Mathematical models of energy homeostasis

Diabetes and obesity present a mounting global challenge. Clinicians are increasingly turning to mechanism-based mathematical models for a quantitative definition of physiological defects such as insulin resistance, glucose intolerance and elevated obesity set points, and for predictions of the likely outcomes of therapeutic interventions. However, a very large range of such models is available, making a judicious choice difficult. To better inform this choice, here we present the most important models published to date in a uniform format, discussing similarities and differences in terms of the decisions faced by modellers. We review models for glucostasis, based on the glucose-insulin feedback control loop, and consider extensions to long-term energy balance, dislipidaemia and obesity.     

The structure and properties of materials used in advanced drug delivery systems

The various requirements placed on materials that might serve as suitable components in drug delivery systems are discussed. Special attention is paid to the interactions between the drug delivery constructs and the biological environment, using the interactions in the vascular compartment of the body as an example. Two alternative general approaches are compared: (a) “controlled drug release”, which aims to reduce or eliminate side effects by producing a steady therapeutic concentration of drug in the body; (b) “site-selective drug delivery”, which aims to ensure that the drug is delivered to the site of its biochemical and disease-related site of action, at the same time maintaining the drug inactive elsewhere in the body. It is concluded that materials for delivering drugs to selected sites of disease within the body must be designed to utilise the unique features (structure, function, rhythm) of the main elements involved in the disease. Equally important is to design drug carriers that do not interact non-specifically within the body so that their specific action would be prevented. It is difficult to see how this could be achieved using materials entirely “foreign” to the body. Utilising the primary structures used by the biological systems (proteins, glycoproteins, carbohydrates) and creating novel higher structures (secondary, tertiary, quartenary) that mimic the native material is the logical way forward in the search for new drug delivery systems, and we need to turn more and more to the molecular basis of biology for guidance and inspiration.     

数学建模案例的编写与使用

从数学建模案例教学的可能性与必要性出发，本文陈述浙江大学近年来在数学建模系列课程教学过程中编写和使用数学建模教学案例的经验和方法。     

Otic drug delivery systems: formulation principles and recent developments

Disorders of the ear severely impact the quality of life of millions of people, but the treatment of these disorders is an ongoing, but often overlooked challenge particularly in terms of formulation design and product development. The prevalence of ear disorders has spurred significant efforts to develop new therapeutic agents, but perhaps less innovation has been applied to new drug delivery systems to improve the efficacy of ear disease treatments. This review provides a brief overview of physiology, major diseases, and current therapies used via the otic route of administration. The primary focuses are on the various administration routes and their formulation principles. The article also presents recent advances in otic drug deliveries as well as potential limitations. Otic drug delivery technology will likely evolve in the next decade and more efficient or specific treatments for ear disease will arise from the development of less invasive drug delivery methods, safe and highly controlled drug delivery systems, and biotechnology targeting therapies.     

Enhanced oral bioavailability and intestinal lymphatic transport of a hydrophilic drug using liposomes

A liposome system was evaluated for oral delivery of a poorly bioavailable hydrophilic drug. The system was prepared from proliposome, which consisted of negatively charged phosphatidylcholine, whereas cefotaxime was chosen as the model drug. An in vivo study was carried out on nine rats according to a three-way crossover design to compare the oral bioavailability of cefotaxime from the liposomal formulation with that of an aqueous drug solution and a physical mixture of cefotaxime with blank liposomes. The results indicated that the extent of bioavailability of cefotaxime was increased approximately 2.7 and 2.3 times compared with that of the aqueous solution and the physical mixture, respectively. In a separate study, simultaneous determination of cefotaxime in intestinal lymph (collected from the mesenteric lymph duct) and in plasma (collected from the tail vein) revealed that its concentration was consistently higher in the lymph than in the plasma when administered via the liposomal formulation, whereas the reverse was observed with the aqueous solution. Thus, the results indicated that the liposomes system has the potential of increasing the oral bioavailability of poorly bioavailable hydrophilic drugs and also promote their lymphatic transport in the intestinal lymph.     

石墨烯纳米材料在药物释放和基因传递中的应用

石墨烯纳米材料由于其独特的结构和优良的机械、光学和电学性能,已经在物理、化学和材料科学等领域广泛应用。最新研究表明其特殊的属性可应用在生物医学领域的,综述了石墨烯纳米材料在生物医学领域如药物释放和基因传递中的应用,最后指出了石墨烯纳米材料在生物医学领域应用中目前存在的问题。     

On computational homogenization of microscale crack propagation

The effective response of microstructures undergoing crack propagation is studied by homogenizing the response of statistical volume elements (SVEs). Because conventional boundary conditions (Dirichlet, Neumann and strong periodic) all are inaccurate when cracks intersect the SVE boundary, we herein use first order homogenization to compare the performance of these boundary conditions during the initial stage of crack propagation in the microstructure, prior to macroscopic localization. Using weakly periodic boundary conditions that lead to a mixed formulation with displacements and boundary tractions as unknowns, we can adapt the traction approximation to the problem at hand to obtain better convergence with increasing SVE size. In particular, we show that a piecewise constant traction approximation, which has previously been shown to be efficient for stationary cracks, is more efficient than the conventional boundary conditions in terms of convergence also when crack propagation occurs on the microscale. The performance of the method is demonstrated by examples involving grain boundary crack propagation modelled by conventional cohesive interface elements as well as crack propagation modelled by means of the extended finite element method in combination with the concept of material forces. © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd.     

A patient-specific computational model of hypoxia-modulated radiation resistance in glioblastoma using 18F-FMISO-PET

Glioblastoma multiforme (GBM) is a highly invasive primary brain tumour that has poor prognosis despite aggressive treatment. A hallmark of these tumours is diffuse invasion into the surrounding brain, necessitating a multi-modal treatment approach, including surgery, radiation and chemotherapy. We have previously demonstrated the ability of our model to predict radiographic response immediately following radiation therapy in individual GBM patients using a simplified geometry of the brain and theoretical radiation dose. Using only two pre-treatment magnetic resonance imaging scans, we calculate net rates of proliferation and invasion as well as radiation sensitivity for a patient''s disease. Here, we present the application of our clinically targeted modelling approach to a single glioblastoma patient as a demonstration of our method. We apply our model in the full three-dimensional architecture of the brain to quantify the effects of regional resistance to radiation owing to hypoxia in vivo determined by [¹⁸F]-fluoromisonidazole positron emission tomography (FMISO-PET) and the patient-specific three-dimensional radiation treatment plan. Incorporation of hypoxia into our model with FMISO-PET increases the model–data agreement by an order of magnitude. This improvement was robust to our definition of hypoxia or the degree of radiation resistance quantified with the FMISO-PET image and our computational model, respectively. This work demonstrates a useful application of patient-specific modelling in personalized medicine and how mathematical modelling has the potential to unify multi-modality imaging and radiation treatment planning.     

A composite computational model of liver glucose homeostasis. II. Exploring system behaviour

Using a composite model of the glucose homeostasis system, consisting of seven interconnected submodels, we enumerate the possible behaviours of the model in response to variation of liver insulin sensitivity and dietary glucose variability. The model can reproduce published experimental manipulations of the glucose homeostasis system and clearly illustrates several important properties of glucose homeostasis—boundedness in model parameters of the region of efficient homeostasis, existence of an insulin sensitivity that allows effective homeostatic control and the importance of transient and oscillatory behaviour in characterizing homeostatic failure. Bifurcation analysis shows that the appearance of a stable limit cycle can be identified.     

A composite computational model of liver glucose homeostasis. I. Building the composite model

A computational model of the glucagon/insulin-driven liver glucohomeostasis function, focusing on the buffering of glucose into glycogen, has been developed. The model exemplifies an ‘engineering’ approach to modelling in systems biology, and was produced by linking together seven component models of separate aspects of the physiology. The component models use a variety of modelling paradigms and degrees of simplification. Model parameters were determined by an iterative hybrid of fitting to high-scale physiological data, and determination from small-scale in vitro experiments or molecular biological techniques. The component models were not originally designed for inclusion within such a composite model, but were integrated, with modification, using our published modelling software and computational frameworks. This approach facilitates the development of large and complex composite models, although, inevitably, some compromises must be made when composing the individual models. Composite models of this form have not previously been demonstrated.     

The counter-current backmixing model for fluid bed reactors — computational aspects and model modifications

Numerical solution of differential equations describing the counter-current backmixing model of Fryer and Potter is very difficult due to the boundary value nature of the problem. Several numerical methods (shooting, superposition and finite difference) have been described and tested on a problem with a single first-order reaction in an isothermal fluid bed reactor. It was found that the finite difference method is the most stable method and provides accurate solution over the entire range of parameters that were investigated, while the shooting and the superposition methods could not produce accurate solutions for some parameter values. Also, some modifications of the Fryer and Potter model such as: compartment models and conversion to an initial value type of problem (Jayraman-Kulkarni-Doraiswamy model), have been described. Results obtained from compartment models are in close agreement with predictions obtained from the original Fryer and Potter model. This paper is dedicated to Dr L K Doraiswamy on his sixtieth birthday. Computations reported in this paper were carried out by N Nasif, J G Daly and S H Lane.     

Mathematical Modelling of Wave Propagation in a Rod of Time-Dependent Material

A numerical procedure to study one-dimensional waves in a rod, taking into account arbitrary rheological properties, is considered. The procedure is based on direct mathematical modelling of wave propagation in a rod of variable crosssection. Elastic-viscoplastic waves resulting from the impact of a rigid body, including repeated collisions and rebounds, are analyzed. This revised version was published online in July 2006 with corrections to the Cover Date.     

环境敏感性水凝胶在药物控释系统中的应用

论述了温度敏感性水凝胶、pH敏感性水凝胶及温度/pH双重敏感性水凝胶的结构、性质及在药物控释体系中的应用.     

Magnetic nanoparticles: recent developments in drug delivery system

Nanostructured functional materials have demonstrated their great potentials in medical applications, attracting increasing attention because of the opportunities in cancer therapy and the treatment of other ailments. This article reviews the problems and recent advances in the development of magnetic NPs for drug delivery.     

碳纳米管内药物传输机理及其发展趋势

针对纳米科学技术发展对药物传输方式所带来的革命性变化,综合介绍了基于碳纳米管的分子传输机理的研究结果,指出了相关重要研究结果在药物传输领域中的潜在应用;同时,结合最新研究结果,分析了碳纳米管内药物传输研究的发展趋势,提出了尚需进一步研究的若干问题。     

Development of ocular drug delivery systems using molecularly imprinted soft contact lenses

Recently, significant advances have been made in order to optimize drug delivery to ocular tissues. The main problems in ocular drug delivery are poor bioavailability and uncontrollable drug delivery of conventional ophthalmic preparations (e.g. eye drops). Hydrogels have been investigated since 1965 as new ocular drug delivery systems. Increase of hydrogel loading capacity, optimization of drug residence time on the ocular surface and biocompatibility with the eye tissue has been the main focus of previous studies. Molecular imprinting technology provided the opportunity to fulfill the above-mentioned objectives. Molecularly imprinted soft contact lenses (SCLs) have high potentials as novel drug delivery systems for the treatment of eye disorders. This technique is used for the preparation of polymers with specific binding sites for a template molecule. Previous studies indicated that molecular imprinting technology could be successfully applied for the preparation of SCLs as ocular drug delivery systems. Previous research, particularly in vivo studies, demonstrated that molecular imprinting is a versatile and effective method in optimizing the drug release behavior and enhancing the loading capacity of SCLs as new ocular drug delivery systems. This review highlights various potentials of molecularly imprinted contact lenses in enhancing the drug-loading capacity and controlling the drug release, compared to other ocular drug delivery systems. We have also studied the effects of contributing factors such as the type of comonomer, template/functional monomer molar ratio, crosslinker concentration in drug-loading capacity, and the release properties of molecularly imprinted hydrogels.     

Preparation and in vitro evaluation of pH, time-based and enzyme-degradable pellets for colonic drug delivery

The preparation of pH-dependent, time-based and enzyme degradable pellets was investigated for use as an oral colonic drug delivery system. It was expected that drug would be released immediately once the pellets reached the colon. The pellets were prepared using extrusion-spheronizing equipment and subsequently coated with three layers of three functional polymers by an air-suspension technique. The core consisted of 5-aminosalicylic acid (5-ASA) as a model drug, CaP as an enzyme-degradable material and microcrystalline cellulose (MCC) as an additive. As far as the three coated layers were concerned, the outer layer was coated with Eudragit L30D-55 for protection against gastrointestinal juices, the intermediate layer was coated with ethylcellulose (EC) to inhibit drug release during passage through the small intestine, and the inner film was coated with pectin for swelling and enzyme-degradation, which required a 30, 10, and 12% weight gain, respectively. Several micromeritic properties of the core pellets, including particle size distribution, particle size, degree of circularity, and friability, were evaluated to investigate the effects of the formulations of the cores and preparation conditions. Also, dissolution testing of the cores showed that the presence of calcium pectinate (CaP) markedly increased the drug release rate from the cores, as determined by scanning electron microscopy (SEM). In-vitro release studies indicated that the coated pellets completely protected the drug release in 0.1 mol/L HCl, while the drug release was delayed for 3-4 hr in pH 6.8 PBS. A synergistic effect of enzyme dependence for the coated pellets was seen following removal of the coated layer and during contact with colonic enzymes. Consequently, it was possible to achieve colon-specific drug delivery using this triple-dependence system.     

Mathematical models and program packages for calculating pollutant transport in the atmosphere

Three mathematical models and program packages for modeling pollution of the atmosphere and the ground surface with pollutants from a source of technogenic dusting are presented. Experimental data are used to verify the programs. Translated from Inzhenerno-Fisicheskii Zhurnal, Vol. 71, No. 3, pp. 509–515, May–June 1998.     

Electrospun nanofibrous materials for tissue engineering and drug delivery

Abstract

The electrospinning technique, which was invented about 100 years ago, has attracted more attention in recent years due to its possible biomedical applications. Electrospun fibers with high surface area to volume ratio and structures mimicking extracellular matrix (ECM) have shown great potential in tissue engineering and drug delivery. In order to develop electrospun fibers for these applications, different biocompatible materials have been used to fabricate fibers with different structures and morphologies, such as single fibers with different composition and structures (blending and core-shell composite fibers) and fiber assemblies (fiber bundles, membranes and scaffolds). This review summarizes the electrospinning techniques which control the composition and structures of the nanofibrous materials. It also outlines possible applications of these fibrous materials in skin, blood vessels, nervous system and bone tissue engineering, as well as in drug delivery.     

Mathematical modelling of adult hippocampal neurogenesis: effects of altered stem cell dynamics on cell counts and bromodeoxyuridine-labelled cells

In the adult hippocampus, neurogenesis—the process of generating mature granule cells from adult neural stem cells—occurs throughout the entire lifetime. In order to investigate the involved regulatory mechanisms, knockout (KO) experiments, which modify the dynamic behaviour of this process, were conducted in the past. Evaluating these KOs is a non-trivial task owing to the complicated nature of the hippocampal neurogenic niche. In this study, we model neurogenesis as a multicompartmental system of ordinary differential equations based on experimental data. To analyse the results of KO experiments, we investigate how changes of cell properties, reflected by model parameters, influence the dynamics of cell counts and of the experimentally observed counts of cells labelled by the cell division marker bromodeoxyuridine (BrdU). We find that changing cell proliferation rates or the fraction of self-renewal, reflecting the balance between symmetric and asymmetric cell divisions, may result in multiple time phases in the response of the system, such as an initial increase in cell counts followed by a decrease. Furthermore, these phases may be qualitatively different in cells at different differentiation stages and even between mitotically labelled cells and all cells existing in the system.