IDEAS home Printed from https://ideas.repec.org/a/wsi/ijmpcx/v20y2009i01ns0129183109013522.html
   My bibliography  Save this article

A Mathematical Model For Training Impulse And Lactate Influx And Outflux During Exercise

Author

Listed:
  • JOHN F. MOXNES

    (Department for Protection, Norwegian Defence Research Establishment, P. O. Box 25, N-2007 Kjeller, Norway)

  • KJELL HAUSKEN

    (Faculty of Social Sciences, University of Stavanger, N-4036 Stavanger, Norway)

Abstract

This paper provides a mathematical description based on the theory of differential equations, for the dynamics of lactate production and removal. Analytical and numerical results for training/exercise of endurance of athletes are presented based on the common concept of training impulse (Trimp). The relationships between activity, production rate, and removal strategies of lactate are studied. Parameters are estimated from published data. A model for optimum removal of lactate after exercise is developed. The model provides realistic predictions when compared with experimental results. We show some specific examples for the usefulness of the mathematical model by studying some recent problems discussed in the literature. (a) Is interval exercise more beneficial than steady-state exercise? (b) What is the optimum aerobic power during recovery? We discuss whether steady-state exercise gives higher Trimp than interval exercise, when imposing an upper boundary for the lactate concentration as a constraint. The model allows for testing all imaginable kinds of steady-state and interval exercises in search of the optimal exercise regime for individuals with various kinds of characteristics. In general, the dynamic model constitute a powerful tool describing the processes by which the concentration of lactate can be studied and controlled to decrease fatigue and increase endurance.

Suggested Citation

  • John F. Moxnes & Kjell Hausken, 2009. "A Mathematical Model For Training Impulse And Lactate Influx And Outflux During Exercise," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 147-177.
  • Handle: RePEc:wsi:ijmpcx:v:20:y:2009:i:01:n:s0129183109013522
    DOI: 10.1142/S0129183109013522
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0129183109013522
    Download Restriction: Access to full text is restricted to subscribers

    File URL: https://libkey.io/10.1142/S0129183109013522?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. anonymous, 1993. "Profile of Jacob Frenkel," The Region, Federal Reserve Bank of Minneapolis, issue Dec, pages 14-22.
    2. Fernando Cabral & Alexandre Lago & Jason A. C. Gallas, 1993. "A Picture Book Of Two Families Of Cubic Maps," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 4(03), pages 553-568.
    3. Gary Gorton & James A. Kahn & Raghuram G. Rajan & ary, 1993. "Pricing bank loans," Proceedings 415, Federal Reserve Bank of Chicago.
    4. Unknown, 1993. "The Maputo Market Study: Research Methods," Food Security Collaborative Working Papers 55997, Michigan State University, Department of Agricultural, Food, and Resource Economics.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Santos, Ana Paula & Tschirley, David L., 1999. "The Effects of Maize Trade with Malawi on Price Levels in Mozambique: Implications for Trade and Development Policy," Food Security Collaborative Policy Briefs 55213, Michigan State University, Department of Agricultural, Food, and Resource Economics.
    2. Howard, Julie A. & Jeje, Jose Jaime & Kelly, Valerie A. & Boughton, Duncan, 2000. "Comparing Yields and Profitability in MADER's High- and Low-Input Maize Programs: 1997/98 Survey Results and Analysis," Food Security Collaborative Working Papers 56038, Michigan State University, Department of Agricultural, Food, and Resource Economics.
    3. Howard, Julie A. & Low, Jan W. & Jeje, Jose Jaime & Boughton, Duncan & Massingue, Jaquelino & Maredia, Mywish K., 2001. "Constraints and Strategies for the Development of the Seed System in Mozambique," Food Security Collaborative Working Papers 56045, Michigan State University, Department of Agricultural, Food, and Resource Economics.
    4. Howard, Julie A. & Jeje, Jose Jaime & Tschirley, David L. & Strasberg, Paul J. & Crawford, Eric W. & Weber, Michael T., 1998. "What Makes Agricultural Intensification Profitable for Mozambican Smallholders? An Appraisal of the Inputs Subsector and the 1996/97 DNER/SG2000 Program, Volume I: Summary," Food Security Collaborative Working Papers 56029, Michigan State University, Department of Agricultural, Food, and Resource Economics.
    5. S. Panda & K. Banerjee & M. Basu, 2005. "Determination Of Eoq Of Multi-Item Inventory Problems Through Nonlinear Goal Programming With Penalty Function," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 539-553.
    6. Unknown, 1997. "Smallholder Cash Cropping, Food Cropping and Food Security in Northern Mozambique: Summary, Conclusions and Policy Recommendations," Food Security Collaborative Working Papers 56022, Michigan State University, Department of Agricultural, Food, and Resource Economics.
    7. Tschirley, David L., 1998. "Planificando pela Seca em Moçambique: Balanceando os Papéis da Ajuda Alimentar e dos Mercados de Alimentos," Food Security Collaborative Working Papers 56027, Michigan State University, Department of Agricultural, Food, and Resource Economics.
    8. Tania Bucic & Liem Viet Ngo, 2012. "Examining Drivers Of Collaborative Inbound Open Innovation: Empirical Evidence From Australian Firms," International Journal of Innovation Management (ijim), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1-24.
    9. Tschirley, David L. & Abdula, Danilo Carimo & Weber, Michael T., 2006. "Toward Improved Maize Marketing and Trade Policies to Promote Household Food Security in Central and Southern Mozambique," Food Security Collaborative Working Papers 56065, Michigan State University, Department of Agricultural, Food, and Resource Economics.
    10. Benfica, Rui M.S. & Arlindo, Pedro & Weber, Michael T. & Tschirley, David L., 2000. "Representative Characteristics of Rural Households in Areas of Central and Southern Mozambique Affected by the 2000 Floods," Food Security Collaborative Policy Briefs 55214, Michigan State University, Department of Agricultural, Food, and Resource Economics.
    11. Tschirley, David L., 1998. "Planning for Drought in Mozambique: Balancing the Roles of Food Aid and Food Markets," Food Security Collaborative Working Papers 56026, Michigan State University, Department of Agricultural, Food, and Resource Economics.
    12. Tschirley, David L. & Abdula, Danilo Carimo, 2007. "Toward Improved Marketing and Trade Policies to Promote Household Food Security in Central and Southern Mozambique: 2007 Update," Food Security Collaborative Working Papers 56068, Michigan State University, Department of Agricultural, Food, and Resource Economics.
    13. Tschirley, David L. & Santos, Ana Paula, 1995. "Who Eats Yellow Maize? Preliminary Results of a Survey of Consumer Maize Preferences in Maputo, Mozambique," Food Security International Development Working Papers 54697, Michigan State University, Department of Agricultural, Food, and Resource Economics.
    14. Unknown, 1994. "Quem Come Milho Amarelo? Alguns Resultados Preliminares de um Inquérito sobre as Preferências dos Consumidores de Farinha de Milho na Cidade de Maputo," Food Security Collaborative Working Papers 56018, Michigan State University, Department of Agricultural, Food, and Resource Economics.
    15. Unknown, 1996. "Smallholder Cash Cropping, Food Cropping, and Food Security in Northern Mozambique: Research Methods," Food Security Collaborative Working Papers 56021, Michigan State University, Department of Agricultural, Food, and Resource Economics.
    16. Benfica, Rui M.S. & Arlindo, Pedro & Weber, Michael T. & Tschirley, David L., 2000. "Características dos Agregados Familiares Rurais nas Zonas Afectadas pelas Cheias do Ano 2000 no Centro e Sul de Moçambique," Food Security Collaborative Working Papers 56040, Michigan State University, Department of Agricultural, Food, and Resource Economics.
    17. Unknown, 1994. "Who Eats Yellow Maize? Some Preliminary Results of a Survey of Consumer Maize Meal Preferences in Maputo," Food Security Collaborative Working Papers 56017, Michigan State University, Department of Agricultural, Food, and Resource Economics.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:ijmpcx:v:20:y:2009:i:01:n:s0129183109013522. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijmpc/ijmpc.shtml .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.