom</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E13</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E13</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E12</ci>
<ci>E23</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">4</cn>
</apply>
<ci>E22</ci>
<ci>E31</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>E31</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>E21</ci>
<ci>E32</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>detc</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x12denom</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_2="equations" component_1="interface"/>
<map_variables variable_2="E11" variable_1="E11"/>
<map_variables variable_2="E22" variable_1="E22"/>
<map_variables variable_2="E33" variable_1="E33"/>
<map_variables variable_2="E12" variable_1="E12"/>
<map_variables variable_2="E13" variable_1="E13"/>
<map_variables variable_2="E21" variable_1="E21"/>
<map_variables variable_2="E23" variable_1="E23"/>
<map_variables variable_2="E31" variable_1="E31"/>
<map_variables variable_2="E32" variable_1="E32"/>
<map_variables variable_2="Tdev11" variable_1="Tdev11"/>
<map_variables variable_2="Tdev22" variable_1="Tdev22"/>
<map_variables variable_2="Tdev33" variable_1="Tdev33"/>
<map_variables variable_2="Tdev12" variable_1="Tdev12"/>
<map_variables variable_2="Tdev13" variable_1="Tdev13"/>
<map_variables variable_2="Tdev21" variable_1="Tdev21"/>
<map_variables variable_2="Tdev23" variable_1="Tdev23"/>
<map_variables variable_2="Tdev31" variable_1="Tdev31"/>
<map_variables variable_2="Tdev32" variable_1="Tdev32"/>
<map_variables variable_2="mu1" variable_1="mu1"/>
<map_variables variable_2="a1" variable_1="a1"/>
<map_variables variable_2="b1" variable_1="b1"/>
<map_variables variable_2="x11" variable_1="x11"/>
<map_variables variable_2="x21" variable_1="x21"/>
<map_variables variable_2="mu2" variable_1="mu2"/>
<map_variables variable_2="a2" variable_1="a2"/>
<map_variables variable_2="b2" variable_1="b2"/>
<map_variables variable_2="x12" variable_1="x12"/>
<map_variables variable_2="x22" variable_1="x22"/>
</connection>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="interface">
<component_ref component="equations"/>
</component_ref>
</group>
<rdf:RDF>
<rdf:Seq rdf:about="rdf:#9d60cc15-8934-4d0e-b916-26d94367186c">
<rdf:li rdf:resource="rdf:#3ff6aff2-ee55-4b11-a807-5756cdcf6425"/>
<rdf:li rdf:resource="rdf:#ad9de0f1-b81c-4669-a4db-9d9230de29d2"/>
<rdf:li rdf:resource="rdf:#aef22418-3df3-4181-9392-4ace80bfcb05"/>
</rdf:Seq>
<rdf:Description rdf:about="">
<dc:publisher>University of Auckland</dc:publisher>
<cmeta:comment rdf:resource="rdf:#5cb89bae-aa60-4c3d-990c-c74e15702092"/>
<dcterms:created rdf:resource="rdf:#18caf162-2160-44ff-972b-95b77eac21d5"/>
<dc:creator rdf:resource="rdf:#82d3db8b-7c0e-4a9e-a418-2a978bca14bc"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#82d3db8b-7c0e-4a9e-a418-2a978bca14bc">
<vCard:ORG rdf:resource="rdf:#0f3159c2-2238-48bc-aee0-93d555a50688"/>
<vCard:EMAIL rdf:resource="rdf:#4e6b1d70-dccc-4ffd-9193-3bebd66bb5b2"/>
<vCard:N rdf:resource="rdf:#79498ae9-887c-4058-9b94-2d9991c22ec6"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4e6b1d70-dccc-4ffd-9193-3bebd66bb5b2">
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
<rdf:value/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4e466546-212e-477f-9683-fad45b97b69b">
<vCard:Given>A</vCard:Given>
<vCard:Family>Ehret</vCard:Family>
<vCard:Other>E</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5a4d00d5-7746-42ce-b657-de4cc2dcdbd1">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#46fe0f8a-03f5-4200-974c-37d93637312b"/>
</rdf:Description>
<rdf:Description rdf:about="#interface">
<cmeta:comment rdf:resource="rdf:#58e4b000-57ba-4ab9-9ca1-d8df1fa1aec0"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e93e6d99-5da8-40ac-b156-3fab8b334c0c">
<dcterms:W3CDTF>2006-03-01 00:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="#equations">
<cmeta:comment rdf:resource="rdf:#5a9674fe-e33e-44f0-b347-c797990532c5"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8fe91c21-b06a-4b03-955b-fa0d64886b4a">
<dcterms:W3CDTF>2007-01-24</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#828dd465-dd45-4e3e-9073-7b068911eb37">
<vCard:FN>Vignesh Kumar</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e18ba1ae-af0c-4d31-a9f0-ed54350ffcbd">
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
<rdf:value>jash042@ec.auckland.ac.nz</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5a9674fe-e33e-44f0-b347-c797990532c5">
<rdf:value>
In this simple model we only have one component, which holds the
six equations.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#cb8315fa-c495-444e-ae71-7dea10d22177">
<bqs:Pubmed_id/>
<bqs:JournalArticle rdf:resource="rdf:#3bd21819-008b-4b84-8ed5-163c52f45621"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#58e4b000-57ba-4ab9-9ca1-d8df1fa1aec0">
<rdf:value>
We'll use this component as the "interface" to the model, all
other components are hidden via encapsulation in this component.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3bd21819-008b-4b84-8ed5-163c52f45621">
<dc:creator rdf:resource="rdf:#9d60cc15-8934-4d0e-b916-26d94367186c"/>
<dc:title>A Polyconvex Anisotropic Strain-Energy Function for Soft Collagenous Tissues</dc:title>
<bqs:volume>5(1)</bqs:volume>
<bqs:first_page>17</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#a0431872-d0b7-40ee-afe3-805ba688d7f6"/>
<dcterms:issued rdf:resource="rdf:#e93e6d99-5da8-40ac-b156-3fab8b334c0c"/>
<bqs:last_page>26</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#492afb46-c125-4b96-9c42-ac70045aa7ba">
<vCard:Given>Jesse</vCard:Given>
<vCard:Family>Ashton</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5cb89bae-aa60-4c3d-990c-c74e15702092">
<dc:creator rdf:resource="rdf:#828dd465-dd45-4e3e-9073-7b068911eb37"/>
<rdf:value>This CellML file deals with the introduction of an exponential polyconvex anisotropic strain energy function, for use with modeling applications in regards to soft biological tissues.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#PoleZero">
<bqs:reference rdf:resource="rdf:#8971e08c-fccc-4831-88f3-57e701b7ef4a"/>
<bqs:reference rdf:resource="rdf:#cb8315fa-c495-444e-ae71-7dea10d22177"/>
<cmeta:comment rdf:resource="rdf:#11d1a4cc-624a-4552-a9d9-bf3517ca524d"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1f274b34-9523-4c3e-804d-d9ee65d44796">
<vCard:Given>D</vCard:Given>
<vCard:Family>Mavrilas</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#fcdc7d35-3582-4c8c-bd7a-832c9036776e">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#85b6b216-334e-43a2-93c7-aea5befcafeb">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value>
<rdf:Bag>
<rdf:li>polyconvex</rdf:li>
<rdf:li>soft tissue</rdf:li>
<rdf:li>constitutive material law</rdf:li>
<rdf:li>mechanical constitutive laws</rdf:li>
<rdf:li>anisotropic strain-energy</rdf:li>
</rdf:Bag>
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#11d1a4cc-624a-4552-a9d9-bf3517ca524d">
<dc:creator rdf:resource="rdf:#c0bbcf35-7d1c-462c-92de-356e84a984c7"/>
<rdf:value>This is a CellML version of the Polyconvex constitutive material law for Orthotropic, Incompressible materials, defining the relation between the nine independent strain components and the stress components. It is assumed that the strain components will be controlled externally by the application using this CellML model.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#41814ac0-fe67-4ade-9ea3-d5e74429ac7d">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#4b76fdab-3310-491b-9958-2502e94288d4"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ad9de0f1-b81c-4669-a4db-9d9230de29d2">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#4e466546-212e-477f-9683-fad45b97b69b"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3ff6aff2-ee55-4b11-a807-5756cdcf6425">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#92b9a5b8-ac94-459d-b03b-96479482fea0"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0f3159c2-2238-48bc-aee0-93d555a50688">
<vCard:Orgname>Auckland Bioengineering Institute</vCard:Orgname>
<vCard:Orgunit>University of Auckland</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8971e08c-fccc-4831-88f3-57e701b7ef4a">
<dc:subject rdf:resource="rdf:#85b6b216-334e-43a2-93c7-aea5befcafeb"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a0431872-d0b7-40ee-afe3-805ba688d7f6">
<dc:title>Biomechanics and modelling in mechanobiology</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#79498ae9-887c-4058-9b94-2d9991c22ec6">
<vCard:Given>Jesse</vCard:Given>
<vCard:Family>Ashton</vCard:Family>
<vCard:Other/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e6cc1f7a-9e0f-4dad-bf85-11e051be2dd1">
<vCard:ORG rdf:resource="rdf:#fcdc7d35-3582-4c8c-bd7a-832c9036776e"/>
<vCard:EMAIL rdf:resource="rdf:#e18ba1ae-af0c-4d31-a9f0-ed54350ffcbd"/>
<vCard:N rdf:resource="rdf:#492afb46-c125-4b96-9c42-ac70045aa7ba"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#18caf162-2160-44ff-972b-95b77eac21d5">
<dcterms:W3CDTF>2007-01-24T00:00:00+13:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#92b9a5b8-ac94-459d-b03b-96479482fea0">
<vCard:Given>M</vCard:Given>
<vCard:Family>Itskov</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#49c2e415-5f8c-4d10-880a-5c8557b53008">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#117ade7b-2261-43b0-a974-32f9873a6edc"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c0bbcf35-7d1c-462c-92de-356e84a984c7">
<vCard:FN>Vignesh Kumar</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="">
<dcterms:created rdf:resource="rdf:#8fe91c21-b06a-4b03-955b-fa0d64886b4a"/>
<dc:creator rdf:resource="rdf:#e6cc1f7a-9e0f-4dad-bf85-11e051be2dd1"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#aef22418-3df3-4181-9392-4ace80bfcb05">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#1f274b34-9523-4c3e-804d-d9ee65d44796"/>
</rdf:Description>
</rdf:RDF>
</model>
