Mathematical modeling of drug delivery from cylindrical implantable devices

A mechanistic mathematical model applicable to the controlled dispersed‐drug release from cylindrical device such as implantable drug delivery system was derived. Analytical solutions based on the pseudosteady state approximation are derived taken account an exact external medium volume. The model prediction is accurate when the initial drug load is higher than the drug solubility in the polymer. The results obtained are compared with the analytical solutions available in the literature. The equations are corroborated by comparison with experimental profiles reported in the literature for sink conditions and non sink conditions. The evolution of concentration distribution profiles is compared for different volume of external medium. A reduction in the volume of the external solution leads to an increase in the concentration on the surface of the device, which determines decreases in the release of drug. One criterion for determining whether the volume of external solution should be considered for the prediction of drug release from cylindrical devices is established. This criterion is based on establishing a maximum percentage error allowed in the values of amount of drug released. The usefulness of the model is focused in the design of implant for controlled release of drug into a small volume of external medium of release. Copyright © 2014 John Wiley & Sons, Ltd.     

Multilevel computations of dispersed drug release

We study a mathematical model of drug release from controlled delivery systems with initial drug loading higher than solubility. The model combines dissolution, diffusion, swelling, and erosion mechanisms of drug delivery. Multilevel methods are introduced to solve the governing system of diffusion equations numerically with better accuracy and lower computational costs compared with the finite element methods. Numerical examples are given to demonstrate the advantages of the multilevel methods. Numerical solutions are compared to exact and approximate solutions of the reduced models. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

药物从柱型高聚物基体内扩散释放的活动边界问题

采用修正积分法,得到了药物从柱形高聚物基体内扩散释放的活动边界问题的近似解析解,给出了扩散边界和药物释放分数的计算公式及其在不同初装浓度下的计算结果。计算结果与实验结果是一致的。进而,对药物从片形、柱形、球形等不同几何形状的基体内的释放问题进行了对照,分析了基体的不同几何形状对药物释放的影响。还给出了药物从柱形基体内扩散释放的有效时间的近似计算公式。这对临床实验具有一定的指导意义,也为进一步研究药物从柱型高聚物基体内扩散释放问题以及缓释制剂的设计提供了理论工具。     

Single machine scheduling problem with controllable processing times and resource dependent release times

We consider two single machine scheduling problems with resource dependent release times and processing times, in which the release times and processing times are linearly decreasing functions of the amount of resources consumed. The objective is to minimize the total cost of makespan and resource consumption function that is composed of release time reduction and processing time reduction. In the first problem, the cost of reducing a unit release time for each job is common. We show that the problem can be solved in polynomial time. The second problem assumes different reduction costs of job release times. We show that the problem can be reduced polynomially from the partition problem and thus, is NP-complete.     

Network Design for Express Shipment Delivery

Service network design problems arise at airlines (passenger and cargo), trucking companies, railroads, etc., wherever there is a need to determine cost minimizing routes and schedules, given constraints on resource availability and level of service. We focus on a particular service network design application, namely, the express shipment delivery problem, and we develop models and a solution technique designed specifically for large-scale express delivery problems with time windows. Using data from an express delivery company, we demonstrate that our approach can produce savings in total operating costs and provide a valuable tool for making decisions at strategic and tactical levels.     

Mathematical modeling of the receptor-mediated endocytosis process of targeted therapeutic agents in drug delivery systems

In this paper, we propose mathematical models to describe receptor-mediated endocytosis processes. One is a stochastic differential model for the agent-target binding process. The mean extinction time and a standard variation over time profile are evaluated. The other is an age-structured model for demonstrating endocytosis and lysosome processes. A targeted drug delivery system has a complex process in how it is to deliver drug molecules in terms of administration, transportation in blood and across membranes to intracellular space, and inhibition to microtubule polymerization. In particular, receptor-mediated endocytosis of targeted therapeutic agents, such as antibody drug conjugates or ligand-targeted liposome encapsulated nanoparticles, is a key step in understanding the drug delivery mechanism. We discuss stochastic quasi steady state approximation when agent-target complex does not appreciably vary compared with the free agents. This reduces the number of the systems and the parameters; however, an initial time phase cannot be captured. In addition, we discuss the strengths and weaknesses when the age-structured model induces the reduced model compared with the full model that considers endocytosis and lysosome processes. If the total mean retention time until payload release in intracellular space is known, then the age-structured model with the Erlang distribution may fairly predict data of the released payload over time profile with far fewer parameters; however, induced compartments lose their physical meaning and describe only a delay.     

Optimization models for radiotherapy patient scheduling

The efficient radiotherapy patient scheduling, within oncology departments, plays a crucial role in order to ensure the delivery of the right treatment at the right time. In this context, generating a high quality solution is a challenging task, since different goals (i.e., all the activities are scheduled as soon as possible, the patient waiting time is minimized, the device utilization is maximized) could be achieved and a large set of constraints (i.e., every device can be used by only one patient at time, the treatments have to be performed in an exact time order) should be taken into account. We propose novel optimization models dealing with the efficient outpatient scheduling within a radiotherapy department defined in such a way to represent different real-life situations. The effectiveness of the proposed models is evaluated on randomly generated problems and on a real case situation. The results are very encouraging since the developed optimization models allow to overcome the performance of human experts (i.e., the number of patients that begin the radiotherapy treatment is maximized).      

带有拒绝的单机和同型机排序问题

研究了带有拒绝的单机和同型机排序问题. 对于单机情形, 工件的惩罚费用是对应加工时间的\alpha倍.如果工件有到达时间, 目标为最小化时间表长与惩罚费用之和, 证明了这个问题是可解的.如果所有工件在零时刻到达, 目标为最小化总完工时间与惩罚费用之和, 也证明了该问题是可解的.对于同型机排序问题, 研究了工件分两批在线实时到达的情形, 目标为最小化时间表长与惩罚费用之和.针对机器台数2和m, 分别给出了竞争比为2和4-2/m的在线算法.     

无阻塞概率下的排队效率分析

排队在日常生活当中屡见不鲜,为了使顾客排队等待的时间尽可能减少,除了合理安排工作人员的服务质量及服务设备外,还应该考虑如何安排排队更有效。本文在通讯系统排队问题分析的基础上,在假设阻塞概率趋近于零的情况下,比较了不同排队方式下的效率,得出结论：排成一个大队要优于排成几个小队。     

Alternate risk measures for emergency medical service system design

The stochastic nature of emergency service requests and the unavailability of emergency vehicles when requested to serve demands are critical issues in constructing valid models representing real life emergency medical service (EMS) systems. We consider an EMS system design problem with stochastic demand and locate the emergency response facilities and vehicles in order to ensure target levels of coverage, which are quantified using risk measures on random unmet demand. The target service levels for each demand site and also for the entire service area are specified. In order to increase the possibility of representing a wider range of risk preferences we develop two types of stochastic optimization models involving alternate risk measures. The first type of the model includes integrated chance constraints (ICCs ), whereas the second type incorporates ICCs  and a stochastic dominance constraint. We develop solution methods for the proposed single-stage stochastic optimization problems and present extensive numerical results demonstrating their computational effectiveness.     

考虑多种类型缺陷的软件可靠性模型研究

本文提出一种考虑多种类型缺陷的软件可靠性模型,并构建了缺陷检测和剔除两个过程的模型。具体分类情况,可以根据模型的检验方法(拟合准则和预测有效性度量)和模型复杂度来具体决定,如果有测试人员的分类建议或者分类数据,可以结合模型共同决定。为了说明问题,本文给出四种类型缺陷的具体模型,并对实际数据集进行了拟合。通过模型比较,验证了多种类型缺陷模型的有效性。最后,通过构建软件最优发布时间策略对模型进行了应用。研究结果为软件开发和测试提供了理论参考。     

基于承诺交货期的两阶通用件库存模型

在一个两阶段生产系统中,针对第二阶段应用单通用件的情况,引入承诺交货期因素,分别建立了第一阶段无通用件、单通用件、双通用件库存模型,考查了承诺交货期对通用件库存模型总成本的影响,分析了三类模型相应的最优库存水平。通过算例,说明了在一个第二阶段采用单通用件的两阶段生产系统中,当通用件与非通用件的单位采购成本相同时,并非第一阶段使用越多的通用件,总成本就越低。     

A conservation law with spatially localized sublinear damping

We consider a general conservation law on the circle, in the presence of a sublinear damping. If the damping acts on the whole circle, then the solution becomes identically zero in finite time, following the same mechanism as the corresponding ordinary differential equation. When the damping acts only locally in space, we show a dichotomy: if the flux function is not zero at the origin, then the transport mechanism causes the extinction of the solution in finite time, as in the first case. On the other hand, if zero is a non-degenerate critical point of the flux function, then the solution becomes extinct in finite time only inside the damping zone, decays algebraically uniformly in space, and we exhibit a boundary layer, shrinking with time, around the damping zone. Numerical illustrations show how similar phenomena may be expected for other equations.     

Flux tracking in drug delivery

The dynamics of diffusive and stress-induced transport in polymeric delivery systems was investigated. Partial and ordinary differential equations were first written to describe drug release behaviors in Maxwell and Maxwell–Voigt materials. The time constants governing the flux and concentration responses of a permeating species were determined from a Laplace transform solution of the original model. A “tracking strategy”, based on the estimated characteristic times, was proposed to estimate the delivery rate and the concentration near the exit side of the membrane. The methodology was more efficient at times greater than the time constant and the prediction error decreased further as the process approached steady state. Numerical illustrations and comparisons made with published data show the effectiveness of the proposed approach in describing the influence of the Young modulus, viscosity and relaxation time on the transient regime.     

工件可转包加工的排序问题研究

研究工件可以转包加工的单台机排序问题: 有n个工件, 在零时刻已经到达一个单台机处, 每个工件可以由加工者自有的单台机器加工或者转包给其他机器加工. 如果工件被转包加工, 那么其完工时间等于在自有机器上的加工时间, 而产生的加工费用与在自有机器上加工的费用不同. 假设被转包加工的工件的完工时间和加工费用与转包加工机器的总负载没有关系.目标函数是最小化工件最大完工时间与总加工费用的加权和. 该问题已经被证明是NP-难的. 最后给出该问题的伪多项式时间最优算法, 并且提出一个完全多项式时间近似方案(FPTAS).     

An adaptive characteristics method for advective-diffusive transport

An adaptive characteristics method is presented for the solution of advective-diffusive groundwater transport problems. The method decomposes the transport processes into advective and diffusive transport components. Advective flows are defined by using a streamtube incrementing procedure, based on the method of characteristics, to define the position of advective front. Diffusive transport orthogonal to the front is represented by an array of propagating streamtube elements, with dimension determined from analytical solution of the one-dimensional diffusion equation. Adaptive time scaling is used to moderate the dimensions and aspect ratios of the advective and diffusive streamtube elements as appropriate to the dominant transport mechanism. Finite differences are used to solve for transport ahead of the advancing front. The distribution of streamtubes are predetermined from a direct boundary element algorithm. Comparison with analytical results for a one-dimensional transport geometry indicates agreement for Peclet numbers between zero and infinity. Solution for transport in two-dimensional domains illustrates excellent agreement for Peclet numbers from zero to 25.     

Theoretical study of diffusional release of a dispersed solute from cylindrical polymeric matrix: A novel configuration for providing zero-order release profile

In the context of controlled release drug delivery approaches, the systems providing zero-order release kinetics have special advantages. Through employing these systems, drug concentration could be maintained within the therapeutic window over release time; thus maximum effectiveness alongside minimized side effects of the drug are achieved. However, obtaining zero-order drug release is extremely challenging. One of the main obstacles is the fact that implemented devices should be designed to overcome the decreasing mass transfer driving force, especially, in polymeric systems in which diffusion mechanism is dominant. In this study, we developed a new configuration of a polymeric matrix containing dispersed solute which provides sustained zero-order release. A combination of two innovative approaches including separating baffles and a two-layer coating was proposed to be incorporated into the conventional cylindrical polymeric matrix to induce zero-order release behavior. Then, an approximate mathematical model was developed to investigate the performance of the system under different conditions. The simulated results showed the potential of proposed configuration to be used as a carrier for sustained zero-order release.     

Incorporating manufacturing lead times in joint production-marketing models: A review and some future directions

In many industries the pricing of a product over time can be used to manage demand for the product. Lead time, or promised delivery time is often a significant factor in price negotiations. However, the production planning literature has largely treated pricing decisions as exogeneous while focusing on the allocation of production capacity between products over time. On the other hand, the marketing literature has generally ignored the effects of capacity constraints and focused on the effects of pricing. In this paper, we begin by reviewing the existing literature on integrative production-marketing research, focusing on those models that consider lead times and capacity. We suggest a number of directions for future research that take advantage of recent developments in production planning models, as well as explicit modeling of feedback loops governing key parameters, which suggest a broader view of the problem.     

Sensitivity analysis of release time of software reliability models incorporating testing effort with multiple change-points

To accurately model software failure process with software reliability growth models, incorporating testing effort has shown to be important. In fact, testing effort allocation is also a difficult issue, and it directly affects the software release time when a reliability criteria has to be met. However, with an increasing number of parameters involved in these models, the uncertainty of parameters estimated from the failure data could greatly affect the decision. Hence, it is of importance to study the impact of these model parameters. In this paper, sensitivity of the software release time is investigated through various methods, including one-factor-at-a-time approach, design of experiments and global sensitivity analysis. It is shown that the results from the first two methods may not be accurate enough for the case of complex nonlinear model. Global sensitivity analysis performs better due to the consideration of the global parameter space. The limitations of different approaches are also discussed. Finally, to avoid further excessive adjustment of software release time, interval estimation is recommended for use and it can be obtained based on the results from global sensitivity analysis.     

Solving Planning and Design Problems in the Process Industry Using Mixed Integer and Global Optimization

This contribution gives an overview on the state-of-the-art and recent advances in mixed integer optimization to solve planning and design problems in the process industry. In some case studies specific aspects are stressed and the typical difficulties of real world problems are addressed. Mixed integer linear optimization is widely used to solve supply chain planning problems. Some of the complicating features such as origin tracing and shelf life constraints are discussed in more detail. If properly done the planning models can also be used to do product and customer portfolio analysis. We also stress the importance of multi-criteria optimization and correct modeling for optimization under uncertainty. Stochastic programming for continuous LP problems is now part of most optimization packages, and there is encouraging progress in the field of stochastic MILP and robust MILP. Process and network design problems often lead to nonconvex mixed integer nonlinear programming models. If the time to compute the solution is not bounded, there are already a commercial solvers available which can compute the global optima of such problems within hours. If time is more restricted, then tailored solution techniques are required.