Mathematical analysis of a model for the growth of the bovine corpus luteum
Type
ArticleAuthors
Prokopiou, Sotiris A.Byrne, Helen M.

Jeffrey, Mike R.
Robinson, Robert S.
Mann, George E.
Owen, Markus R.
KAUST Grant Number
KUK-C1-013-04Date
2013-12-13Online Publication Date
2013-12-13Print Publication Date
2014-12Permanent link to this record
http://hdl.handle.net/10754/598765
Metadata
Show full item recordAbstract
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.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).Publisher
Springer NatureJournal
Journal of Mathematical BiologyPubMed ID
24337679ae974a485f413a2113503eed53cd6c53
10.1007/s00285-013-0722-2
Scopus Count
Collections
Publications Acknowledging KAUST SupportRelated articles
- Fibroblast growth factor 2 is more dynamic than vascular endothelial growth factor A during the follicle-luteal transition in the cow.
- Authors: Robinson RS, Nicklin LT, Hammond AJ, Schams D, Hunter MG, Mann GE
- Issue date: 2007 Jul
- Regulation of angiogenesis-related prostaglandin f2alpha-induced genes in the bovine corpus luteum.
- Authors: Zalman Y, Klipper E, Farberov S, Mondal M, Wee G, Folger JK, Smith GW, Meidan R
- Issue date: 2012 Mar
- Regulation of corpus luteum development and maintenance: specific roles of angiogenesis and action of prostaglandin F2alpha.
- Authors: Miyamoto A, Shirasuna K, Shimizu T, Bollwein H, Schams D
- Issue date: 2010
- Endocrine and cellular characteristics of corpora lutea from cows with a delayed post-ovulatory progesterone rise.
- Authors: Robinson RS, Hammond AJ, Nicklin LT, Schams D, Mann GE, Hunter MG
- Issue date: 2006 Aug
- Nitric oxide stimulates progesterone and prostaglandin E2 secretion as well as angiogenic activity in the equine corpus luteum.
- Authors: Ferreira-Dias G, Costa AS, Mateus L, Korzekwa AJ, Galvão A, Redmer DA, Lukasik K, Szóstek AZ, Woclawek-Potocka I, Skarzynski DJ
- Issue date: 2011 Jan