Water transport in the arterial wall--a theoretical study

Asymmetry of tensile versus compressive elasticity and permeability contributes to the regulation of exchanges in collagen gels

The Starling principle describes exchanges between blood and tissues based on the balance of hydrostatic and osmotic flows. However, the permeation properties of the main constituent of tissues, namely, collagen, in response to the stress exerted by blood pressure remain poorly characterized. Here, we develop an instrument to determine the elasticity and permeability of collagen gels under tensile and compressive stress based on measuring the temporal change in pressure in an air cavity sealed at the outlet of a collagen slab. Data analysis with an analytical model reveals a drop in the permeability and enhanced strain stiffening of native collagen gels under compression versus tension, both effects being essentially lost after chemical cross-linking. Furthermore, we report the control of the permeability of native collagen gels using sinusoidal fluid injection, an effect explained by the asymmetric response in tension and compression. We lastly suggest that blood-associated pulsations could contribute to exchanges within tissues.

From arteries to boreholes: transient response of a poroelastic cylinder to fluid injection

The radially outward flow of fluid through a porous medium occurs in many practical problems, from transport across vascular walls to the pressurization of boreholes in the subsurface. When the driving pressure is non-negligible relative to the stiffness of the solid structure, the poromechanical coupling between the fluid and the solid can control both the steady state and the transient mechanics of the system. Very large pressures or very soft materials lead to large deformations of the solid skeleton, which introduce kinematic and constitutive nonlinearity that can have a non-trivial impact on these mechanics. Here, we study the transient response of a poroelastic cylinder to sudden fluid injection. We consider the impacts of kinematic and constitutive nonlinearity, both separately and in combination, and we highlight the central role of driving method in the evolution of the response. We show that the various facets of nonlinearity may either accelerate or decelerate the transient response relative to linear poroelasticity, depending on the boundary conditions and the initial geometry, and that an imposed fluid pressure leads to a much faster response than an imposed fluid flux.

A Small Deformation Thermoporomechanics Finite Element Model and Its Application to Arterial Tissue Fusion

Understanding the impact of thermally and mechanically loading biological tissue to supraphysiological levels is becoming of increasing importance as complex multiphysical tissue-device interactions increase. The ability to conduct accurate, patient specific computer simulations would provide surgeons with valuable insight into the physical processes occurring within the tissue as it is heated or cooled. Several studies have modeled tissue as porous media, yet fully coupled thermoporomechanics (TPM) models are limited. Therefore, this study introduces a small deformation theory of modeling the TPM occurring within biological tissue. Next, the model is used to simulate the mass, momentum, and energy balance occurring within an artery wall when heated by a tissue fusion device and compared to experimental values. Though limited by its small strain assumption, the model predicted final tissue temperature and water content within one standard deviation of experimental data for seven of seven simulations. Additionally, the model showed the ability to predict the final displacement of the tissue to within 15% of experimental results. These results promote potential design of novel medical devices and more accurate simulations allowing for scientists and surgeons to quickly, yet accurately, assess the effects of surgical procedures as well as provide a first step toward a fully coupled large deformation TPM finite element (FE) model.

From arteries to boreholes: steady-state response of a poroelastic cylinder to fluid injection

The radially outward flow of fluid into a porous medium occurs in many practical problems, from transport across vascular walls to the pressurization of boreholes. As the driving pressure becomes non-negligible relative to the stiffness of the solid structure, the poromechanical coupling between the fluid and the solid has an increasingly strong impact on the flow. For very large pressures or very soft materials, as is the case for hydraulic fracturing and arterial flows, this coupling can lead to large deformations and, hence, to strong deviations from a classical, linear-poroelastic response. Here, we study this problem by analysing the steady-state response of a poroelastic cylinder to fluid injection. We consider the qualitative and quantitative impacts of kinematic and constitutive nonlinearity, highlighting the strong impact of deformation-dependent permeability. We show that the wall thickness (thick versus thin) and the outer boundary condition (free versus constrained) play a central role in controlling the mechanics.

Radial flow through deformable porous shells

The problem of radially directed fluid flow through a deformable porous shell is considered. General nonlinear diffusion equations are developed for spherical, cylindrical and planar geometries. Solutions for steady flow are found in terms of an exact integral and perturbation solutions are also developed. For unsteady flow, perturbation methods are used to find approximate small-time solutions and a solution valid for slow compression rates. These solutions are used to investigate the deformation of the porous material with comparisons made between the planar and the cylindrical geometries.

Contribution of macromolecular structure to the retention of low-density lipoprotein at arterial branch points

BACKGROUND

Extracellular deposition of low-density lipoprotein (LDL) in the arterial wall is an essential early step in atherosclerosis. This process preferentially occurs at arterial branch points, reflecting a regional variation in lipoprotein-arterial wall interactions. In this study, we characterized the submicron microstructure of arterial wall collagen and elastin to evaluate its potential role in regional LDL deposition.

METHODS AND RESULTS

With 2-photon microscopy, we used the intrinsic optical properties of collagen and elastin to determine the arterial wall macromolecular microstructure in fresh porcine and murine arteries. This optical approach generated unique nondestructive en face 3-dimensional views of the wall. The collagen/elastin microstructure was found to vary with the topology of the arterial bed. A nearly confluent elastin surface layer was present throughout but was missing at atherosclerosis-susceptible branch points, exposing dense collagen-proteoglycan complexes. In LDL binding studies, this luminal elastin layer limited LDL penetration, whereas its absence at the branches resulted in extensive LDL binding. Furthermore, LDL colocalized with proteoglycans with a sigmoidal dose dependence (inflection point, approximately 130 mg LDL/dL). Ionic strength and competing anions studies were consistent with the initial interaction of LDL with proteoglycans to be electrostatic in nature.

CONCLUSIONS

This optical sectioning approach provided a robust 3-dimensional collagen/elastin microstructure of the arterial wall in fresh samples. At atherosclerosis-susceptible vascular branch points, the absence of a luminal elastin barrier and the presence of a dense collagen/proteoglycan matrix contribute to increased retention of LDL.

The hydromechanics of hydrocephalus: steady-state solutions for cylindrical geometry

Hydrocephalus is a state in which the circulation of cerebrospinal fluid is disturbed. This fluid, produced within the brain at a constant rate, moves through internal cavities in it (ventricles), then exits through passages so that it may be absorbed by the surrounding membranes (meninges). Failure of fluid to move properly through these passages results in the distention of the passages and the ventricles. Ultimately, this distention causes large displacements and distortion of brain tissue as well as an increase of fluid in the extracellular space of the brain (edema). We use a two-phase model of fluid-saturated material to simulate the steady state of the hydrocephalic brain. Analytic solutions for the displacement of brain tissue and the distribution of edema for the annular regions of an idealized cylindrical geometry and small-strain theory are found. The solutions are used for a large-deformation analysis by superposition of the responses obtained for incrementally increasing loading. The effects of structural and hydraulic differences of white and gray brain matter, and the ependymal lining surrounding the ventricles, are examined. The results reproduce the characteristic steady-state distribution of edema seen in hydrocephalus, and are compared with experiment.

Effect of pressure on transmural fluid flow in different de-endothelialised arteries

The effect of pressure on filtration across different de-endothelialised arteries has been studied experimentally, and the existing theoretical model is validated. Segments of different arteries are excised, de-endothelialised and cannulated. Bovine serum albumin Krebs solution is used as perfusate. Transmural water flux is measured by following the movement of an air bubble in a calibrated capillary, which connects the artery to a pressure reservoir; the pressure of which is varied. The hydraulic conductivity Lp is calculated from the flux values. Using available experimental parameters in the case of the thoracic and abdominal aorta, a theoretical model is validated using the experimental results. As the elastic constant for the carotid artery is not available, the theoretical model is used to calculate the elastic constant at different transmural pressures. The values calculated are in the range -4.9 x 10(-8) to -5.7 x 10(-9) cm2 dyne-1 between 50 and 135 mm Hg. Both theoretical and experimental results show a decrease in Lp values with an increase in transmural pressure for the thoracic and abdominal aorta, whereas a different trend is observed in the case of the carotid artery. The Lp values increase at 90 mm Hg, as compared with 50 mm Hg, and with a further increase in transmural pressure the values decrease.

Flow-induced deformation from pressurized cavities in absorbing porous tissues

The behaviour of a cavity during an injection of fluid into biological tissue is considered. High cavity pressure drives fluid into the neighbouring tissue where it is absorbed by capillaries and lymphatics. The tissue is modelled as a nonlinear deformable porous medium with the injected fluid absorbed by the tissue at a rate proportional to the local pressure. A model with a spherical cavity in an infinite medium is used to find the pressure and displacement of the tissue as a function of time and radial distance. Analytical and numerical solutions for a step change in cavity pressure show that the flow induces a radial compression in the medium together with an annular expansion, the net result being an overall expansion of the medium. Thus any flow induced deformation of the material will aid in the absorption of fluid.

Interstitial pressure, volume, and flow during infusion into brain tissue

A model of infusion-induced swelling in the brain is presented, in which gray and white matter are treated as poroelastic media. The distributions of interstitial pressure, flow, and volume are derived for steady-state and transient infusion protocols. A significant percentage increase in interstitial volume is predicted near the injection site, despite only a modest increase in tissue-averaged fluid content there. The model also can be used to estimate mechanical parameters of brain tissue, such as its hydraulic permeability, shear modulus, and Lamé constant. A solute transport equation that incorporates tissue swelling is also presented. This work suggests that knowing the distribution of swelling induced by infusion is a prerequisite to describing interstitial transport of solutes.

Comparison of models for flow induced deformation of soft biological tissue

The behaviour of a deformable porous medium during the flow of fluid under a pressure difference is examined for both infinitesimal and finite deformations. Models for both cases are solved for the problem of steady one-dimensional compression and compared with experimental data from Parker et al. (J. appl. Mech. 54, 794-800, 1987) for a polyurethane sponge. The purpose of this study is to identify a simple model which agrees qualitatively with these published results. To relate the stress relations for biological tissues to the data for polymer sponges (Parker et al., 1987) a translation of 1.1 kPa was introduced. This allows for some structural differences between the two media. It was found that the infinitesimal models were adequate up to 20% strain, but significant divergence occurred for higher strains. A finite deformation model with the permeability depending exponentially on the strain gave the most consistent results and required the fitting of only two parameters.