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Whole body heat balance during the human thoracic hyperthermia

  • Biomedical Engineering
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Abstract

A whole-body heat balance model during hyperthermia is developed. In the model, local temperature is calculated using a finite-element model. The perfusion blood, along with its energy, is circulated to the rest of the body, where the heat dissipation is calculated using lumped segments. With this model the effects of the electromagnetic power dosage on the body core temperature and the responses of other body elements are analysed for the human thoracic hyperthermia.

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Abbreviations

C p(i, j):

tissue specific heat in layerj of segmenti, J kg−1 °C−1

C pb :

blood specific heat, J kg−1 °C−1

COLDS :

integrated output from skin cold receptors, °C

DILAT :

total efferent skin vasodilation command, m3 s−1

ERROR :

output from thermoreceptors, °C

F s(i):

view factor ofS(i), dimensionless

H c(i):

convection heat transfer coefficient for segmenti, W m−2 °C−1

H r(i):

radiation heat transfer coefficient for segmenti, W m−2 °C−1

i :

segment number

j :

layer number in a segment

k(i, j) :

tissue thermal conductivity in layerj of segmenti, W m−1 °C−1

\(\dot m_b \) :

blood mass perfusion rate per unit volume of tissue;\(\dot m_b = \rho _b \omega \rho _t \), kgm-3s-1

\(\dot m_b {{C_{pb} } \mathord{\left/ {\vphantom {{C_{pb} } {\rho _t }}} \right. \kern-\nulldelimiterspace} {\rho _t }}\) :

in W kg−1 °C−1

N :

total number of segments

P skin :

saturation pressure of water at skin temperature, torr

P air :

partial pressure of water vapour at air temperature, torr

Q cond :

heat transfer due to conduction, W

Q conv :

convective heat transfer at a skin surface, W

Q em, body :

total body EM energy deposition, W

Q em :

rate of electromagnetic energy deposition, W

Q ‴em :

EM energy deposition per unit volume of tissue, W m−3

Q met, body :

total body metabolic rate, W

Q met, b(i,j):

basal metabolic rate in layerj of segmenti, W

Q ‴met :

metabolic heat per unit volume of tissue, W m−3

Q met :

rate of metabolic heating, W

Q per f :

heat transfer due to blood perfusion, W

Q rad :

radiation heat transfer at a skin surface, W

Q res :

respiration heat transfer, W

Q res, l :

latent (insensible) respiration heat transfer, W

Q res, d :

dry (sensible) respiration heat transfer, W

Q ‴res :

respiration heat transfer per unit volume of lung tissue, W m−3

Q sweat(i):

heat transfer due to sweating from the skin of segmenti, W

Q sweat, b(i):

basal evaporation rate from the skin of segmenti, W

Q work :

heating by muscle work, W

R :

thermal resistance, °C W−1

r :

radius, m

r c :

radius at mid-volume, m

S(i) :

surface area of segmenti, m 2

SKINC (i) :

fraction of vasoconstriction command applicable to skin of segmenti, dimensionaless

SKINRS (i) :

fraction of all skin receptors in segmenti, dimensionless

SKINS (i) :

fraction of sweating command applicable to skin of segmenti, dimensionless

SKINV (i) :

fraction of vasodilation command applicable to skin of segmenti, dimensionless

STRIC :

total efferent skin vasoconstriction command, dimensionless

SWEAT :

total efferent sweat command, W

T sur :

surrounding temperature, °C

T a :

arterial temperature, °C

T air :

air temperature, °C

T(i, j) :

tissue temperature in layerj of segmenti, °C

T pa :

pulmonary arterial temeprature, °C

T pv :

pulmonary venous temperature, °C

T sa :

systemic arterial temperature, °C

T sv :

systemic venous temperature, °C

\(\dot V\left( {i,j} \right)\) :

tissue volume in layerj of segmenti, m3

\(\dot V\) :

cardiac output or total blood volume flow rate, m3 s−1

\(\dot V_{pa} \) :

pulmonary arterial blood volume flow rate, m3 s−1

\(\dot V_{pv} \) :

pulmonary venous blood volume flow rate, m3 s−1

\(\dot V_{sa} \) :

systemic arterial blood volume flow rate (cardiac output), m3 s−1

\(\dot V_{sv} \) :

systemic venous blood volume flow rate, m3 s−1

\(\dot V\left( i \right)\) :

blood flow rate to segmenti, m3 s−1

\(\dot V\left( {i,j} \right)\) :

blood flow rate to layerj of segmenti, m3 s−1

WARMS :

integrated output from skin warm receptors, °C

w :

skin wettedness, dimensionless

ρ (i, j):

tissue density in layerj of segmenti, kg m−3

ρb :

blood density, kg m−3

δ(i, j):

tissue electrical conductivity in layerj of segmenti

ω(i, j):

blood volume perfusion rate per unit mass of tissue in layerj of segmenti, m3 kg−1 s−1

ωb(i, j):

basal blood volume perfusion rate per unit mass of tissue in layerj of segmenti, m3 kg−1 s−1

ϕ:

relative humidity

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Authors and Affiliations

  1. Department of Mechanical Engineering & Applied Mechanics, The University of Michigan, 48109, Ann Arbor, MI, USA

    Zheng Lou & Wen-Jei Yang

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  1. Zheng Lou
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  2. Wen-Jei Yang
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Lou, Z., Yang, WJ. Whole body heat balance during the human thoracic hyperthermia. Med. Biol. Eng. Comput. 28, 171–181 (1990). https://doi.org/10.1007/BF02441774

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  • DOI: https://doi.org/10.1007/BF02441774

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