Modeling of a glucose sensitive composite membrane for closed-loop insulin delivery

Design and Optimization of a Nanoparticulate Pore Former as a Multifunctional Coating Excipient for pH Transition-Independent Controlled Release of Weakly Basic Drugs for Oral Drug Delivery

Bioavailability of weakly basic drugs may be disrupted by dramatic pH changes or unexpected pH alterations in the gastrointestinal tract. Conventional organic acids or enteric coating polymers cannot address this problem adequately because they leach out or dissolve prematurely, especially during controlled release applications. Thus, a non-leachable, multifunctional terpolymer nanoparticle (TPN) made of cross-linked poly(methacrylic acid) (PMAA)-polysorbate 80-grafted-starch (PMAA-PS 80-g-St) was proposed to provide pH transition-independent release of a weakly basic drug, verapamil HCl (VER), by a rationally designed bilayer-coated controlled release bead formulation. The pH-responsive PMAA and cross-linker content in the TPN was first optimized to achieve the largest possible increase in medium uptake alongside the smallest decrease in drug release rate at pH 6.8, relative to pH 1.2. Such TPNs maintained an acidic microenvironmental pH (pH_m) when loaded in ethylcellulose (EC) films, as measured using pH-indicating dyes. Further studies of formulations revealed that with the 1:2 VER:TPN ratio and 19% coating weight gain, bilayer-coated beads maintained a constant release rate over the pH transition and exhibited extended release up to 18 h. These results demonstrated that the multifunctional TPN as a pH_m modifier and pH-dependent pore former could overcome the severe pH-dependent solubility of weakly basic drugs.

Connecting Rodent and Human Pharmacokinetic Models for the Design and Translation of Glucose-Responsive Insulin

Despite considerable progress, development of glucose-responsive insulins (GRIs) still largely depends on empirical knowledge and tedious experimentation-especially on rodents. To assist the rational design and clinical translation of the therapeutic, we present a Pharmacokinetic Algorithm Mapping GRI Efficacies in Rodents and Humans (PAMERAH) built upon our previous human model. PAMERAH constitutes a framework for predicting the therapeutic efficacy of a GRI candidate from its user-specified mechanism of action, kinetics, and dosage, which we show is accurate when checked against data from experiments and literature. Results from simulated glucose clamps also agree quantitatively with recent GRI publications. We demonstrate that the model can be used to explore the vast number of permutations constituting the GRI parameter space and thereby identify the optimal design ranges that yield desired performance. A design guide aside, PAMERAH more importantly can facilitate GRI's clinical translation by connecting each candidate's efficacies in rats, mice, and humans. The resultant mapping helps to find GRIs that appear promising in rodents but underperform in humans (i.e., false positives). Conversely, it also allows for the discovery of optimal human GRI dynamics not captured by experiments on a rodent population (false negatives). We condense such information onto a "translatability grid" as a straightforward, visual guide for GRI development.

Unprecedented homotopy perturbation method for solving nonlinear equations in the enzymatic reaction of glucose in a spherical matrix

The theory of glucose-responsive composite membranes for the planar diffusion and reaction process is extended to a microsphere membrane. The theoretical model of glucose oxidation and hydrogen peroxide production in the chitosan-aliginate microsphere has been discussed in this manuscript for the first time. We have successfully reported an analytical derived methodology utilizing homotopy perturbation to perform the numerical simulation. The influence and sensitive analysis of various parameters on the concentrations of gluconic acid and hydrogen peroxide are also discussed. The theoretical results enable to predict and optimize the performance of enzyme kinetics.

Rational Design of Glucose-Responsive Insulin Using Pharmacokinetic Modeling

A glucose responsive insulin (GRI) is a therapeutic that modulates its potency, concentration, or dosing of insulin in relation to a patient's dynamic glucose concentration, thereby approximating aspects of a normally functioning pancreas. Current GRI design lacks a theoretical basis on which to base fundamental design parameters such as glucose reactivity, dissociation constant or potency, and in vivo efficacy. In this work, an approach to mathematically model the relevant parameter space for effective GRIs is induced, and design rules for linking GRI performance to therapeutic benefit are developed. Well-developed pharmacokinetic models of human glucose and insulin metabolism coupled to a kinetic model representation of a freely circulating GRI are used to determine the desired kinetic parameters and dosing for optimal glycemic control. The model examines a subcutaneous dose of GRI with kinetic parameters in an optimal range that results in successful glycemic control within prescribed constraints over a 24 h period. Additionally, it is demonstrated that the modeling approach can find GRI parameters that enable stable glucose levels that persist through a skipped meal. The results provide a framework for exploring the parameter space of GRIs, potentially without extensive, iterative in vivo animal testing.

Numerical simulation of a glucose sensitive composite membrane closed-loop insulin delivery system

Closed-loop insulin delivery system works on pH modulation by gluconic acid production from glucose, which in turn allows regulation of insulin release across membrane. Typically, the concentration variation of gluconic acid can be numerically modeled by a set of non-linear, non-steady state reaction diffusion equations. Here, we report a simpler numerical approach to time and position dependent diffusivity of species using finite difference and differential quadrature (DQ) method. The results are comparable to that obtained by analytical method. The membrane thickness directly determines the concentrations of the glucose and oxygen in the system, and inversely to the gluconic acid. The advantage with the DQ method is that its parameter values need not be altered throughout the analysis to obtain the concentration profiles of the glucose, oxygen and gluconic acid. Our work would be useful for modeling diabetes and other systems governed by such non-linear and non-steady state reaction diffusion equations.

Part-2: Analytical Expressions of Concentrations of Glucose, Oxygen, and Gluconic Acid in a Composite Membrane for Closed-Loop Insulin Delivery for the Non-steady State Conditions

A mathematical model developed by Abdekhodaie and Wu (J Membr Sci 335:21-31, 2009), which describes a dynamic process involving an enzymatic reaction and diffusion of reactants and product inside glucose-sensitive composite membrane has been discussed. This theoretical model depicts a system of non-linear non-steady state reaction diffusion equations. These equations have been solved using new approach of homotopy perturbation method and analytical solutions pertaining to the concentrations of glucose, oxygen, and gluconic acid are derived. These analytical results are compared with the numerical results, and limiting case results for steady state conditions and a good agreement is observed. The influence of various kinetic parameters involved in the model has been presented graphically. Theoretical evaluation of the kinetic parameters like the maximal reaction velocity (V _max) and Michaelis-Menten constants for glucose and oxygen (K _g and K _ox) is also reported. This predicted model is very much useful for designing the glucose-responsive composite membranes for closed-loop insulin delivery.

Swelling of glucose-responsive gels functionalized with boronic acid

A model is developed for the elastic response of a glucose-sensitive gel functionalized with boronic acid under swelling in aqueous solutions of glucose with various pH. A gel is treated as a three-phase medium composed of a solid phase (partially ionized polymer network), solvent (water), and solute (mobile glucose molecules and ions). Constitutive equations are derived by means of the free energy imbalance inequality for three-dimensional deformation with finite strains. Numerical analysis demonstrates the ability of the model to describe the effects of pH, molar fraction of glucose, and concentration of functional groups on equilibrium water uptake diagrams under unconstrained and constrained swelling.

The Mathematical Theory of Diffusion and Reaction in Enzymes Immoblized Artificial Membrane. The Theory of the Non-Steady State

In this paper, mathematical model pertaining to the decomposition of enzyme-substrate complex in an artificial membrane is discussed. Here the transport through liquid membrane phases is considered. The model involves the system of non-linear reaction diffusion equations. The non-linear terms in this model are related to Michaelis-Menten reaction scheme. Approximate analytical expressions for the concentrations of substrate and product have been derived by solving the system of non-linear reaction diffusion equations using new approach of homotopy perturbation method for all values of Michaelis-Menten constant, diffusion coefficient, and rate constant. Approximate flux expression for substrate and product for non-steady-state conditions are also reported. A comparison of the analytical approximation and numerical simulation is also presented. The results obtained in this work are valid for the entire solution domain.

Analytical expressions for the steady-state concentrations of glucose, oxygen and gluconic acid in a composite membrane for closed-loop insulin delivery

The mathematical model of Abdekhodaie and Wu (J Membr Sci 335:21-31, 2009) of glucose-responsive composite membranes for closed-loop insulin delivery is discussed. The glucose composite membrane contains nanoparticles of an anionic polymer, glucose oxidase and catalase embedded in a hydrophobic polymer. The model involves the system of nonlinear steady-state reaction-diffusion equations. Analytical expressions for the concentration of glucose, oxygen and gluconic acid are derived from these equations using the Adomian decomposition method. A comparison of the analytical approximation and numerical simulation is also presented. An agreement between analytical expressions and numerical results is observed.

An autonomous drug release system based on chemo-mechanical energy conversion "Organic Engine" for feedback control of blood glucose

A novel autonomous drug release system was fabricated and tested. The system consists of two integrated units: decompression unit and drug release unit. The decompression unit was fabricated by separating a cylindrical cell into a top cell (gas phase) and a bottom cell (liquid phase) by glucose oxidase (GOD) enzyme immobilized membrane. The enzyme membrane recognizes glucose and converts chemical energy found in glucose to mechanical energy. The linear correlation between glucose concentration and de-pressure slope of the top cell was revealed as applying glucose solution to the bottom cell. Afterward, the drug release unit which utilizes the energy of the decompression unit as a power source was fabricated and evaluated by recording its release actions. The drug release unit was made to release at a constant quantity of drug in the liquid phase. The system was then fabricated by combining the decompression unit and the drug release unit. And it was evaluated in an open loop and in a closed loop by applying a mixture of glucose solution (100 mmol/l) and NADH(+) using glucose dehydrogenase enzyme (GDH) as a glucose reducer. Glucose concentration decreased gradually in the closed loop and, as a consequence, interval time of the GDH release became longer. In other words, an inverse correlation between actuation interval of the system and glucose concentration was shown. As a result, the possibility of feedback control of glucose concentration by the drug release system without external energy was confirmed.