Showing papers by "Nicholas A. Peppas published in 2004"

Hydrogels for oral delivery of therapeutic proteins.

Abstract: In recent years there has been significant new interest in the development of transmucosal (mostly oral) pharmaceutical formulations for the delivery of therapeutic proteins. Emphasis has been given to the molecular design of new carriers for the delivery of insulin, calcitonin and various types of interferons for the treatment of diabetes, osteoporosis, multiple sclerosis and cancer. Most popular carriers include advanced designs of swollen hydrogels prepared from neutral or intelligent polymeric networks. In this review, the most successful of such systems are presented and their promise in the field described.

Stimuli-sensitive hydrogels: ideal carriers for chronobiology and chronotherapy

Abstract: The development of solid-phase peptide synthesis in the early 1960s and recombinant DNA technology in the early 1970s boosted the scientific interest of utilizing proteins and peptides as potential therapeutic agents to battle poorly controlled diseases. While there has been rapid progress in the development and synthesis of new proteins and peptides as potential therapeutic agents, the formulation and development of the associated delivery systems is lacking. The development of delivery systems is equally important due to the problems of stability, low bioavailability and short half-life of proteins and peptides. The main problem in this field is that low stability leads to low bioavailability. In this review we draw attention to chrono-pharmacological drug-delivery systems, which can be used to match the delivery of therapeutic agents with the biological rhythm. They are very important especially in endocrinology and in vaccine therapy. We show that the treatment of hypopituitary dwarfism by administration of human growth-hormone-releasing hormone (GHRH) is more effective when GHRH is administered in a pulsatile manner that exhibits a period characteristic of the patient's circadian rhythm. Here we examine how to design novel chrono-pharmacological drug-delivery systems that should be able to release the therapeutic agents at predetermined intervals.

Responsive and recognitive hydrogels using star polymers.

Abstract: Polymeric networks that have inherent capabilities to recognize different molecules and chemical changes in their environment are the next generation of materials that will aid in the diagnosis and treatment of diseases. We have prepared new networks based on star polymers that were designed to be responsive and recognitive. Using molecular imprinting with D-glucose and crosslinking with poly(ethylene glycol) dimethacrylate with an ethylene glycol chain of nominal molecular weight 600, we prepared star polymer networks, which exhibited over 300% more uptake for D-glucose compared to D-fructose. Using copolymerization with methacrylic acid, we prepared star polymer networks with pH-sensitivity, which showed a sharp transition in swelling around a pH of 4.5.

Origins and development of biomedical engineering within chemical engineering

Abstract: Over the past 45 years, the field of biomedical engineering has found a welcome home in academic chemical engineering departments and in companies working with artificial organs, medical devices, and pharmaceutical formulations. The contributions of chemical engineers to the definition and the growth of the field have been important and at times seminal. The development and early contributions in the biomedical field with special emphasis on the contributions of chemical engineers is examined. © 2004 American Institute of Chemical Engineers AIChE J, 50: 536–546, 2004

Effect of Poly (Ethylene Glycol) Molecular Weight and Microparticle Size on Oral Insulin Delivery from P(MAA-g-EG) Microparticles

Abstract: Five years of successful work in our lab have shown that graft copolymer networks of poly(methacrylic acid-g-ethylene) [P(MAA-g-EG)], are very promising candidates for oral drug delivery. In an acidic environment, these copolymers form interpolymer complexes, protecting the active agent from the harsh environment of the gastrointestinal tract. At high pH, these complexes dissociate, causing the polymer to swell and release the drug. Films of P(MAA-g-EG) with a monomer ratio of 1:1 (MAA:EG) were prepared by free radical solution UV-polymerization, washed in order to remove the unreacted monomer, and crushed to form microparticles with different particle size distribution. Previous studies in our lab have focused on using polymer disks in their swelling studies. The swelling properties of polymer disks vs. crushed particles were investigated via equilibrium swelling experiments in this study. Another goal in this study is to compare different PEG chain length (MW-400 and MW-1000) and different particle size (150-212 microns, 90-150 microns and 25-90 microns) in their loading and release behavior. After 6 hours of exposing the polymer with the insulin solution we achieved approximately 90% of insulin loading.

Structural and dynamic response of neutral and intelligent networks in biomedical environments

Abstract: Publisher Summary As biomedical materials are becoming more advanced and sophisticated, advanced techniques of combinatorial chemistry and molecular design are becoming of utmost importance in order to achieve better design and desirable response to the biological environment. In particular, hydrophilic polymer networks have attained new importance in this field, as they are particularly prone to molecular or structural changes. Their structure can be modified by copolymerization to achieve hydrophilicity or hydrophobicity. In addition, the presence of selected functional groups can make these networks responsive to environmental changes. This chapter presents an analysis of the structural and biological properties of polymer networks, both neutral and responsive. It outlines the significance of these properties in biomedical applications. An overview of currently pursued hydrogels technologies is also provided.

Modeling of water transport in and release from glucose-sensitive swelling-controlled release systems based on poly(diethylaminoethyl methacrylate-g-ethylene glycol)

Abstract: The glucose-sensitive behavior of glucose-sensitive, poly(diethylaminoethyl methacrylate-g-ethylene glycol) hydrogels was modeled and analyzed in the case of exposure to glucose solutions. Gel microparticles were prepared with molar ratios of 10:1 diethylaminoethyl methacrylate to poly(ethylene glycol) of molecular weights 200, 400, and 1000, using tetra(ethylene glycol) dimethacrylate as a cross-linking agent. Glucose oxidase and catalase was immobilized in the matrix during polymerization. The equilibrium and dynamic swelling properties of these hydrogels were investigated. The pH-dependent equilibrium swelling characteristics showed a sharp transition between the swollen state and the collapsed state at a pH of 7.0. Microparticles showed rapid swelling and collapse under the influence of pulsatile pH changes. The glucose-sensitive behavior of the gels due to glucose oxidase was also studied. Diffusion and relaxation models were used to predict swelling of single microparticles under different pH and gl...

Cellular evaluation of insulin transmucosal delivery.

Abstract: P(MAA-g-EG) microparticles have been extensively investigated as carriers for oral delivery of proteins such as insulin. In this study, we investigated the effect of the molecular weight of the PEG tethered chains in the copolymer network and of the microparticle size on the transepithelial electrical resistance (TEER) and insulin epithelial permeability, using monolayers of human intestinal epithelial Caco-2 cells. Two molecular weights of the PEG chains, 400 and 1000, were investigated, as well as three different dry microparticle sizes: 25-90, 90-150 and 150-212 μm. Their effect on the cell monolayer integrity was studied by monitoring TEER as a fraction of time and determining insulin permeability. The presence of insulin-loaded P(MAA-g-EG) microparticles decreases the TEERs value by 50% with respect to the control. This disruption of the cell monolayer was recovered in 3 h after the removal of the polymer microparticles. Within the range of PEG molecular weights studied, there was no significant chan...

Molecular and cellular foundations of biomaterials

Abstract: The new biomaterials. Cell-material interactions. Polymeric biomaterials for nerve regeneration. Structural and dynamic response of neutral and intelligent networks in biomedical environments. Biomaterials and gene therapy. Surface-erodible biomaterials for drug delivery.

The future of intelligent therapeutics

Abstract: Smart delivery in response to recognition of undesirable biological compounds calls for advanced designs of drug delivery carriers. Recognitive proteins and protein binding domains reveal molecular architectures with specific chemical moieties that provide a framework for selective recognition of a target molecule in aqueous environment. Developments of particular interest to the field will have a wide and far reaching impact and will cover intelligent biomolecule-modulated drug and protein delivery, nano-scale patterning and recognition of biological molecules for micro-diagnostic devices, and site or ligand-specific interaction with cells and tissues. Introduction Recent advances in the discovery and delivery of drugs to cure chronic diseases are achieved by combination of intelligent material design with advances in nanotechnology. Since many drugs act as protagonists or antagonists to different chemicals in the body, a delivery system that can respond to the concentrations of certain molecules in the body is invaluable. For this purpose, intelligent therapeutics or “smart drug delivery” calls for the design of the newest generation of sensitive materials based on molecular recognition. Biomimetic polymeric networks can be prepared by designing interactions between the building blocks of biocompatible networks and the desired specific ligands and by stabilizing these interactions by a three-dimensional structure. These structures are at the same time flexible enough to allow for diffusion of solvent and ligand into and out of the networks. Synthetic networks that can be designed to recognize and bind biologically significant molecules are of great importance and influence a number of emerging technologies. These artificial materials can be used as unique systems or incorporated into existing drug delivery technologies that can aid in the removal or delivery of biomolecules and restore the natural profiles of compounds in the body. Nanoscale Structures in Intelligent Therapeutics In recent years, there has been considerable work in preparing materials and finding new uses for nanoscale structures based on biomaterials. Uses such as carriers for controlled and targeted drug delivery, micropatterned devices, systems for biological recognition, have shown the versatility of these biopolymeric materials as indicated by Langer and Peppas [1]. Of specific interest to us are applications requiring the patterning of vinyls, methacrylates and acrylates during reaction allowing for the formation of nanoscale three-dimensional structures. These micropatterned structures may be used for a host of applications including cell adhesion, separation processes, the so called “factory-on-a-chip” microscale reactors, and microfluidic devices. Electronic devices have now reached a stage of dimensions comparable to those of biological macromolecules. This raises exciting possibilities for combining microelectronics and biotechnology to develop new technologies with unprecedented power and versatility. While molecular electronics use the unique self-assembly, switching and dynamic capabilities of molecules to miniaturize electronic devices, nanoscale biosystems use the power of microelectronics to design ultrafast/ultrasmall biocompatible devices, including implants, that can revolutionize the field of bioengineering. Thus, in recent years we have seen an explosion in the field of novel microfabricated and nanofabricated devices for drug delivery. Such devices seek to develop a platform of well controlled functions in the microor nano-level. They include nanoparticulate systems, recognitive molecular systems, biosensing devices, and microfabricated and microelectronic devices. For example, polymer surfaces in contact with biological fluids, cells, or cellular components can be tailored to provide specific recognition properties or to resist binding depending on the intended application and environment. Engineering the molecular design of biomaterials by controlling recognition and specificity is the first step in coordinating and duplicating complex biological and physiological processes. The design of surfaces for cellular recognition and adhesion, analyte recognition, and surface passivity encompasses a number of techniques such as surface grafting (ultraviolet radiation, ionizing radiation, electron beam irradiation). Certain techniques can change the chemical nature of surfaces and produce areas of differing chemistry as well as surfaces and polymer matrices with binding regimes for a given analyte. In addition, biomimetic methods are now used to build biohybrid systems or even biomimetic materials (mimicking biological recognition) for drug delivery, drug targeting, and tissue engineering devices [2]. The synthesis and characterization of biomimetic gels and molecularly imprinted drug release and protein delivery systems is a significant focus of recent research. Configurational biomimetic imprinting of an important analyte on an intelligent gel leads to preparation of new biomaterials that not only recognize the analyte but also act therapeutically by locally or systemically releasing an appropriate drug. Nanoimprinting and Therapeutics The design of a precise macromolecular chemical architecture that can recognize target molecules from an ensemble of closely related molecules has a large number of potential applications [3]. The main thrust of research in this field has included separation processes (chromatography, capillary electrophoresis, solid-phase extraction, membrane separations), immunoassays and antibody mimics, biosensor recognition elements, and catalysis and artificial enzymes. Nanoimprinting creates stereo-specific three-dimensional binding cavities based on the template of interest. Efforts for the imprinting of large molecules and proteins have focused upon two-dimensional surface imprinting, a method of recognition at a surface rather than within a bulk polymer matrix. More recently, by using an epitope approach and imprinting a short peptide chain representing an exposed fragment of the total protein, three-dimensional imprinting of proteins within a bulk matrix has been successfully prepared. There is a variety of microelectronic devices that have been studied for controlled drug delivery systems [1]. Sensors represent another area where microfabrication and nanotechnology for drug delivery can be important. For example, scientists are building capacitor-based sensors which have been tested in vitro in model blood vessels. One concept is to implant such systems in small animals to measure blood pressure during cardiovascular studies. In another case, small sensors are being used to measure intraocular pressure for glaucoma patients. For in vivo sensors, issues of biocompatibility will be important, and packaging issues may become significant. To address such issues, in one case an electrochemical sensor array was developed to put inside a biocompatible tube which can be monitored by telemetry. This sensor was designed so that it could monitor such substances as pH, carbon dioxide and oxygen. Another interesting approach involves the development of microfabricated microneedles. This type of approach can have a remarkable effect in enhancing the delivery of drugs without causing significant pain to the patient. Microneedles are able to do this without pain because they don’t penetrate deep enough into the skin layers that contain nerves, but are able to penetrate far enough into the skin for the therapeutic compounds to enter the center of circulation. There are numerous techniques for microfabrication of patterned polymer surfaces and microchips for drug delivery. While silicon has been the choice material for much of the research done with MEMS, the methacrylates and acrylates provide a rapid and inexpensive base for future work. Several applications have already been suggested including patterned surfaces for cell adhesion, biosensors, microfluidic devices, and arrays for chemical screening. Initial work has been directed at creating a microfluidic pump directed by oscillating electrical current. It is possible for pH sensitive hydrogels to be created that deswell when connected to an external electrical source. The development of nanoparticulate systems for drug delivery applications has taken a level of sophistication never before seen in the field of drug delivery [4]. Using intelligent polymers, it is now possible to design new devices for intelligent therapeutics. Such systems can be employed for auto-feedback drug delivery, whereby the hydrogel will be connected to a biosensor and will respond to fast changes in the external biological conditions. This idea may be used to develop novel insulin delivery systems. Another particularly novel use of these systems is for the release of human calcitonin. Nanoparticles and Intelligent Therapeutics New promising methods of delivery of chemotherapeutic agents using nanoscale structures have been recently reported. For example, biorecognition of various sugar-containing copolymers can be used for the release of chemotherapeutic agents. Particles in the submicron range possess very high surface to volume ratios thus allowing for intimate interaction between the surface of the particles and the gastro-intestinal mucus. Additionally, carriers in the particulate form should be able to diffuse further into the mucus layer enabling them to reach the cells of the epithelial layer. The particle size and surface properties, namely, their relative hydrophobicity, are the main factors affecting the particles’ effectiveness in prolonging their transit time in the GI tract and protecting the active agents from degradation. An alternative method of targeting drugs to specific sites is by use of bioadhesive and mucoadhesive nanostructures. Such systems usually consist of hydrogen-bonded structures such as poly(acrylic acid)-based hydrogels which adhere to the mucosa due to

Complexation hydrogels as oral delivery vehicles for insulin-transferrin conjugates

Abstract: Protein bioconjugation is being currently investigated as a strategy to improve oral absorption of proteins. By conjugating proteins of therapeutic interest, such as insulin, to macromolecular PEG chains or other proteins, such as transferrin (Tf), the enzymatic stability of the protein drug and its transport characteristics across the intestinal epithelium may be improved. Complexation graft copolymers of poly(methacrylic acid-g-ethylene glycol), have also shown to be excellent carriers for oral protein delivery. In this work we demonstrated the use of complexation hydrogels as delivery vehicles for insulin-transferrin bioconjugates. Introduction: Complexation graft copolymers of poly(methacrylic acid-g-ethylene glycol), designated as P(MAA-g-EG), have been shown to be effective in oral delivery of insulin. Their hydrogen bonding complexation/decomplexation characteristics render these responsive hydrogels able to protect the insulin in the harsh, acidic environment of the stomach before releasing the bioactive agent in the small intestine. Further, these network structures can inhibit the activity of Ca dependent proteolytic enzymes [1], and increase the residence time of the drug in the small intestine by mucoadhesion. Oral administration of insulin entrapped in polymer microparticles resulted in high bioavailability of the drug in diabetic rats [2]. One of the other effective strategies for enhancing bioavailability of proteins exploits the receptor-mediated endocytotic pathway used by the cells for selective and efficient uptake of specific macromolecules required for various cell processes. By coupling proteins and peptides to ligands that can recognize specific receptors on the epithelial cells, transcellular delivery of these macromolecular biopharmaceuticals may be achieved [3]. Since only those molecules that are conjugated to the ligands are transcytosed, this process eliminates the potential side effects associated with the unspecific transport via the paracellular pathway. Researchers have used insulin-transferrin conjugates for enhancing the oral bioavailability of insulin [4]. Transferrin is a naturally occurring protein involved in the uptake of iron by the cells that binds specific receptors on the epithelial cells and is endocytosed. We are investigating the use of the complexation hydrogel as a delivery vehicle for the insulin conjugates. Since the insulin conjugates thus released from the polymer microparticles will have better enzymatic resistance and enhanced permeability across the epithelium, high bioavailability of the drug could be achieved. In this work we investigated the loading and release profiles of transferrin and insulin-transferrin conjugates from P(MAA-g-EG) microparticles. Experimental: Polymer Synthesis: Polymer microparticles of 150-210 μm size rage were prepared by free radical UV polymerization as described elsewhere [5]. The initial monomer feed ratio of MAA:EG was 1:1. Tetraethylene glycol dimethacrylate (TEGDMA) was added as a crosslinker at 0.75 mol% of the total monomer. 1-Hydroxylcyclohexyl phenyl ketone (Irgacure-184) was used as the free-radical initiator and added in the amount of 0.1 wt% of the monomer mixture. Conjugate Synthesis and Analysis: The conjugates were synthesized by coupling the proteins via succinimidyl 3-(2-pyridyldithio)propionate (SPDP), an amine reactive heterobifunctional crosslinker [4, 6]. Briefly, The N-terminal amino groups of bovine insulin (2 mg/ml) were protected by reaction with dimethylmaleic anhydride (DMMA) at a controlled pH of 6.8-7.0. Following this, the reaction products were dialyzed overnight (MWCO 3500) to remove the unreacted DMMA. The dialyzed protein was then reacted with 1 mg SPDP dissolved in minimum quantity of dimethylformamide for 2 hr. Insulin-PDP thus prepared was then dialyzed overnight and reacted with human holo transferrin-PDP complex (Tf-PDP) prepared by a similar procedure. The PDP:protein ratio was measured spectrophotometrically by measuring absorbance at 343 nm after reaction with 25 mM dithiothreitol (DTT) solution [6]. The conjugate was purified by size exclusion chromatography by elution on a Sephacryl-S200 column and protein modifications were confirmed by mass spectroscopy. The insulin: transferrin ratio in the conjugates was also measured to determine the number of insulin molecules coupled to a single transferrin molecule. Protein Loading and Release Studies: The proteins were loaded into the polymer microparticles by equilibrium partitioning from a concentrated protein solution at pH 6.8 [7, 8]. Briefly 140 mg of polymer particles were soaked in protein solution for 6 hr. The microparticles were then collapsed by addition of 20 ml of 0.1 M HCl, filtered through 0.45 μm pore size membrane, and freeze dried for 24 hrs. The release studies were performed in a USP II dissolution apparatus. 10 mg of the protein loaded particles were placed in 50 ml pH 2.0 buffer solution. 50 μl samples were withdrawn at different time points and analyzed by reversed phase HPLC. After 1 hr, the pH was increased to 7.4 by addition of NaOH solution. The samples were withdrawn and analyzed for 2 hrs. The fractional release of the protein from the formulations, defined here as the ratio of the amount released at any time (Mt) to the total amount released at the end of release experiment (M∞) was calculated. Results: Mass spectroscopy analysis of the prepared conjugates confirmed both the Nterminal primary amine blocking and PDP attachment to the lysine primary amine at β-29 position of insulin. Insulin conjugation to Tf was also confirmed by mass spectroscopy. The loading and release were performed initially for Tf as a preliminary step towards the development of conjugate loaded formulation since the Tf molecule is significantly larger (hydrodynamic radius, Rh, of 40Ǻ) as compared to insulin (Rh=20Ǻ). Hence the diffusion of Tf in and out of the polymer network may be significantly hindered. The release profile of Tf from P(MAA-g-EG) microparticles is shown in Fig. 1. The loading efficiency in these studies, based on the initial protein present in the loading solution was 54.6± 4.7% and the release efficiency based on the loaded amount was 64.4± 6.7%. The loading and release profiles of the conjugates from the polymer formulation was also studied in this work. 0 0.2 0.4 0.6 0.8 1 1.2 0 30 60 90 120 150 180 210 240 270 Time (min) Fr ac tio n of tr an sf er rin re le as ed

Biomimetic, molecularly imprinted hydrogels for recognition and capture of high molecular weight proteins

Abstract: A novel molecularly imprinted (MIP) hydrogel consisting of methacrylic acid (MAA), 2dimethylaminoethyl methacrylamide (DMAEM), and acrylamide (Aam) were fabricated using free radical polymerization in the presence of the template molecule lysozyme. Kinetic binding studies revealed a rapid recognition of template molecule where 95% of lysozyme was bound after 20 min. The imprinting efficiency of these matrices also exhibited 21% more binding of lysozyme after 20 min compared to non-imprinted control polymer. To study the specificity of the MIP hydrogel formulation to lysozyme, MIP polymers were placed into solution with similarly sized molecules pepsin and soybean trypsin inhibitor. These binding studies indicated less than 2% binding of these molecules to MIP polymers and validated our MIP process. These novel polymers have the potential as tissue engineering scaffolds and drug delivery

Modeling and control of the behavior of glucose sensing devices

Abstract: Hydrogels made of glucose oxidase-containing graft copolymers of dimethyl aminoethyl methacrylate and ethylene glycol, or glucose oxidase-containing P(DMAEMg-EG) copolymers, have been shown to deliver insulin upon exposure to glucose. The glucose oxidase reacts with glucose to form gluconic acid. The production of gluconic acid decreases the pH, which results in the swelling of the hydrogel complex. Once the mesh size has increased, insulin is released from the complex. Previous work has shown that P(DMAEM-g-EG) hydrogels have exhibited pH sensitive swelling and deswelling. Current work focuses on the design of novel hydrogels that allow for insulin release in diabetic patients that is similar to that of healthy, non-diabetic patients. To evaluate the effectiveness of proposed hydrogels, dynamic models of glucose and insulin are being developed for both healthy patients and diabetic patients in order to compare the dynamic responses of the hydrogels to those of a healthy pancreas. In healthy patients, the models show how insulin and glucose dynamics are dependent on each other throughout the body, while in diabetics the hydrogel complex dynamics are included as the primary insulin source. Understanding glucose and insulin dynamics is necessary in order develop control strategies for hydrogels used in glucose regulation. Introduction: The main objective of this research was to contribute to the medical field by providing new therapeutic methods and improved devices for insulin delivery in diabetic patients. With the new therapies developed we should be able to: (i) determine when exactly should insulin be delivered to the patient; and (ii) avoid unnecessary and premature insulin delivery. A major goal and contribution of this research were the design and development of glucose-responsive, gel-based devices for insulin delivery that can be used over a prolonged period of time. These systems are known as self-regulated drug delivery systems. A significant distinction of our research is the reliance on robust control theory to establish performance objectives for the proposed hydrogel device, as well as optimal control theory to guide the selection of optimal parameter values for the synthesis of the gel. We have developed a series of novel self-regulated, glucoseand pH-sensitive gels for insulin delivery. We have experimented already with novel hydrogels in which the swelling ratio and the resulting mesh size change reversibly as a function of environmental parameters such as pH or temperature. These reversible changes allow for the release of drugs or the permeation of solutes depending on surrounding environmental conditions. Poly(methacrylic acid) (PMAA) exhibits interpolymer complexation with poly(ethylene glycol) (PEG) as the protons of the carboxylic acid groups on PMAA form hydrogen bonds with the ether groups on the PEG chain. This complexation forms only at pH low enough to insure substantial protonation of the carboxylic acid groups. Complexation of free chains of PMAA with PEG in solution has been studied. We have also shown that poly(dimethyl aminoethyl methacrylate) and poly(ethylene glycol) exhibit the same type of hydrogen bonding, except that the pH dependence is such that the systems decomplex at low pH and complex at high pH values. Summary of Proposed Models We developed models describing the dynamics of glucose and insulin in both healthy and diabetic patients. The models were developed by representing the body as a system consisting of several compartments. Glucose and insulin dynamics were determined by deriving mass balance equations for each individual compartment. Although compartmental models have been used in the past to describe insulin and glucose dynamics, we believe that ours is a novel contribution to the field in four ways. First, we incorporate an accurate model of a meal disturbance into both models, we incorporate an accurate model of the effects of exercise on glucose levels into both models, we attempt to characterize both interpatient and intrapatient uncertainty among model parameters such as the basal values of insulin and glucose in each compartment and we incorporate insulin release dynamics from the hydrogel systems into the diabetic patient model. The model is used to determine the structure of the hydrogel system having insulin release dynamics that most resembles the dynamics of the pancreas. In addition to the use of hydrogels, we also use the models to design effective glucose control algorithms for implantable, self-regulating insulin pumps. Results We focused on studying the effects of linearization and feedback control on existing models, most notably the model created by Bergman et al (1) and modified by Furler et al (2). ) ( ) ( 1 t D XG G G P dt dG b + − − − = (1) ) ( 3 2 b I I P X P dt dX − + − = (2)