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Whole body heat balance during the human thoracic hyperthermia

  • Zheng Lou
  • Wen-Jei Yang
Biomedical Engineering

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.

Key words

Computer simulation Finite-element methods Hyperthermia Lumped model Thoracic tumour Whole-body heat balance 

List of symbols

Cp(i, j)

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

Cpb

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

Fs(i)

view factor ofS(i), dimensionless

Hc(i)

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

Hr(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

Pskin

saturation pressure of water at skin temperature, torr

Pair

partial pressure of water vapour at air temperature, torr

Qcond

heat transfer due to conduction, W

Qconv

convective heat transfer at a skin surface, W

Qem, body

total body EM energy deposition, W

Qem

rate of electromagnetic energy deposition, W

Qem

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

Qmet, body

total body metabolic rate, W

Qmet, b(i,j)

basal metabolic rate in layerj of segmenti, W

Qmet

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

Qmet

rate of metabolic heating, W

Qper f

heat transfer due to blood perfusion, W

Qrad

radiation heat transfer at a skin surface, W

Qres

respiration heat transfer, W

Qres, l

latent (insensible) respiration heat transfer, W

Qres, d

dry (sensible) respiration heat transfer, W

Qres

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

Qsweat(i)

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

Qsweat, b(i)

basal evaporation rate from the skin of segmenti, W

Qwork

heating by muscle work, W

R

thermal resistance, °C W−1

r

radius, m

rc

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

Tsur

surrounding temperature, °C

Ta

arterial temperature, °C

Tair

air temperature, °C

T(i, j)

tissue temperature in layerj of segmenti, °C

Tpa

pulmonary arterial temeprature, °C

Tpv

pulmonary venous temperature, °C

Tsa

systemic arterial temperature, °C

Tsv

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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Copyright information

© IFMBE 1990

Authors and Affiliations

  • Zheng Lou
    • 1
  • Wen-Jei Yang
    • 1
  1. 1.Department of Mechanical Engineering & Applied MechanicsThe University of MichiganAnn ArborUSA

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