Kinetic modelling of the role of the aldehyde dehydrogenase enzyme and the breast cancer resistance protein in drug resistance and transport

A compartmental model for the in vitro uptake kinetics of the anti-cancer agent topotecan (TPT) has been extended from a previously published model. The extended model describes the drug activity and delivery of the pharmacologically active form to the DNA target as well as the catalysis of the aldehyde dehydrogenase (ALDH) enzyme and the elimination of drug from the cytoplasm via the efflux pump. Verification of the proposed model is achieved using scanning-laser microscopy data from live human breast cancer cells. Before estimating the unknown model parameters from the experimental in vitro data it is essential to determine parameter uniqueness (or otherwise) from this imposed output structure. This is formally performed as a structural identifiability analysis, which demonstrates that all of the unknown model parameters are uniquely determined by the output structure corresponding to the experiment.     

Structural identifiability analysis via symmetries of differential equations

Results and derivations are presented for the generation of a local Lie algebra that represents the ‘symmetries’ of a set of coupled differential equations. The subalgebra preserving the observation defined on the model structure is found, thus giving all transformations of the system that preserve its structure. It is shown that this is equivalent to the similarity transformation approach (Evans, Chapman, Chappell, & Godfrey, 2002) for structural identifiability analysis and as such is a method of generating such transformations for this approach. This provides another method for performing structural identifiability analysis on nonlinear state-space models that has the possibility of extension to PDE type models. The analysis is easily automated and performed in Mathematica, and this is demonstrated by application of the technique to a number of practical examples from the literature.     

Pharmacokinetic modelling of the anti-malarial drug artesunate and its active metabolite dihydroartemisinin

A four compartment mechanistic mathematical model is developed for the pharmacokinetics of the commonly used anti-malarial drug artesunate and its principle metabolite dihydroartemisinin following oral administration of artesunate. The model is structurally unidentifiable unless additional constraints are imposed. Combinations of mechanistically derived constraints are considered to assess their effects on structural identifiability and on model fits. Certain combinations of the constraints give rise to locally or globally identifiable model structures.     

Reprint of “Pharmacokinetic modelling of the anti-malarial drug artesunate and its active metabolite dihydroartemisinin”

A four compartment mechanistic mathematical model is developed for the pharmacokinetics of the commonly used anti-malarial drug artesunate and its principle metabolite dihydroartemisinin following oral administration of artesunate. The model is structurally unidentifiable unless additional constraints are imposed. Combinations of mechanistically derived constraints are considered to assess their effects on structural identifiability and on model fits. Certain combinations of the constraints give rise to locally or globally identifiable model structures.     

Variable forgetting factors in parameter estimation

This paper is concerned with the influence of forgetting factors on the consistency of prediction error methods of identification. Based on Ljung's analysis of the off-line case, it is shown that the use of forgetting factors can give rise to identifiability problems, unless the behaviour of these factors over time satisfied certain conditions. The main theorem covers the cases when the factors are deterministic functions of time or calculated via an adaptive mechanism.     

Structural identifiability and indistinguishability analyses of the Minimal Model and a Euglycemic Hyperinsulinemic Clamp model for glucose-insulin dynamics

Many mathematical models have been developed to describe glucose-insulin kinetics as a means of analysing the effective control of diabetes. This paper concentrates on the structural identifiability analysis of certain well-established mathematical models that have been developed to characterise glucose-insulin kinetics under different experimental scenarios. Such analysis is a pre-requisite to experiment design and parameter estimation and is applied for the first time to these models with the specific structures considered. The analysis is applied to a basic (original) form of the Minimal Model (MM) using the Taylor Series approach and a now well-accepted extended form of the MM by application of the Taylor Series approach and a form of the Similarity Transformation approach. Due to the established inappropriate nature of the MM with regard to glucose clamping experiments an alternative model describing the glucose-insulin dynamics during a Euglycemic Hyperinsulinemic Clamp (EIC) experiment was considered. Structural identifiability analysis of the EIC model is also performed using the Taylor Series approach and shows that, with glucose infusion as input alone, the model is structurally globally identifiable. Additional analysis demonstrates that the two different model forms are structurally distinguishable for observation of both glucose and insulin.     

Modelling of tumour growth and cytotoxic effect of docetaxel in xenografts

One of the major sources of information on physiological and pathophysiological effects in pre-clinical oncology studies is the xenografted tumour animal model. However, measurement of tumour volume over time potentially masks a range of biological changes that the xenograft is undergoing. In this paper a mechanistic model of tumour growth in xenografts is presented that can be used to investigate the mode of drug action with respect to phenotypic changes. The model encapsulates key histological biomarkers and spatial constraints. The unknown model parameters are first shown to be uniquely identifiable from the proposed experimental studies, and then estimated from the resulting data using the anti-cancer agent docetaxel.     

Parameter identifiability of space-time MIMO radar

In multiple-input multiple-output (MIMO) radar, the maximum number of targets which can be uniquely identified, also known as the parameter identifiability, is one of the most basic issues. In this paper, the parameter identifiability is extended from the space-only MIMO radar to the space-time MIMO radar. According to the parameter identifiability conditions derived, the maximum number of targets which can be identified by the space-time MIMO radar is presented. Comparing with space-only MIMO radar, the parameter identifiability of space-time MIMO radar is significantly enhanced by exploiting both the spatial and temporal characteristics of the transmitted waveforms. The results are validated by several numerical examples.     

序贯实验设计方法在变换反应动力学方程模型参数估值研究中的应用

根据序贯实验设计原理,提出用于 B_(110-2)催化剂的动力学模型参数估值程序,并提出B_(110-2)催化剂的中温变换反应本征动力学方程。     

相位的可辨识性及极大似然反褶积

本文所述系统有两个特点:输入为不可量测的随机信号;系统可以具有不稳定的零点或者说系统可以是非最小相位的.文中研究了将一类输入信号与具有正确相位的脉冲响应从输出信号中分开的条件,并对以状态空间模型为基础的极大似然反褶积方法进行了改进.利用合成数据进行了仿真研究,仿真结果验证了非最小相位系统的可辨识性.     

Direct electrochemistry and electrocatalysis of myoglobin immobilized in zirconium phosphate nanosheets film

Myoglobin (Mb) is incorporated on a novel matrix—zirconium phosphate nanosheets (ZrPNS) and immobilized at a glassy carbon electrode surface. UV–vis spectra and electrochemical measurements show that the matrix is well biocompatible and can retain the bioactivity of immobilized Mb. The direct electron transfer between Mb and electrode exhibits a couple of well-defined redox peaks. The cathodic and anodic peaks are located at −0.340 and −0.280 V vs. Ag/AgCl, respectively. The ZrPNS can improve the electron transfer between Mb and electrode with an electron transfer constant of 5.6 s⁻¹. Meanwhile, the catalytic ability of the protein toward the reduction of H₂O₂, O₂, NaNO₂, trichloroacetic acid (TCA) is also studied and a third-generation biosensor is subsequently fabricated. The linear range of biosensor to H₂O₂ is from 8 × 10⁻⁷ to 1.28 × 10⁻⁵ M with the limit detection of 1.4 × 10⁻⁷ M. The small apparent Michaelis–Menten constant (34 μM) suggests that Mb/ZrPNS film performs good affinity with H₂O₂. The biosensor also exhibits acceptable stability and reproducibility. This work paves a way to develop other biologic active materials in this kind of nanosheets for constructing novel biosensors.     

An implementation of the Expectation-Maximisation (EM) algorithm for population pharmacokinetic–pharmacodynamic modelling in ACSLXTREME

An implementation of the Expectation-Maximisation (EM) algorithm in ACSLXTREME (AEGIS Technologies) for the analyses of population pharmacokinetic–pharmacodynamic (PKPD) data is demonstrated. The parameter estimation results are compared with those from NONMEM (Globomax) using the first order conditional estimate method. The estimates are comparable and it is concluded that the EM algorithm is a useful technique in population pharmacokinetic–pharmacodynamic modelling. The implementation also demonstrates the ease with which parameter estimation algorithms for population data can be implemented in simulation software packages.     

LFT modelling and identification of anaerobic digestion

In this paper, a reduced order model of anaerobic digestion is first proposed, with the main goal to develop an efficient tool for process monitoring and control. Then, in order to perform parameter estimation, the model has been rewritten in a linear fractional transformation (LFT) formulation, using a symbolic tool originally developed for linear models and modified for the processing of nonlinear models. Two different test cases have been considered. In a first case, the data used for parameter identification have been generated by simulating the well known and more complex ADM1 model, considering waste activated sludge as substrate. In a second case, experimental data were collected on a laboratory scale equipment, operated in a semi-batch experiment, performing the anaerobic digestion of ultra-filtered cheese-whey.     

Identification of Wiener systems with binary-valued output observations

This work is concerned with identification of Wiener systems whose outputs are measured by binary-valued sensors. The system consists of a linear FIR (finite impulse response) subsystem of known order, followed by a nonlinear function with a known parametrization structure. The parameters of both linear and nonlinear parts are unknown. Input design, identification algorithms, and their essential properties are presented under the assumptions that the distribution function of the noise is known and the nonlinearity is continuous and invertible. It is shown that under scaled periodic inputs, identification of Wiener systems can be decomposed into a finite number of core identification problems. The concept of joint identifiability of the core problem is introduced to capture the essential conditions under which the Wiener system can be identified with binary-valued observations. Under scaled full-rank conditions and joint identifiability, a strongly convergent algorithm is constructed. The algorithm is shown to be asymptotically efficient for the core identification problem, hence achieving asymptotic optimality in its convergence rate. For computational simplicity, recursive algorithms are also developed.     

Direct electron transfer of myoglobin in mesoporous silica KIT-6 modified on screen-printed electrode

A disposable hydrogen peroxide biosensor was developed based on the direct electron transfer of myoglobin (Mb) on mesopores KIT-6 modified screen-printed electrode (SPE) which was manually performed to fabricate the planar carbon electrodes. KIT-6 is a new material which can absorb abundant of Mb molecules. A mixture of Mb and KIT-6 was immobilized with nafion on electrode. The cyclic voltammetry experiment indicated that a pair of stable and well-defined reduction peaks with a formal potentials of −0.35, and −0.28 V versus saturated calomel electrode (SCE) was obtained, using the present modified electrode in phosphate buffer saline (0.05 M, pH 7.0) at scan rate of 100 mV s⁻¹, characteristic of Mb heme Fe(III)/Fe(II) redox couple. The heterogeneous electron transfer rate constant k_s was estimated to be 16.93 s⁻¹. And the formal potential was pH-dependent, having two slopes of −54.7 and −49.3 mV/pH which illustrated one electron transfer. This modified electrode was applied to detect H₂O₂ with sensitivity of 55.68 mA M⁻¹ cm⁻². Infrared spectrum and UV–vis absorption spectra of immobilized Mb film were recorded. In conclusion, KIT-6 increases the electron transfer activity of Mb and this kind of H₂O₂ biosensor is low cost for using disposable.     

An augmented subcutaneous type 1 diabetic patient modelling and design of adaptive glucose control

In the present work, an augmented subcutaneous (SC) model of type 1 diabetic patients (T1DP) is proposed first by estimating the model parameters with the aid of nonlinear least square method using the physiological data. Next, a nonlinear adaptive controller is proposed to tackle two important issues of intra-patient variability (IPV) and uncertain meal disturbance (MD). The proposed patient model agrees quite well with the responses of one of the most popular existing nonlinear model used in the research of artificial pancreas. Further, the developed adaptive control is shown to be capable of providing desired glycemic control without feed-forward action for meal compensation or safety algorithms to avoid hypoglycemia. Due to the simple structure and capability of handling intra-patient variability of the adaptive controller, it can find immediate applicability in the development of the in-silico artificial pancreas.     

参数估计法检测与诊断铁路运输车减振装置故障

本文利用参数估计法检测与诊断铁路运输车减振装置故障,并分别对6自由度和4自由度模型进行了仿真和模拟实验.     

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.     

Decoupled delay estimation in the identification of differential delay systems

Based on the variable projection functional in nonlinear least-squares theory, the estimation of pure time delay is decoupled from the determination of the remaining system parameters for a class of differential delay models. The approach utilizes input-output data on a fixed finite time interval and avoids estimating unknown initial conditions. Results of a simulation study are summarized for several examples.     

Optimal activation policies for continuous scanning observations in parameter estimation of distributed systems

The problem of determining an optimal measurement scheduling for identification of unknown parameters in distributed systems described by partial differential equations is discussed. The discrete-scanning observations are performed by an optimal selection of measurement data from spatially fixed sensors. In the adopted approach, the sensor scheduling problem is converted to a constrained optimal control problem. In this framework, the control value represents the selected sensor configuration. Thus the control variable is constrained to take values in a discrete set and switchings between sensors may occur in continuous time. By applying the control parameterization enhancing transform technique, a computational procedure for solving the optimal scanning measurement problem is obtained. The numerical scheme is then tested on a computer example regarding an advection-diffusion problem.