Dermal Heat Transport Analysis for Transcutaneous O₂ Measurement

Heat from a transcutaneous oxygen electrode is transmitted locally to the blood beneath it causing a shift in the HbO₂ dissociation curve. This increases the local PO₂, and allows a measurable PO₂, at the skin surface. The temperature effect on the HbO₂, curve must be accounted for in in vivo calibration of Ptco₂, data. To do this, the capillary blood temperature beneath the electrode must be known. A heat balance is written around the capillary blood with heat being conducted in from the electrode and carried out by two means: conduction to deep tissue; and transport away by the flowing capillary blood. The following equation is the steady state solution of the heat transport problem:

T₈ = ±

where Z = ± = 0.17

T₈, = capillary blood temperature

T₁ = electrode temperature

T_o = body temperature

ρ = blood density

P = cutaneous perfusion

δ = dermal capillary depth

k = thermal conductivity of skin

C± = heat capacity of blood

This solution shows the capillary blood temperature may be calculated if the T₁ and T_o are measured and the physiologic constants in 2 are known. 2 is a dimensionless heat transport number which represents the relative importance of perfusion to conduction effects on the deterring T₈, and may be used as a data correlating parameter. Z = 0.17 is obtained using literature values for the physiological constants. This analysis used in conjunction with a mass transport analysis for oxygen will produce a theoretically based correlation scheme for in vivo calibration of heated transcutaneous oxygen electrodes.