Dermal Heat Transport Analysis for Transcutaneous O 2 Measurement

Heat from a transcutaneous oxygen electrode is transmitted locally to the blood beneath it causing a shift in the HbO 2 dissociation curve. This increases the local PO 2 , and allows a measurable PO 2 , at the skin surface. The temperature effect on the HbO 2 , curve must be accounted for in in vivo calibration of Ptco 2 , 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: T 8 = ± where Z = ± = 0.17 T 8 , = capillary blood temperature T 1 = 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 T 1 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 T 8 , 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.