The Balance of Fluid and Osmotic Pressures across Active Biological Membranes with Application to the Corneal Endothelium.

The movement of fluid and solutes across biological membranes facilitates the transport of nutrients for living organisms and maintains the fluid and osmotic pressures in biological systems. Understanding the pressure balances across membranes is crucial for studying fluid and electrolyte homeostasis in living systems, and is an area of active research. In this study, a set of enhanced Kedem-Katchalsky (KK) equations is proposed to describe fluxes of water and solutes across biological membranes, and is applied to analyze the relationship between fluid and osmotic pressures, accounting for active transport mechanisms that propel substances against their concentration gradients and for fixed charges that alter ionic distributions in separated environments.

A structural model for the in vivo human cornea including collagen-swelling interaction.

A structural model of the in vivo cornea, which accounts for tissue swelling behaviour, for the three-dimensional organization of stromal fibres and for collagen-swelling interaction, is proposed. Modelled as a binary electrolyte gel in thermodynamic equilibrium, the stromal electrostatic free energy is based on the mean-field approximation. To account for active endothelial ionic transport in the in vivo cornea, which modulates osmotic pressure and hydration, stromal mobile ions are shown to satisfy a modified Boltzmann distribution.

Three-dimensional modeling of metabolic species transport in the cornea with a hydrogel intrastromal inlay.

Purpose: Intrastromal inlays for refractive correction of presbyopia are being adopted into clinical practice. An important concern is the effect of the inlay on the long-term health of the cornea due to disturbances in the concentration profiles of metabolic species. A three-dimensional metabolic model for the cornea is employed to investigate oxygen, glucose, and lactate ion transport in the cornea and to estimate changes in species concentrations induced by the introduction of a hydrogel inlay.

THREE-DIMENSIONAL MODELING OF METABOLIC SPECIES TRANSPORT IN THE CORNEA WITH A HYDROGEL INTRASTROMAL INLAY.

Purpose: Intrastromal inlays for refractive correction of presbyopia are being adopted into clinical practice. An important concern is the effect of the inlay on the long-term health of the cornea due to disturbances in the concentration profiles of metabolic species. A 3-D metabolic model for the cornea is employed to investigate oxygen, glucose and lactate ion transport in the cornea and to estimate changes in species concentrations induced by the introduction of a hydrogel inlay.

Three-dimensional distribution of transverse collagen fibers in the anterior human corneal stroma.

Purpose: Recent investigations of human corneal structure and biomechanics have shown that stromal collagen fibers (lamellae) are organized into a complex, highly intertwined three-dimensional meshwork of transverse oriented fibers that increases stromal stiffness and controls corneal shape. The purpose of this study was to characterize the three-dimensional distribution of transverse collagen fibers along the major meridians of the cornea using an automated method to rapidly quantify the collagen fibers' angular orientation.

Methods: Three eyes from three donors were perfusion-fixed under pressure, excised, and cut into four quadrants.

Mechanisms of self-organization for the collagen fibril lattice in the human cornea.

The transparency of the human cornea depends on the regular lattice arrangement of the collagen fibrils and on the maintenance of an optimal hydration--the achievement of both depends on the presence of stromal proteoglycans (PGs) and their linear sidechains of negatively charged glycosaminoglycans (GAGs). Although the GAGs produce osmotic pressure by the Donnan effect, the means by which they exert positional control of the lattice is less clear. In this study, a theoretical model based on equilibrium thermodynamics is used to describe restoring force mechanisms that may control and maintain the fibril lattice and underlie corneal transparency.

The role of 3-D collagen organization in stromal elasticity: a model based on X-ray diffraction data and second harmonic-generated images.

Examining the cross-section of the human cornea with second harmonic-generated (SHG) imaging shows that many lamellae do not lie parallel to the cornea's anterior surface but have inclined trajectories that take them through the corneal thickness with a depth-dependent distribution. A continuum mechanics-based model of stromal elasticity is developed based on orientation information extracted and synthesized from both X-ray scattering studies and SHG imaging. The model describes the effects of inclined lamella orientation by introducing a probability function that varies with depth through the stroma, which characterizes the range and distribution of lamellae at inclined angles.

Depth-dependent transverse shear properties of the human corneal stroma.

Purpose: To measure the transverse shear modulus of the human corneal stroma and its profile through the depth by mechanical testing, and to assess the validity of the hypothesis that the shear modulus will be greater in the anterior third due to increased interweaving of lamellae.

Methods: Torsional rheometry was used to measure the transverse shear properties of 6 mm diameter buttons of matched human cadaver cornea pairs. One cornea from each pair was cut into thirds through the thickness with a femtosecond laser and each stromal third was tested individually.

Multiscale modeling framework of transdermal drug delivery.

This study addresses the modeling of transdermal diffusion of drugs to better understand the permeation of molecules through the skin, especially the stratum corneum, which forms the main permeation barrier to percutaneous permeation. In order to ensure reproducibility and predictability of drug permeation through the skin and into the body, a quantitative understanding of the permeation barrier properties of the stratum corneum (SC) is crucial. We propose a multiscale framework of modeling the multicomponent transdermal diffusion of molecules.

Finite element modeling of acousto-mechanical coupling in the cat middle ear.

The function of the middle ear is to transfer acoustic energy from the ear canal to the cochlea. An essential component of this system is the tympanic membrane. In this paper, a new finite element model of the middle ear of the domestic cat is presented, generated in part from cadaver anatomy via microcomputed tomographic imaging.

Simulating and interpreting Kelvin probe force microscopy images on dielectrics with boundary integral equations.

Kelvin probe force microscopy (KPFM) is designed for measuring the tip-sample contact potential differences by probing the sample surface, measuring the electrostatic interaction, and adjusting a feedback circuit. However, for the case of a dielectric (insulating) sample, the contact potential difference may be ill defined, and the KPFM probe may be sensing electrostatic interactions with a certain distribution of sample trapped charges or dipoles, leading to difficulty in interpreting the images. We have proposed a general framework based on boundary integral equations for simulating the KPFM image based on the knowledge about the sample charge distributions (forward problem) and a deconvolution algorithm solving for the trapped charges on the surface from an image (inverse problem).

A resolution study for electrostatic force microscopy on bimetallic samples using the boundary element method.

Electrostatic force microscopy (EFM) is a special design of non-contact atomic force microscopy used for detecting electrostatic interactions between the probe tip and the sample. Its resolution is limited by the finite probe size and the long-range characteristics of electrostatic forces. Therefore, quantitative analysis is crucial to understanding the relationship between the actual local surface potential distribution and the quantities obtained from EFM measurements.

Using the method of homogenization to calculate the effective diffusivity of the stratum corneum with permeable corneocytes.

The stratum corneum is the outermost layer of the skin, which acts as a barrier membrane against the penetration of molecules into and out of the body. It has a biphasic structure consisting of keratinized cells (corneocytes) that are embedded in a lipid matrix. The macroscopic transport properties of the stratum corneum are functions of its microstructure and the transport properties of the corneocytes and the lipid matrix, and are of considerable interest in the context of transdermal drug delivery and quantifying exposure to toxins, as well as for determining the relation of skin disorders to disruption of the stratum corneum barrier.

Finite element modeling of coupled diffusion with partitioning in transdermal drug delivery.

The finite element method is employed to simulate two-dimensional (axisymmetric) drug diffusion from a finite drug reservoir into the skin. The numerical formulation is based on a general mathematical model for multicomponent nonlinear diffusion that takes into account the coupling effects between the different components. The presence of several diffusing components is crucial, as many transdermal drug delivery formulations contain one or more permeation enhancers in addition to the drug.

Computational modeling of mechanical anisotropy in the cornea and sclera.

Purpose: To determine the biomechanical deformation of the cornea resulting from tissue cutting and removal by use of a new computational model and to investigate the effect of mechanical anisotrophy resulting from the fibrillar architecture.

Setting: Department of Mechanical Engineering, Stanford University, Stanford, California, USA.

Methods: A mathematical model for a typical lamella that explicitly accounts for the strain energy of the collagen fibrils, extrafibrillar matrix, and proteoglycan cross-linking was developed.

A 3D model of muscle reveals the causes of nonuniform strains in the biceps brachii.

Biomechanical models generally assume that muscle fascicles shorten uniformly. However, dynamic magnetic resonance (MR) images of the biceps brachii have recently shown nonuniform shortening along some muscle fascicles during low-load elbow flexion (J. Appl.

Application of Padé via Lanczos approximations for efficient multifrequency solution of Helmholtz problems.

This paper addresses the efficient solution of acoustic problems in which the primary interest is obtaining the solution only on restricted portions of the domain but over a wide range of frequencies. The exterior acoustics boundary value problem is approximated using the finite element method in combination with the Dirichlet-to-Neumann (DtN) map. The restriction domain problem is formally posed in transfer function form based on the finite element solution.