Compartmental modelling of the pharmacokinetics of a breast cancer resistance protein

A mathematical model for the pharmacokinetics of Hoechst 33342 following administration into a culture medium containing a population of transfected cells (HEK293 hBCRP) with a potent breast cancer resistance protein inhibitor, Fumitremorgin C (FTC), present is described. FTC is reported to almost completely annul resistance mediated by BCRP in vitro. This non-linear compartmental model has seven macroscopic sub-units, with 14 rate parameters. It describes the relationship between the concentration of Hoechst 33342 and FTC, initially spiked in the medium, and the observed change in fluorescence due to Hoechst 33342 binding to DNA. Structural identifiability analysis has been performed using two methods, one based on the similarity transformation/exhaustive modelling approach and the other based on the differential algebra approach. The analyses demonstrated that all models derived are uniquely identifiable for the experiments/observations available. A kinetic modelling software package, namely FACSIMILE (MPCA Software, UK), was used for parameter fitting and to obtain numerical solutions for the system equations. Model fits gave very good agreement with in vitro data provided by AstraZeneca across a variety of experimental scenarios.     

Multidisciplinary modelling of biomedical systems

This paper describes general principles and example results of a new software tool being developed for physiologically-based modelling of biomedical systems within a multidisciplinary framework. The aim is to overcome some limitations of currently available software designed either for general purpose or for highly specialised modelling applications. In fact, general purpose tools usually impose explicit coding of mathematical model equations or non-intuitive system representations, whereas specialised software use domain-specific notations that allow efficient and convenient model building only for special classes of systems. The aim of the present study is to pursue intuitive representation of various, possibly interacting, types of biological systems described as interconnected physical components, such as mass and energy storage elements, active and passive transport or biochemical transformations. The presented software generates automatically the mathematical model equations that can be coded in different formats. This allows interoperability with other existing software, e.g. for numerical simulation, symbolic analysis or text processing. A multi-domain structural language has been defined for an intuitive, hierarchical and self-explanatory specification of physiological models. The proposed strategies may become useful for dissemination and integration of multidisciplinary modelling knowledge.     

Indistinguishability and identifiability of kinetic models for the MurC reaction in peptidoglycan biosynthesis

An important question in Systems Biology is the design of experiments that enable discrimination between two (or more) competing chemical pathway models or biological mechanisms. In this paper analysis is performed between two different models describing the kinetic mechanism of a three-substrate three-product reaction, namely the MurC reaction in the cytoplasmic phase of peptidoglycan biosynthesis. One model involves ordered substrate binding and ordered release of the three products; the competing model also assumes ordered substrate binding, but with fast release of the three products. The two versions are shown to be distinguishable; however, if standard quasi-steady-state assumptions are made distinguishability cannot be determined. Once model structure uniqueness is ensured the experimenter must determine if it is possible to successfully recover rate constant values given the experiment observations, a process known as structural identifiability. Structural identifiability analysis is carried out for both models to determine which of the unknown reaction parameters can be determined uniquely, or otherwise, from the ideal system outputs. This structural analysis forms an integrated step towards the modelling of the full pathway of the cytoplasmic phase of peptidoglycan biosynthesis.     

The role of knowledge modelling techniques in software development: a general approach based on a knowledge management tool

The aim of the paper is to discuss the use of knowledge models to formulate general applications. First, the paper presents the recent evolution of the software field where increasing attention is paid to conceptual modelling. Then, the current state of knowledge modelling techniques is described where increased reliability is available through the modern knowledge-acquisition techniques and supporting tools. The knowledge structure manager (KSM) tool is described next. First, the concept of knowledge area is introduced as a building block where methods to perform a collection of tasks are included together with the bodies of knowledge providing the basic methods to perform the basic tasks. Then, the CONCEL language to define vocabularies of domains and the LINK language for methods formulation are introduced. Finally, the object-oriented implementation of a knowledge area is described and a general methodology for application design and maintenance supported by KSM is proposed. To illustrate the concepts and methods, an example of system for intelligent traffic management in a road network is described. This example is followed by a proposal of generalization for reuse of the resulting architecture. Finally, some concluding comments are made regarding the feasibility of using the knowledge modelling tools and methods for general application design.     

Numerical and visual evaluation of hydrological and environmental models using the Monte Carlo analysis toolbox

The detailed evaluation of mathematical models and the consideration of uncertainty in the modeling of hydrological and environmental systems are of increasing importance, and are sometimes even demanded by decision makers. At the same time, the growing complexity of models to represent real-world systems makes it more and more difficult to understand model behavior, sensitivities and uncertainties. The Monte Carlo Analysis Toolbox (MCAT) is a Matlab library of visual and numerical analysis tools for the evaluation of hydrological and environmental models. Input to the MCAT is the result of a Monte Carlo or population evolution based sampling of the parameter space of the model structure under investigation. The MCAT can be used off-line, i.e. it does not have to be connected to the evaluated model, and can thus be used for any model for which an appropriate sampling can be performed. The MCAT contains tools for the evaluation of performance, identifiability, sensitivity, predictive uncertainty and also allows for the testing of hypotheses with respect to the model structure used. In addition to research applications, the MCAT can be used as a teaching tool in courses that include the use of mathematical models.     

统计机器学习中参数可辨识性研究及其关键问题

参数可辨识性研究在统计机器学习中具有重要的理论意义和应用价值.参数可辨识性是关于模型参数能否被惟一确定的性质.在包含物理参数的学习模型中,可辨识性不仅是物理参数获得正确估计的前提条件,更重要的是,它反映了学习机器中由参数决定的物理特征.为扩展到未来类人智能机器研究的考察视角,我们将学习模型纳入"知识与数据共同驱动模型"的框架中讨论.在此框架下,我们提出两个关键问题.第一是参数可辨识性准则问题.该问题考察与可辨识性密切相关的各种判断准则,其中知识驱动子模型与数据驱动子模型的耦合方式为参数可辨识性问题提供了新的研究空间.第二是参数可辨识性与机器学习理论和应用相关联的研究.该研究包括可辨识性对参数估计、模型选择、学习算法、学习动态过程、奇异学习理论、贝叶斯推断等内容的深刻影响.     

Factors affecting the identifiability of compartmental models

The identifiability of compartmental models is analysed through a series of examples which have been used to describe physiological or pharmacokinetic processes. Emphasis is placed on aspects of experimental identifiability which have hitherto received little attention in identifiability analysis. It is shown that where a single-input, single-output experiment results in non-identifiability or local identifiability, it is often possible to improve the situation by measuring more responses or simultaneously perturbing more inputs. Identifiability is then shown usually to depend on whether the observation gains are known and on the shape of the inputs, when more than one is applied. The relative merits of the Laplace transform and normal mode methods of analysing identifiability are discussed and illustrated with a substantial example. The identifiability analysis of a nonlinear compartmental model, with state-dependent rate coefficients, is presented. It is shown that inclusion of a neglected (nonlinear) relationship can make a previously non-identifiable model uniquely identifiable.     

“It was an artefact not the result”: A note on systems dynamic model development tools

Environmental modelling is done more and more by practising ecologists rather than computer scientists or mathematicians. This is because there is a broad spectrum of development tools available that allows graphical coding of complex models of dynamic systems and help to abstract from the mathematical issues of the modelled system and the related numerical problems for estimating solutions. In this contribution, we study how different modelling tools treat a test system, a highly non-linear predator–prey model, and how the numerical solutions vary. We can show that solutions (a) differ if different development tools are chosen but the same numerical procedure is selected; (b) depend on undocumented implementation details; (c) vary even for the same tool but for different versions; and (d) are generated but with no notifications on numerical problems even if these could be identified. We conclude that improved documentation of numeric methods used in the modelling software is essential to make sure that process based models formulated in terms of these modelling packages do not become “black box” models due to uncertainty in integration methods.     

Mathematical modelling in science and mathematics education

Scientific research involves mathematical modelling in the context of an interactive balance between theory, experiment and computation. However, computational methods and tools are still far from being appropriately integrated in the high school and university curricula in science and mathematics. In this paper, it is discussed the relevance of mathematical modelling and illustrated how a computer modelling tool (Modellus, a free tool available on the Internet and developed at FCTUNL) can be used to embed modelling in high school and undergraduate courses. Modellus allows students to create and explore mathematical models using functions, differential and iterative equations, and visualize the behaviour of mathematical objects.     

Parameter identification and model verification in systems of partial differential equations applied to transdermal drug delivery

The purpose of this paper is to present some numerical tools which facilitate the interpretation of simulation or data fitting results and which allow computation of optimal experimental designs. They help to validate mathematical models describing the dynamical behavior of a biological, chemical, or pharmaceutical system, without requiring a priori knowledge about the physical or chemical background. Although the ideas are quite general, we will concentrate our attention to systems of one-dimensional partial differential equations and coupled ordinary differential equations. A special application model serves as a case study and is outlined in detail. We consider the diffusion of a substrate through cutaneous tissue, where metabolic reactions are included in form of Michaelis–Menten kinetics. The goal is to simulate transdermal drug delivery, where it is supposed that experimental data are available for substrate and metabolic fluxes. Numerical results are included based on laboratory data to show typical steps of a model validation procedure, i.e., the interpretation of confidence intervals, the compliance with physical laws, the identification and elimination of redundant model parameters, the computation of optimum experimental designs and the identifiability of parameters by determining weight distributions.     

CHEOPS: A tool-integration platform for chemical process modelling and simulation

A large number of modelling tools exist for the construction and solution of mathematical models of chemical processes. Each (chemical) process modelling tool provides its own model representation and model definition functions as well as its own solution algorithms, which are used for performing computer-aided studies for the process under consideration. However, in order to support reusability of existing models and to allow for the combined use of different modelling tools for the study of complex processes, model integration is needed. This paper presents a concept for an integration platform that allows for the integration of modelling tools, combining their models to build up a process model and performing computer-aided studies based on this integrated process model. In order to illustrate the concept without getting into complicated algorithmic issues, we focus on steady-state simulation using models comprising only algebraic equations. The concept is realized in the component-based integration platform CHEOPS, which focuses on integrating and solving existing models rather than providing its own modelling capabilities.     

Design of a multimodel of a dairy cows herd attacked by mastitis

We present the building of a discrete event multimodel simulation tool of livestock farming systems, regrouping several mathematical models, and reproducing cattle herd performances through an individual based model. The main goal of this simulator is to study and predict consequences of mastitis occurrences on dairy herds taking into account individual characteristics of animals and seasonal and livestock parameters. The model presented is the result of a close collaboration between epidemiologists and simulationists and we were able to use real field data from animal experiments. The project includes a domain analysis of dairy herd systems in France, using an object oriented approach and Unified Modelling Language tools. The software, written in Java, is to become a decision-aid tool for stock breeder advisors.     

Identification and Identifiability of Unknown Parameters in Multibody Dynamic Systems

Assessing design changes in mechanical systems from simulationresults requires both accurate dynamic models and accurate values forparameters in the models. Model parameters are often unavailable ordifficult to measure. This study details an identification procedure fordetermining optimal values for unknown or estimated model parametersfrom experimental test data. The resulting optimization problem issolved by Levenberg–Marquardt methods. Partial derivative matricesneeded for the optimization are computed through sensitivity analysis.The sensitivity equations to be solved are generated analytically.Unfortunately, not all parameters can be uniquely determined using anidentification procedure. An issue of parameter identifiability remains.Since a global identifiability test is impractical for even the simplestmodels, a local identifiability test is developed. Two examples areprovided. The first example highlights the test for parameteridentifiability, while the second shows the usefulness of parameteridentification by determining vehicle suspension parameters fromexperimentally measured data.     

Agent-Based Simulation of Animal Behaviour

In the biological literature on animal behaviour, in addition to real experiments and field studies, also simulation experiments are a useful source of progress. Often specific mathematical modelling techniques are adopted and directly implemented in a programming language. Modelling more complex agent behaviours is less adequate using the usually adopted mathematical modelling techniques. The literature on AI and Agent Technology offers more specific methods to design and implement (also more complex) intelligent agents and agent societies on a conceptual level. One of these methods is the compositional multi-agent system design method DESIRE. In this paper it is shown how (depending on the complexity of the required behaviour) a simulation model for animal behaviour can be designed at a conceptual level in an agent-based manner. Different models are shown for different types of behaviour, varying from purely reactive behaviour to pro-active, social and adaptive behaviour. The compositional design method for multi-agent systems DESIRE and its software environment supports the conceptual and detailed design, and execution of these models. A number of experiments reported in the literature on animal behaviour have been simulated for different agent models.     

MIGA, A Software Tool for Nonlinear System Modelling with Modular Neural Networks

This paper presents a software tool suitable for dynamic system modelling. The models generated by this tool are modular neural networks, see [1]. Each module behaves like a functional block and is connected to the other modules like in classical block diagrams. This tool allows the inclusion of a priori knowledge and, furthermore, to extract physical information from the models, once the system has learned. The modelling tool is capable of automatic model generation, parameter estimation and model validation.     

Application of evolutionary optimisers in data-based calibration of Activated Sludge Models

Modelling activated sludge systems has become an accepted practice in Wastewater Treatment Plant (WWTP) design, teaching and research, and Activated Sludge Models (ASM) are by far the most widely used models for activated sludge systems. In most ASM applications, calibration is based on more or less ad-hoc and trial and error approaches. Calibration of the ASMs remains the weakest link in the overall process of modelling biological wastewater treatment. In this paper, a calibration approach is proposed where the need for expert knowledge and modeller effort is significantly reduced. The calibration approach combines identifiability analysis and evolutionary optimisers to automate the ASM calibration. Identifiability analysis is used to deal with poor identifiability of the model structures and evolutionary optimisers are used to identify the model parameters. The applied evolutionary optimisers are Genetic Algorithms and Differential Evolution. Performance of the evolutionary optimisers is compared with a previously proposed calibration approach based on Monte Carlo simulations. All methods were capable of calibrating the model when given enough computation time. However, some of the evolutionary optimisation methods had an advantage in terms of computation time against the Monte Carlo method.     

DAISY: a decision support design methodology for complex,experience-centered domains

Users at different levels of domain experience have very different needs. For example, a system designed to assist domain novices may frustrate experts and vice-versa. This is one of several challenges specific to building decision support systems for experience-centered domains. A second challenge in working with complex experience-centered domains is that it is hard for non-experts to understand the domain in order to model it. In this paper we present DAISY, the design aid for intelligent support systems. It is a software design methodology for constructing decision support systems in complex, experience-based domains. DAISY address the specialized challenges of these domains by augmenting existing cognitive engineering methodologies. In particular, DAISY provides a method for identifying the specialized needs of users within a specific range of domain experience. Thus, it can help software designers to understand "What does the domain expert need?" or "What does a trained novice need?" To help system designers manage the complexity of modeling unfamiliar experience-centered domains, it provides a tool called a time/activity matrix. To illustrate each of DAISY's steps, we used the development of a decision support system called Fox. Fox assists expert military planners by rapidly generating alternative plans. This is a cognitively difficult, time critical task with life and death consequences     

Design techniques of a computer program for the identification of processes and the simulation of water quality in aquatic systems

In order to support environmental scientists in finding an “adequate” model for the system they are investigating, a computer program is necessary that allows its users to perform simulations for different models, to assess the identifiability and to estimate the values of model parameters (using measured data), and to estimate prediction uncertainty. These requirements, especially that of providing much freedom in model formulation, are difficult to realize in such a program. In this paper, it is shown how object-oriented program design techniques were employed to facilitate the realization of an identification and simulation program for aquatic systems (AQUASIM) that is very flexible with regard to model formulation and that provides methods of sensitivity analysis, parameter estimation and uncertainty analysis in addition to simulation. It is the goal of this paper to encourage developers of environmental software to revise previously used program structures and to employ modern program design techniques.     

Automatic fuzzy-rule assessment and its application to the modelling of nitrogen leaching for large regions

 Diffuse nutrient emissions from agricultural land is one of the major sources of pollution for ground water, rivers and coastal waters. The quantification of pollutant loads requires mathematical modelling of water and nutrient cycles. The deterministic simulation of nitrogen dynamics, represented by complicated highly non-linear processes, requires the application of detailed models with many parameters and large associated data bases. The operation of those models within integrated assessment tools or decision support systems for large regions is often not feasible. Fuzzy rule based modelling provides a fast, transparent and parameter parsimonious alternative. Besides, it allows regionalisation and integration of results from different models and measurements at a higher generalised level and enables explicit consideration of expert knowledge. In this paper an algorithm for the assessment of fuzzy rules for fuzzy modelling using simulated annealing is presented. The fuzzy rule system is applied to simulate nitrogen leaching for selected agricultural soils within the 23687 km² Saale River Basin. The fuzzy rules are defined and calibrated using results from simulation experiments carried out with the deterministic modelling system SWIM. Monthly aggregated time series of simulated water balance components (e.g. percolation and evapotranspiration), fertilization amounts, resulting nitrogen leaching and crop parameters are used for the derivation of the fuzzy rules. The 30-year simulation period was divided into 20 years for training and 10 years for validation, with the latter taken from the middle part of the period. Three specific fuzzy rule systems were created from the simulation experiments, one for each selected soil profile. Each rule system includes 15 rules as well as one prescribed rules from expert knowledge and 7 input variables. The performance of the fuzzy rule system is satisfactory for the assessment of nitrate leaching on annual to long term time steps. The approach allows rapid scenario analysis for large regions and has the potential to become part of decision support systems for generalised integrated assessment of water and nutrients in macroscale regions.