Lumped-parameter tissue temperature-blood perfusion model of a cold-stressed fingertip

Abstract

A lumped-parameter model of a fingertip is presented. The semispherical model includes the effects of heat storage, heat exchange with the environment, and heat transport by blood perfusion. The thermal insulation on the surface of the fingertip is represented by the overall heat transfer coefficient that is calculated by common engineering formulas. The model is solved analytically for the simple case of constant blood perfusion rate. The general case of variable blood perfusion rates is solved by an Euler finite difference technique. At this stage, the model does not include active control mechanisms of blood perfusion. Thus the effects of cold-induced vasodilatation have to be superimposed and are modeled by symmetrical triangular waveforms because these were found to best depict the behavior of fingers exposed to cold environments. Results of this model were compared with experimental data obtained in two separate studies. One included 60-min infrared thermograms of the dorsal surface of bare hands of sedentary subjects horizontally suspended on a fish net in a 0 degree C environment. Another study, on gloved finger temperatures, involved 0 and -6.7 degrees C environments. Fingertip (nail bed) temperatures of both these studies were compared with model predictions. Blood perfusion rates were assumed and adjusted within physiologically reasonable limits. Comparison of measured and computed temperature records showed very good conformity in both cases studied.