Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T23:04:50.540Z Has data issue: false hasContentIssue false
  • English
  • Français

Validation of a mathematical model of the bovine estrous cycle for cows with different estrous cycle characteristics

Published online by Cambridge University Press:  15 February 2017

H. M. T. Boer ,
S. T. Butler ,
C. Stötzel ,
M. F. W. te Pas ,
R. F. Veerkamp  and
H. Woelders
H. M. T. Boer
Affiliation:
Wageningen UR Livestock Research, Animal Breeding and Genomics Centre, 8200 AB Lelystad, The Netherlands
S. T. Butler
Affiliation:
Animal & Grassland Research and Innovation Centre, Teagasc, Moorepark, Fermoy, P61 C997 Co. Cork, Ireland
C. Stötzel
Affiliation:
Computational Systems Biology Group, Department of Numerical Analysis and Modeling, Konrad-Zuse-Zentrum für Informationstechnik Berlin, Takustraβe 7 14195 Berlin, Germany
M. F. W. te Pas
Affiliation:
Wageningen UR Livestock Research, Animal Breeding and Genomics Centre, 8200 AB Lelystad, The Netherlands
R. F. Veerkamp
Affiliation:
Wageningen UR Livestock Research, Animal Breeding and Genomics Centre, 8200 AB Lelystad, The Netherlands
H. Woelders*
Affiliation:
Wageningen UR Livestock Research, Animal Breeding and Genomics Centre, 8200 AB Lelystad, The Netherlands
*
†E-mail: [email protected]
Get access

Abstract

A recently developed mechanistic mathematical model of the bovine estrous cycle was parameterized to fit empirical data sets collected during one estrous cycle of 31 individual cows, with the main objective to further validate the model. The a priori criteria for validation were (1) the resulting model can simulate the measured data correctly (i.e. goodness of fit), and (2) this is achieved without needing extreme, probably non-physiological parameter values. We used a least squares optimization procedure to identify parameter configurations for the mathematical model to fit the empirical in vivo measurements of follicle and corpus luteum sizes, and the plasma concentrations of progesterone, estradiol, FSH and LH for each cow. The model was capable of accommodating normal variation in estrous cycle characteristics of individual cows. With the parameter sets estimated for the individual cows, the model behavior changed for 21 cows, with improved fit of the simulated output curves for 18 of these 21 cows. Moreover, the number of follicular waves was predicted correctly for 18 of the 25 two-wave and three-wave cows, without extreme parameter value changes. Estimation of specific parameters confirmed results of previous model simulations indicating that parameters involved in luteolytic signaling are very important for regulation of general estrous cycle characteristics, and are likely responsible for differences in estrous cycle characteristics between cows.

Keywords

mathematical modelestrous cyclebovineparameter identificationvalidation
Type
Research Article
Information
animal , Volume 11 , Issue 11 , November 2017 , pp. 1991 - 2001
Copyright
© The Animal Consortium 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Baldwin, RL 1995. Modelling ruminant digestion and metabolism. Chapman & Hall, New York, USA. pp. 469–518.Google Scholar
Boer, HMT, Apri, M, Molenaar, J, Stötzel, C, Veerkamp, RF and Woelders, H 2012. Candidate mechanisms underlying atypical progresterone profiles as deduced from parameter perturbations in a mathematical model of the bovine estrous cycle. Journal of Dairy Science 95, 3837–3851.CrossRefGoogle Scholar
Boer, HMT, Röblitz, S, Stötzel, C, Veerkamp, RF, Kemp, B and Woelders, H 2011a. Mechanisms regulating follicle wave patterns in the bovine estrous cycle investigated with a mathematical model. Journal of Dairy Science 94, 5987–6000.Google Scholar
Boer, HMT, Stötzel, C, Röblitz, S, Deuflhard, P, Veerkamp, RF and Woelders, H 2011b. A simple mathematical model of the bovine estrous cycle: follicle development and endocrine interactions. Journal of Theoretical Biology 278, 20–31.CrossRefGoogle ScholarPubMed
Boer, HMT, Veerkamp, RF, Beerda, B and Woelders, H 2010. Estrous behavior in dairy cows: identification of underlying mechanisms and gene functions. Animal 4, 446–453.Google Scholar
Bondouy, M and Röblitz, S 2012. Mathematical modeling of follicular development in bovine estrous cycles. ZIB-Report 12-26 (August 2012) ISSN 2192-7782, Konrad-Zuse-Zentrum für Informationstechnik Berlin, Takustraβe 7 14195 Berlin, Germany.Google Scholar
Cornish-Bowden, A 2005. Making systems biology work in the 21st century. Genome Biology 6, 317–317.Google Scholar
Cornish-Bowden, A, Cárdenas, ML, Letelier, JC and Soto-Andrade, J 2007. Beyond reductionism: metabolic circularity as a guiding vision for a real biology of systems. Proteomics 6, 839–845.Google Scholar
Cummins, SB, Lonergan, P, Evans, ACO and Butler, ST 2012. Genetic merit for fertility traits in Holstein cows: II. Ovarian follicular and corpus luteum dynamics, reproductive hormones and estrus behaviour. Journal of Dairy Science 95, 3698–3710.CrossRefGoogle Scholar
Dierkes, T, Röblitz, S, Wade, M and Deuflhard, P 2013. Parameter identification in large kinetic networks with BioPARKIN, arXiv CoRR eprints 1303.4928. Retrieved on 02 January 2014 from http://arxiv.org/abs/1303.4928.Google Scholar
Fernández Slezak, D, Suárez, C, Cecchi, GA, Marshall, G and Stolovitzky, G 2010. When the optimal is not the best: parameter estimation in complex biological models. PLoS One 5, e13283.Google Scholar
Kaneko, H, Kishi, H, Watanabe, G, Taya, K, Sasamoto, S and Hasegawa, Y 1995. Changes in plasma concentrations of immunoreactive inhibin, estradiol and FSH associated with follicular waves during the estrous cycle of the cow. Journal of Reproduction and Development 41, 311–320.Google Scholar
Martin, O, Blanc, F, Agabriel, J, Disenhaus, C, Dupont, J, Ponsart, C, Paccard, P, Pires, J, Fréret, S, Elis, S, Gatien, J, Salvetti, P and Friggens, NC 2012. A bovine reproductive physiology model to predict interactions between nutritional status and reproductive management. Canadian Journal of Animal Science 92, 557–558.Google Scholar
Martin, O, Friggens, NC, Dupont, J, Salvetti, P, Freret, S, Rame, C, Elis, S, Gatien, J, Disenhaus, C and Blanc, F 2013. Data-derived reference profiles with corepresentation of progesterone, estradiol, LH, and FSH dynamics during the bovine estrous cycle. Theriogenology 79, 331–343.Google Scholar
McNamara, JP and Shields, SL 2013. Reproduction during lactation of dairy cattle: integrating nutritional aspects of reproductive control in a systems research approach. Animal Frontiers 3, 76–83.CrossRefGoogle Scholar
Nguyen, PT, Conley, AJ, Soboleva, TK and Lee, RS 2012. Multilevel regulation of steroid synthesis and metabolism in the bovine placenta. Molecular Reproduction and Development 79, 239–254.Google Scholar
Shorten, PR, Peterson, AJ, O’Connell, AR, Juengel, JL, McNatty, KP and Soboleva, TK 2010. A mathematical model of pregnancy recognition in mammals. Journal of Theoretical Biology 266, 62–69.Google Scholar
Soboleva, TKA, Peterson, J, Pleasants, AB, McNatty, KP and Rhodes, FM 2000. A model of follicular development and ovulation in sheep and cattle. Animal Reproduction Science 28, 45–57.Google Scholar
Soboleva, T, Pleasants, AB, Van Rens, BTTM, Van Der Lende, T and Peterson, A 2004. A dynamic model for ovulation rate reveals an effect of the estrogen receptor genotype on ovarian follicular development in the pig. Journal of Animal Science 82, 2329–2332.Google Scholar
Stötzel, C, Plöntzke, J, Heuwieser, W and Röblitz, S 2012. Advances in modeling of the bovine estrous cycle: synchronization with PGF2α. Theriogenology 78, 1415–1428.Google Scholar
Vetharaniam, I, Peterson, AJ, McNatty, KP and Soboleva, TK 2010. Modelling female reproductive function in farmed animals. Animal Reproduction Science 122, 164–173.Google Scholar
Wiltbank, M, Lopez, H, Sartori, R, Sangsritavong, S and Gumen, A 2006. Changes in reproductive physiology of lactating dairy cows due to elevated steroid metabolism. Theriogenology 65, 17–29.Google Scholar
Supplementary material: File

Boer supplementary material

Figure S1

Download Boer supplementary material(File)
File 19.9 KB
Supplementary material: File

Boer supplementary material

Figure S2

Download Boer supplementary material(File)
File 71.2 KB
Supplementary material: File

Boer supplementary material

Figure S3

Download Boer supplementary material(File)
File 65.8 KB
Supplementary material: File

Boer supplementary material

Figure S4

Download Boer supplementary material(File)
File 66.2 KB
Supplementary material: File

Boer supplementary material

Figure S5

Download Boer supplementary material(File)
File 72.8 KB
Supplementary material: File

Boer supplementary material

Table S1

Download Boer supplementary material(File)
File 24.9 KB
Supplementary material: File

Boer supplementary material

Table S2

Download Boer supplementary material(File)
File 24.7 KB
Supplementary material: File

Boer supplementary material

Table S3

Download Boer supplementary material(File)
File 32 KB
Supplementary material: File

Boer supplementary material

Table S4

Download Boer supplementary material(File)
File 44 KB