Net albumin transport across the wall of the rabbit common carotid artery perfused in situ.

We have studied the transport of radioactively labelled albumin in the rabbit common carotid artery perfused in situ at 100 cm H2O luminal pressure in the anaesthetized living animal, assessing the distribution of concentration across the wall by means of sequential frozen sectioning. We have compared the findings with those of experiments in which we have attempted to saturate the wall with label. Our findings support the belief that there is a net transport of macromolecules across the arterial wall. They show in addition that the wall is inhomogeneous. The distribution volume for label is greater in the adventitia than the media, which appears to offer a larger resistance. The transport process is seemingly dominantly diffusional.

Modeling of coronary capillary flow.

The coronary capillary flow is analyzed theoretically based on the laws of continuum mechanics. The capillary is considered as a long, elastic and permeable vessel loaded externally by tissue pressure. It is subjected to periodic length changes, together with adjacent myocytes. Capillary flow is driven by arteriolar-venular pressure differences. Ultrafiltration due to transmural hydrostatic and osmotic pressure gradients is included in the model. Consideration of mass conservation leads to a nonlinear flow equation. The results show that under stable physiological conditions ultrafiltration is of minor importance. The analysis of untethered capillaries predicts regional differences in capillary flow. In all regions, but more so in the subendocardium, capillaries undergo significant periodic volume changes, giving rise to intramyocardial pumping. In the deeper layers, capillary wall elasticity is of major importance. In the subepicardium, the possible capillary length-changes with adjacent myocytes tend to enhance systolic/diastolic volume differences. The predicted patterns of the overall capillary flow in the left ventricular (LV) wall are in good qualitative agreement with measured coronary phasic flow, showing systolic retrograde arterial inflow, accelerated venal outflow, and diastolic rapid filling accompanied by venal retrograde flow. Analysis of the flow in tethered capillary shows significant effect of the collagen attachments between the surrounding myocytes and the capillary wall. The advantage of the continuum analysis is demonstrated in the present study by its ability to elucidate and evaluate the role of flow controlling mechanisms and their complex interactions.

Ciliary fluid transport: theory and experiment.

The essence of the discrete-cilia approach to model cilia action was presented, the basic building block being the concentrated force, or Stokeslet. Properties of single Stokeslets and infinite arrays of Stokeslets were discussed. Applications of the theory to the feeding of microorganisms, fluid transport above a ciliary patch, and fluid flow inside a ciliated tube were discussed. In the first two cases experiments exist, and the theory fits well with experiment. The third suggests a possible mechanism for sperm movement up the oviduct.

Simulations of three-dimensional ciliary beats and cilia interactions.

A new set of equations describing the time evolution of torsion and curvature for an inextensible curve is developed. Combined with our recently developed Slender Body Theory approach to such problems, these equations were applied to simulate three-dimensional ciliary beats, while allowing for cilia interactions. The computer animation technique, which was originally designed to display two-dimensional beats, has been enhanced to accommodate the new three-dimensional results.

Ciliary motion modeling, and dynamic multicilia interactions.

This paper presents a rigorous and accurate modeling tool for ciliary motion. The hydrodynamics analysis, originally suggested by Lighthill (1975), has been modified to remove computational problems. This approach is incorporated into a moment-balance model of ciliary motion in place of the previously used hydrodynamic analyses, known as Resistive Force Theory. The method is also developed to include the effect of a plane surface at the base of the cilium, and the effect of the flow fields produced by neighboring cilia. These extensions were not possible with previous work using the Resistive Force Theory hydrodynamics. Performing reliable simulations of a single cilium as well as modeling multicilia interactions is now possible. The result is a general method which could now be used for detailed modeling of the mechanisms for generating ciliary beat patterns and patterns of metachronal interactions in arrays of cilia. A computer animation technique was designed and applied to display the results.

A model of herd grazing as a travelling wave, chemotaxis and stability.

Possible constitutive models are examined for the formation of a herd, under the assumption that a herd forms a travelling wave while grazing. Under quite general conditions, it is found that the only possibility for a travelling wave is a balance between food seeking and natural dispersion, such as in chemotaxis. The stability of the travelling wave previously conjectured, is shown both for one- and two-dimensional perturbations.

Mathematical model of blood flow in a coronary capillary.

The coronary capillary flow is analyzed theoretically based on continuum mechanics. The capillary is a long, elastic, and permeable vessel loaded externally by tissue pressure, and it is subject to possible periodic length changes, together with adjacent myocytes. Capillary flow is driven by arteriolar-venular pressure difference. Ultrafiltration due to transmural hydrostatic and osmotic gradients is included, and consideration of mass conservation leads to a nonlinear flow equation. The results show that under physiological conditions ultrafiltration is of minor importance, and the analysis predicts regional differences in capillary flow. In regions with high tissue pressure (subendocardium), capillaries undergo significant periodic volume changes, giving rise to intramyocardial pumping. In those regions, capillary wall elasticity is of major importance. In regions with low tissue pressure (subepicardium), the possible periodic capillary length changes are predominant. The predicted flow patterns are in good qualitative agreement with measured epicardial phasic flow. In conclusion, the methodological advantage of a distributive analysis is demonstrated by its ability to elucidate and evaluate the role of flow determinants and their complex interactions.

Fluid transport in a thick layer above an active ciliated surface.

The discrete cilia approach is employed to describe the flow field above an active ciliated surface in a layer of finite depth. The infinite-size cilia surface model predicts a uniform flow above the cilia surface. Modifications as a result of a finitely extending cilia surface inside a finite-size dish predict a backward parabolic profile above an active cilia surface. Experiments are described which demonstrate a good fit between theoretical predictions and observations. The results provide a sound physical basis for the proper interpretation of fluid-flow observations close to an active ciliary field.

The propulsion of mucus by cilia.

The presence of cilia on epithelia of the respiratory tract was reported more than 150 yr ago, and the two-layer model of mucus transport was put forward more than 50 yr ago. However, it is only in the last 10 yr or so that the motion of mucus-propelling cilia of the mammalian respiratory system has been adequately described, and fluid dynamic studies have developed far enough to allow descriptions of the mechanisms by which ciliary movement is coupled to mucus transport. In this review, scientific developments on the study of cilia and mucus, and interactions between them, are drawn together to further understanding of mucociliary clearance mechanisms of the respiratory tract. The study of the cilia incorporates a discussion of the internal mechanics and biochemistry of the ciliary axoneme, the physical principles of the beat pattern, and the (weak) metachronal coordination of cilia in the lung. Mucus rheology plays a central role in mucociliary transport with the rheologic properties of the mucus determining the effective functioning of this clearance mechanism. Theoretical models provide information on the mechanical principles of the beat pattern as well as providing reliable estimates of the transport rates. Although airflow is not thought to contribute to mucus transport in the normal state, high frequency ventilation and coughing may make significant contributions.

Cilia internal mechanism and metachronal coordination as the result of hydrodynamical coupling.

We present a simple but realistic model for the internal bend-generating mechanism of cilia, using parameters obtained from the analysis of data of the beat of a single cilium, and incorporate it into a recently developed dynamical model. Comparing the results to experimental data for two-dimensional beats, we demonstrate that the model captures the essential features of the motion, including many properties that are not built in explicitly. The beat pattern and frequency change in response to increased viscosity and the presence of neighboring cilia in a realistic fashion. Using the model, we are able to investigate multicilia configurations such as rows of cilia and two-dimensional arrays of cilia. When two adjacent model cilia start beating at different phase, they synchronize within two cycles, as observed in experiments in which two flagella beating out of phase are brought close together. Examination of various multicilia configurations shows that metachronal patterns (i. e., beats with a constant phase difference between neighboring cilia) evolve autonomously. This provides modeling evidence in support of the conjecture that metachronism may occur as a self-organized phenomenon due to hydrodynamical interactions between the cilia.