Self-Excited Oscillations in a Collapsible Channel With Applications to Retinal Venous pulsation

Stewart, Philip; Foss, Alexander

doi:10.1017/s1446181119000117

Cited by 4 publications

(5 citation statements)

References 50 publications

(123 reference statements)

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“…To construct a theoretical model for this pressure transmission, we treat each vessel as a long collapsible tube formed by multiple regions in series, where each region represents a different external pressure environment. This approach is similar to our previous work to understand the onset of retinal venous pulsation [12,13], where we were able to deduce a threshold for the onset of large amplitude oscillations in blood pressure as a function of the (relatively normal) pressures in the eye and the brain. However, the acute CSF pressure increases considered in this study will be of significantly larger amplitude (and on a vastly different timescale) to normal CSF pressure fluctuations in the brain.…”

Section: Introductionsupporting

confidence: 57%

“…In region 1, the perturbation cross-sectional area becomes (for n ≥ 0) wavefront as shown in figure 3. Using a similar argument, we calculate the area of the compressed vessel in region 3 as 13)…”

Section: Discussionmentioning

confidence: 99%

“…There are then two boundary conditions between region 1 and 2 in the form of conservation of flux and pressure in the form 3. Using a similar argument, we calculate the area of the compressed vessel in region 3 as 13)…”

Section: Data Accessibilitymentioning

confidence: 99%

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Shock wave propagation along the central retinal blood vessels

Spelman

Stewart

2020

Proc. R. Soc. A.

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Retinal haemorrhage is often observed following brain injury. The retinal circulation is supplied (drained) by the central retinal artery (vein) which enters (leaves) the eye through the optic nerve at the optic disc; these vessels penetrate the nerve immediately after passing through a region of cerebrospinal fluid (CSF). We consider a theoretical model for the blood flow in the central retinal vessels, treating each as multi-region collapsible tubes, where we examine how a sudden change in CSF pressure (mimicking an injury) drives a large amplitude pressure perturbation towards the eye. In some cases, this wave can steepen to form a shock. We show that the region immediately proximal to the eye (within the optic nerve where the vessels are strongly confined by the nerve fibres) can significantly reduce the amplitude of the pressure wave transmitted into the eye. When the length of this region is consistent with clinical measurements, the CSF pressure perturbation generates a wave of significantly lower amplitude than the input, protecting the eye from damage. We construct an analytical framework to explain this observation, showing that repeated rapid propagation and reflection of waves along the confined section of the vessel distributes the perturbation over a longer lengthscale.

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Section: Introductionsupporting

confidence: 57%

Section: Discussionmentioning

confidence: 99%

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Shock wave propagation along the central retinal blood vessels

Spelman

Stewart

2020

Proc. R. Soc. A.

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“…Meanwhile, Stewart et al (2009) invoked the long-wave approximation and built a 1D model to study the global and local instabilities in collapsible tubes. This model was then used extensively to investigate the effect of the pre-tension of the soft wall (Stewart et al, 2010), the effect of the length of the downstream rigid segment (Xu et al, 2013(Xu et al, , 2014, and the model was also applied to understand retinal venous pulsation (Stewart and Foss, 2019).…”

Section: Re = Rementioning

confidence: 99%

Reduced modeling and global instability of finite-Reynolds-number flow in compliant rectangular channels

Wang¹,

Christov²

2022

Preprint

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Experiments have shown that flow in compliant microchannels can become unstable at a much lower Reynolds number than the corresponding flow in a rigid conduit. Therefore, it has been suggested that the wall's elastic compliance can be exploited towards new modalities of microscale mixing. While previous studies mainly focused on the local instability induced by the fluid-structure interactions (FSIs) in the system, we derive a new one-dimensional (1D) model to study the FSI's effect on the global instability. The proposed 1D FSI model is tailored to long, shallow rectangular microchannels with a deformable top wall, similar to the experiments. Going beyond the usual lubrication flows analyzed in these geometries, we include finite fluid inertia and couple the reduced flow equations to a reduced 1D wall deformation equation. Although a quantitative comparison to previous experiments is quite difficult, the behaviors of the proposed derived model show qualitatively agreement with the experimental observations, and capture several key effects. Specifically, we find the critical conditions under which the inflated base state of the 1D FSI model is linearly unstable to infinitesimal perturbations. The critical Reynolds numbers predicted are in agreement with experimental observations. The unstable modes are highly oscillatory, with frequencies close to the natural frequency of the wall, suggesting that the observed instabilities are resonance phenomena. Furthermore, during the start-up from an undeformed initial state, self-sustained oscillations can be triggered due to FSIs. Our proposed modeling framework can be applied to other microfluidic systems with similar geometric scale separation, even under different operation conditions.

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“…Meanwhile, Stewart et al (2009) invoked the long-wave approximation and built a 1-D model to study the global and local instabilities in collapsible tubes. This model was then used extensively to investigate the effect of the pretension of the soft wall (Stewart et al 2010), the effect of the length of a downstream rigid segment (Xu et al 2013(Xu et al , 2014 and the model was also applied to understand retinal venous pulsation (Stewart & Foss 2019).…”

Section: Introductionmentioning

confidence: 99%

Reduced modelling and global instability of finite-Reynolds-number flow in compliant rectangular channels

Wang

Christov²

2022

J. Fluid Mech.

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Experiments have shown that flow in compliant microchannels can become unstable at a much lower Reynolds number than the corresponding flow in a rigid conduit. Therefore, it has been suggested that the wall's elastic compliance can be exploited towards new modalities of microscale mixing. While previous studies mainly focused on the local instability induced by the fluid–structure interactions (FSIs) in the system, we derive a one-dimensional (1-D) model to study the FSI's effect on the global instability. The proposed 1-D FSI model is tailored to long, shallow rectangular microchannels with a deformable top wall, similar to the experiments. Going beyond the usual lubrication flows analysed in these geometries, we include finite fluid inertia and couple the reduced flow equations to a novel reduced 1-D wall deformation equation. Although a quantitative comparison with previous experiments is difficult, the behaviours of the proposed model show, qualitatively, agreement with the experimental observations, and capture several key effects. Specifically, we find the critical conditions under which the inflated base state of the 1-D FSI model is linearly unstable to infinitesimal perturbations. The critical Reynolds numbers predicted are in agreement with experimental observations. The unstable modes are highly oscillatory, with frequencies close to the natural frequency of the wall, suggesting that the observed instabilities are resonance phenomena. Furthermore, during the start-up from an undeformed initial state, self-sustained oscillations can be triggered by FSI. Our modelling framework can be applied to other microfluidic systems with similar geometric scale separation under different operating conditions.

show abstract

Self-Excited Oscillations in a Collapsible Channel With Applications to Retinal Venous pulsation

Cited by 4 publications

References 50 publications

Shock wave propagation along the central retinal blood vessels

Shock wave propagation along the central retinal blood vessels

Reduced modeling and global instability of finite-Reynolds-number flow in compliant rectangular channels

Reduced modelling and global instability of finite-Reynolds-number flow in compliant rectangular channels

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