A Modification of Murray's Law for Shear-Thinning Rheology

摘要: This study reformulates Murray's well-known principle of minimum work as applied to the cardiovascular system include effects shear-thinning rheology blood. The viscous behavior is described using extended modified power law (EMPL), which a time-independent, but rheological constitutive equation. resulting minimization problem solved numerically for typical parameter ranges. non-Newtonian analysis still predicts classical cubic diameter dependence volume flow rate and branching law. current also constant wall shear stress throughout vascular tree, albeit with numerical value about 15-25% higher than Newtonian analysis. Thus, experimentally observed deviations from or predicted in vasculature cannot likely be attributed blood's behavior. Further differences between predictions analyses are highlighted, limitations discussed. Finally, range limits applicability results human arterial tree