Blood pressure regulation is commonly addressed in terms of local mechanisms such as vascular resistance, compliance and neurohumoral control. However, the human vasculature encompasses multiple quasi-closed flow loops under both physiological and pathological conditions. To test whether these loops could influence pressure dynamics beyond local control, we address the role of vascular topology in blood pressure regulation. Using one dimensional flow simulation models, we compared pressure dynamics in open vascular segments and closed vascular loops. We found that in open segments pressure fades away and remains spatially localized, whereas in closed loops pressure can keep circulating around the loop even if resistance in one spot is modified. Since parallel pathways within loops are dynamically coupled rather than independent, pressure changes in one place can affect the entire closed loop, allowing system level pressure patterns to emerge. Also, we assessed the temporal evolution of pressure fluctuations within closed vascular loops in normotensive and hypertensive parameter regimes, before and after loop breaking intervention. This topological approach helps clarifying why drugs or local interventions may fail to lower blood pressure in looped vascular architectures, providing a theoretical interpretation of some forms of resistant hypertension. Because disrupting a loop restores pressure relaxation, it may also help explain the disproportionate pressure changes observed after topology altering events like thrombosis, vascular surgery or embolization of arteriovenous malformations and shunts. Therefore, vascular topology can influence cardiovascular physiology by coupling local pressure flow relations to global constraints on blood pressure regulation, with physiological, pathological and clinical implications.
Blood pressure regulation is generally described in terms of local mechanisms acting along the vascular tree, including cardiac output, vascular resistance, compliance, neurohumoral control, renal feedback, etc ( ). These approaches implicitly model the vasculature as a branching, open network in which pressure gradients dissipate locally and regulation is understood through pointwise balances. This view accounts for many physiological and pharmacological observations, yet struggles to explain sclinical phenomena appearing intrinsically nonlocal. Examples include resistant hypertension despite multi-target pharmacological treatment, system-wide hemodynamic effects induced by arteriovenous shunts and disproportionate pressure changes following surgical or interventional procedures that alter vascular connectivity rather than local resistance (Narechania and Agarwal et al. 2025). These effects are attributed to parameter heterogeneity, compensatory mechanisms or unobserved regulatory pathways, while the possibility that global vascular topology itself constrains pressure dynamics is rarely addressed. Human circulation is not purely tree-like but contains multiple looped configurations, including, e.g., the Circle of Willis, collateral arterial rings, portal-systemic shunts, renal microvascular loops, arteriovenous fistulas (Nardelli et Our aim is to assess whether topology-driven global pressure modes contribute to hypertension when vascular pressure regulation is examined from a topological perspective. We analyze pressure dynamics in both open vascular segments and closed-loop configurations, introducing a distinction between locally driven flow and topology-induced modes. Closed vascular loops are treated as domains that admit global pressure modes not reducible to local sources or sinks, allowing these modes to persist even in the presence of local dissipation. We perform simulations using physiologically scaled dynamical models to compare pressure behavior in open vascular segments and closed vascular loops. We measure relaxation times and spatial patterns of pressure fluctuations to determine when pressure acts as a global mode rather than a locally regulated quantity. Then, we test whether this behavior differs between normotensive and hypertensive parameter regimes and under topology-altering procedures.
We will proceed as follows. First, we introduce the dynamical model and the assumptions underlying the representation of pressure evolution in open and closed vascular domains. Second, we analyze how vascular topology shapes pressure relaxation and global mode organization under normotensive and hypertensive parameter regimes. Finally, we examine the effects of topology-altering interventions, focusing on how loop disruption modifies pressure persistence and spatial organization.
Vascular segments were represented as one-dimensional continuous domains embedded in space but evolving only along their arclength coordinate. Two geometries were considered: an open segment of length 𝐿 with two terminal boundaries and a closed loop of identical length with periodic identification of endpoints. The spatial coordinate was denoted by 𝑥 ∈ [0, 𝐿] for the open case and by 𝑥 ∈ 𝕊 1 for the closed case. Pressure 𝑝(𝑥, 𝑡) was treated as a scalar field evolving in time 𝑡 according to conservation and constitutive relations that approximate low Reynolds number hemodynamic behavior at mesoscopic scales. Our model does not resolve individual vessels or branching but rather aims to capture effective dynamics along an equivalent path, allowing isolation of topological effects independent of detailed anatomy. All parameters were chosen to lie within physiologically plausible ranges for arterial pressure fluctuations.
Governing equations for pressure evolution. Pressure dynamics were modeled using a linear transport diffusion equation with damping and external forcing (Abramson, Bishop, and where 𝐷 > 0 is an effective pressure diffusivity with units of cm 2 s -1 , 𝛾 > 0 is a linear damping coefficient with units of s -1 and 𝑓(𝑡) is a temporally varying forcing term representing cardiac input. The diffusion term captures spatial redistribution of pressure due to vascular compliance and wave propagation at scales larger than individual vessels. The damping term represents energy loss due to viscous dissipation and peripheral outflow. The forcing term was taken to be spatially uniform to focus on intrinsic spatial organization rather than localized sources. which eliminates boundaries and enforce topological closure. These two conditions differ only in topology, not in local dynamics. All comparisons were performed using identical parameter values and forcing functions to ensure that differences arise exclusively from the presence or absence of topological closure.
Temporal forcing and parameter scaling. The forcing term was defined as a sinusoidal signal
where 𝐴 is the forcing amplitude measured in mm Hg and 𝜈 is the ca
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