- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2009-11-17 15:28:47+13:00
- Desc:
- Removed links from the citation and added documentation ready to link to Hanne's image.
- Permanent Source URI:
- http://models.cellml.org/workspace/waugh_sherratt_2007/rawfile/f93224810c0bf5dfa4b947c3178ab82c133bd631/waugh_sherratt_2007_d.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : waugh_model_2007.xml
CREATED : 8th November 2007
LAST MODIFIED : 8th November 2007
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.1 Specification.
DESCRIPTION : This file contains a CellML description of Waugh and Sherratt's 2006 mathematical model of macrophage dynamics in diabetic wound healing.
CHANGES:
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="waugh_model_2007" name="waugh_model_2007">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modeling the effects of treating diabetic wounds with engineered skin substitutes</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This CellML version of the model runs in PCEnv to recreate the results in the published paper. The model has also been checked in COR and the units are consistent. This particular version of the model represents wound healing in a diabetic patient treated with Dermagraft.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Wounds in diabetic patients can take much longer to heal than they would in a healthy individual; some taking up to 18 months to heal properly. This suggests the normal wound healing process is disrupted in some way in diabetic patients, but despite intensive research, the mechanisms underlying this process are still relatively poorly understood. However, by piecing together the information which has been obtained, it is possible to develop a simple mathematical model of the wound healing process and how it is influenced by diabetes.
</para>
<para>
The first stage of the wound healing process is inflammation, and macrophages are some of the first cells to be recruited to the site of injury. They are derived from monocytes and they differentiate into one of three types depending on the chemical stimulus they receive, namely; cytocidal (or killer), inflammatory, and repair macrophages. Killer macrophages remove bacteria and other debris from the wound site by phagocytosis, inflammatory macrophages secrete cytokines and chemokines to attract fibroblasts and endothelial cells to the wound and encourage their proliferation, while repair macrophages help to remodel the extracellular matrix of the wound. The ratio of inflammatory to repair macrophages seems to be a key determinant of the rate of wound healing.
</para>
<para>
In diabetic patients cell proliferation is often impaired, endothelial cells are more likely to undergo apoptosis, blood glucose levels are elevated, blood vessel growth is impaired, and there can be decreased collagen deposition at the wound site. Macrophage removal to the lymph nodes may also be impaired, which might explain the presence of macrophages at the wound site long after the inflammatory stage when they would have normally been cleared in a healthy individual.
</para>
<para>
To date, mathematical models of wound healing have tended to focus on the cell proliferation and repair stages of the wound process. However, in diabetic patients it seems the inflammatory phase should be modelled instead. In the paper described here, Helen Waugh and Jonathan Sherratt address this issue by developing a basic mathematical model of the inflammatory stage of the wound healing process, in particular focusing on the behaviour of the macrophage populations. This model is an extension of their previous 2006 model (also described in CellML) and in addition to investigating the kinetics of inflammatory macrophages, repair macrophages and TGF-beta, the current model also describes changing PDGF, collagen density, hyaluronan concentration and fibroblast dynamics. These variables were chosen, in particular, because they are components of two commercially available engineering skin substitutes; Apligraf and Dermagraft, which can be used in diabetic wound healing, and are considered in the current 2007 mathematical model described here.
</para>
<para>
Apligraf is an artificial skin comprising a dermal layer and an epidermal layer of cells seeded onto a bioabsorbable scaffold. Although Apligraf possesses an epidermal layer of keratinocytes the mathematical model discussed here focuses on the dermal components of the therapy - namely neonatal fibroblasts, TGF-beta, PDGF, collagen and hyaluronan. Similarly Dermagraft comprises fibroblasts seeded onto a Vicryl scaffold and it also contains TGF-beta, PDGF, collagen and hyaluronan. However unlike Apligraf, Dermagraft does not possess an epidermal layer of keratinocytes, and the relative density of fibroblasts and concentrations of growth factors and fibres vary slightly.
</para>
<para>
Model simulations suggest that the key component in the successful healing of diabetic wounds appear to be hyaluronan concentration and effect wound healing therapies work by increasing the amount of hyaluronan in the wound environment. Model simulation data agree with time-to-healing results observed in clinical trials and the model assists in our understanding of why diabetic wounds do not heal and how treatments promote wound closure.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
Modeling the effects of treating diabetic wounds with engineered skin substitutes, Helen V. Waugh and Jonathan A. Sherratt, 2007, <emphasis>Wound Repair and Regeneration</emphasis>, 15, 556-565. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=17650100&query_hl=1&itool=pubmed_docsum">PubMed ID: 17650100</ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="waugh_2007.png"/>
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</mediaobject>
<caption>Schematic diagram of the mathematical model describing macrophage and fibroblast dynamics in diabetic wound healing.</caption>
</informalfigure>
</sect1>
</article>
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<geq/>
<ci> time </ci>
<cn cellml:units="day"> 0.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 28.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="pg_per_mm3_per_day"> 1.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 28.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 29.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="pg_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 29.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 35.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="pg_per_mm3_per_day"> 1.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 35.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 36.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="pg_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 36.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 42.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="pg_per_mm3_per_day"> 1.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 42.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 43.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="pg_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 43.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 49.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="pg_per_mm3_per_day"> 1.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 49.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 50.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="pg_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 50.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 56.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="pg_per_mm3_per_day"> 1.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 56.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 57.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="pg_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 57.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 63.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="pg_per_mm3_per_day"> 1.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 63.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 64.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="pg_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 64.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 70.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="pg_per_mm3_per_day"> 1.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 70.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 71.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="pg_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 71.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 77.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="pg_per_mm3_per_day"> 1.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 77.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 78.0 </cn>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="pg_per_mm3_per_day"> 0.0 </cn>
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</component>
<component cmeta:id="F" name="F">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="F">
<dc:title>F</dc:title>
<dcterms:alternative>fibroblast density</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="cells_per_mm3" public_interface="out" name="F" initial_value="50.0"/>
<variable units="cells_per_mm3_per_day" name="Apligraf"/>
<variable units="per_day" public_interface="in" name="k10"/>
<variable units="mm3_per_cells" public_interface="in" name="k3"/>
<variable units="mm3_per_cells" public_interface="in" name="k5"/>
<variable units="mm3_per_microg" public_interface="in" name="k6"/>
<variable units="per_day" public_interface="in" name="d4"/>
<variable units="cells_per_mm3" public_interface="in" name="phi_I"/>
<variable units="cells_per_mm3" public_interface="in" name="phi_R"/>
<variable units="cells_per_mm3_per_day" public_interface="in" name="M_P"/>
<variable units="microg_per_mm3" public_interface="in" name="C"/>
<variable units="day" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> F </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci> M_P </ci>
<apply>
<times/>
<ci> k10 </ci>
<ci> F </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<apply>
<times/>
<ci> k3 </ci>
<apply>
<plus/>
<ci> phi_I </ci>
<ci> phi_R </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k5 </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> k6 </ci>
<ci> C </ci>
</apply>
</apply>
</apply>
</apply>
<ci> Apligraf </ci>
</apply>
<apply>
<times/>
<ci> d4 </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci> Apligraf </ci>
<piecewise>
<piece>
<cn cellml:units="cells_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 0.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 28.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="cells_per_mm3_per_day"> 8000.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 28.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 29.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="cells_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 29.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 35.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="cells_per_mm3_per_day"> 8000.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 35.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 36.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="cells_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 36.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 42.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="cells_per_mm3_per_day"> 8000.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 42.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 43.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="cells_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 43.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 49.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="cells_per_mm3_per_day"> 8000.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 49.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 50.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="cells_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 50.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 56.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="cells_per_mm3_per_day"> 8000.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 56.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 57.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="cells_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 57.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 63.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="cells_per_mm3_per_day"> 8000.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 63.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 64.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="cells_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 64.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 70.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="cells_per_mm3_per_day"> 8000.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 70.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 71.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="cells_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 71.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 77.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="cells_per_mm3_per_day"> 8000.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 77.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 78.0 </cn>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="cells_per_mm3_per_day"> 0.0 </cn>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component cmeta:id="C" name="C">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="C">
<dc:title>C</dc:title>
<dcterms:alternative>collagen concentration</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="microg_per_mm3" public_interface="out" name="C" initial_value="10.0"/>
<variable units="microg_per_mm3_per_day" name="Apligraf"/>
<variable units="microg_per_cells_per_day" public_interface="in" name="k11"/>
<variable units="dimensionless" public_interface="in" name="f_T"/>
<variable units="dimensionless" public_interface="in" name="g_C"/>
<variable units="mm3_per_cells_per_day" public_interface="in" name="d5"/>
<variable units="cells_per_mm3" public_interface="in" name="F"/>
<variable units="day" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> C </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> k11 </ci>
<ci> F </ci>
<ci> f_T </ci>
<ci> g_C </ci>
</apply>
<ci> Apligraf </ci>
</apply>
<apply>
<times/>
<ci> d5 </ci>
<ci> F </ci>
<ci> C </ci>
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</apply>
</apply>
<apply>
<eq/>
<ci> Apligraf </ci>
<piecewise>
<piece>
<cn cellml:units="microg_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 0.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 28.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="microg_per_mm3_per_day"> 18.75 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 28.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 29.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="microg_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 29.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 35.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="microg_per_mm3_per_day"> 18.75 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 35.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 36.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="microg_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 36.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 42.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="microg_per_mm3_per_day"> 18.75 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 42.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 43.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="microg_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 43.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 49.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="microg_per_mm3_per_day"> 18.75 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 49.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 50.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="microg_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 50.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 56.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="microg_per_mm3_per_day"> 18.75 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 56.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 57.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="microg_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 57.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 63.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="microg_per_mm3_per_day"> 18.75 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 63.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 64.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="microg_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 64.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 70.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="microg_per_mm3_per_day"> 18.75 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 70.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 71.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="microg_per_mm3_per_day"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 71.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 77.0 </cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="microg_per_mm3_per_day"> 18.75 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="day"> 77.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<cn cellml:units="day"> 78.0 </cn>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="microg_per_mm3_per_day"> 0.0 </cn>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component cmeta:id="H" name="H">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="H">
<dc:title>H</dc:title>
<dcterms:alternative>hyaluronan concentration</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="microg_per_mm3" public_interface="out" name="H" initial_value="0.01"/>
<variable units="microg_per_mm3_per_day" name="Apligraf"/>
<variable units="microg_per_cells_per_day" public_interface="in" name="k12"/>
<variable units="per_day" public_interface="in" name="d6"/>
<variable units="cells_per_mm3" public_interface="in" name="F"/>
<variable units="day" public_interface="in" name="time"/>
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<times/>
<ci> k12 </ci>
<ci> F </ci>
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<ci> Apligraf </ci>
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<times/>
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<ci> H </ci>
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<rdf:Description rdf:about="K_T">
<dc:title>K_T</dc:title>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="M_P">
<dc:title>M_P</dc:title>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="f_T">
<dc:title>f_T</dc:title>
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<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
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<vCard:FN>Catherine Lloyd</vCard:FN>
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<dc:publisher>The University of Auckland, Bioengineering Institute</dc:publisher>
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<dcterms:W3CDTF>2007-11-28T00:00:00+00:00</dcterms:W3CDTF>
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<vCard:Given>Jonathan</vCard:Given>
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<vCard:Other>A</vCard:Other>
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<vCard:FN>Catherine Lloyd</vCard:FN>
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<rdf:value>This is a CellML description of Waugh and Sherratt's 2006 mathematical model of macrophage dynamics in diabetic wound healing.</rdf:value>
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<vCard:Given>Catherine</vCard:Given>
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<dc:title>Modeling the effects of treating diabetic wounds with engineered skin substitutes</dc:title>
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Waugh and Sherratt's 2006 mathematical model of macrophage dynamics in diabetic wound healing.
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<dc:title>Wound Repair and Regeneration</dc:title>
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