American Institute of Mathematical Sciences

Advanced
2011, 8(3): 723-732. doi: 10.3934/mbe.2011.8.723

Optimal nutritional intake for fetal growth

Chanakarn Kiataramkul 1, , Graeme Wake 2, , Alona Ben-Tal 3, and  Yongwimon Lenbury 4,

1. 

Department of Mathematics, Mahidol University, Bangkok 10400, Thailand & National Research Centre for Growth and Development, Auckland, New Zealand
2. 

National Research Centre for Growth and Development & Institute of Information and Mathematical Sciences, Massey University, Private Bag 102904, Albany, Auckland
3. 

Institute of Information and Mathematical Sciences, Massey University, Private Bag 102904, Albany, Auckland, New Zealand
4. 

Department of Mathematics, Mahidol University, Bangkok 10400, Thailand & Center of Excellence in Mathematics,, PERDO Commission on Higher Education, Si Ayudhya Rd., Bangkok 10400, New Zealand

Received  August 2010 Revised  November 2010 Published  June 2011

The regular nutritional intake of an expectant mother clearly affects the weight development of the fetus. Assuming the growth of the fetus follows a deterministic growth law, like a logistic equation, albeit dependent on the nutritional intake, the ideal solution is usually determined by the birth-weight being pre-assigned, for example, as a percentage of the mother's average weight. This problem can then be specified as an optimal control problem with the daily intake as the control, which appears in a Michaelis-Menten relationship, for which there are well-developed procedures to follow. The best solution is determined by requiring minimum total intake under which the preassigned birth weight is reached. The algorithm has been generalized to the case where the fetal weight depends in a detailed way on the cumulative intake, suitably discounted according to the history. The optimality system is derived and then solved numerically using an iterative method for the specific values of parameter. The procedure is generic and can be adapted to any growth law and any parameterisation obtained by the detailed physiology.
Keywords: controlled nutrition, dynamical system., Logistic.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Chanakarn Kiataramkul, Graeme Wake, Alona Ben-Tal, Yongwimon Lenbury. Optimal nutritional intake for fetal growth. Mathematical Biosciences & Engineering, 2011, 8 (3) : 723-732. doi: 10.3934/mbe.2011.8.723
References:
[1]

C. W. Clark, "Bioeconomics: The Optimal Management of Renewable Resources,", Wiley, (1976). Google Scholar

[2]

H. R. Joshi, Optimal control of an HIV immunology model,, Optim. Control Appl. Methods, 23 (2002), 199. doi: 10.1002/oca.710. Google Scholar

[3]

E. Jung, S. Lenhart and Z. Feng, Optimal control of treatments in a two-strain tuberculosis model,, Discrete and Continuous Dynamical Systems-Series B, 2 (2002), 473. doi: 10.3934/dcdsb.2002.2.473. Google Scholar

[4]

K. L. Gatford, J. A. Owens, S. Li, T. J. M. Moss, J. P. Newnham, J. R. G. Challis and D. M. Sloboda, Repeated betamethasone treatment of pregnant sheep programspersistent reductions in circulating IGF-I and IGF-binding proteins in progeny,, Am. J. Physiol. Endocrinol. Metab., 295 (2008), 170. doi: 10.1152/ajpendo.00047.2008. Google Scholar

[5]

D. Kirschner, S. Lenhart and S. Serbis, Optimal control of the chemotherapy of HIV,, J. Math. Biol., 35 (1997), 775. doi: 10.1007/s002850050076. Google Scholar

[6]

S. Lenhart and J. T. Workman, Optimal control applied to biological models,, in, (2007). Google Scholar

[7]

L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelize and E. F. Mishchenko, "The Mathematical Theory of Optimal Processes" (ed. L. W. Neustadt),, Interscience Publishers John Wiley & Sons, (1962). Google Scholar

[8]

D. A. Redmer, J. M. Wallace and L. P. Reynolds, Effect of nutrient intake during pregnancy on fetal and placental growth and vascular development,, Domestic Animal Endocrinology, 27 (2004), 199. doi: 10.1016/j.domaniend.2004.06.006. Google Scholar

[9]

G. Wu, F. W. Bazer, T. A. Cudd, C. J. Meininger and T. E. Spencer, Maternal nutrition and fetal development,, Journal of Nutrition, 134 (2004), 2169. Google Scholar

[10]

G. Wu, F. W. Bazer, J. M. Wallace and T. E. Spencer, Board-invited review: Intraurine growth retardation: Implications for the animal sciences,, Journal of Animal Science, 84 (2006), 2316. doi: 10.2527/jas.2006-156. Google Scholar

[11]

G. Zaman, Y. H. Kang and I. H. Jung, Optimal vaccination and treatment in the SIR epidemic model,, Proc. KSIAM, 3 (2007), 31. Google Scholar

show all references

References:
[1]

C. W. Clark, "Bioeconomics: The Optimal Management of Renewable Resources,", Wiley, (1976). Google Scholar

[2]

H. R. Joshi, Optimal control of an HIV immunology model,, Optim. Control Appl. Methods, 23 (2002), 199. doi: 10.1002/oca.710. Google Scholar

[3]

E. Jung, S. Lenhart and Z. Feng, Optimal control of treatments in a two-strain tuberculosis model,, Discrete and Continuous Dynamical Systems-Series B, 2 (2002), 473. doi: 10.3934/dcdsb.2002.2.473. Google Scholar

[4]

K. L. Gatford, J. A. Owens, S. Li, T. J. M. Moss, J. P. Newnham, J. R. G. Challis and D. M. Sloboda, Repeated betamethasone treatment of pregnant sheep programspersistent reductions in circulating IGF-I and IGF-binding proteins in progeny,, Am. J. Physiol. Endocrinol. Metab., 295 (2008), 170. doi: 10.1152/ajpendo.00047.2008. Google Scholar

[5]

D. Kirschner, S. Lenhart and S. Serbis, Optimal control of the chemotherapy of HIV,, J. Math. Biol., 35 (1997), 775. doi: 10.1007/s002850050076. Google Scholar

[6]

S. Lenhart and J. T. Workman, Optimal control applied to biological models,, in, (2007). Google Scholar

[7]

L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelize and E. F. Mishchenko, "The Mathematical Theory of Optimal Processes" (ed. L. W. Neustadt),, Interscience Publishers John Wiley & Sons, (1962). Google Scholar

[8]

D. A. Redmer, J. M. Wallace and L. P. Reynolds, Effect of nutrient intake during pregnancy on fetal and placental growth and vascular development,, Domestic Animal Endocrinology, 27 (2004), 199. doi: 10.1016/j.domaniend.2004.06.006. Google Scholar

[9]

G. Wu, F. W. Bazer, T. A. Cudd, C. J. Meininger and T. E. Spencer, Maternal nutrition and fetal development,, Journal of Nutrition, 134 (2004), 2169. Google Scholar

[10]

G. Wu, F. W. Bazer, J. M. Wallace and T. E. Spencer, Board-invited review: Intraurine growth retardation: Implications for the animal sciences,, Journal of Animal Science, 84 (2006), 2316. doi: 10.2527/jas.2006-156. Google Scholar

[11]

G. Zaman, Y. H. Kang and I. H. Jung, Optimal vaccination and treatment in the SIR epidemic model,, Proc. KSIAM, 3 (2007), 31. Google Scholar

[1]

Mariko Arisawa, Hitoshi Ishii. Some properties of ergodic attractors for controlled dynamical systems. Discrete & Continuous Dynamical Systems - A, 1998, 4 (1) : 43-54. doi: 10.3934/dcds.1998.4.43
[2]

Radosław Kurek, Paweł Lubowiecki, Henryk Żołądek. The Hess-Appelrot system. Ⅲ. Splitting of separatrices and chaos. Discrete & Continuous Dynamical Systems - A, 2018, 38 (4) : 1955-1981. doi: 10.3934/dcds.2018079
[3]

Sébastien Court. Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part II: The nonlinear system.. Evolution Equations & Control Theory, 2014, 3 (1) : 83-118. doi: 10.3934/eect.2014.3.83
[4]

Sébastien Court. Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part I: The linearized system.. Evolution Equations & Control Theory, 2014, 3 (1) : 59-82. doi: 10.3934/eect.2014.3.59
[5]

Tomás Caraballo, Francisco Morillas, José Valero. Asymptotic behaviour of a logistic lattice system. Discrete & Continuous Dynamical Systems - A, 2014, 34 (10) : 4019-4037. doi: 10.3934/dcds.2014.34.4019
[6]

Paweł Lubowiecki, Henryk Żołądek. The Hess-Appelrot system. I. Invariant torus and its normal hyperbolicity. Journal of Geometric Mechanics, 2012, 4 (4) : 443-467. doi: 10.3934/jgm.2012.4.443
[7]

P.K. Newton. The dipole dynamical system. Conference Publications, 2005, 2005 (Special) : 692-699. doi: 10.3934/proc.2005.2005.692
[8]

Ellina Grigorieva, Evgenii Khailov. A nonlinear controlled system of differential equations describing the process of production and sales of a consumer good. Conference Publications, 2003, 2003 (Special) : 359-364. doi: 10.3934/proc.2003.2003.359
[9]

Dina Kalinichenko, Volker Reitmann, Sergey Skopinov. Asymptotic behavior of solutions to a coupled system of Maxwell's equations and a controlled differential inclusion. Conference Publications, 2013, 2013 (special) : 407-414. doi: 10.3934/proc.2013.2013.407
[10]

Liangchen Wang, Yuhuan Li, Chunlai Mu. Boundedness in a parabolic-parabolic quasilinear chemotaxis system with logistic source. Discrete & Continuous Dynamical Systems - A, 2014, 34 (2) : 789-802. doi: 10.3934/dcds.2014.34.789
[11]

Ke Lin, Chunlai Mu. Global dynamics in a fully parabolic chemotaxis system with logistic source. Discrete & Continuous Dynamical Systems - A, 2016, 36 (9) : 5025-5046. doi: 10.3934/dcds.2016018
[12]

Giuseppe Viglialoro, Thomas E. Woolley. Eventual smoothness and asymptotic behaviour of solutions to a chemotaxis system perturbed by a logistic growth. Discrete & Continuous Dynamical Systems - B, 2018, 23 (8) : 3023-3045. doi: 10.3934/dcdsb.2017199
[13]

Dorota Bors, Robert Stańczy. Dynamical system modeling fermionic limit. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 45-55. doi: 10.3934/dcdsb.2018004
[14]

Xiangnan He, Wenlian Lu, Tianping Chen. On transverse stability of random dynamical system. Discrete & Continuous Dynamical Systems - A, 2013, 33 (2) : 701-721. doi: 10.3934/dcds.2013.33.701
[15]

Jianfeng Feng, Mariya Shcherbina, Brunello Tirozzi. Dynamical behaviour of a large complex system. Communications on Pure & Applied Analysis, 2008, 7 (2) : 249-265. doi: 10.3934/cpaa.2008.7.249
[16]

Michel Duprez, Guillaume Olive. Compact perturbations of controlled systems. Mathematical Control & Related Fields, 2018, 8 (2) : 397-410. doi: 10.3934/mcrf.2018016
[17]

Achilles Beros, Monique Chyba, Oleksandr Markovichenko. Controlled cellular automata. Networks & Heterogeneous Media, 2019, 14 (1) : 1-22. doi: 10.3934/nhm.2019001
[18]

Mika Yoshida, Kinji Fuchikami, Tatsuya Uezu. Realization of immune response features by dynamical system models. Mathematical Biosciences & Engineering, 2007, 4 (3) : 531-552. doi: 10.3934/mbe.2007.4.531
[19]

Howard A. Levine, Yeon-Jung Seo, Marit Nilsen-Hamilton. A discrete dynamical system arising in molecular biology. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 2091-2151. doi: 10.3934/dcdsb.2012.17.2091
[20]

Karsten Keller, Sergiy Maksymenko, Inga Stolz. Entropy determination based on the ordinal structure of a dynamical system. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3507-3524. doi: 10.3934/dcdsb.2015.20.3507

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (8)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences