title: The haemodynamics of multiple sequential stenoses and the criteria for a critical stenosis.
abstract: BACKGROUND
  Occlusive arterial disease is usually multi-focal but the cumulative functional effect of multiple arterial stenoses is not fully understood. We tested the hypothesis that a non-linear pressure/flow model (DeltaP=k1Q+k2Q2) that has been validated for single stenoses is also valid for multiple stenoses arranged in series.
  
  
  METHODS
  The pressure/flow characteristics of three dissimilar modelled stenoses were measured individually and in different combinations using a hydraulic flow rig.
  
  
  RESULTS
  The combined effect of multiple stenoses fitted the non-linear model accurately (R2=0.99) and approximated to the sum of the k1 and k2 parameters for each individual stenosis. For multiple stenoses the cumulative k1 was less than the predicted and the series order of the individual stenoses consistently altered the combined effect.
  
  
  CONCLUSIONS
  A sequence of multiple stenoses is functionally equivalent to a single equivalent stenosis of greater functional severity and can be represented by a single viscous (k1) and inertial (k2) pressure loss coefficient. This finding allows the term 'critical stenosis' to be defined precisely in terms of the functional effect rather than the anatomical appearance, particularly where disease is multi-focal.
mesh_terms: D001157:Arterial Occlusive Diseases / Q000473:pathology / Q000503:physiopathology*; D001158:Arteries / Q000473:pathology; D001783:Blood Flow Velocity; D001809:Blood Viscosity; D003251:Constriction, Pathologic; D006439:Hemodynamics; D018056:Hemorheology; D006801:Humans; D008955:Models, Cardiovascular; D008961:Models, Structural