2015
DOI: 10.1007/s11538-015-0089-1
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Oscillations and Multiple Equilibria in Microvascular Blood Flow

Abstract: We investigate the existence of oscillatory dynamics and multiple steady-state flow rates in a network with a simple topology and in vivo microvascular blood flow constitutive laws. Unlike many previous analytic studies, we employ the most biologically relevant models of the physical properties of whole blood. Through a combination of analytic and numeric techniques, we predict in a series of two-parameter bifurcation diagrams a range of dynamical behaviors, including multiple equilibria flow configurations, s… Show more

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Cited by 8 publications
(14 citation statements)
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“…Such behaviors could even be reproduced in in vitro artificial capillary networks through which blood was pumped 72 . The dynamic system has been studied and it has been shown to have several equilibria 28,73‐75 . These equilibria stability has been studied, showing different types of behaviors even for simple bifurcations 75 .…”
Section: Resultsmentioning
confidence: 99%
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“…Such behaviors could even be reproduced in in vitro artificial capillary networks through which blood was pumped 72 . The dynamic system has been studied and it has been shown to have several equilibria 28,73‐75 . These equilibria stability has been studied, showing different types of behaviors even for simple bifurcations 75 .…”
Section: Resultsmentioning
confidence: 99%
“…The dynamic system has been studied and it has been shown to have several equilibria 28,73‐75 . These equilibria stability has been studied, showing different types of behaviors even for simple bifurcations 75 . When the nonlinear plasma skimming law is included, the oscillating states could be related to these observations.…”
Section: Resultsmentioning
confidence: 99%
“…Therefore, analysing these models has been an area of interest for biologists and mathematicians alike. For some recent investigations; see [1], [6], [7], [16], [20], [30]- [32], [35]. This is an extension of our preliminary work that appeared in Proceedings of the 26th IEEE Chinese Control and Decision Conference (CCDC), pp.…”
Section: Introductionmentioning
confidence: 81%
“…For this, we fix the other parameters as follows: γ = 0.3, n = 10, and vary β in the range [0.5, 1]. For each value of β in this range, we compute the values of τ c , τ suf f and τ noc , which define the boundaries of the necessary and sufficient condition (16), sufficient condition (18) and the condition (19) for non-oscillatory convergence. This plot is presented in Fig.…”
Section: ) Mackey-glass Equationmentioning
confidence: 99%
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