Lubrication theory and similarity methods are used to determine the spreading rate of a localized monolayer of insoluble surfactant on the surface of a thin viscous film, in the limit of weak capillarity and weak surface diffusion. If the total mass of surfactant increases as tα, then at early times, when spreading is driven predominantly by Marangoni forces, a planar (axisymmetric) region of surfactant is shown to spread as t(1 + α)/3 (t(1 + α)/4). A shock exists at the leading edge of the monolayer; asymptotic methods are used to show that a wavetrain due to capillary forces exists ahead of the shock at small times, but that after a finite time it is swamped by diffusive effects. For α < ½ (α < 1), the diffusive lengthscale at the shock grows faster than the length of the monolayer, ultimately destroying the shock; subsequently, spreading is driven by diffusion, and proceeds as t½. The asymptotic results are shown to be good approximations of numerical solutions of the governing partial differential equations in the appropriate limits. Additional forces are also considered: weak vertical gravity can also destroy the shock in finite time, while effects usually neglected from lubrication theory are important only early in spreading. Experiments have shown that the severe thinning of the film behind the shock can cause it to rupture: the dryout process is modelled by introducing van der Waals forces.

Aquaporins are membrane channels that facilitate water movement across cell membranes. In plants, aquaporins contribute to water relations. Here, we establish a new link between aquaporin-dependent tissue hydraulics and auxin-regulated root development in Arabidopsis thaliana. We report that most aquaporin genes are repressed during lateral root formation and by exogenous auxin treatment. Auxin reduces root hydraulic conductivity both at the cell and whole-organ levels. The highly expressed aquaporin PIP2;1 is progressively excluded from the site of the auxin response maximum in lateral root primordia (LRP) whilst being maintained at their base and underlying vascular tissues. Modelling predicts that the positive and negative perturbations of PIP2;1 expression alter water flow into LRP, thereby slowing lateral root emergence (LRE). Consistent with this mechanism, pip2;1 mutants and PIP2;1-overexpressing lines exhibit delayed LRE. We conclude that auxin promotes LRE by regulating the spatial and temporal distribution of aquaporin-dependent root tissue water transport.

Intramuscular fluid pressures were recorded in the vastus medialis of seven healthy male volunteers. Pressures were measured simultaneously at three different sites in the muscle by a catheter-tip transducer with extremely low volume-displacement characteristics and by two extracorporeal transducers connected to slit catheters. All three recording systems gave qualitatively similar results provided the catheters had inner diameters exceeding 0.53 mm and allowed measurement of pressures lasting as short as 1 s. Wick catheters yielded slower responses than slit catheters. At any position intramuscular fluid pressure increased linearly with force up to maximal voluntary contraction (MVC). However, slopes of these curves varied greatly mainly because the pressure was also a linear function of the distance from the fascia. The highest recorded pressure was 570 Torr. At prolonged submaximal contractions intramuscular fluid pressure oscillated independent of contraction force. The linearity of both the pressure-force relationship and the pressure-depth relationship is compatible with a simple model based on the law of Laplace because the muscle fibers are curved during contraction in this muscle. It is hypothesized that blood flow is first compromised deep in the muscle where pressure is highest and in general at lower stress or tension in short bulging muscles with great curvature of the fibers compared with long slender ones.

▪ Abstract Almost all vessels carrying fluids within the body are flexible, and interactions between an internal flow and wall deformation often underlie a vessel's biological function or dysfunction. Such interactions can involve a rich range of fluid-mechanical phenomena, including nonlinear pressure-drop/flow-rate relations, self-excited oscillations of single-phase flow at high Reynolds number and capillary-elastic instabilities of two-phase flow at low Reynolds number. We review recent advances in understanding the fundamental mechanics of flexible-tube flows, and discuss physiological applications spanning the cardiovascular system (involving wave propagation and flow-induced instabilities of blood vessels), the respiratory system (involving phonation, the closure and reopening of liquid-lined airways, and Marangoni flows on flexible surfaces), and elsewhere in the body (involving active peristaltic transport driven by fluid-structure/muscle interactions).

Objectives : The luminal surface of the gut is lined with a monolayer of epithelial cells that acts as a nutrient absorptive engine and protective barrier. To maintain its integrity and functionality, the epithelium is renewed every few days. Theoretical models are powerful tools that can be used to test hypotheses concerning the regulation of this renewal process, to investigate how its dysfunction can lead to loss of homeostasis and neoplasia, and to identify potential therapeutic interventions. Here we propose a new multiscale model for crypt dynamics that links phenomena occurring at the subcellular, cellular and tissue levels of organisation. Methods : At the subcellular level, deterministic models characterise molecular networks, such as cell-cycle control and Wnt signalling. The output of these models determines the behaviour of each epithelial cell in response to intra-, inter-and extracellular cues. The modular nature of the model enables us to easily modify individual assumptions and analyse their effects on the system as a whole. Results : We perform virtual microdissection and labelling-index experiments, evaluate the impact of various model extensions, obtain new insight into clonal expansion in the crypt, and compare our predictions with recent mitochondrial DNA mutation data. Conclusions : We demonstrate that relaxing the assumption that stem-cell positions are fixed enables clonal expansion and niche succession to occur. We also predict that the presence of extracellular factors near the base of the crypt alone suffices to explain the observed spatial variation in nuclear beta-catenin levels along the crypt axis.