<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : flynn_model_2002.xml
CREATED : 12th June 2004
LAST MODIFIED : 27th April 2004
AUTHOR : Catherine Lloyd
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 Flynn et al.'s 2002 model-based approach for assessing the efficacy of radioimmunotherapy.
CHANGES:
27/04/2005 - PJV - Added units to cn elements where they were missing
--><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="flynn_green_pedley_boxer_dearling_watson_boden_begent_2002_version01" name="flynn_green_pedley_boxer_dearling_watson_boden_begent_2002_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>A Model-Based Approach for Assessing the Efficacy of Radioimmunotherapy</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 is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Radioimmunotherapy (RIT) is a treatment for cancer which combines radiation and immune therapy using monoclonal antibodies. RIT uses a radioactive material attached to specially designed antibodies to locate cancer within the body. Antibodies are defense proteins which are naturally produced by the body's immune system in order to fight infections caused by bacteria and other foreign pathogens. The antibodies used in RIT are monoclonal antibodies (MAbs) which are developed in the laboratory in order to recognise marker molecules on the surface of tumor cells. These antibodies are then modified to bind the radioactive metal Yttrium-90, which delivers high levels of local radiation to the tumour and subsequently destroys it.
</para>
<para>
The effectiveness of RIT is known to depend on at least six factors, including:
</para>
<itemizedlist>
<listitem>
<para>the totla absorbed dose and pattern of delivery;</para>
</listitem>
<listitem>
<para>radiosensitivity;</para>
</listitem>
<listitem>
<para>rate of repair of sublethal damage;</para>
</listitem>
<listitem>
<para>ongoing cancer proliferation during treatment;</para>
</listitem>
<listitem>
<para>tumour heterogeneity; and</para>
</listitem>
<listitem>
<para>tumour size.</para>
</listitem>
</itemizedlist>
<para>
Therefore no single parameter is a good indicator of how effective the RIT has been. Instead, several factors have to be simulataneously considered in order to get a more accurate characterisation of the biological effect.
</para>
<para>
The aim of this study by Flynn <emphasis>et al.</emphasis> was to develop a mathematical model that would relate the absorbed dose and its pattern of delivery to tumour response by incorporating information on each of the six influencing factors (see <xref linkend="fig_reaction_diagram"/> below). The mathemtical model was then used to optimise therapeutic efficacy in mice by matching the antibody and radionuclide characteristics while ensuring recoverable marrow toxicity.
</para>
<para>
The model has been described here in CellML (the raw CellML description of the Flynn <emphasis>et al.</emphasis> 2002 model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>).
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www3.interscience.wiley.com/cgi-bin/abstract/90511815/ABSTRACT">A Model-Based Approach for the Optimization of Radioimmunotherapy through Antibody Design and Radionuclide Selection</ulink>, Aiden A. Flynn, Alan J. Green, R. Barbara Pedley, Geoffrey M. Boxer, Jason Dearling, Rebecca Watson, Robert Boden, and Richard H. J. Begent, 2002, <ulink url="http://www3.interscience.wiley.com/cgi-bin/jhome/28741">
<emphasis>Cancer</emphasis>
</ulink>, 94, 1249-1257. (<ulink url="http://www3.interscience.wiley.com/cgi-bin/fulltext/90511815/HTMLSTART">Full text (HTML)</ulink> and <ulink url="http://www3.interscience.wiley.com/cgi-bin/fulltext/90511815/PDFSTART">PDF</ulink> versions of the article are available to subscribers on the <emphasis>Cancer</emphasis> website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11877753&dopt=Abstract">PubMed ID: 11877753</ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>reaction diagram</title>
</objectinfo>
<imagedata fileref="flynn_2002.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram of the three compartment model representing blood (B), viable tumour (V), and hypoxic tumour (H). Flow between compartments is governed by flow rate constants.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<units name="hour">
<unit units="second" multiplier="3600.0"/>
</units>
<units name="per_hour">
<unit units="hour" exponent="-1"/>
</units>
<units name="Gy">
<unit units="joule"/>
<unit units="gram" prefix="kilo" exponent="-1"/>
</units>
<units name="per_Gy">
<unit units="Gy" exponent="-1"/>
</units>
<units name="Bq">
<unit units="becquerel"/>
</units>
<units name="MBq">
<unit units="becquerel" prefix="mega"/>
</units>
<units name="eV">
<unit units="joule" multiplier="1.602E-19"/>
</units>
<units name="MeV">
<unit units="eV" prefix="mega"/>
</units>
<units name="Gy_per_second">
<unit units="Gy"/>
<unit units="second" exponent="-1"/>
</units>
<units name="Gy_per_Bq_second">
<unit units="Gy"/>
<unit units="becquerel" exponent="-1"/>
<unit units="second" exponent="-1"/>
</units>
<units name="g_Gy_per_MeV">
<unit units="gram"/>
<unit units="Gy"/>
<unit units="MeV" exponent="-1"/>
</units>
<units name="per_gram">
<unit units="gram" exponent="-1"/>
</units>
<units name="per_gram_second">
<unit units="gram" exponent="-1"/>
<unit units="second" exponent="-1"/>
</units>
<component name="environment">
<variable units="hour" public_interface="out" name="time"/>
</component>
<component cmeta:id="B" name="B">
<rdf:RDF>
<rdf:Description rdf:about="B">
<dc:title>B</dc:title>
<dcterms:alternative>antibody concentration in the blood</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="per_gram" public_interface="out" name="B" initial_value="0.4"/>
<variable units="per_gram_second" name="lamda_Bo"/>
<variable units="per_gram_second" public_interface="in" name="lamda_Vi"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>B</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci> lamda_Bo </ci>
<ci> lamda_Vi </ci>
</apply>
</apply>
<ci> B </ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="V" name="V">
<rdf:RDF>
<rdf:Description rdf:about="V">
<dc:title>V</dc:title>
<dcterms:alternative>antibody concentration in the viable tumour</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="per_gram" public_interface="out" name="V"/>
<variable units="per_gram_second" name="lamda_Vo"/>
<variable units="per_gram_second" public_interface="in" name="lamda_Vi"/>
<variable units="per_gram_second" public_interface="in" name="lamda_Ho"/>
<variable units="per_gram" public_interface="in" name="B"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>V</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> lamda_Vi </ci>
<ci> B </ci>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> lamda_Vo </ci>
<ci> lamda_Ho </ci>
</apply>
<ci> V </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="H" name="H">
<rdf:RDF>
<rdf:Description rdf:about="H">
<dc:title>H</dc:title>
<dcterms:alternative>antibody concentration in the hypoxic tumour</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="per_gram" public_interface="out" name="H"/>
<variable units="per_gram_second" name="lamda_Hi"/>
<variable units="per_gram_second" public_interface="in" name="lamda_Ho"/>
<variable units="per_gram" public_interface="in" name="V"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>H</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci> lamda_Hi </ci>
<ci> V </ci>
</apply>
</apply>
<apply>
<times/>
<ci> lamda_Ho </ci>
<ci> H </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="antibody_dose_rate" name="antibody_dose_rate">
<rdf:RDF>
<rdf:Description rdf:about="antibody_dose_rate">
<dc:title>antibody_dose_rate</dc:title>
<dcterms:alternative>antibody dose-rate in the viable tumour</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="Gy_per_Bq_second" public_interface="out" name="RV"/>
<variable units="Gy_per_Bq_second" public_interface="out" name="RH"/>
<variable units="g_Gy_per_MeV" name="K" initial_value="1.6E-6"/>
<variable units="dimensionless" name="n_beta"/>
<variable units="MeV" name="Eav"/>
<variable units="dimensionless" name="phi"/>
<variable units="MBq" name="A0"/>
<variable units="dimensionless" name="VV"/>
<variable units="dimensionless" name="VH"/>
<variable units="dimensionless" name="HV"/>
<variable units="dimensionless" name="HH"/>
<variable units="per_gram" public_interface="in" name="V"/>
<variable units="per_gram" public_interface="in" name="H"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>RV</ci>
<apply>
<times/>
<ci> A0 </ci>
<ci> Eav </ci>
<ci> n_beta </ci>
<ci> K </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> V </ci>
<apply>
<times/>
<ci> phi </ci>
<ci> VV </ci>
</apply>
</apply>
<apply>
<times/>
<ci> H </ci>
<apply>
<times/>
<ci> phi </ci>
<ci> VH </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>RH</ci>
<apply>
<times/>
<ci> A0 </ci>
<ci> Eav </ci>
<ci> n_beta </ci>
<ci> K </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> V </ci>
<apply>
<times/>
<ci> phi </ci>
<ci> HV </ci>
</apply>
</apply>
<apply>
<times/>
<ci> H </ci>
<apply>
<times/>
<ci> phi </ci>
<ci> HH </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="S" name="S">
<rdf:RDF>
<rdf:Description rdf:about="S">
<dc:title>S</dc:title>
<dcterms:alternative>surviving fraction</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="Gy_per_Bq_second" public_interface="out" name="S"/>
<variable units="dimensionless" name="RE"/>
<variable units="MBq" name="D"/>
<variable units="per_Gy" public_interface="in" name="alpha"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>S</ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha </ci>
<ci> D </ci>
</apply>
</apply>
<ci> RE </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="response_models">
<variable units="dimensionless" public_interface="out" name="total_probability"/>
<variable units="dimensionless" public_interface="out" name="probability_of_typeB_damage"/>
<variable units="dimensionless" public_interface="out" name="probability_of_typeA_damage"/>
<variable units="dimensionless" name="P"/>
<variable units="Gy_per_second" name="R"/>
<variable units="hour" name="T"/>
<variable units="per_hour" name="mu"/>
<variable units="per_Gy" public_interface="in" name="alpha"/>
<variable units="hour" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>total_probability</ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> P </ci>
<apply>
<int/>
<bvar>
<ci> time </ci>
</bvar>
<lowlimit>
<cn cellml:units="hour"> 0 </cn>
</lowlimit>
<uplimit>
<ci> T </ci>
</uplimit>
<apply>
<times/>
<ci> R </ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci> mu </ci>
</apply>
<apply>
<minus/>
<ci> T </ci>
<ci> time </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>probability_of_typeB_damage</ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<apply>
<power/>
<ci> P </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<int/>
<bvar>
<ci> time </ci>
</bvar>
<lowlimit>
<cn cellml:units="hour"> 0 </cn>
</lowlimit>
<uplimit>
<ci> time </ci>
</uplimit>
<ci> R </ci>
<apply>
<int/>
<bvar>
<ci> T </ci>
</bvar>
<lowlimit>
<cn cellml:units="hour"> 0 </cn>
</lowlimit>
<uplimit>
<ci> T </ci>
</uplimit>
<ci> R </ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci> mu </ci>
</apply>
<apply>
<minus/>
<ci> T </ci>
<ci> time </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>probability_of_typeB_damage</ci>
<apply>
<times/>
<ci> alpha </ci>
<apply>
<int/>
<bvar>
<ci> time </ci>
</bvar>
<lowlimit>
<cn cellml:units="hour"> 0 </cn>
</lowlimit>
<uplimit>
<ci> time </ci>
</uplimit>
<ci> R </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="model_parameters">
<variable units="per_Gy" public_interface="out" name="alpha"/>
<variable units="per_gram_second" public_interface="out" name="lamda_Vi"/>
<variable units="per_gram_second" public_interface="out" name="lamda_Ho"/>
</component>
<connection>
<map_components component_2="environment" component_1="B"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="V"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="H"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="response_models"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="V" component_1="B"/>
<map_variables variable_2="B" variable_1="B"/>
</connection>
<connection>
<map_components component_2="H" component_1="V"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="B"/>
<map_variables variable_2="lamda_Vi" variable_1="lamda_Vi"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="S"/>
<map_variables variable_2="alpha" variable_1="alpha"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="response_models"/>
<map_variables variable_2="alpha" variable_1="alpha"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="V"/>
<map_variables variable_2="lamda_Vi" variable_1="lamda_Vi"/>
<map_variables variable_2="lamda_Ho" variable_1="lamda_Ho"/>
</connection>
<connection>
<map_components component_2="model_parameters" component_1="H"/>
<map_variables variable_2="lamda_Ho" variable_1="lamda_Ho"/>
</connection>
<connection>
<map_components component_2="antibody_dose_rate" component_1="V"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="antibody_dose_rate" component_1="H"/>
<map_variables variable_2="H" variable_1="H"/>
</connection>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Bag rdf:about="rdf:#4427fcc1-8842-4991-a26d-3b47c5852302">
<rdf:li>immunology</rdf:li>
<rdf:li>tumour dynamics</rdf:li>
<rdf:li>antibody kinetics</rdf:li>
<rdf:li>radioimmunotherapy</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#9287dfaf-c4e4-4f2d-9fdd-5596d2114dfc">
<rdf:li rdf:resource="rdf:#74f956a4-db75-4799-9e1a-c965bb68f414"/>
<rdf:li rdf:resource="rdf:#0f08fca6-8d95-4f0d-83d6-0219098b4673"/>
<rdf:li rdf:resource="rdf:#95656c83-b790-4610-bd25-6b5bcdf76706"/>
<rdf:li rdf:resource="rdf:#f88e5ebf-4d66-4e95-8936-6f06408269b4"/>
<rdf:li rdf:resource="rdf:#3d691a7b-a424-47a7-816a-bab339aa9647"/>
<rdf:li rdf:resource="rdf:#f829cc7b-1863-4f98-98a2-adb10685e5a9"/>
<rdf:li rdf:resource="rdf:#1adea706-ff95-4e41-810e-eda19ab5b283"/>
<rdf:li rdf:resource="rdf:#e7f0f757-c23d-42b8-bfc7-775552b0c187"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#aaefdab2-c5a7-4587-bd20-1dbd1ff71a54">
<vCard:Given>Robert</vCard:Given>
<vCard:Family>Boden</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#2559a994-35e5-4b1a-bc6d-aa1a25b5514c">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#2fb690d3-cc2c-4ba6-9447-f51c8ca16568">
<vCard:ORG rdf:resource="rdf:#41c85800-7178-4346-ab82-df48521c34dc"/>
<vCard:EMAIL rdf:resource="rdf:#7ca58e3a-27f3-49e0-ba14-4a3321ecf146"/>
<vCard:N rdf:resource="rdf:#2559a994-35e5-4b1a-bc6d-aa1a25b5514c"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e7f0f757-c23d-42b8-bfc7-775552b0c187">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#7ac4a48c-1bda-43ec-ab08-44ccdb927fe3"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#95656c83-b790-4610-bd25-6b5bcdf76706">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#d54195f3-9426-484a-bb0a-ffe27db659d3"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d0c6558a-7de7-44fd-b820-6dc0d7e22235">
<dc:creator rdf:resource="rdf:#7b72266b-b6b9-46eb-b936-ec25212d7bee"/>
<rdf:value>
This is the CellML description of Flynn et al.'s 2002 model-based approach for assessing the efficacy of radioimmunotherapy.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7b72266b-b6b9-46eb-b936-ec25212d7bee">
<vCard:FN>Catherine Lloyd</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#dd60bb9d-ac3b-48d2-b98b-2c4287c4a3a7">
<dc:creator rdf:resource="rdf:#9287dfaf-c4e4-4f2d-9fdd-5596d2114dfc"/>
<dc:title>
A Model-Based Approach for the Optimization of Radioimmunotherapy through Antibody Design and Radionuclide Selection
</dc:title>
<bqs:volume>94</bqs:volume>
<bqs:first_page>1249</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#38532dc2-2245-4854-bb6b-94dfef9d7f55"/>
<dcterms:issued rdf:resource="rdf:#f5b78163-d110-4d72-a1e1-1f41e23395d5"/>
<bqs:last_page>1257</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#599d8475-8a53-4f7f-8763-b1c66a17ba91">
<vCard:Given>Jason</vCard:Given>
<vCard:Family>Dearling</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#57422d26-996b-4c0b-bc59-11319334b245">
<bqs:Pubmed_id>11877753</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#dd60bb9d-ac3b-48d2-b98b-2c4287c4a3a7"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1b7754f0-1482-4b33-b178-15aec7a1c9da">
<dc:subject rdf:resource="rdf:#1aee7d56-8dc2-45c9-9901-f41dbfbf2e96"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#15a606f7-d7c9-4f28-b810-2d024e1fe0f2">
<vCard:Given>Geoffrey</vCard:Given>
<vCard:Family>Boxer</vCard:Family>
<vCard:Other>M</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:publisher>
The University of Auckland, Bioengineering Institute
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Flynn et al.'s 2002 model-based approach for assessing the efficacy of radioimmunotherapy.
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