Mathematical analysis of a model for the growth of the bovine corpus luteum
| Autor: | Markus R. Owen, George E Mann, Helen M. Byrne, Sotiris A. Prokopiou, Robert S Robinson, Mike R. Jeffrey |
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| Rok vydání: | 2013 |
| Předmět: |
medicine.medical_specialty
Stromal cell Angiogenesis Uterus Neovascularization Physiologic Biology Luteal phase Fibroblast growth factor Models Biological Corpus luteum 03 medical and health sciences Follicle 0302 clinical medicine Corpus Luteum Pregnancy Internal medicine Luteal Cells medicine Animals Computer Simulation Piecewise smooth systems Progesterone 030304 developmental biology Cell Proliferation Sliding bifurcations 0303 health sciences 030219 obstetrics & reproductive medicine Cell growth Applied Mathematics Endothelial Cells Agricultural and Biological Sciences (miscellaneous) Cell biology Endocrinology medicine.anatomical_structure Modeling and Simulation Cattle Female Fibroblast Growth Factor 2 |
| Zdroj: | Prokopiou, S, Byrne, H, Jeffrey, M R, Robinson, RL, Mann, G & Owen, M 2013, ' Mathematical analysis of a model for the growth of the bovine corpus luteum ', Journal of Mathematical Biology, vol. 69, pp. 1515-1546 . https://doi.org/10.1007/s00285-013-0722-2 |
| ISSN: | 1432-1416 0303-6812 |
| DOI: | 10.1007/s00285-013-0722-2 |
| Popis: | © 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. |
| Databáze: | OpenAIRE |
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