×

zbMATH — the first resource for mathematics

A generalized compartmental model to estimate the fibre mass in the ruminoreticulum: I. Estimating parameters of digestion. (English) Zbl 1400.92152
Summary: Parameters related to the microbial digestion of nutrients in the ruminoreticulum have been estimated by fitting mathematical models to degradation profiles generated from kinetic studies. In the present paper, we propose a generalized compartmental model of digestion (GCMD) based on implicit theoretical concepts and the gamma probability density function to estimate fibre digestion parameters. The proposed model is consistent to a broader compartmental model presented in a companion paper that integrates aspects of fibre digestion and passage. Different versions of the GCMD were generated by increasing the integer order of time dependency of the gamma function. These versions were fitted to 192 published fibre degradation profiles that were obtained using an in vitro fermentation technique. The quality of fit was evaluated based on the frequency of minimum sum of squares of errors (SSE), the number of runs of signs of residuals, and its likelihood probability calculated according to the Akaike’s information criterion. The likelihood of the proposed model was also compared to a discrete lag time model (DLT), which is commonly used to interpret fibre degradation profiles. The GCMD had superior quality of fit compared to the DLT and was considered more likely in describing 68.75% of the profiles evaluated. Only 9.38% of the degradation profiles that were fitted to the DLT model had a lower SSE. Even though the degradation profiles studied were generated by incubating feed samples up to 96h, the true asymptotic limit of fibre degradation can only be achieved by long-term fermentations. This fact leads to questioning the uniformity of the potentially digestible fibre fraction and a further approach based on GCMD-type model was used to account for its heterogeneous nature.

MSC:
92C30 Physiology (general)
Software:
GraphPad Prism; Prism; R
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Agricultural and Food Research Council, Energy and protein requirements of ruminants, (1993), CAB International Walingford, 159pp
[2] Burnham, K.P.; Anderson, D.R., Model selection and multi-model inference: A practical information—theoretic approach, (2002), Springer NY, USA, 488pp · Zbl 1005.62007
[3] Dhanoa, M.S.; France, J.; Siddons, R.C.; Lopez, S.; Buchanan-Smith, J.G., A non-linear compartmental model to describe forage degradation kinetics during incubation in polyester bags in the rumen, Br. J. nutr., 73, 3-15, (1995)
[4] Ellis, W.C.; Matis, J.H.; Hill, T.H.; Murphy, M.R., Methodology for estimating digestion and passage kinetics of forages, (), 682-756
[5] Ellis, W.C.; Mahlooji, M.; Matis, J.H., Models for estimating parameters of neutral detergent fiber digestion by ruminal microorganisms, J. anim. sci., 83, 1591-1601, (2005)
[6] France, J.; Thornley, J.H.M.; Lopez, S.; Siddons, R.C.; Dhanoa, M.S.; Van Soest, P.J.; Gill, M., On the two-compartment model for estimating the rate and extent of feed degradation in the rumen, J. theor. biol., 146, 269-287, (1990)
[7] France, J.; Dijkstra, J.; Dhanoa, M.S.; Baldwin, R.L., Biomathematical applications in ruminant nutrition, J. Frank. inst., 335B, 241-258, (1998) · Zbl 0923.92035
[8] Huhtanen, P.; Nousiainen, J.; Rinne, M., Recent developments in forage evaluation with special reference to practical applications, Agric. food sci., 15, 293-323, (2006)
[9] Huntington, J.A.; Givens, D.I., The in situ technique for studying the rumen degradation of feeds: a review of the procedure, Nutr. abstr. rev. (ser. B), 65, 63-93, (1995)
[10] Matis, J.H., Gamma time-dependency in Blaxter’s compartmental model, Biometrics, 28, 597-602, (1972)
[11] Matis, J.H.; Tolley, H.D., On the stochastic modeling of tracer kinetics, Fed. proc., 39, 104-109, (1980)
[12] Matis, J.H.; Wehrly, T.E.; Ellis, W.C., Some generalized stochastic compartmental models for digesta flow, Biometrics, 45, 703-720, (1989) · Zbl 0715.62200
[13] McDonald, I., A revised model for the estimation of protein degradability in the rumen, J. agric. sci., 96, 251-252, (1981)
[14] Mertens, D.R., 1973. Application of theoretical mathematical models to cell wall digestion and forage intake in ruminants. Ph.D. Dissertation, Cornell University, Ithaca, USA, 217pp.
[15] Mertens, D.R., Dietary fiber components: relationship to the rate and extent of ruminal digestion, Fed. proc., 36, 187-192, (1977)
[16] Mertens, D.R., Rate and extent of digestion, (), 13-47
[17] Mertens, D.R.; Loften, J.R., The effect of starch on forage fiber digestion kinetics in vitro, J. dairy sci., 63, 1437-1446, (1980)
[18] Motulsky, H.J.; Christopoulos, A., Fitting models to biological data using linear and nonlinear regression. A practical guide to curve Fitting, (2003), GraphPad Software Inc. San Diego, USA, 351pp · Zbl 1081.62100
[19] Nocek, J.E., in situ and other methods to estimate ruminal protein and energy digestibility: a review, J. dairy sci., 71, 2051-2069, (1988)
[20] National Research Council, Nutrients requirements of beef cattle, (2000), National Academy Press Washington, 242pp
[21] National Research Council, Nutrient requirements of dairy cattle, (2001), National Academy Press Washington, 381pp
[22] Ørskov, E.R.; McDonald, I., The protein degradability in the rumen from incubation measurements weighted according to rate of passage, J. agric. sci., 92, 499-503, (1979)
[23] Pereira, J.C.; Vieira, R.A.M.; Gonzalez, J.C.; Alvir, M.; Queiroz, A.C., Ruminal degradability of agroindustrial by-products (portuguese), Rev. bras. zoot. (braz. J. anim. sci.), 29, 2359-2366, (2000)
[24] Pitt, R.E.; Cross, T.L.; Pell, A.N.; Schofield, P.; Doane, P.H., Use of in vitro gas production models in ruminal kinetics, Math. biosci., 159, 145-163, (1999) · Zbl 0945.92008
[25] R Development Core Team, R: A language and environment for statistical computing, ISBN: 3-900051-07-0, (2007), R Foundation for Statistical Computing Vienna, URL
[26] Russell, J.B., Rumen microbiology and its role in ruminant nutrition, (2002), James B. Russell Ithaca, 120pp
[27] Schofield, P.; Pitt, R.E.; Pell, A.N., Kinetics of fiber digestion from in vitro gas production, J. anim. sci., 72, 2980-2991, (1994)
[28] Tedeschi, L.O., Assessment of the adequacy of mathematical models, Agric. syst., 89, 225-247, (2006)
[29] Van Milgen, J.; Baumont, R., Models based on variable fractional digestion rates to describe ruminal in situ digestion, Br. J. nutr., 73, 793-807, (1995)
[30] Van Milgen, J.; Murphy, M.R.; Berger, L.L., A compartmental model to analyse ruminal digestion, J. dairy sci., 74, 2515-2529, (1991)
[31] Van Soest, P.J., Nutritional ecology of the ruminant, (1994), Cornell University Press Ithaca, 476pp
[32] Van Soest, P.J.; Robertson, J.B., Analysis of forages and fibrous foods. A laboratory manual for animal science 613, (1985), Cornell University Ithaca, 202pp
[33] Van Soest, P.J., Van Amburgh, M.E., Robertson, J.B., Knaus, W.F., 2005. Validation of the 2.4 times lignin factor for ultimate extent of NDF digestion, and curve peeling rate of fermentation curves into pools. In: Proceedings of the Cornell Nutrition Conference, Ithaca, pp. 139-149.
[34] Vanzant, E.S.; Cochran, R.C.; Titgemeyer, E.C., Standardization of in situ techniques for ruminant feedstuff evaluation, J. anim. sci., 76, 2717-2729, (1998)
[35] Vieira, R.A.M.; Pereira, J.C.; Malafaia, P.A.M.; Queiroz, A.C., Application of non-linear models in the description of in situ degradation profiles of the elephant grass (pennisetum purpureum schum., mineiro variety), Anim. feed sci. technol., 66, 197-210, (1997)
[36] Vieira, R.A.M., Tedeschi, L.O., Cannas, A., 2008. A generalized compartmental model to estimate the fibre mass in the ruminoreticulum: 2. Integrating digestion and passage. J. Theor. Biol., this issue, doi:10.1016/j.jtbi.2008.08.013. · Zbl 1400.92153
[37] Waldo, D.R.; Smith, I.W.; Cox, L.L., Model of cellulose disappearance from the rumen, J. dairy sci., 55, 125-129, (1972)
[38] Wilson, J.R., Organization of forage plant tissues, (), 1-32
[39] Zwietering, M.H.; Jongenburger, I.; Rombouts, F.M.; Van’t Riet, K., Modelling the bacterial growth curve, Appl. environ. microbiol., 56, 1875-1881, (1990)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.