Mathematical analysis of a model for the growth of the bovine corpus luteum

Handle URI:
http://hdl.handle.net/10754/598765
Title:
Mathematical analysis of a model for the growth of the bovine corpus luteum
Authors:
Prokopiou, Sotiris A.; Byrne, Helen M.; Jeffrey, Mike R.; Robinson, Robert S.; Mann, George E.; Owen, Markus R.
Abstract:
The corpus luteum (CL) is an ovarian tissue that grows in the wound space created by follicular rupture. It produces the progesterone needed in the uterus to maintain pregnancy. Rapid growth of the CL and progesterone transport to the uterus require angiogenesis, the creation of new blood vessels from pre-existing ones, a process which is regulated by proteins that include fibroblast growth factor 2 (FGF2). In this paper we develop a system of time-dependent ordinary differential equations to model CL growth. The dependent variables represent FGF2, endothelial cells (ECs), luteal cells, and stromal cells (like pericytes), by assuming that the CL volume is a continuum of the three cell types. We assume that if the CL volume exceeds that of the ovulated follicle, then growth is inhibited. This threshold volume partitions the system dynamics into two regimes, so that the model may be classified as a Filippov (piecewise smooth) system. We show that normal CL growth requires an appropriate balance between the growth rates of luteal and stromal cells. We investigate how angiogenesis influences CL growth by considering how the system dynamics depend on the dimensionless EC proliferation rate, {Mathematical expression}. We find that weak (low {Mathematical expression}) or strong (high {Mathematical expression}) angiogenesis leads to 'pathological' CL growth, since the loss of CL constituents compromises progesterone production or delivery. However, for intermediate values of {Mathematical expression}, normal CL growth is predicted. The implications of these results for cow fertility are also discussed. For example, inadequate angiogenesis has been linked to infertility in dairy cows. © 2013 Springer-Verlag Berlin Heidelberg.
Citation:
Prokopiou SA, Byrne HM, Jeffrey MR, Robinson RS, Mann GE, et al. (2013) Mathematical analysis of a model for the growth of the bovine corpus luteum. Journal of Mathematical Biology 69: 1515–1546. Available: http://dx.doi.org/10.1007/s00285-013-0722-2.
Publisher:
Springer Nature
Journal:
Journal of Mathematical Biology
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
13-Dec-2013
DOI:
10.1007/s00285-013-0722-2
PubMed ID:
24337679
Type:
Article
ISSN:
0303-6812; 1432-1416
Sponsors:
SAP acknowledges support from the Schools of Biosciences and Mathematical Sciences at the University of Nottingham in the form of a PhD studentship. MRJ's research is supported by EPSRC grant EP/J001317/1. This publication was based in part on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorProkopiou, Sotiris A.en
dc.contributor.authorByrne, Helen M.en
dc.contributor.authorJeffrey, Mike R.en
dc.contributor.authorRobinson, Robert S.en
dc.contributor.authorMann, George E.en
dc.contributor.authorOwen, Markus R.en
dc.date.accessioned2016-02-25T13:40:46Zen
dc.date.available2016-02-25T13:40:46Zen
dc.date.issued2013-12-13en
dc.identifier.citationProkopiou SA, Byrne HM, Jeffrey MR, Robinson RS, Mann GE, et al. (2013) Mathematical analysis of a model for the growth of the bovine corpus luteum. Journal of Mathematical Biology 69: 1515–1546. Available: http://dx.doi.org/10.1007/s00285-013-0722-2.en
dc.identifier.issn0303-6812en
dc.identifier.issn1432-1416en
dc.identifier.pmid24337679en
dc.identifier.doi10.1007/s00285-013-0722-2en
dc.identifier.urihttp://hdl.handle.net/10754/598765en
dc.description.abstractThe corpus luteum (CL) is an ovarian tissue that grows in the wound space created by follicular rupture. It produces the progesterone needed in the uterus to maintain pregnancy. Rapid growth of the CL and progesterone transport to the uterus require angiogenesis, the creation of new blood vessels from pre-existing ones, a process which is regulated by proteins that include fibroblast growth factor 2 (FGF2). In this paper we develop a system of time-dependent ordinary differential equations to model CL growth. The dependent variables represent FGF2, endothelial cells (ECs), luteal cells, and stromal cells (like pericytes), by assuming that the CL volume is a continuum of the three cell types. We assume that if the CL volume exceeds that of the ovulated follicle, then growth is inhibited. This threshold volume partitions the system dynamics into two regimes, so that the model may be classified as a Filippov (piecewise smooth) system. We show that normal CL growth requires an appropriate balance between the growth rates of luteal and stromal cells. We investigate how angiogenesis influences CL growth by considering how the system dynamics depend on the dimensionless EC proliferation rate, {Mathematical expression}. We find that weak (low {Mathematical expression}) or strong (high {Mathematical expression}) angiogenesis leads to 'pathological' CL growth, since the loss of CL constituents compromises progesterone production or delivery. However, for intermediate values of {Mathematical expression}, normal CL growth is predicted. The implications of these results for cow fertility are also discussed. For example, inadequate angiogenesis has been linked to infertility in dairy cows. © 2013 Springer-Verlag Berlin Heidelberg.en
dc.description.sponsorshipSAP acknowledges support from the Schools of Biosciences and Mathematical Sciences at the University of Nottingham in the form of a PhD studentship. MRJ's research is supported by EPSRC grant EP/J001317/1. This publication was based in part on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherSpringer Natureen
dc.subjectAngiogenesisen
dc.subjectCorpus luteumen
dc.subjectPiecewise smooth systemsen
dc.subjectSliding bifurcationsen
dc.titleMathematical analysis of a model for the growth of the bovine corpus luteumen
dc.typeArticleen
dc.identifier.journalJournal of Mathematical Biologyen
dc.contributor.institutionUniversity of Nottingham, Nottingham, United Kingdomen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionUniversity of Bristol, Bristol, United Kingdomen
kaust.grant.numberKUK-C1-013-04en

Related articles on PubMed

All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.