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

Prokopiou, Sotiris A.; Byrne, Helen M.; Jeffrey, Mike R.; Robinson, Robert S.; Mann, George E.; Owen, Markus R.

Authors

Sotiris A. Prokopiou

Helen M. Byrne

Mike R. Jeffrey

George E. Mann

MARKUS OWEN markus.owen@nottingham.ac.uk
Professor of Mathematical Biology



Abstract

© 2013, Springer-Verlag Berlin Heidelberg. 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, ρ. We find that weak (low ρ 5 or strong (high ρ5) angiogenesis leads to ‘pathological’ CL growth, since the loss of CL constituents compromises progesterone production or delivery. However, for intermediate values of ρ5, 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.

Journal Article Type Article
Publication Date 2014-12
Journal Journal of Mathematical Biology
Print ISSN 0303-6812
Electronic ISSN 1432-1416
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 69
Pages 1515-1546
APA6 Citation Prokopiou, S. A., Byrne, H. M., Jeffrey, M. R., Robinson, R. S., Mann, G. E., & Owen, M. R. (2014). Mathematical analysis of a model for the growth of the bovine corpus luteum. Journal of Mathematical Biology, 69, 1515-1546. https://doi.org/10.1007/s00285-013-0722-2
DOI https://doi.org/10.1007/s00285-013-0722-2
Keywords Corpus luteum ; Angiogenesis ; Piecewise smooth systems ; Sliding bifurcations
Publisher URL http://link.springer.com/article/10.1007%2Fs00285-013-0722-2
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information The final publication is available at Springer via https://dx.doi.org/10.1007/s00285-013-0722-2

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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