Estimating umbilical cord flow resistance from measurements of the whole cord

Measuring umbilical blood pressure in utero is challenging and for this reason non-invasive methods are required. However, the total vessel blood pressure drop can be estimated using numerical and empirical results by studying the mechanics of fluids in coiled and straight tubes. Two key findings emerge from such an analysis. Firstly, the total pressure drop along a vessel at a given blood flow-rate depends on both the tightness of the coils and the total cord length. Relatively short and straight cords exhibit low pressure, while long, tightly coiled cords with large width exhibit high pressure. It follows that an estimate of the pressure requires three measurements: the full cord length, its average width and number of coils. Using this result we propose two prototype indices for clinical testing that estimate umbilical cord flow resistance. The umbilical pressure index (P_X) and flow index (Q_X) quantify the deviation of a cord geometry from defined typical conditions by considering the steady pressure drop and flow-rate, respectively. These indices can be quickly calculated, and require only a single additional measurement to the conventional umbilical coiling index (UCI); namely the cord coiling width. Unlike the UCI, these indices are derived from blood-flow properties and provide a measure of the relative flow-resistance inherent to a cord geometry. Furthermore, the pressure index can be applied to irregularities, including loose true knots, which we show must be accounted for.