Sequential deposition of microdroplets on patterned surfaces.

We use a combination of experiments and numerical modelling to investigate the influence of physico-chemical-patterned substrates on the spreading of fluid deposited as a partially overlapping sequence of droplets via inkjet printing. Our investigation is motivated by the manufacture of polymeric organic light-emitting-diode displays, where the substrate is textured with a regular array of shallow recessed regions (pixels) that are highly wetting compared to the remainder of the substrate. We examine the roles of topography and wettability patterning separately and in combination. On a substrate with uniform wettability, we find that the presence of bounding side walls enhances the local spreading and facilitates fluid coverage of the entire recessed region, but containment within the pixel is not guaranteed. In contrast, wettability patterning alone leads to robust containment of the fluid within the wetting region, but fluid coverage is reduced in the absence of side walls. Our theoretical calculations use a simplified numerical model of fluid redistribution via purely capillary effects, augmented by a Cox-Voinov spreading law. The neglect of fluid viscosity in this model means that, after an initial period of agreement, the predicted evolution is faster than in the experiments. Nonetheless, the simplified model achieves excellent predictions both for the liquid morphologies and for the conditions required for successful pixel filling on substrates with topographical and wettability variations.

Bubble propagation on a rail: a concept for sorting bubbles by size.

We demonstrate experimentally that the introduction of a rail, a small height constriction, within the cross-section of a rectangular channel could be used as a robust passive sorting device in two-phase fluid flows. Single air bubbles carried within silicone oil are generally transported on one side of the rail. However, for flow rates marginally larger than a critical value, a narrow band of bubble sizes can propagate (stably) over the rail, while bubbles of other sizes segregate to the side of the rail. The width of this band of bubble sizes increases with flow rate and the size of the most stable bubble can be tuned by varying the rail width. We present a complementary theoretical analysis based on a depth-averaged theory, which is in qualitative agreement with the experiments. The theoretical study reveals that the mechanism relies on a non-trivial interaction between capillary and viscous forces that is fully dynamic, rather than being a simple modification of capillary static solutions.

Discussion: "Comparison of Statistical Methods for Assessing Spatial Correlations Between Maps of Different Arterial Properties" (Rowland, E. M., Mohamied, Y., Chooi, K. Y., Bailey, E. L., and Weinberg, P. D., 2015, ASME J. Biomech. Eng., 137(10), p. 101003): An Alternative Approach Using Segmentation Based on Local Hemodynamics.

The biological response of living arteries to mechanical forces is an important component of the atherosclerotic process and is responsible, at least in part, for the well-recognized spatial variation in atherosusceptibility in man. Experiments to elucidate this response often generate maps of force and response variables over the arterial surface, from which the force-response relationship is sought. Rowland et al. discussed several statistical approaches to the spatial autocorrelation that confounds the analysis of such maps and applied them to maps of hemodynamic stress and vascular response obtained by averaging these variables in multiple animals. Here, we point out an alternative approach, in which discrete surface regions are defined by the hemodynamic stress levels they experience, and the stress and response in each animal are treated separately. This approach, applied properly, is insensitive to autocorrelation and less sensitive to the effect of confounding hemodynamic variables. The analysis suggests an inverse relation between permeability and shear that differs from that in Rowland et al. Possible sources of this difference are suggested.

ClinCirc identifies alterations of the circadian peripheral oscillator in critical care patients.

BackgroundAssessing circadian rhythmicity from infrequently sampled data is challenging; however, these types of data are often encountered when measuring circadian transcripts in hospitalized patients.MethodsWe present ClinCirc. This method combines 2 existing mathematical methods (Lomb-Scargle periodogram and cosinor) sequentially and is designed to measure circadian oscillations from infrequently sampled clinical data. The accuracy of this method was compared against 9 other methods using simulated and frequently sampled biological data. ClinCirc was then evaluated in 13 intensive care unit (ICU) patients as well as in a separate cohort of 29 kidney-transplant recipients. Finally, the consequences of circadian alterations were investigated in a retrospective cohort of 726 kidney-transplant recipients.ResultsClinCirc had comparable performance to existing methods for analyzing simulated data or clock transcript expression of healthy volunteers. It had improved accuracy compared with the cosinor method in evaluating circadian parameters in PER2:luc cell lines. In ICU patients, it was the only method investigated to suggest that loss of circadian oscillations in the peripheral oscillator was associated with inflammation, a feature widely reported in animal models. Additionally, ClinCirc was able to detect other circadian alterations, including a phase shift following kidney transplantation that was associated with the administration of glucocorticoids. This phase shift could explain why a significant complication of kidney transplantation (delayed graft dysfunction) oscillates according to the time of day kidney transplantation is performed.ConclusionClinCirc analysis of the peripheral oscillator reveals important clinical associations in hospitalized patients.FundingUK Research and Innovation (UKRI), National Institute of Health Research (NIHR), Engineering and Physical Sciences Research Council (EPSRC), National Institute on Academic Anaesthesia (NIAA), Asthma+Lung UK, Kidneys for Life.

Effects of sleep disturbance on dyspnoea and impaired lung function following hospital admission due to COVID-19 in the UK: a prospective multicentre cohort study.

BACKGROUND: Sleep disturbance is common following hospital admission both for COVID-19 and other causes. The clinical associations of this for recovery after hospital admission are poorly understood despite sleep disturbance contributing to morbidity in other scenarios. We aimed to investigate the prevalence and nature of sleep disturbance after discharge following hospital admission for COVID-19 and to assess whether this was associated with dyspnoea. METHODS: CircCOVID was a prospective multicentre cohort substudy designed to investigate the effects of circadian disruption and sleep disturbance on recovery after COVID-19 in a cohort of participants aged 18 years or older, admitted to hospital for COVID-19 in the UK, and discharged between March, 2020, and October, 2021. Participants were recruited from the Post-hospitalisation COVID-19 study (PHOSP-COVID). Follow-up data were collected at two timepoints: an early time point 2-7 months after hospital discharge and a later time point 10-14 months after hospital discharge. Sleep quality was assessed subjectively using the Pittsburgh Sleep Quality Index questionnaire and a numerical rating scale. Sleep quality was also assessed with an accelerometer worn on the wrist (actigraphy) for 14 days. Participants were also clinically phenotyped, including assessment of symptoms (ie, anxiety [Generalised Anxiety Disorder 7-item scale questionnaire], muscle function [SARC-F questionnaire], dyspnoea [Dyspnoea-12 questionnaire] and measurement of lung function), at the early timepoint after discharge. Actigraphy results were also compared to a matched UK Biobank cohort (non-hospitalised individuals and recently hospitalised individuals). Multivariable linear regression was used to define associations of sleep disturbance with the primary outcome of breathlessness and the other clinical symptoms. PHOSP-COVID is registered on the ISRCTN Registry (ISRCTN10980107). FINDINGS: 2320 of 2468 participants in the PHOSP-COVID study attended an early timepoint research visit a median of 5 months (IQR 4-6) following discharge from 83 hospitals in the UK. Data for sleep quality were assessed by subjective measures (the Pittsburgh Sleep Quality Index questionnaire and the numerical rating scale) for 638 participants at the early time point. Sleep quality was also assessed using device-based measures (actigraphy) a median of 7 months (IQR 5-8 months) after discharge from hospital for 729 participants. After discharge from hospital, the majority (396 [62%] of 638) of participants who had been admitted to hospital for COVID-19 reported poor sleep quality in response to the Pittsburgh Sleep Quality Index questionnaire. A comparable proportion (338 [53%] of 638) of participants felt their sleep quality had deteriorated following discharge after COVID-19 admission, as assessed by the numerical rating scale. Device-based measurements were compared to an age-matched, sex-matched, BMI-matched, and time from discharge-matched UK Biobank cohort who had recently been admitted to hospital. Compared to the recently hospitalised matched UK Biobank cohort, participants in our study slept on average 65 min (95% CI 59 to 71) longer, had a lower sleep regularity index (-19%; 95% CI -20 to -16), and a lower sleep efficiency (3·83 percentage points; 95% CI 3·40 to 4·26). Similar results were obtained when comparisons were made with the non-hospitalised UK Biobank cohort. Overall sleep quality (unadjusted effect estimate 3·94; 95% CI 2·78 to 5·10), deterioration in sleep quality following hospital admission (3·00; 1·82 to 4·28), and sleep regularity (4·38; 2·10 to 6·65) were associated with higher dyspnoea scores. Poor sleep quality, deterioration in sleep quality, and sleep regularity were also associated with impaired lung function, as assessed by forced vital capacity. Depending on the sleep metric, anxiety mediated 18-39% of the effect of sleep disturbance on dyspnoea, while muscle weakness mediated 27-41% of this effect. INTERPRETATION: Sleep disturbance following hospital admission for COVID-19 is associated with dyspnoea, anxiety, and muscle weakness. Due to the association with multiple symptoms, targeting sleep disturbance might be beneficial in treating the post-COVID-19 condition. FUNDING: UK Research and Innovation, National Institute for Health Research, and Engineering and Physical Sciences Research Council.

A microstructural model of tendon failure.

Collagen fibrils are the most important structural component of tendons. Their crimped structure and parallel arrangement within the tendon lead to a distinctive non-linear stress-strain curve when a tendon is stretched. Microstructural models can be used to relate microscale collagen fibril mechanics to macroscale tendon mechanics, allowing us to identify the mechanisms behind each feature present in the stress-strain curve. Most models in the literature focus on the elastic behaviour of the tendon, and there are few which model beyond the elastic limit without introducing phenomenological parameters. We develop a model, built upon a collagen recruitment approach, that only contains microstructural parameters. We split the stress in the fibrils into elastic and plastic parts, and assume that the fibril yield stretch and rupture stretch are each described by a distribution function, rather than being single-valued. By changing the shapes of the distributions and their regions of overlap, we can produce macroscale tendon stress-strain curves that generate the full range of features observed experimentally, including those that could not be explained using existing models. These features include second linear regions occurring after the tendon has yielded, and step-like failure behaviour present after the stress has peaked. When we compare with an existing model, we find that our model reduces the average root mean squared error from 4.53MPa to 2.29MPa, and the resulting parameter values are closer to those found experimentally. Since our model contains only parameters that have a direct physical interpretation, it can be used to predict how processes such as ageing, disease, and injury affect the mechanical behaviour of tendons, provided we can quantify the effects of these processes on the microstructure.

The influence of invariant solutions on the transient behaviour of an air bubble in a Hele-Shaw channel.

We hypothesize that dynamical systems concepts used to study the transition to turbulence in shear flows are applicable to other transition phenomena in fluid mechanics. In this paper, we consider a finite air bubble that propagates within a Hele-Shaw channel containing a depth-perturbation. Recent experiments revealed that the bubble shape becomes more complex, quantified by an increasing number of transient bubble tips, with increasing flow rate. Eventually, the bubble changes topology, breaking into multiple distinct entities with non-trivial dynamics. We demonstrate that qualitatively similar behaviour to the experiments is exhibited by a previously established, depth-averaged mathematical model and arises from the model's intricate solution structure. For the bubble volumes studied, a stable asymmetric bubble exists for all flow rates of interest, while a second stable solution branch develops above a critical flow rate and transitions between symmetric and asymmetric shapes. The region of bistability is bounded by two Hopf bifurcations on the second branch. By developing a method for a numerical weakly nonlinear stability analysis we show that unstable periodic orbits (UPOs) emanate from the first Hopf bifurcation. Moreover, as has been found in shear flows, the UPOs are edge states that influence the transient behaviour of the system.

The mechanics of airway closure.

We describe how surface-tension-driven instabilities of the lung's liquid lining may lead to pulmonary airway closure via the formation of liquid bridges that occlude the airway lumen. Using simple theoretical models, we demonstrate that this process may occur via a purely fluid-mechanical "film collapse" or through a coupled, fluid-elastic "compliant collapse" mechanism. Both mechanisms can lead to airway closure in times comparable with the breathing cycle, suggesting that surface tension is the primary mechanical effect responsible for the closure observed in peripheral regions of the human lungs. We conclude by discussing the influence of additional effects not included in the simple models, such as gravity, the presence of pulmonary surfactant, respiratory flow and wall motion, the airways' geometry, and the mechanical structure of the airway walls.

On the Feasibility of Automated Mechanical Ventilation Control Through EIT.

OBJECTIVE: This paper aims to demonstrate the feasibility of coupling electrical impedance tomography (EIT) with models of lung function in order to recover parameters and inform mechanical ventilation control. METHODS: A compartmental ordinary differential equation model of lung function is coupled to simulations of EIT, assuming accurate modeling and movement tracking, to generate time series values of bulk conductivity. These values are differentiated and normalized against the total air volume flux to recover regional volumes and flows. These ventilation distributions are used to recover regional resistance and elastance properties of the lung. Linear control theory is used to demonstrate how these parameters may be used to generate a patient-specific pressure mode control. RESULTS: Ventilation distributions are shown to be recoverable, with Euclidean norm errors in air flow below 9% and volume below 3%. The parameters are also shown to be recoverable, although errors are higher for resistance values than elastance. The control constructed is shown to have minimal seminorm resulting in bounded magnitudes and minimal gradients. CONCLUSION: The recovery of regional ventilation distributions and lung parameters is feasible with the use of EIT. These parameters may then be used in model based control schemes to provide patient-specific care. SIGNIFICANCE: For pulmonary-intensive-care patients mechanical ventilation is a life saving intervention, requiring careful calibration of pressure settings. Both magnitudes and gradients of pressure can contribute to ventilator induced lung injury. Retrieving regional lung parameters allows the design of patient-specific ventilator controls to reduce injury.

On the buckling of elastic rings by external confinement.

We report the results of an experimental and numerical investigation into the buckling of thin elastic rings confined within containers of circular or regular polygonal cross section. The rings float on the surface of water held in the container and controlled removal of the fluid increases the confinement of the ring. The increased compressive forces can cause the ring to buckle into a variety of shapes. For the circular container, finite perturbations are required to induce buckling, whereas in polygonal containers the buckling occurs through a linear instability that is closely related to the canonical Euler column buckling. A model based on Kirchhoff-Love beam theory is developed and solved numerically, showing good agreement with the experiments and revealing that in polygons increasing the number of sides means that buckling occurs at reduced levels of confinement.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'

Finite-Reynolds-number effects in steady, three-dimensional airway reopening.

Motivated by the physiological problem of pulmonary airway reopening, we study the steady propagation of an air finger into a buckled elastic tube, initially filled with viscous fluid. The system is modeled using geometrically non-linear, Kirchhoff-Love shell theory, coupled to the free-surface Navier-Stokes equations. The resulting three-dimensional, fluid-structure-interaction problem is solved numerically by a fully coupled finite element method. Our study focuses on the effects of fluid inertia, which has been neglected in most previous studies. The importance of inertial forces is characterized by the ratio of the Reynolds and capillary numbers, ReCa, a material parameter. Fluid inertia has a significant effect on the system's behavior, even at relatively small values of ReCa. In particular, compared to the case of zero Reynolds number, fluid inertia causes a significant increase in the pressure required to drive the air finger at a given speed.

Spatial comparison between wall shear stress measures and porcine arterial endothelial permeability.

A better understanding of how hemodynamic factors affect the integrity and function of the vascular endothelium is necessary to appreciate more fully how atherosclerosis is initiated and promoted. A novel technique is presented to assess the relation between fluid dynamic variables and the permeability of the endothelium to macromolecules. Fully anesthetized, domestic swine were intravenously injected with the albumin marker Evans blue dye, which was allowed to circulate for 90 min. After the animals were euthanized, silicone casts were made of the abdominal aorta and its iliac branches. Pulsatile flow calculations were subsequently made in computational regions derived from the casts. The distribution of the calculated time-dependent wall shear stress in the external iliac branches was directly compared on a point-by-point basis with the spatially varying in vivo uptake of Evans blue dye in the same arteries. The results indicate that in vivo endothelial permeability to albumin decreases with increasing time-average shear stress over the normal range. Additionally, endothelial permeability increases slightly with oscillatory shear index.