Model for calculating skin perfusion from heat flux measured with a double heated transcutaneous pO₂ electrode

Abstract

The heat flux q into the skin from a heated transcutaneous pO₂ electrode depends on the blood flow rate in the skin. Previous studies by Jaszczak et al. have provided a model for calculating the ‘areic’ blood flow rate, i.e. the blood flow rate divided by surface area. The calculation requires measuring the heat flux with and without blood flow, q₁ and q₂, and knowing the core temperature under the electrode T_c. The present model provides an equation for calculating the ‘volumic’ blood flow rate, i.e. the blood flow rate divided by skin volume: where a is the thermal diffusivity of the skin (0.13 10^-6 m²/s), l_c is a depth parameter, and R is the ratio (q₁-q₂)/q₂. l_C, T_C, and q₂ are related by: q₂=· (T_E - T_C)/l_C where T_E is the electrode temperature and X is the thermal conductivity of the skin (0.544 W/(m K). If standard values for l_C and T_C are used, measuring the heat flux after blood flow is stopped becomes superfluous.

The experimental heat flux data of Jaszczak et al. measured with a special double thermostattet pO₂ electrode at 45 °C placed on the volar side of the forearm provided a calculated blood flow of 64 (ml/min)/(100 ml) with the present model. This is about 60 % higher than their value measured with the ¹³³Xe washout technique, but all approximations made in the present model tend to give too low rather than too high values.

Key-words:

• calculation algorithms
• mathematical model