Microvascular dysfunction induces a hyperdynamic circulation; a mathematical exploration

Background: The discordance between the macrocirculation and microcirculation in septic shock has been recognised but never explained. I present a novel mathematical hypothesis as to how heterogenous microcirculatory flow distribution directly induces a hyperdynamic circulation and how elevated central venous pressure induces microcirculatory dysfunction. Methods: I explore the tube law and modified Poiseuille resistance for compliant blood vessels. Using these equations a new equation is developed incorporating time constants, elastance of the vessel, unstressed volume and wave reflections that demonstrates the relationship between volume of a microcirculatory vessel and total flow through it. Results: The relationship is demonstrated to be constant at zero until the unstressed volume is reached after which it increases exponentially. By considering n of these vessels in parallel, I demonstrate that the summed flow is minimised when flow is equally distributed among the n vessels, while it is maximised when all flow goes through one vessel alone, thereby demonstrating that heterogenous microvascular perfusion leads to increased total flow. It is shown that if conditions of wave reflection are right then a hyperdynamic circulation with high cardiac output develops. It is also demonstrated that high central venous pressure increases wave reflections and necessarily leads to microvascular perfusion heterogeneity if cardiac output is to be maintained. Conclusions: Microvascular impairment in septic shock directly leads to a hyperdynamic circulation with high cardiac output. High central venous pressures impair the microcirculation. Decades of clinical findings can now be explained mathematically. Implications for hemodynamic therapy for septic shock are discussed.