- Author:
- Geoff Nunns <gnunns1@jhu.edu>
- Date:
- 2010-03-25 17:39:43+13:00
- Desc:
- Corrected unit inconsistencies, naming of variables. Added model status and issue number.
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/liu_hu_peng_liu_1999/rawfile/1012c1b7a5cdd037fc006e3e77e6a1d7c3dfc5a3/liu_hu_peng_liu_1999.cellml
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<!--
This CellML file was generated on 25/03/2010 at 5:00:45 at p.m. using:
COR (0.9.31.1351)
Copyright 2002-2010 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk
CellML 1.0 was used to generate this model
http://www.cellml.org/
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<title>Mathematical modeling and qualitative analysis of insulin therapies</title>
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<title>Model Status</title>
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This CellML model runs in PCenv, COR and OpenCell to recreate the published results. The initial conditions were not explicitly defined in the paper, but were extrapolated from Table 1 and Figure 2. The model was then run until it reached a steady state, and new intial values were taken from the steady state.
</para>
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<sect1 id="sec_structure">
<title>Model Structure</title>
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Many hormones are secreted pulsatilely with periods of about one hour. These rhythms are on a different timescale to circadian rhythms, suggesting they are regulated by distinct mechanisms. Neither does it seem likely these hormone oscillations are completely controlled at the molecular or cellular level. Instead, the authors of the model described here suggest they probably originate from system dynamics. They propose a dynamical model for the secretory system of the hypothalamic-pituitary-adrenal (HPA) axis (see the figure below). Comparison of model simulation results with experimental data demonstrate the mathematical model captures the essence of the hormone dynamics.
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ABSTRACT: We propose a dynamical model for the pulsatile secretion of the hypothalamo-pituitary-adrenal axis. This model takes into account both the binding of hormone with proteins in the plasma and tissues and mutual interactions of the hormones in the system. The deductions from
this model are in good agreement with experiment results.
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<caption>Schematic diagram of the hormone flow and interactions between the different components of the hypothalamic-pituitary-adrenal (HPA) axis which are described by the mathematical model. CRH represents corticotropin releasing hormone, ACTH represents corticotropin, and CBG is corticosteroid binding globulin. Red arrows represent hormone disposal, while black arrows represent flow between the different glands and plasma. + represents a stimulatory effect while - represents an inhibitory effect.</caption>
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The complete original paper reference is cited below:
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A dynamical model for the pulsatile secretion of the hypothalamo-pituitary-adrenal axis, Yi-Wei Liu, Zhi-Hong Hu, Jian-Hua Peng, and Bing-Zheng Liu, 1999, Mathematical and Computer Modelling, 29 (Issue 4), 103-110. (No Pubmed ID)
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<variable name="a13" units="per_microg_l2" public_interface="in"/>
<variable name="a14" units="per_microg_l" public_interface="in"/>
<variable name="a15" units="per_microg_l2" public_interface="in"/>
<variable name="time" units="minute" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>ACTH</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci>a9</ci>
<apply>
<times/>
<ci>a10</ci>
<ci>CRH</ci>
</apply>
<apply>
<times/>
<ci>a11</ci>
<apply>
<power/>
<ci>CRH</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>a12</ci>
<ci>CRH</ci>
</apply>
<apply>
<times/>
<ci>a13</ci>
<apply>
<power/>
<ci>CRH</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>a14</ci>
<ci>Free_Cortisol</ci>
</apply>
<apply>
<times/>
<ci>a15</ci>
<apply>
<power/>
<ci>Free_Cortisol</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>lambda2</ci>
<ci>ACTH</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="Free_Cortisol">
<variable name="Free_Cortisol" units="microg_l" initial_value="6.51" public_interface="out"/>
<variable name="lambda3_" units="first_order_rate_constant" public_interface="in"/>
<variable name="CRH" units="microg_l" public_interface="in"/>
<variable name="ACTH" units="microg_l" public_interface="in"/>
<variable name="CBG_Bound_Cortisol" units="microg_l" public_interface="in"/>
<variable name="Albumin_Bound_Cortisol" units="microg_l" public_interface="in"/>
<variable name="a16" units="zeroth_order_rate_constant" public_interface="in"/>
<variable name="a17" units="first_order_rate_constant" public_interface="in"/>
<variable name="a18" units="second_order_rate_constant" public_interface="in"/>
<variable name="a19" units="first_order_rate_constant" public_interface="in"/>
<variable name="a20" units="second_order_rate_constant" public_interface="in"/>
<variable name="a21" units="per_microg_l" public_interface="in"/>
<variable name="a22" units="per_microg_l2" public_interface="in"/>
<variable name="a23" units="per_microg_l" public_interface="in"/>
<variable name="a24" units="per_microg_l2" public_interface="in"/>
<variable name="a25" units="first_order_rate_constant" public_interface="in"/>
<variable name="a26" units="first_order_rate_constant" public_interface="in"/>
<variable name="time" units="minute" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Free_Cortisol</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>a16</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>a17</ci>
<ci>CRH</ci>
</apply>
<apply>
<times/>
<ci>a18</ci>
<apply>
<power/>
<ci>CRH</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>a19</ci>
<ci>ACTH</ci>
</apply>
<apply>
<times/>
<ci>a20</ci>
<apply>
<power/>
<ci>ACTH</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>a21</ci>
<ci>CRH</ci>
</apply>
<apply>
<times/>
<ci>a22</ci>
<apply>
<power/>
<ci>CRH</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>a23</ci>
<ci>ACTH</ci>
</apply>
<apply>
<times/>
<ci>a24</ci>
<apply>
<power/>
<ci>ACTH</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>a25</ci>
<ci>CBG_Bound_Cortisol</ci>
</apply>
<apply>
<times/>
<ci>a26</ci>
<ci>Albumin_Bound_Cortisol</ci>
</apply>
</apply>
<apply>
<times/>
<ci>lambda3_</ci>
<ci>Free_Cortisol</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="CBG_Bound_Cortisol">
<variable name="CBG_Bound_Cortisol" units="microg_l" initial_value="60.61" public_interface="out"/>
<variable name="lambda4_" units="first_order_rate_constant" public_interface="in"/>
<variable name="Free_Cortisol" units="microg_l" public_interface="in"/>
<variable name="a27" units="first_order_rate_constant" public_interface="in"/>
<variable name="time" units="minute" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>CBG_Bound_Cortisol</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>a27</ci>
<ci>Free_Cortisol</ci>
</apply>
<apply>
<times/>
<ci>lambda4_</ci>
<ci>CBG_Bound_Cortisol</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="Albumin_Bound_Cortisol">
<variable name="Albumin_Bound_Cortisol" units="microg_l" initial_value="12.61" public_interface="out"/>
<variable name="lambda5_" units="first_order_rate_constant" public_interface="in"/>
<variable name="Free_Cortisol" units="microg_l" public_interface="in"/>
<variable name="a28" units="first_order_rate_constant" public_interface="in"/>
<variable name="time" units="minute" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Albumin_Bound_Cortisol</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>a28</ci>
<ci>Free_Cortisol</ci>
</apply>
<apply>
<times/>
<ci>lambda5_</ci>
<ci>Albumin_Bound_Cortisol</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="model_parameters">
<variable name="a1" units="zeroth_order_rate_constant" initial_value="0.000017" public_interface="out"/>
<variable name="a2" units="zeroth_order_rate_constant" initial_value="0.0023" public_interface="out"/>
<variable name="a3" units="first_order_rate_constant" initial_value="0.6" public_interface="out"/>
<variable name="a4" units="second_order_rate_constant" initial_value="45" public_interface="out"/>
<variable name="a5" units="per_microg_l" initial_value="36" public_interface="out"/>
<variable name="a6" units="per_microg_l2" initial_value="216" public_interface="out"/>
<variable name="a7" units="per_microg_l" initial_value="0.28" public_interface="out"/>
<variable name="a8" units="per_microg_l2" initial_value="0.36" public_interface="out"/>
<variable name="a9" units="zeroth_order_rate_constant" initial_value="0.0003" public_interface="out"/>
<variable name="a10" units="first_order_rate_constant" initial_value="0.18" public_interface="out"/>
<variable name="a11" units="second_order_rate_constant" initial_value="150" public_interface="out"/>
<variable name="a12" units="per_microg_l" initial_value="18" public_interface="out"/>
<variable name="a13" units="per_microg_l2" initial_value="460" public_interface="out"/>
<variable name="a14" units="per_microg_l" initial_value="0.46" public_interface="out"/>
<variable name="a15" units="per_microg_l2" initial_value="0.1" public_interface="out"/>
<variable name="a16" units="zeroth_order_rate_constant" initial_value="0.04" public_interface="out"/>
<variable name="a17" units="first_order_rate_constant" initial_value="150" public_interface="out"/>
<variable name="a18" units="second_order_rate_constant" initial_value="3800" public_interface="out"/>
<variable name="a19" units="first_order_rate_constant" initial_value="57" public_interface="out"/>
<variable name="a20" units="second_order_rate_constant" initial_value="2600" public_interface="out"/>
<variable name="a21" units="per_microg_l" initial_value="200" public_interface="out"/>
<variable name="a22" units="per_microg_l2" initial_value="9400" public_interface="out"/>
<variable name="a23" units="per_microg_l" initial_value="10" public_interface="out"/>
<variable name="a24" units="per_microg_l2" initial_value="320" public_interface="out"/>
<variable name="a25" units="first_order_rate_constant" initial_value="0.04" public_interface="out"/>
<variable name="a26" units="first_order_rate_constant" initial_value="0.00097" public_interface="out"/>
<variable name="a27" units="first_order_rate_constant" initial_value="0.57" public_interface="out"/>
<variable name="a28" units="first_order_rate_constant" initial_value="0.0017" public_interface="out"/>
<variable name="lambda1" units="first_order_rate_constant" initial_value="0.059" public_interface="out"/>
<variable name="lambda2" units="first_order_rate_constant" initial_value="0.028" public_interface="out"/>
<variable name="lambda3_" units="first_order_rate_constant" initial_value="0.67" public_interface="out"/>
<variable name="lambda4_" units="first_order_rate_constant" initial_value="0.06" public_interface="out"/>
<variable name="lambda5_" units="first_order_rate_constant" initial_value="0.001" public_interface="out"/>
</component>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="CRH" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="ACTH" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Free_Cortisol" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="CBG_Bound_Cortisol" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Albumin_Bound_Cortisol" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="CRH" component_2="Free_Cortisol"/>
<map_variables variable_1="CRH" variable_2="CRH"/>
<map_variables variable_1="Free_Cortisol" variable_2="Free_Cortisol"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="CRH" component_2="ACTH"/>
<map_variables variable_1="CRH" variable_2="CRH"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="CRH" component_2="model_parameters"/>
<map_variables variable_1="a1" variable_2="a1"/>
<map_variables variable_1="a2" variable_2="a2"/>
<map_variables variable_1="a3" variable_2="a3"/>
<map_variables variable_1="a4" variable_2="a4"/>
<map_variables variable_1="a5" variable_2="a5"/>
<map_variables variable_1="a6" variable_2="a6"/>
<map_variables variable_1="a7" variable_2="a7"/>
<map_variables variable_1="a8" variable_2="a8"/>
<map_variables variable_1="lambda1" variable_2="lambda1"/>
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<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="ACTH" component_2="Free_Cortisol"/>
<map_variables variable_1="ACTH" variable_2="ACTH"/>
<map_variables variable_1="Free_Cortisol" variable_2="Free_Cortisol"/>
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<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="ACTH" component_2="model_parameters"/>
<map_variables variable_1="a9" variable_2="a9"/>
<map_variables variable_1="a10" variable_2="a10"/>
<map_variables variable_1="a11" variable_2="a11"/>
<map_variables variable_1="a12" variable_2="a12"/>
<map_variables variable_1="a13" variable_2="a13"/>
<map_variables variable_1="a14" variable_2="a14"/>
<map_variables variable_1="a15" variable_2="a15"/>
<map_variables variable_1="lambda2" variable_2="lambda2"/>
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<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="CBG_Bound_Cortisol" component_2="Free_Cortisol"/>
<map_variables variable_1="CBG_Bound_Cortisol" variable_2="CBG_Bound_Cortisol"/>
<map_variables variable_1="Free_Cortisol" variable_2="Free_Cortisol"/>
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<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Albumin_Bound_Cortisol" component_2="Free_Cortisol"/>
<map_variables variable_1="Albumin_Bound_Cortisol" variable_2="Albumin_Bound_Cortisol"/>
<map_variables variable_1="Free_Cortisol" variable_2="Free_Cortisol"/>
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<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Free_Cortisol" component_2="model_parameters"/>
<map_variables variable_1="a16" variable_2="a16"/>
<map_variables variable_1="a17" variable_2="a17"/>
<map_variables variable_1="a18" variable_2="a18"/>
<map_variables variable_1="a19" variable_2="a19"/>
<map_variables variable_1="a20" variable_2="a20"/>
<map_variables variable_1="a21" variable_2="a21"/>
<map_variables variable_1="a22" variable_2="a22"/>
<map_variables variable_1="a23" variable_2="a23"/>
<map_variables variable_1="a24" variable_2="a24"/>
<map_variables variable_1="a25" variable_2="a25"/>
<map_variables variable_1="a26" variable_2="a26"/>
<map_variables variable_1="lambda3_" variable_2="lambda3_"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="CBG_Bound_Cortisol" component_2="model_parameters"/>
<map_variables variable_1="a27" variable_2="a27"/>
<map_variables variable_1="lambda4_" variable_2="lambda4_"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Albumin_Bound_Cortisol" component_2="model_parameters"/>
<map_variables variable_1="a28" variable_2="a28"/>
<map_variables variable_1="lambda5_" variable_2="lambda5_"/>
</connection>
</model>
