The time-evolution of DCIS size distributions with applications to breast cancer growth and progression.
Identifieur interne : 003415 ( Main/Exploration ); précédent : 003414; suivant : 003416The time-evolution of DCIS size distributions with applications to breast cancer growth and progression.
Auteurs : James G. Dowty [Australie] ; Graham B. Byrnes [France] ; Dorota M. Gertig [Australie]Source :
- Mathematical medicine and biology : a journal of the IMA [ 1477-8602 ] ; 2014.
Descripteurs français
- KwdFr :
- Adulte d'âge moyen, Bases de données factuelles, Carcinome intracanalaire non infiltrant (anatomopathologie), Carcinome intracanalaire non infiltrant (imagerie diagnostique), Carcinome intracanalaire non infiltrant (étiologie), Concepts mathématiques, Femelle, Fonctions de vraisemblance, Humains, Invasion tumorale (anatomopathologie), Mammographie (), Modèles biologiques, Sujet âgé, Tumeurs du sein (anatomopathologie), Tumeurs du sein (imagerie diagnostique), Tumeurs du sein (étiologie), Évolution de la maladie.
- MESH :
- anatomopathologie : Carcinome intracanalaire non infiltrant, Invasion tumorale, Tumeurs du sein.
- imagerie diagnostique : Carcinome intracanalaire non infiltrant, Tumeurs du sein.
- étiologie : Carcinome intracanalaire non infiltrant, Tumeurs du sein.
- Adulte d'âge moyen, Bases de données factuelles, Concepts mathématiques, Femelle, Fonctions de vraisemblance, Humains, Mammographie, Modèles biologiques, Sujet âgé, Évolution de la maladie.
English descriptors
- KwdEn :
- Aged, Breast Neoplasms (diagnostic imaging), Breast Neoplasms (etiology), Breast Neoplasms (pathology), Carcinoma, Intraductal, Noninfiltrating (diagnostic imaging), Carcinoma, Intraductal, Noninfiltrating (etiology), Carcinoma, Intraductal, Noninfiltrating (pathology), Databases, Factual, Disease Progression, Female, Humans, Likelihood Functions, Mammography (statistics & numerical data), Mathematical Concepts, Middle Aged, Models, Biological, Neoplasm Invasiveness (pathology).
- MESH :
- diagnostic imaging : Breast Neoplasms, Carcinoma, Intraductal, Noninfiltrating.
- etiology : Breast Neoplasms, Carcinoma, Intraductal, Noninfiltrating.
- pathology : Breast Neoplasms, Carcinoma, Intraductal, Noninfiltrating, Neoplasm Invasiveness.
- statistics & numerical data : Mammography.
- Aged, Databases, Factual, Disease Progression, Female, Humans, Likelihood Functions, Mathematical Concepts, Middle Aged, Models, Biological.
Abstract
Ductal carcinoma in situ (DCIS) lesions are non-invasive tumours of the breast that are thought to precede most invasive breast cancers (IBCs). As individual DCIS lesions are initiated, grow and invade (i.e. become IBC), the size distribution of the DCIS lesions present in a given human population will evolve. We derive a differential equation governing this evolution and show, for given assumptions about growth and invasion, that there is a unique distribution which does not vary with time. Further, we show that any initial distribution converges to this stationary distribution exponentially quickly. Therefore, it is reasonable to assume that the stationary distribution governs the size of DCIS lesions in human populations which are relatively stable with respect to the determinants of breast cancer. Based on this assumption and the size data of 110 DCIS lesions detected in a mammographic screening programme between 1993 and 2000, we produce maximum likelihood estimates for certain growth and invasion parameters. Assuming that DCIS size is proportional to a positive power p of the time since tumour initiation, we estimate p to be 0.50 with a 95% confidence interval of (0.35, 0.71). Therefore, we estimate that DCIS lesions follow a square-root growth law and hence that they grow rapidly when small and relatively slowly when large. Our approach and results should be useful for other mathematical studies of cancer, especially those investigating biological mechanisms of invasion.
DOI: 10.1093/imammb/dqt014
PubMed: 23873441
Affiliations:
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Dowty</name><affiliation wicri:level="4"><nlm:affiliation>Melbourne School of Population and Global Health, University of Melbourne, Level 3/207 Bouverie St., Carlton 3053, Australia jdowty@unimelb.edu.au.</nlm:affiliation><country wicri:rule="url">Australie</country><wicri:regionArea>Melbourne School of Population and Global Health, University of Melbourne, Level 3/207 Bouverie St., Carlton 3053</wicri:regionArea><orgName type="university">Université de Melbourne</orgName><placeName><settlement type="city">Melbourne</settlement><region type="état">Victoria (État)</region></placeName></affiliation></author><author><name sortKey="Byrnes, Graham B" sort="Byrnes, Graham B" uniqKey="Byrnes G" first="Graham B" last="Byrnes">Graham B. Byrnes</name><affiliation wicri:level="1"><nlm:affiliation>International Agency for Research on Cancer, 150 Cours Albert Thomas, 69372 Lyon cedex 08, France.</nlm:affiliation><country xml:lang="fr">France</country><wicri:regionArea>International Agency for Research on Cancer, 150 Cours Albert Thomas, 69372 Lyon cedex 08</wicri:regionArea><wicri:noRegion>69372 Lyon cedex 08</wicri:noRegion><wicri:noRegion>69372 Lyon cedex 08</wicri:noRegion></affiliation></author><author><name sortKey="Gertig, Dorota M" sort="Gertig, Dorota M" uniqKey="Gertig D" first="Dorota M" last="Gertig">Dorota M. Gertig</name><affiliation wicri:level="4"><nlm:affiliation>Victorian Cytology Service, 752 Swanston Street, Carlton 3053, Australia and Melbourne School of Population and Global Health, University of Melbourne, Level 3/207 Bouverie St., Carlton 3053, Australia.</nlm:affiliation><country xml:lang="fr">Australie</country><wicri:regionArea>Victorian Cytology Service, 752 Swanston Street, Carlton 3053, Australia and Melbourne School of Population and Global Health, University of Melbourne, Level 3/207 Bouverie St., Carlton 3053</wicri:regionArea><orgName type="university">Université de Melbourne</orgName><placeName><settlement type="city">Melbourne</settlement><region type="état">Victoria (État)</region></placeName></affiliation></author></analytic><series><title level="j">Mathematical medicine and biology : a journal of the IMA</title><idno type="eISSN">1477-8602</idno><imprint><date when="2014" type="published">2014</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Aged</term><term>Breast Neoplasms (diagnostic imaging)</term><term>Breast Neoplasms (etiology)</term><term>Breast Neoplasms (pathology)</term><term>Carcinoma, Intraductal, Noninfiltrating (diagnostic imaging)</term><term>Carcinoma, Intraductal, Noninfiltrating (etiology)</term><term>Carcinoma, Intraductal, Noninfiltrating (pathology)</term><term>Databases, Factual</term><term>Disease Progression</term><term>Female</term><term>Humans</term><term>Likelihood Functions</term><term>Mammography (statistics & numerical data)</term><term>Mathematical Concepts</term><term>Middle Aged</term><term>Models, Biological</term><term>Neoplasm Invasiveness (pathology)</term></keywords><keywords scheme="KwdFr" xml:lang="fr"><term>Adulte d'âge moyen</term><term>Bases de données factuelles</term><term>Carcinome intracanalaire non infiltrant (anatomopathologie)</term><term>Carcinome intracanalaire non infiltrant (imagerie diagnostique)</term><term>Carcinome intracanalaire non infiltrant (étiologie)</term><term>Concepts mathématiques</term><term>Femelle</term><term>Fonctions de vraisemblance</term><term>Humains</term><term>Invasion tumorale (anatomopathologie)</term><term>Mammographie ()</term><term>Modèles biologiques</term><term>Sujet âgé</term><term>Tumeurs du sein (anatomopathologie)</term><term>Tumeurs du sein (imagerie diagnostique)</term><term>Tumeurs du sein (étiologie)</term><term>Évolution de la maladie</term></keywords><keywords scheme="MESH" qualifier="anatomopathologie" xml:lang="fr"><term>Carcinome intracanalaire non infiltrant</term><term>Invasion tumorale</term><term>Tumeurs du sein</term></keywords><keywords scheme="MESH" qualifier="diagnostic imaging" xml:lang="en"><term>Breast Neoplasms</term><term>Carcinoma, Intraductal, Noninfiltrating</term></keywords><keywords scheme="MESH" qualifier="etiology" xml:lang="en"><term>Breast Neoplasms</term><term>Carcinoma, Intraductal, Noninfiltrating</term></keywords><keywords scheme="MESH" qualifier="imagerie diagnostique" xml:lang="fr"><term>Carcinome intracanalaire non infiltrant</term><term>Tumeurs du sein</term></keywords><keywords scheme="MESH" qualifier="pathology" xml:lang="en"><term>Breast Neoplasms</term><term>Carcinoma, Intraductal, Noninfiltrating</term><term>Neoplasm Invasiveness</term></keywords><keywords scheme="MESH" qualifier="statistics & numerical data" xml:lang="en"><term>Mammography</term></keywords><keywords scheme="MESH" qualifier="étiologie" xml:lang="fr"><term>Carcinome intracanalaire non infiltrant</term><term>Tumeurs du sein</term></keywords><keywords scheme="MESH" xml:lang="en"><term>Aged</term><term>Databases, Factual</term><term>Disease Progression</term><term>Female</term><term>Humans</term><term>Likelihood Functions</term><term>Mathematical Concepts</term><term>Middle Aged</term><term>Models, Biological</term></keywords><keywords scheme="MESH" xml:lang="fr"><term>Adulte d'âge moyen</term><term>Bases de données factuelles</term><term>Concepts mathématiques</term><term>Femelle</term><term>Fonctions de vraisemblance</term><term>Humains</term><term>Mammographie</term><term>Modèles biologiques</term><term>Sujet âgé</term><term>Évolution de la maladie</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Ductal carcinoma in situ (DCIS) lesions are non-invasive tumours of the breast that are thought to precede most invasive breast cancers (IBCs). As individual DCIS lesions are initiated, grow and invade (i.e. become IBC), the size distribution of the DCIS lesions present in a given human population will evolve. We derive a differential equation governing this evolution and show, for given assumptions about growth and invasion, that there is a unique distribution which does not vary with time. Further, we show that any initial distribution converges to this stationary distribution exponentially quickly. Therefore, it is reasonable to assume that the stationary distribution governs the size of DCIS lesions in human populations which are relatively stable with respect to the determinants of breast cancer. Based on this assumption and the size data of 110 DCIS lesions detected in a mammographic screening programme between 1993 and 2000, we produce maximum likelihood estimates for certain growth and invasion parameters. Assuming that DCIS size is proportional to a positive power p of the time since tumour initiation, we estimate p to be 0.50 with a 95% confidence interval of (0.35, 0.71). Therefore, we estimate that DCIS lesions follow a square-root growth law and hence that they grow rapidly when small and relatively slowly when large. Our approach and results should be useful for other mathematical studies of cancer, especially those investigating biological mechanisms of invasion.</div></front></TEI><affiliations><list><country><li>Australie</li><li>France</li></country><region><li>Victoria (État)</li></region><settlement><li>Melbourne</li></settlement><orgName><li>Université de Melbourne</li></orgName></list><tree><country name="Australie"><region name="Victoria (État)"><name sortKey="Dowty, James G" sort="Dowty, James G" uniqKey="Dowty J" first="James G" last="Dowty">James G. Dowty</name></region><name sortKey="Gertig, Dorota M" sort="Gertig, Dorota M" uniqKey="Gertig D" first="Dorota M" last="Gertig">Dorota M. Gertig</name></country><country name="France"><noRegion><name sortKey="Byrnes, Graham B" sort="Byrnes, Graham B" uniqKey="Byrnes G" first="Graham B" last="Byrnes">Graham B. Byrnes</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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