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  <doc>
    <id>1273</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2011-04-27</completedDate>
    <publishedDate>2011-04-27</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A mathematical model of the human menstrual cycle for the administration of GnRH analogues</title>
    <abstract language="eng">This study presents a differential equation model for the feedback mechanisms between Gonadotropin-releasing Hormone (GnRH), Follicle-Stimulating Hormone (FSH), Luteinizing Hormone (LH), development of follicles and corpus luteum, and the production of estradiol (E2), progesterone (P4), inhibin A (IhA), and inhibin B (IhB) during the female menstrual cycle. &#13;
In contrast to other models, this model does not involve delay differential equations and is based on deterministic modelling of the GnRH pulse pattern, which allows for faster simulation times and efficient parameter identification. &#13;
These steps were essential to tackle the task of developing a mathematical model for the administration of GnRH analogues. &#13;
The focus of this paper is on model development for GnRH receptor binding and the integration of a pharmacokinetic/pharmacodynamic model for the GnRH agonist Nafarelin and the GnRH antagonist Cetrorelix into the menstrual cycle model. &#13;
The final mathematical model describes the hormone profiles (LH, FSH, P4, E2) throughout the menstrual cycle in 12 healthy women.&#13;
Moreover, it correctly predicts the changes in the cycle following single and multiple dose administration of Nafarelin or Cetrorelix at different stages in the cycle.</abstract>
    <identifier type="serial">11-16</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-12732</identifier>
    <enrichment key="SourceTitle">Appeared in: Journal of Theoretical Biology 321 (2013) pp. 8-27</enrichment>
    <author>Susanna Röblitz</author>
    <submitter>Susanna Röblitz</submitter>
    <author>Claudia Stötzel</author>
    <author>Peter Deuflhard</author>
    <author>Hannah M. Jones</author>
    <author>David-Olivier Azulay</author>
    <author>Piet van der Graaf</author>
    <author>Steven Martin</author>
    <series>
      <title>ZIB-Report</title>
      <number>11-16</number>
    </series>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>human menstrual cycle</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>systems biology</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>mathematical modelling</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>GnRH analogues</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>differential equations</value>
    </subject>
    <collection role="msc" number="65L09">Inverse problems</collection>
    <collection role="msc" number="90C31">Sensitivity, stability, parametric optimization</collection>
    <collection role="msc" number="92C30">Physiology (general)</collection>
    <collection role="msc" number="92C42">Systems biology, networks</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="projects" number="GynSys">GynSys</collection>
    <collection role="projects" number="MATHEON-A18">MATHEON-A18</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1273/ZR_11_16.pdf</file>
  </doc>
  <doc>
    <id>1274</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2011-06-14</completedDate>
    <publishedDate>2011-06-14</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Advances in modelling of the bovine estrous cycle: Administration of PGF2alpha</title>
    <abstract language="eng">Our model of the bovine estrous cycle is a set of ordinary differential equations which generates hormone profiles of successive estrous cycles with several follicular waves per cycle. It describes the growth and decay of the follicles and the corpus luteum, as well as the change of the key substances over time. In this work we describe recent improvements of this model, including the introduction of new components, and elimination of time delays. We validate our model by showing that the simulations agree with observations from synchronization studies and with measured progesterone data after a single dose administration of synthetic prostaglandin F2alpha.</abstract>
    <identifier type="serial">11-17</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-12740</identifier>
    <enrichment key="SourceTitle">Appeared in: Theriogenology 78 (2012), pp. 1415-1428</enrichment>
    <author>Claudia Stötzel</author>
    <submitter>Claudia Stötzel</submitter>
    <author>Julia Plöntzke</author>
    <author>Susanna Röblitz</author>
    <series>
      <title>ZIB-Report</title>
      <number>11-17</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cow</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>reproduction</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>hormone patterns</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>differential equations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>systems biology</value>
    </subject>
    <collection role="msc" number="92C30">Physiology (general)</collection>
    <collection role="msc" number="92C42">Systems biology, networks</collection>
    <collection role="msc" number="92C50">Medical applications (general)</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="projects" number="MATHEON-A18">MATHEON-A18</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1274/ZR_11_17_Bovine_PGF.pdf</file>
  </doc>
  <doc>
    <id>1774</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-02-14</completedDate>
    <publishedDate>2013-02-14</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Modeling potassium balance in dairy cows</title>
    <abstract language="eng">Potassium is fundamental for cell functioning including signal transduction, acid-base- and water-metabolism. &#13;
Since diet of dairy cows is generally rich in potassium, hypokalemia was not in the focus of research for long time. Furthermore, hypokalemia was not frequently diagnosed because blood potassium content is difficult to measure. In recent years, measurement methods have been improved. Nowadays hypokalemia is increasingly diagnosed in cows with disorders such as abomasal displacement, ketosis or down cow syndrome, calling for intensified research on this topic. &#13;
In this report we describe the development of a basic mechanistic, dynamic model of potassium balance based on ordinary differential and algebraic equations. Parameter values are obtained from data of a clinical trial in which potassium balance and the influence of therapeutic intervention in glucose and electrolyte metabolism on potassium balance in non-lactating dairy cows were studied. The model is formulated at a high abstraction level and includes information and hypotheses from literature. This work represents a first step towards the understanding and design of effective prophylactic feed additives and treatment strategies.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-17749</identifier>
    <author>Julia Plöntzke</author>
    <submitter>Julia Ploentzke</submitter>
    <author>Mascha Berg</author>
    <author>Amiya Olany</author>
    <author>Sabine Leonhard-Marek</author>
    <author>Kerstin-Elisabeth Müller</author>
    <author>Susanna Röblitz</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-09</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>systems biology</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>differential equations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>metabolism</value>
    </subject>
    <collection role="msc" number="92C30">Physiology (general)</collection>
    <collection role="msc" number="92C42">Systems biology, networks</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="projects" number="BovSys">BovSys</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1774/ZR-13-09.pdf</file>
  </doc>
</export-example>
