Abstract
Until now, the measurement of carbon dioxide blood pressure is done ex vivo, using an invasive process. This paper describes a first step toward a novel noninvasive process for in vivo measurement of this pressure. As first approximation, the blood solution is modeled as a simple aqueous solution of carbon dioxide in a cylindrical rigid canalization. The drift flux model and the Young-Laplace equation are employed to describe the fluid behavior. The numerical model relates the carbon dioxide pressure through the mixture pressure and velocity. The spatial distributions of these parameters are implemented to create linear mathematical relations between the mean mixture pressure and the radial velocity variation. As long as we are interested in a noninvasive measuring of the carbon dioxide pressure, a response model is proposed to describe the ultrasound signal backscattered by the considered solution. The linear relations are applied to deduce the carbon dioxide pressure through the measured radial velocity difference, using two computing methods of ultrasound signal. A comparative study is made between them showing the more appropriate process to compute the carbon dioxide pressure.