# Whole body heat balance during the human thoracic hyperthermia

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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.

### Key words

Computer simulation Finite-element methods Hyperthermia Lumped model Thoracic tumour Whole-body heat balance### List of symbols

*C*_{p}(i, j)tissue specific heat in layer

*j*of segment*i*, 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, m

^{3}s^{−1}*ERROR*output from thermoreceptors, °C

*F*_{s}(i)view factor of

*S(i)*, dimensionless*H*_{c}(i)convection heat transfer coefficient for segment

*i*, W m^{−2}°C^{−1}*H*_{r}(i)radiation heat transfer coefficient for segment

*i*, W m^{−2}°C^{−1}*i*segment number

*j*layer number in a segment

*k(i, j)*tissue thermal conductivity in layer

*j*of segment*i*, 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

^{-3}s^{-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 layer

*j*of segment*i*, 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 segment

*i*, W*Q*_{sweat, b}(i)basal evaporation rate from the skin of segment

*i*, 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 segment

*i, m*^{2}*SKINC (i)*fraction of vasoconstriction command applicable to skin of segment

*i*, dimensionaless*SKINRS (i)*fraction of all skin receptors in segment

*i*, dimensionless*SKINS (i)*fraction of sweating command applicable to skin of segment

*i*, dimensionless*SKINV (i)*fraction of vasodilation command applicable to skin of segment

*i*, 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 layer

*j*of segment*i*, °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 layer

*j*of segment*i*, m^{3}- \(\dot V\)
cardiac output or total blood volume flow rate, m

^{3}s^{−1}- \(\dot V_{pa} \)
pulmonary arterial blood volume flow rate, m

^{3}s^{−1}- \(\dot V_{pv} \)
pulmonary venous blood volume flow rate, m

^{3}s^{−1}- \(\dot V_{sa} \)
systemic arterial blood volume flow rate (cardiac output), m

^{3}s^{−1}- \(\dot V_{sv} \)
systemic venous blood volume flow rate, m

^{3}s^{−1}- \(\dot V\left( i \right)\)
blood flow rate to segment

*i*, m^{3}s^{−1}- \(\dot V\left( {i,j} \right)\)
blood flow rate to layer

*j*of segment*i*, m^{3}s^{−1}*WARMS*integrated output from skin warm receptors, °C

*w*skin wettedness, dimensionless

- ρ (
*i, j*) tissue density in layer

*j*of segment*i*, kg m^{−3}- ρ
*b* blood density, kg m

^{−3}- δ(
*i, j*) tissue electrical conductivity in layer

*j*of segment*i*- ω(
*i, j*) blood volume perfusion rate per unit mass of tissue in layer

*j*of segment*i*, m^{3}kg^{−1}s^{−1}- ω
_{b}(*i, j*) basal blood volume perfusion rate per unit mass of tissue in layer

*j*of segment*i*, m^{3}kg^{−1}s^{−1}- ϕ
relative humidity

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