The Development of a Mathematical Human Thermal Model

  • Eugene H. Wissler


Human thermal behavior is determined by the combined effect of physiological and physical phenomena. Physiological factors discussed separately in previous chapters, act in a coordinated complementary manner to regulate bodily temperature. Institution provides qualitative understanding of some interactions, but an analytical approach is required to develop a quantitative understanding of human thermal regulation.


Human Thermal Model Mean Body Density Respiratory Heat Loss Metabolic Heat Generation Whole-body Metabolic Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References and Supplementary Reading

  1. Asmussen E, Nielsen M (1946) Studies on the regulation of respiration in heavy work. Acta Physiol Scand 12:171–188CrossRefGoogle Scholar
  2. Åstrand P-O, Rodahl K (1970) Textbook of work physiology. McGraw-Hill, New YorkGoogle Scholar
  3. Babb TG, Wyrick BL, DeLorey DS, Chase PJ, Mabel Y, Feng MY (2008) Fat distribution and end-expiratory lung volume in lean and obese men and women. Chest 134:704–711CrossRefPubMedGoogle Scholar
  4. Ball SD, Altene TS, Swan PD (2004) Comparison of anthropometry to DXA: a new prediction equation for men. Eur J Clin Nutr 58:1525–1531CrossRefPubMedGoogle Scholar
  5. Bittel JHM (1987) Heat debt as an index for cold adaptation in men. J Appl Physiol 62:1627–1634CrossRefGoogle Scholar
  6. Bittel JHM, Nonotte-Varly C, Liecchi-Gonnot GH, Savourey GLMJ, Hanniquet AM (1988) Physical fitness and thermoregulatory reactions in a cold environment in men. J Appl Physiol 65:1984–1989CrossRefPubMedGoogle Scholar
  7. Borisov BK, Marei AN (1974) Weight parameters of adult human skeleton. Health Phys 27:224–229PubMedGoogle Scholar
  8. Brozek J, Grande F, Anderson T, Keys A (1963) Densitometric analysis of body composition: revisions of some quantitative assumptions. Ann NY Acad Sci 110:113–140CrossRefGoogle Scholar
  9. Budd GM, Warhaft N (1966) Body temperature, shivering, blood pressure and heart rate during a standard cold stress in Australia and Antarctica. J Physiol 186:216–232CrossRefPubMedGoogle Scholar
  10. Budd GM, Brotherhood JR, Beasley FA, Hendrie AL, Jeffery SE, Lincoln GJ, Solaga AT (1993) Effects of acclimatization to cold baths on men's responses to whole-body cooling in air. Eur J Appl Physiol 67:438–449CrossRefGoogle Scholar
  11. Carroll JF, Chiapa AL, Rodriquez M, Phelps DR, Cardarelli KM, Vishwanatha JK, Bae S, Cardarelli R (2008) Visceral fat, waist circumference, and BMI: impact of race/ethnicity. Integrativ Physiol 16:600–607Google Scholar
  12. Christ A, Kainz W, Hahn EG, Honegger K, Zefferer M, Neufeld E, Rascher W, Janka R, Bautz W, Chen J, Kiefer B, Schmitt P, Hollenbach H-P, Shen J, Oberle M, Szczerba D, Kam A, Guag JW, Kuster N (2010) The virtual family – development of surface based anatomical models of two adults and two children for dosimetric simulations. Phys Med Biol 55:N23–N38CrossRefGoogle Scholar
  13. Clarys JP, Martin AD, Drinkwater DT, Marfell-Jones MJ (1987) The skinfold: myth and reality. J Sports Sci 5(1):3–33CrossRefGoogle Scholar
  14. Davidson LE, Wang J, Thornton JC, Kaleem Z, Silva-Palacios F, Pierson RN, Heymsfield SB, Gallagher D (2011) Predicting fat percent by skinfolds in racial groups: Durnin and Womersley revisited. Med Sci Sports Exerc 43:542–549CrossRefPubMedGoogle Scholar
  15. de Hanson RG (1974) Respiratory heat loss at increased core temperature. J Appl Physiol 37:103–107CrossRefGoogle Scholar
  16. Dempster P, Aitkens S (1995) A new air displacement method for the determination of human body composition. Med Sci Sports Exerc 27:1692–1697CrossRefGoogle Scholar
  17. Dube P-A, Imbeau D, Dubeau D, Lebel L, Kolus A (2015) Removing the thermal component from heart rate provides an accurate \( \dot{\mathrm{V}}{\mathrm{O}}_2 \) estimation in forest work. Appl Ergon 54:148–157CrossRefGoogle Scholar
  18. Durnin JVGA, Womersley J (1974) Body fat assessed from total body density and its estimation from skinfold thickness: measurements on 481 men and women aged 16 to 72 years. Br J Nutr 32:77–79CrossRefGoogle Scholar
  19. Elia M (1992) Organ and tissue contribution to metabolic rate. In: Kinney JM, Tucker HN (eds) Energy metabolism: tissue determinants and cellular corollaries. Raven Press, New York, pp 61–77Google Scholar
  20. Ellis KJ (2000) Human body composition: in vivo methods. Physiol Rev 80:649–680CrossRefGoogle Scholar
  21. Eston RG, Rowlands AV, Charlesworth S, Davies A, Hoppitt T (2005) Prediction of DXA-determined whole body fat from skinfolds: importance of including skinfolds from the thigh and calf in young, healthy men and women. Eur J Clin Nutr 59:695–702CrossRefGoogle Scholar
  22. Fanger PO (1970) Thermal comfort. Danish Technical Press, CopenhagenGoogle Scholar
  23. Farnworth B, Sweeney D (2016) The testing of immersion suit thermal protection: Can we rely on the thermal manikin? Joint Canadian-US National Standard for Marine Lifesaving Appliances: Immersion Suit. Report prepared under Underwriters Laboratories Contract Number 2016-01Google Scholar
  24. Forbes GB, Brown MR, Griffiths HLJ (1988) Arm muscle plus bone area: anthropometry and CAT scan compared. Am J Clin Nutr 47:9290931CrossRefGoogle Scholar
  25. Gabathuler M, Marty CA, Hanselmann KW (2001) Parameterization of incoming longwave radiation in high mountain environments. Phys Geogr 22:99–114CrossRefGoogle Scholar
  26. Gagnon D, Kenny GP (2011) Exercise-rest cycles do not alter local and whole-body heat loss responses. Am J Physiol Regul Inter Comp Physiol 300:R958–R968CrossRefGoogle Scholar
  27. Gagnon D, Jay O, Kenny GP (2013) The evaporative requirement for heat balance determines whole-body sweat rate during exercise under conditions permitting full evaporation. J Physiol 591(11):2925–2935CrossRefPubMedGoogle Scholar
  28. Gallagher D, Belmonte D, Deurenberg P, Wang Z, Krasnow N, Sunyer FX, Heymsfield SB (1998) Organ-tissue mass measurement allows modeling of REE and metabolically active tissue mass. Am J Physiol 275 (Endocrinol Metab 38): E249–E258CrossRefGoogle Scholar
  29. Golden FSC, Hervey GR (1981) The ‘after-drop’ and death after rescue from immersion in cold water. In: Adam JM (ed) Hypothermia ashore and afloat. Aberdeen University Press, Aberdeen, pp 37–56Google Scholar
  30. Haurwirz B (1946) Insolation in relation to cloud density. J Meteor 3:123–124CrossRefGoogle Scholar
  31. Haurwitz B (1945) Insolation in relation to cloudiness and cloud density. J Meteor 2:154–166CrossRefGoogle Scholar
  32. Hayes PA, Cohen J, Sowood PJ (1987) Subcutaneous fat distribution of adult males and females measured by nuclear magnetic resonance RAF. Inst Aviat Med IAM Report 655Google Scholar
  33. Hayes PA, Sowood PJ, Belyavin A, Cohen JB (1988) Sub-cutaneous fat thickness measured by magnetic resonance imaging, ultrasound, and calipers. Med Sci Sports Exerc 20:303–309CrossRefPubMedGoogle Scholar
  34. Heymsfield SB, Lohman T, Wang Z, Going SB (2005) Human body composition, 2nd edn. Human Kinetics Publishers, ChampaignGoogle Scholar
  35. Heymsfield SB, Gallagher D, Mayer L, Beetsch J, Pietrobelli A (2007) Scaling of human body composition to stature: new insights into body mass index. Am J Clin Nutr 86:82–91CrossRefPubMedGoogle Scholar
  36. Himes JH, Roche AF, Siervogel RM (1979) Compressibility of skinfolds and the measurement of subcutaneous fat. Am J Clin Nutr 32:1734–1740CrossRefPubMedGoogle Scholar
  37. Illner K, Brinkmann G, Heller M, Bosy-Westphal MMJ (2000) Metabolically active components of fat free mass and resting energy expenditure in nonobese adults. Am J Physiol Endocrinol Metab 278:E308–E315CrossRefPubMedGoogle Scholar
  38. Ineichen P, Guisan O, Perez R (1990) Ground-reflected radiation and albedo. Solar Energy 44:207–214CrossRefGoogle Scholar
  39. Jackson AS, Stanforth PR, Gagnon J, Rankinen T, Leon AS, Rao DC, Skinner JS, Bouchard C, Wilmore JH (2002) The effect of sex, age and race on estimating body fat from body mass index: the Heritage Family Study. Int J Obes (Lond) 26:789–796CrossRefGoogle Scholar
  40. Janssen I, Heymsfield SB, Wang Z, Ross R (2000) Skeletal muscle mass and distribution in 468 men and women aged 18–88 yr. J Appl Physiol 89:81–88CrossRefPubMedGoogle Scholar
  41. Kantor N, Unger J (2011) The most problematic variable in the course of human-biometeorological comfort assessment – the mean radiant temperature. Cent Eur J Geosci 3:90–100Google Scholar
  42. Kim J, Heshka S, Gallagher D, Kotler DP, Mayer L, Albu J, Shen W, Freda PU, Heymsfield SB (2004) Intermuscular adipose tissue-free skeletal muscle mass; estimation by dual-energy X-ray absorptiometry in adults. J Appl Physiol 97:655–670CrossRefGoogle Scholar
  43. Kubaha K, Fiala D, Toftum J, Taki AH (2004) Hunan projected area factors for detailed direct and diffuse solar radiation analysis. Int J Bioeteorol 49:113–129CrossRefGoogle Scholar
  44. Kuehn LA, Stubbs RA, Weaver RS (1970) Theory of the globe thermometer. J Appl Physiol 29:750–757CrossRefGoogle Scholar
  45. Lanini F (2010) Division of Global radiation into direct radiation and diffuse radiation. Master’s Thesis, University of Bern (Available on the internet)Google Scholar
  46. Lee S, Janssen I, Ross R (2004) Interindividual variation in abdominal subcutaneous and visceral adipose tissue: influence of measurement site. J Appl Physiol 97:948–954CrossRefGoogle Scholar
  47. Liu BHY, Jordan RC (1963/1960) The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Solar Energy 4:1–19CrossRefGoogle Scholar
  48. Magarreiro C, Brto MC, Soares PMM (2014) Assessment of diffuse radiation models for cloudy atmospheric conditions in the Azores region. Solar Energy 108:538–547CrossRefGoogle Scholar
  49. Mariak EZ, White MD, Lewko J, Lyson T, Piekarski P (1999) Direct cooling of the human brain by heat loss from the upper respiratory tract. J Appl Physiol 87:1609–1613CrossRefGoogle Scholar
  50. Martin AD, Ross WD, Drinkwater DT, Clarys JP (1985) Prediction of body fat by skinfold caliper: assumptions and cadaver evidence. Int J Obes 9(Suppl 1):31–39Google Scholar
  51. Mazess RB, Barden H, Bisek J, Hanson J (1990) Dual energy X-ray absorptiometry for total body and regional bone mineral and soft-tissue composition. Am J Clin Nutr 51:1106–1112CrossRefGoogle Scholar
  52. McCutchan JW, Taylor CL (1951) Respiratory heat exchange with varying temperature and humidity of inspired air. J Appl Physiol 4:121–135CrossRefGoogle Scholar
  53. Miller R, Ross WD, Rapp A, Roede M (1980) Sex chromosome aneuploidy and anthropometry: a new proportionality assessment using the phantom stratagem. Am J Med Genet 5:125–135CrossRefGoogle Scholar
  54. Mitchell JW, Nadel ER, Stolwijk JAJ (1972) Respiratory weight loss during exercise. J Appl Physiol 32:474–476CrossRefPubMedGoogle Scholar
  55. Mitsiopoulos N, Baumgartner RN, Heymsfield SB, Lyons W, Gallagher D, Ross R (1998) Cadaver validation of skeletal muscle measurement by magnetic resonance imaging and computerized tomography. J Appl Physiol 85:115–122CrossRefGoogle Scholar
  56. Müller MJ, Wang J, Heymsfield SB, Schautz B, Bosy-Westphal (2013) Advance in the understanding of specific metabolic rates of major organs and tissue in humans. Curr Opin Clin Nutr Metab Care 16:501–508Google Scholar
  57. Notley SR, Fullagar HHK, Lee DS, Matsuda-Nakamura M, Peoples GE, Taylor NAS (2014) Revisiting ventilatory and cardiovascular predictions of whole-body metabolic rate. J Occup Environ Med 56(2):214–223CrossRefGoogle Scholar
  58. Nuckols ML (2013) Integration of active and passive thermal technologies in cold weather apparel and thermo-physiological model validation with localized active heating in cold water diving garments. Final report submitted to the Office of Naval Research, Research Grants N00014-11-1-0290 and N00014-13-1-0140, December 31, 2013Google Scholar
  59. Nunneley SA, Wissler EH, Allan JR (1985) Immersion cooling: effect of clothing and skinfold thickness. Aviat Space Environ Med 56:1177–1183Google Scholar
  60. O’Connor DP, Bray MS, McFarlin BK, Sailor MH, Ellis KJ, Jackson AS (2010) Generalized equations for estimating DXA percent fat of diverse young women and men: the TIGER Study. Med Sci Sports Exerc 42:1959–1965, 2010CrossRefPubMedGoogle Scholar
  61. O’Donovan G, Thomas EL, McCarthy JP, Fitzpatrick J, Durighel G, Mehta S, Morin SX, Goldstone AP, Bell JD (2009) Fat distribution in men of different waist girth, fitness level and exercise habit. Int J Obes (Lond) 33:1356–1362CrossRefGoogle Scholar
  62. Pandolf KB, Givoni B, Goldman RF (1977) Predicting energy expenditure with loads while standing or walking very slowly. J Appl Physiol 43:577–581CrossRefGoogle Scholar
  63. Park S, Tuller SE (2011a) Human body area factors for radiation exchange analysis: standing and walking postures. Int J Biometeorol 55:695–709CrossRefGoogle Scholar
  64. Park S, Tuller SE (2011b) Comparison of human radiation exchange models in outdoor areas. Theor Appl Climatol 105:357–370CrossRefGoogle Scholar
  65. Rahman M, Temple JR, Breitkopf CR, Berenson AB (2009) Racial differences in body fat distribution among reproductive-aged women. Metab Clin Exp 58:1329–1337CrossRefPubMedGoogle Scholar
  66. Reindl DT, Beckman JW, Taylor CLWA, Duffie JA (1990) Diffuse fraction correlations. Solar Energy 45:1–7CrossRefGoogle Scholar
  67. Reno MJ, Hansen CW, Stein JS (2012) Global horizontal irradiance clear sky models: Implementation and analysis. Report SAND2012-2389, Sandia National LaboratoriesGoogle Scholar
  68. Riggs BL, Melton LJ III, Robb RA, Camp JJ, Atkinson EJ, Peterson JM, Rouleau PA, McCollough CH, Bouxsein ML, Khosla S (2004) Population-based study of age and sex differences in bone volumetric density, size, geometry and structure at different skeletal sites. J Bone Miner Res 19:1945–1953CrossRefGoogle Scholar
  69. Ross WD, Marfell-Jones MJ (1991) Kinanthropometry. In: MacDougall JD, Wenger HA, Green HJ (eds) Physiological testing of the high-performance athlete. Human Kinetics, Champaign, IL, pp 2223–2283Google Scholar
  70. Ruan XY, Gallaghher D, Harris T, Albu J, Heymsfield S, Kuznia P, Heshka S (2007) Estimating whole body intermuscular adipose tissue from single cross-sectional magnetic resonance images. J Appl Physiol 102:748–754CrossRefGoogle Scholar
  71. Saltin B, Gagge AP, Bergh U, Stolwijk JAJ (1972) Body temperatures and sweating during exhaustive exercise. J Appl Physiol 32:635–643CrossRefPubMedGoogle Scholar
  72. Sardinha LB, Lohman TG, Teixeira PJ, Guedes DP, Going SV (1998) Comparison of air displacement plethysmography with dual-energy X-ray absorptiometry and 3 field methods for estimating body composition in middle-aged men. Am J Clin Nutr 68:786–793CrossRefGoogle Scholar
  73. Savourey G, Bittel J (1998) Thermoregulatory changes in he cold-induced by physical training in humans. Eur J Appl Physiol 78:379–384CrossRefGoogle Scholar
  74. Shen W, Punyanitya M, Wang ZM, Gallagher D, Onge M-P, Albu J, Heymsfield SB, Heshka S (2004) Total body skeletal muscle and adipose tissue volumes: estimation from single abdominal cross-sectional image. J Appl Physiol 97:2333–2338CrossRefGoogle Scholar
  75. Siri WE (1956) In: Lawrence JH, Tobias CA (eds) Advances in biological and medical physics. Academic, New York, pp 239–280Google Scholar
  76. Siri WE (1961) Body composition from fluid spaces and density: analysis of methods. In: Brozek J, Henschel A (eds) Techniques for measuring body composition. National Academy of Sciences National Research Council, Washington, DC, pp 223–224Google Scholar
  77. Stolwijk JAJ (1974) Expansion of a mathematical model of thermoregulation to include high metabolic rates. NAS-9-7140, Final Report BGoogle Scholar
  78. Supit I, Van Kappel RR (1998) A simple method to estimate global radiation. Solar Energy 63:147–160CrossRefGoogle Scholar
  79. Thorsson S, Lindberg F, Eliasson I, Holmer B (2007) Different methods for estimating the mean radiant temperature in an outdoor urban setting. Int J Climatol 27:1983–1993CrossRefGoogle Scholar
  80. Todd G, Gordon CJ, Groeller H, Taylor NAS (2014) Does intramuscular thermal feedback modulate eccrine sweating in exercising humans? Acta Physiol 212:86–96CrossRefGoogle Scholar
  81. Usui C, Takahashi E, Gando Y, Sanada K, ka J, Miyachi M, Tabata I, Higuchi M (2008) Resting energy expenditure can be assessed by dual-energy X-ray absorptiometry in women regardless of age and fitness. Eur J Clin Nutr 63:529–536CrossRefPubMedGoogle Scholar
  82. Vallerand AL, Savourey G, Bittel JHM (1992) Determination of heat debt in the cold: partitional calorimetry vs. conventional methods. J Appl Physiol 72:1380–1385CrossRefPubMedGoogle Scholar
  83. van der Ploeg GE, Gunn SM, Withers RT, Modra AC (2003) Use of anthropometric variables to predict relative fat determined by a four-compartment body composition model. Eur J Clin Nutr 57:1009–1016CrossRefPubMedGoogle Scholar
  84. Varene P (1986) Computation of respiratory heat exchanges. J Appl Physiol 61:1586–1589CrossRefPubMedGoogle Scholar
  85. Wang Z, Heshka S, Gallagher D, Boozer CN, Kotler DP, Heymsfield SB (2000) Resting energy expenditure-fat-free mass relationship: new insights provided by body composition modeling. Am J Physiol Endocrinol Metab 279:E539–E545CrossRefPubMedGoogle Scholar
  86. Wilmore JH (1969) A simplified method for determining residual lung volume. J Appl Physiol 26:96–100CrossRefGoogle Scholar
  87. Wissler EH (1984) Mathematical simulation of human thermal behavior using whole body models. In: Shitzer A, Eberhart RC (eds) Heat transfer in biology and medicine. Plenum Press, New YorkGoogle Scholar
  88. Wissler EH (2003) Probability of survival during accidental immersion in cld water. Aviat Space Environ Med 74:47–55Google Scholar
  89. Wissler EH (2014) Cold-exposure survival and modeling offshore antiexposure garments. In: Wang F, Gao C (eds) Protective clothing: managing thermal stress. Woodhead Publishing, WalthamGoogle Scholar
  90. Xu X, Turner CA, Santee WR (2011) Survival time prediction in marine environments. J Therm Biol 36:340–335CrossRefGoogle Scholar
  91. Xu X, Rioux TP, MacLeod T, Patel T, Rome MN, Potter AW (2017) Measured body composition and geometrical data of four “virtual family” members for thermoregulatory modeling. Int J Biometeorol 61:477–486CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Eugene H. Wissler
    • 1
  1. 1.Department of Chemical EngineeringThe University of Texas at AustinAustinUSA

Personalised recommendations