European Journal of Applied Physiology

, Volume 118, Issue 2, pp 449–460 | Cite as

A mathematical model of the effects of resistance exercise-induced muscle hypertrophy on body composition

  • Marcella Torres
  • Eric T. Trexler
  • Abbie E. Smith-Ryan
  • Angela Reynolds
Original Article

Abstract

Purpose

Current diet and exercise methods used to maintain or improve body composition often have poor long-term outcomes. We hypothesize that resistance exercise (RE) should aid in the maintenance of a healthy body composition by preserving lean mass (LM) and metabolic rate.

Method

We extended a previously developed energy balance model of human metabolism to include muscle hypertrophy in response to RE. We first fit model parameters to a hypothetical individual to simulate an RE program and then compared the effects of a hypocaloric diet only to the diet with either cardiovascular exercise (CE) or RE. We then simulated a cohort of individuals with different responses to RE by varying the parameters controlling it using Latin Hypercube Sampling (LHS). Finally, we fit the model to mean data from an elderly population on an RE program.

Conclusion

The model is able to reproduce the time course of change in LM in response to RE and can be used to generate a simulated cohort for in silico clinical studies. Simulations suggest that the additional LM generated by RE may shift the body composition to a healthier state.

Keywords

Resistance exercise Dieting Weight loss Muscle hypertrophy Lean mass Mathematical model 

Abbreviations

CE

Cardiovascular exercise

LHS

Latin hypercube sampling

LM

Lean mass

PAL

Physical activity level

RE

Resistance exercise

Supplementary material

421_2017_3787_MOESM1_ESM.pdf (411 kb)
Supplementary material 1 (PDF 411 kb)

References

  1. Alpert SS (1979) A two-reservoir energy model of the human body. Am J Clin Nutr 32(8):1710–1718PubMedGoogle Scholar
  2. Alpert SS (1990) Growth, thermogenesis, and hyperphagia. Am J Clin Nutr 52(5):784–792CrossRefPubMedGoogle Scholar
  3. Alpert SS (2005) A limit on the energy transfer rate from the human fat store in hypophagia. J Theor Biol 233(1):1–13CrossRefPubMedGoogle Scholar
  4. Antonetti VW (1973) The equations governing weight change in human beings. Am J Clin Nutr 26(1):64–71PubMedGoogle Scholar
  5. Avila JJ, Gutierres JA, Sheehy ME, Lofgren IE, Delmonico MJ (2010) Effect of moderate intensity resistance training during weight loss on body composition and physical performance in overweight older adults. Eur J Appl Physiol 109(3):517–525CrossRefPubMedGoogle Scholar
  6. Ballor DL, Katch V, Becque M, Marks C (1988) Resistance weight training during caloric restriction enhances lean body weight maintenance. Am J Clin Nutr 47(1):19–25CrossRefPubMedGoogle Scholar
  7. Borrud L, Flegal K, Looker A, Everhart J, Harris T, Shepherd J (2010) Body composition data for individuals 8 years of age and older: US population, 1999–2004. Vital Health Stat Ser 11 Data Natl Health Surv 250:1–87Google Scholar
  8. Bouchard DR, Soucy L, Sénéchal M, Dionne IJ, Brochu M (2009) Impact of resistance training with or without caloric restriction on physical capacity in obese older women. Menopause 16(1):66–72CrossRefPubMedGoogle Scholar
  9. Bryner RW, Ullrich IH, Sauers J, Donley D, Hornsby G, Kolar M, Yeater R (1999) Effects of resistance vs. aerobic training combined with an 800 calorie liquid diet on lean body mass and resting metabolic rate. J Am Coll Nutr 18(2):115–121CrossRefPubMedGoogle Scholar
  10. Chow CC, Hall KD (2008) The dynamics of human body weight change. PLoS Comput Biol 4(3):e1000045CrossRefPubMedPubMedCentralGoogle Scholar
  11. Christiansen E, Garby L (2002) Prediction of body weight changes caused by changes in energy balance. Eur J Clin investig 32(11):826–830CrossRefGoogle Scholar
  12. Churchward-Venne TA, Tieland M, Verdijk LB, Leenders M, Dirks ML, de Groot LC, van Loon LJ (2015) There are no nonresponders to resistance-type exercise training in older men and women. J Am Med Dir Assoc 16(5):400–411CrossRefPubMedGoogle Scholar
  13. Corral P, Bryan DR, Garvey WT, Gower BA, Hunter GR (2011) Dietary adherence during weight loss predicts weight regain. Obesity 19(6):1177–1181CrossRefPubMedGoogle Scholar
  14. Cunningham JJ (1991) Body composition as a determinant of energy expenditure: a synthetic review and a proposed general prediction equation. Am J Clin Nutr 54(6):963–969CrossRefPubMedGoogle Scholar
  15. Dolezal BA, Potteiger JA (1998) Concurrent resistance and endurance training influence basal metabolic rate in nondieting individuals. J Appl Physiol 85(2):695–700CrossRefPubMedGoogle Scholar
  16. Flatt J-P (2004) Carbohydratefat interactions and obesity examined by a two-compartment computer model. Obes Res 12(12):2013–2022CrossRefPubMedGoogle Scholar
  17. Geliebter A, Maher MM, Gerace L, Gutin B, Heymsfield SB, Hashim SA (1997) Effects of strength or aerobic training on body composition, resting metabolic rate, and peak oxygen consumption in obese dieting subjects. Am J Clin Nutr 66(3):557–563CrossRefPubMedGoogle Scholar
  18. Hall KD (2010a) Predicting metabolic adaptation, body weight change, and energy intake in humans. Am J Physiol Endocrinol Metab 298(3):E449–E466CrossRefPubMedGoogle Scholar
  19. Hall KD (2010b) Mechanisms of metabolic fuel selection: modeling human metabolism and body-weight change. Eng Med Biol Mag IEEE 29(1):36–41CrossRefGoogle Scholar
  20. Hall KD, Jordan PN (2008) Dynamic coordination of macronutrient balance during infant growth: Insights from a mathematical model. FASEB J 22(1 Supplement):305–1Google Scholar
  21. Hall KD, Bain HL, Chow CC (2007) How adaptations of substrate utilization regulate body composition. Int J obes 31(9):1378–1383CrossRefGoogle Scholar
  22. Hall KD, Sacks G, Chandramohan D, Chow CC, Wang YC, Gortmaker SL, Swinburn BA (2011) Quantification of the effect of energy imbalance on bodyweight. Lancet 378(9793):826–837CrossRefPubMedGoogle Scholar
  23. Ho SS, Dhaliwal SS, Hills AP, Pal S (2012) The effect of 12 weeks of aerobic, resistance or combination exercise training on cardiovascular risk factors in the overweight and obese in a randomized trial. BMC Public Health 12(1):704CrossRefPubMedPubMedCentralGoogle Scholar
  24. Hubal MJ, Gordish-Dressman H, Thompson PD, Price TB, Hoffman EP, Angelopoulos TJ, Gordon PM, Moyna NM, Pescatello LS, Visich PS et al (2005) Variability in muscle size and strength gain after unilateral resistance training. Med Sci Sports Exerc 37(6):964–72PubMedGoogle Scholar
  25. Johnstone AM, Murison SD, Duncan JS, Rance KA, Speakman JR (2005) Factors influencing variation in basal metabolic rate include fat-free mass, fat mass, age, and circulating thyroxine but not sex, circulating leptin, or triiodothyronine. Am J Clin Nutr 82(5):941–948PubMedGoogle Scholar
  26. Kozusko FP (2001) Body weight setpoint, metabolic adaption and human starvation. Bull Math Biol 63(2):393–403CrossRefPubMedGoogle Scholar
  27. Leenders M, Verdijk LB, van der Hoeven L, van Kranenburg J, Nilwik R, van Loon LJ (2013) Elderly men and women benefit equally from prolonged resistance-type exercise training. J Gerontol Ser A Biol Sci Med Sci 68(7):769–779CrossRefGoogle Scholar
  28. Livingston EH, Sebastian JL, Huerta S, Yip I, Heber D (2001) Biexponential model for predicting weight loss after gastric surgery for obesity. J Surg Res 101(2):216–224CrossRefPubMedGoogle Scholar
  29. Lo MS, Lin LL, Yao W-J, Ma M-C (2011) Training and detraining effects of the resistance vs. endurance program on body composition, body size, and physical performance in young men. The. J Strength Cond Res 25(8):2246–2254CrossRefPubMedGoogle Scholar
  30. Marino S, Hogue I B, Ray C J, Kirschner D E (2008) A methodology for performing global uncertainty and sensitivity analysis in systems biology. J Theor Biol 254(1):178–196.  https://doi.org/10.1016/j.jtbi.2008.04.011 ISSN 00225193CrossRefPubMedPubMedCentralGoogle Scholar
  31. McKay M (1992) Latin hypercube sampling as a tool in uncertainity analysis of computer models. In: Proceedings of the 1992 Winter Simulation Conference.  https://doi.org/10.1145/167293.167637
  32. Mifflin MD, St Jeor S, Hill LA, Scott BJ, Daugherty SA, Koh Y (1990) A new predictive equation for resting energy expenditure in healthy individuals. Am J Clin Nutr 51(2):241–247CrossRefPubMedGoogle Scholar
  33. Navarro-Barrientos J-E, Rivera DE, Collins LM (2011) A dynamical model for describing behavioural interventions for weight loss and body composition change. Math Comput Model Dyn Syst 17(2):183–203CrossRefPubMedPubMedCentralGoogle Scholar
  34. Nelson KM, Weinsier RL, Long CL, Schutz Y (1992) Prediction of resting energy expenditure from fat-free mass and fat mass. Am J Clin Nutr 56(5):848–856CrossRefPubMedGoogle Scholar
  35. Nicklas BJ, Chmelo E, Delbono O, Carr JJ, Lyles MF, Marsh AP (2015) Effects of resistance training with and without caloric restriction on physical function and mobility in overweight and obese older adults: a randomized controlled trial. Am J Clin Nutr 101(5):991–999CrossRefPubMedPubMedCentralGoogle Scholar
  36. Pavlou KN, Steffee WP, Lerman RH, Burrows BA (1985) Effects of dieting and exercise on lean body mass, oxygen uptake, and strength. Med Sci Sports Exerc 17(4):466–471CrossRefPubMedGoogle Scholar
  37. Payne PR, Dugdale AE (1977) A model for the prediction of energy balance and body weight. Ann Hum Biol 4(6):525–535CrossRefPubMedGoogle Scholar
  38. Peterson MD, Sen A, Gordon PM (2011) Influence of resistance exercise on lean body mass in aging adults: a meta-analysis. Med Sci Sports Exerc 43(2):249CrossRefPubMedPubMedCentralGoogle Scholar
  39. Petrella JK, Kim J-S, Mayhew DL, Cross JM, Bamman MM (2008) Potent myofiber hypertrophy during resistance training in humans is associated with satellite cell-mediated myonuclear addition: a cluster analysis. J Appl Physiol 104(6):1736–1742CrossRefPubMedGoogle Scholar
  40. Sanal E, Ardic F, Kirac S (2013) Effects of aerobic or combined aerobic resistance exercise on body composition in overweight and obese adults: gender differences. a randomized intervention study. Eur J Phys Rehabil Med 49(1):1–11PubMedGoogle Scholar
  41. Saris WH (2001) Very-low-calorie diets and sustained weight loss. Obesity 9(S11):295S–301SCrossRefGoogle Scholar
  42. Scott D, Hirani V (2016) Sarcopenic obesity. Eur Geriatr Med 7(3):214–219CrossRefGoogle Scholar
  43. Shai I, Stampfer MJ (2008) Weight-loss dietscan you keep it off? Am J Clin Nutr 88(5):1185–1186PubMedGoogle Scholar
  44. Song B, Thomas DM (2007) Dynamics of starvation in humans. J Math Biol 54(1):27–43CrossRefPubMedGoogle Scholar
  45. Srikanthan P, Karlamangla AS (2011) Relative muscle mass is inversely associated with insulin resistance and prediabetes. Findings from the third national health and nutrition examination survey. J Clin Endocrinol Metab 96(9):2898–2903CrossRefPubMedGoogle Scholar
  46. Stout JR, Smith-Ryan AE, Fukuda DH, Kendall KL, Moon JR, Hoffman JR, Wilson JM, Oliver JS, Mustad VA (2013) Effect of calcium \(\beta\)-hydroxy-\(\beta\)-methylbutyrate (cahmb) with and without resistance training in men and women 65+ yrs: a randomized, double-blind pilot trial. Exp Gerontol 48(11):1303–1310CrossRefPubMedGoogle Scholar
  47. Thomas DM, Martin CK, Heymsfield S, Redman LM, Schoeller DA, Levine JA (2011) A simple model predicting individual weight change in humans. J Biol Dyn 5(6):579–599CrossRefPubMedPubMedCentralGoogle Scholar
  48. Trexler ET, Smith-Ryan AE, Norton LE (2014) Metabolic adaptation to weight loss: implications for the athlete. J Int Soc Sports Nutr 11(1):1CrossRefGoogle Scholar
  49. Ulen CG, Huizinga MM, Beech B, Elasy TA (2008) Weight regain prevention. Clin Diabetes 26(3):100–113CrossRefGoogle Scholar
  50. Wernbom M, Augustsson J, Thomeé R (2007) The influence of frequency, intensity, volume and mode of strength training on whole muscle cross-sectional area in humans. Sports Med 37(3):225–264CrossRefPubMedGoogle Scholar
  51. Westerterp KR, Donkers JH, Fredrix EW et al (1995) Energy intake, physical activity and body weight: a simulation model. Br J Nutr 73(03):337–347CrossRefPubMedGoogle Scholar
  52. Willis LH, Slentz CA, Bateman LA, Shields AT, Piner LW, Bales CW, Houmard JA, Kraus WE (2012) Effects of aerobic and/or resistance training on body mass and fat mass in overweight or obese adults. J Appl Physiol 113(12):1831–1837CrossRefPubMedPubMedCentralGoogle Scholar
  53. Wilson JM, Lowery RP, Joy JM, Andersen J, Wilson SM, Stout JR, Duncan N, Fuller JC, Baier SM, Naimo MA et al (2014) The effects of 12 weeks of beta-hydroxy-beta-methylbutyrate free acid supplementation on muscle mass, strength, and power in resistance-trained individuals: a randomized, double-blind, placebo-controlled study. Eur J Appl Physiol 114(6):1217–1227CrossRefPubMedPubMedCentralGoogle Scholar
  54. Wing RR, Phelan S (2005) Long-term weight loss maintenance. Am J Clin Nutr 82(1):222S–225SPubMedGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Marcella Torres
    • 1
  • Eric T. Trexler
    • 2
  • Abbie E. Smith-Ryan
    • 2
  • Angela Reynolds
    • 1
  1. 1.Department of Mathematics and Applied MathematicsVirginia Commonwealth UniversityRichmondUSA
  2. 2.Department of Exercise and Sport ScienceUniversity of North Carolina Chapel HillChapel HillUSA

Personalised recommendations