Microvascular dysfunction induces a hyperdynamic circulation; a mathematical exploration

AbstractBackgroundThe 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.MethodsI 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.ResultsThe 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.ConclusionsMicrovascular 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.Clinical PerspectiveResearch in septic shock has focussed on two main components of the circulation; the macrocirculation and microcirculation. Very discordant findings have been observed between the two, to the point that the term ‘uncoupling’ has appeared in the literature in reference to these two circulations. Thus far nobody has put forward a satisfactory physiological explanation as to the mechanism of this discordance. There is a need to understand the physiological mechanisms to guide future attempts and research into methods of resuscitating the septic patient in order to improve circulatory function.This work provides the first theoretical mathematical groundwork as to not only how these circulations are linked, but how they directly influence one another. This sets the framework for future clinical and basic science research and helps us understand how our current resuscitation strategies may work to restore the microcirculation, and when they may start to impair it.