Microvascular dysfunction induces a hyperdynamic circulation; a mathematical exploration

Ivor Popovich
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Abstract

Abstract 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.
微血管功能障碍诱发高动力循环;数学探索
摘要 背景:脓毒性休克的大循环和微循环之间的不协调已得到公认,但从未得到解释。我提出了一个新的数学假说,说明微循环血流分布不均是如何直接诱发高动力循环的,以及中心静脉压升高是如何诱发微循环功能障碍的。方法:我探讨了顺应性血管的管子定律和修正的普瓦休伊阻力。利用这些方程,结合时间常数、血管弹性、非受压容积和波反射,建立了一个新的方程,证明了微循环血管的容积与通过该血管的总流量之间的关系。结果:结果表明,该关系恒定为零,直到达到非应力容积,之后呈指数增长。通过平行考虑 n 个这样的血管,我证明了当流量在 n 个血管中平均分配时,总流量最小,而当所有流量仅通过一个血管时,总流量最大,从而证明了异质微血管灌注会导致总流量增加。研究表明,如果波反射条件合适,就会形成高心输出量的超动力循环。研究还证明,如果要保持心输出量,高中心静脉压会增加波反射,必然导致微血管灌注异质性。结论:脓毒性休克的微血管损伤直接导致高心输出量的高动力循环。中心静脉压力过高会损害微循环。几十年的临床发现现在可以用数学来解释了。讨论了脓毒性休克血液动力学治疗的意义。
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