Comparison of two mathematical models for the study of vascular reactivity

Abstract

This work is based on the premise that fingertip temperature variation during arterial occlusion and subsequent reperfusion can be used as an indirect measurement of vascular reactivity, commonly assessed by directly measuring flow and its temporal alterations in response to arterial occlusion. Temperature of the fingers depends on blood perfusion and environmental factors. The temperature change experienced during hyperemia or high blood flow after occlusion depend on the capacity of the occluded arteries to restore normal circulation or vascular reactivity. This work uses two mathematical models of heat transfer to show the relationship between blood flow and changes in fingertip temperature experienced during vascular occlusion and reperfusion. The models consider different levels of complexity and anatomical detail. One model is a lumped or zero-order model that neglects tissue composition; the second model (first-order model) considers a simplified anatomy of the finger and allows the analysis of tissue composition which cannot be addressed with the lumped system. Thermal models provide a way of estimating the influence of different factors on the dynamic temperature response recorded during the reactivity tests. The models intend to increase the interest of the clinical community in the thermal study of vascular reactivity compared to other techniques that focus on the analysis of flow. The differences of the calculated dynamic temperature during arterial occlusion and reperfusion using both models were analyzed. Such comparison indicated that the zero-order model suffices to analyze the temperature variation during the reactivity test, as long as the proper variation between initial condition and environmental parameters affecting the response is used.