A gastric acid secretion model.

A theory of gastric acid production and self-protection is formulated mathematically and examined for clinical and experimental correlations, implications, and predictions using analytic and numerical techniques. In our model, gastric acid secretion in the stomach, as represented by an archetypal gastron, consists of two chambers, circulatory and luminal, connected by two different regions of ion exchange. The capillary circulation of the gastric mucosa is arranged in arterial-venous arcades which pass from the gastric glands up to the surface epithelial lining of the lumen; therefore the upstream region of the capillary chamber communicates with oxyntic cells, while the downstream region communicates with epithelial cells. Both cell types abut the gastric lumen. Ion currents across the upstream region are calculated from a steady-state oxyntic cell model with active ion transport, while the downstream ion fluxes are (facilitated) diffusion driven or secondarily active. Water transport is considered iso-osmotic. The steady-state model is solved in closed form for low gastric lumen pH. A wide variety of previously performed static and dynamic experiments on ion and CO2 transport in the gastric lumen and gastric blood supply are for the first time correlated with each other for an (at least) semiquantitative test of current concepts of gastric acid secretion and for the purpose of model verification. Agreement with the data is reported with a few outstanding and instructive exceptions. Model predictions and implications are also discussed.

Modulation of lateral transport of membrane components by spatial variations in diffusivity and solubility.

The effect of spatially varying diffusivity and solubility on the efficiency of intramembrane transport is investigated by obtaining solutions to the generalized lateral diffusion equation in which both the diffusion coefficient, D(r), and the partition coefficient, K(r), are functions of position. The mean-time-to-capture by a sink, tc, of particles diffusing in a plane is obtained analytically for the case of a sink surrounded by gradients in D(r) and K(r) with radially symmetrical geometry. It is shown that for particles originating at random locations, tc is shortened dramatically, if in an annular region around the sink, D and K are significantly greater than in the remainder of the plane. Similarly, a viscous boundary layer surrounding a sink is demonstrated to represent a significant barrier for diffusing particles. To investigate more complex geometries, a finite difference numerical integration method is used and is shown to provide comparable results for tc with modest computational power. The same method is used to calculate the tc for particles originating at a source that is joined to the sink by a channel. The increase in the rate with which particles travel from a source to a sink when they are joined by a high diffusivity and/or solubility channel is illustrated by several numerical examples and by graphical representations that show the equilibrium particle density (and hence the effective particle flow) in the presence of different sink, source, and channel combinations. These results are discussed in terms of fluidity domains and other membrane heterogeneities.

Resonance energy transfer from a cylindrical distribution of donors to a plane of acceptors. Location of apo-B100 protein on the human low-density lipoprotein particle.

The resonance energy transfer (RET) from a cylindrical assembly of donors to acceptors in a plane was investigated, and the dependence the average RET rate (kT) on the cylinder's size, shape, and proximity to the acceptor plane was determined. This geometry provides a model for the RET from a donor-containing protein to acceptors embedded in an associated phospholipid mono- or bilayer. The determination of kT for a series of acceptors at different levels in the phospholipid layer is shown to provide information on the protein's relationship to the phospholipid layer. Two models for the donor (D) and acceptor (A) distributions are employed: (a) The D's and A's are uniformly distributed in the cylinder and the plane, respectively, and analytical expressions for kT in terms of experimental parameters are derived. (b) The RET rates between all D, A pairs within the cylinder and in the plane are calculated and averaged for a large number of random D and A distributions. The average transfer rates obtained by the two approaches are in agreement and the width of the frequency distribution of kT for the latter provides an estimate of the error to be expected when, as is usually the case, the true D and A locations are unknown. This methodology is illustrated by analyzing RET from the 37 tryptophan residues of the apo-B100 protein to a series of pyrenylphosphatidylcholine acceptors inserted in the phospholipid monolayer of the human low-density lipoprotein particle, and it is concluded that significant portions of the protein penetrate the phospholipid layer.

Design optimization of a prosthesis stem reinforcing shell in total hip arthroplasty.

The use of a perforated, titanium funicular shell to support the proximal femoral cortex in total hip arthroplasty was evaluated with the aid of both analytical and numerical techniques. The principal interactions between the femoral cortex, the metal shell, the implant stem and the acrylic bone cement were modeled using beam on elastic foundations theory and two-dimensional elasticity theory. Subsequent formulation of this model as a nonlinear design optimization problem enabled the determination of the dimensions of the implant and reinforcing shell which minimized an objective function based on a simplified material failure criterion. Two cases were examined, each with two cervico-diaphyseal angles: case A: with a rigid contact between a proximal prosthesis collar and the calcar femorale and case B: no collar contact (a collarless prosthesis or post-operative loosening). Case A achieved an optimal solution at a stem diameter 11-23 percent of the cortex inner diameter, a stem length to diameter ratio of 12-40, shell diameter 22-53 percent and thickness 0.2-7.2 percent of the cortex inner diameter and thickness, respectively. Case B achieved an optimal solution at a stem diameter 67-92 percent of the cortex inner diameter, length to diameter ratio of 4-6, and no shell. In case A the collar support makes the type of internal fixation unimportant, while in the more realistic case B, the shell is not recommended.