Coarctation of the aorta—a theoretical and experimental analysis of the effects of a centrally located arterial stenosis

Abstract

Aortic coarctation is a local constriction of the aorta that may severely affect haemodynamics. It is therefore important to quantify these effects. Using Bernoulli's equation and the momentum theorem, the pressure drop is described including the pressure recovery distal to the coarctation and the effects of collateral flow; both laminar and turbulent. Assuming the coarctation and collaterals to be stiff, a quadratic relationship between flow and pressure drop is expected for flow through the coarctation and for turbulent collateral flow. For laminar collateral flow, a linear relationship is expected. The coarctation flow was studied in a model consisting of a rigid tube with local constriction, connected to a flooded-level tank, containing a 36 per cent by weight solution of sucrose, with a viscosity equivalent to that of blood at body temperature. The pressure drop across the constriction showed a quadratic relationship to flow in agreement with theoretical expectations. Pressure recovery in this model was very slight (0–4 mm Hg). Nine patients with aortic coarctation were catheterised. Cardiac output and pressure drop across the coarctation were measured at rest and during supine cycle exercise at two different workloads. The relationship between mean pressure drop and cardiac output tended to be either ‘parabolic’ or, in some cases, approximately linear, suggesting that the flow situation in aortic coarctation can be quantified by expressions that either linearly or quadratically relate pressure and flow.