Rendering of the source text

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<!--  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.  
  
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<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>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
    </affiliation>
  </author>
</articleinfo>
<section id="sec_status">
                  <title>Model Status</title>
					<para>
            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.
          </para>
		  <para>
Please note that this CellML model has been implemented in such a manner that it could be used for peforming finite element model simulations on the CMISS software program developed at the Auckland Bioengineering Institute, The University of Auckland. 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>
				</section>
  <sect1 id="sec_structure">
<title>Model Structure</title>
				<para>
ABSTRACT: Polyconvexity of a strain-energy function is a very important mathematical condition, especially in the context of a boundary-value problem. In the present paper, we propose an exponential polyconvex anisotropic strain-energy function. It is given 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. Due to the exponential form, the proposed hyperelastic model is suitable for soft biological tissues. Thus, a good agreement with experimental data on different types of tissues is achieved.</para>

<para>
The 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.
	 <emphasis>Biomechanics and Modeling in Mechanobiology</emphasis>, 5(1), 17-26.  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/16362195">PubMed ID: 16362195</ulink>  </para>
	 
</sect1>
</article>
</documentation>


  

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			</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/>
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											</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/>
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											</apply>
											<ci>E32</ci>
										</apply>
										<apply>
                            <times/>
											<cn cellml:units="dimensionless">4</cn>
											<ci>E12</ci>
											<ci>E31</ci>
										</apply>
									</apply>
									<apply>
                          <power/>
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									</apply>
								</apply>
								<apply>
                        <times/>
									<apply>
                          <power/>
										<ci>detc</ci>		
										<cn cellml:units="dimensionless">2</cn>
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									<ci>x12denom</ci>
									<ci>x22denom</ci>
								</apply>
							</apply>
							<apply>
                      <divide/>
								<apply>
                        <times/>
									<apply>
                          <plus/>
										<apply>
                            <times/>
											<apply>
                              <minus/>
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											</apply>
											<ci>E22</ci>
											<ci>E13</ci>
										</apply>
										<apply>
                            <times/>
											<apply>
                              <minus/>
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											</apply>
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										</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/>
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											<ci>E31</ci>
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										<apply>
                            <times/>
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										</apply>
									</apply>
								</apply>
							</apply>
							<apply>
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								<apply>
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								</apply>
								<ci>x12denom</ci>
							</apply>
						</apply>
					</apply>							
				</apply>
			</apply>
        	</apply>
        </apply>
      </apply>
    </math>


    
  </component>

  <connection>
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    <map_variables variable_2="Tdev11" variable_1="Tdev11"/>
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    <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"/>
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    <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"/>
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    <relationship_ref relationship="encapsulation"/>
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      <component_ref component="equations"/>
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    <vCard:FN>Vignesh Kumar</vCard:FN>
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    <rdf:value>
            In this simple model we only have one component, which holds the
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            We'll use this component as the "interface" to the model, all 
            other components are hidden via encapsulation in this component.
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    <dc:title>A Polyconvex Anisotropic Strain-Energy Function for Soft Collagenous Tissues</dc:title>
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    <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>
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    <vCard:Orgname>The University of Auckland</vCard:Orgname>
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        <rdf:li>polyconvex</rdf:li>
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    <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>
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    <dc:title>Biomechanics and modelling in mechanobiology</dc:title>
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    <vCard:Given>Jesse</vCard:Given>
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