Optimal minimum variance‐entropy control of tumour growth processes based on the Fokker–Planck equation

The authors demonstrated an optimal stochastic control algorithm to obtain desirable cancer treatment based on the Gompertz model. Two external forces as two time‐dependent functions are presented to manipulate the growth and death rates in the drift term of the Gompertz model. These input signals represent the effect of external treatment agents to decrease tumour growth rate and increase tumour death rate, respectively. Entropy and variance of cancerous cells are simultaneously controlled based on the Gompertz model. They have introduced a constrained optimisation problem whose cost function is the variance of a cancerous cells population. The defined entropy is based on the probability density function of affected cells was used as a constraint for the cost function. Analysing growth and death rates of cancerous cells, it is found that the logarithmic control signal reduces the growth rate, while the hyperbolic tangent–like control function increases the death rate of tumour growth. The two optimal control signals were calculated by converting the constrained optimisation problem into an unconstrained optimisation problem and by using the real–coded genetic algorithm. Mathematical justifications are implemented to elucidate the existence and uniqueness of the solution for the optimal control problem.Inspec keywords: optimal control, genetic algorithms, cancer, Fokker‐Planck equation, cellular biophysics, stochastic systems, probability, tumours, entropy, medical control systemsOther keywords: cancer treatment, Gompertz model, time‐dependent functions, process input signals, external treatment agents, tumour growth rate, constrained optimisation problem, cost function, cancerous cells population, probability density function, logarithmic control signal, Fokker‐Planck equation, tumour growth process, optimal control signals, optimal control problem, optimal minimum variance‐entropy control, optimal stochastic control algorithm, tumour death rates, hyperbolic tangent‐like control function, unconstrained optimisation problem, real‐coded genetic algorithm     

Pseudo‐spectral method for controlling the drug dosage in cancer

A mixed chemotherapy–immunotherapy treatment protocol is developed for cancer treatment. Chemotherapy pushes the trajectory of the system towards the desired equilibrium point, and then immunotherapy alters the dynamics of the system by affecting the parameters of the system. A co‐existing cancerous equilibrium point is considered as the desired equilibrium point instead of the tumour‐free equilibrium. Chemotherapy protocol is derived using the pseudo‐spectral (PS) controller due to its high convergence rate and simple implementation structure. Thus, one of the contributions of this study is simplifying the design procedure and reducing the controller computational load in comparison with Lyapunov‐based controllers. In this method, an infinite‐horizon optimal control problem is proposed for a non‐linear cancer model. Then, the infinite‐horizon optimal control of cancer is transformed into a non‐linear programming problem. The efficient Legendre PS scheme is suggested to solve the proposed problem. Then, the dynamics of the system is modified by immunotherapy is another contribution. To restrict the upper limit of the chemo‐drug dose based on the age of the patients, a Mamdani fuzzy system is designed, which is not present yet. Simulation results on four different dynamics cases how the efficiency of the proposed treatment strategy.Inspec keywords: patient treatment, cancer, convergence, linear programming, optimal control, nonlinear programming, nonlinear control systems, Lyapunov methods, drugs, tumoursOther keywords: nonlinear programming problem, efficient Legendre PS scheme, chemo‐drug dose, Mamdani fuzzy system, treatment strategy, pseudospectral method, drug dosage, mixed chemotherapy–immunotherapy treatment protocol, cancer treatment, desired equilibrium point, immunotherapy alters, cancerous equilibrium point, tumour‐free equilibrium, chemotherapy protocol, pseudospectral controller, high convergence rate, simple implementation structure, controller computational load, Lyapunov‐based controllers, infinite‐horizon optimal control problem, nonlinear cancer model     

Effective implicit finite‐difference method for sensitivity analysis of stiff stochastic discrete biochemical systems

Simulation of cellular processes is achieved through a range of mathematical modelling approaches. Deterministic differential equation models are a commonly used first strategy. However, because many biochemical processes are inherently probabilistic, stochastic models are often called for to capture the random fluctuations observed in these systems. In that context, the Chemical Master Equation (CME) is a widely used stochastic model of biochemical kinetics. Use of these models relies on estimates of kinetic parameters, which are often poorly constrained by experimental observations. Consequently, sensitivity analysis, which quantifies the dependence of systems dynamics on model parameters, is a valuable tool for model analysis and assessment. A number of approaches to sensitivity analysis of biochemical models have been developed. In this study, the authors present a novel method for estimation of sensitivity coefficients for CME models of biochemical reaction systems that span a wide range of time‐scales. They make use of finite‐difference approximations and adaptive implicit tau‐leaping strategies to estimate sensitivities for these stiff models, resulting in significant computational efficiencies in comparison with previously published approaches of similar accuracy, as evidenced by illustrative applications.Inspec keywords: biochemistry, sensitivity analysis, stochastic processes, cellular biophysics, probability, fluctuations, master equation, reaction kinetics, finite difference methodsOther keywords: effective implicit finite‐difference method, sensitivity analysis, stiff stochastic discrete biochemical systems, cellular processes, mathematical modelling, deterministic differential equation models, inherently probabilistic‐stochastic models, random fluctuations, Chemical Master Equation, biochemical kinetics, kinetic parameter estimation, systems dynamics, CME models, biochemical reaction systems, finite‐difference approximations, adaptive implicit tau‐leaping strategies, computational efficiencies     

Exploiting intrinsic fluctuations to identify model parameters

Parameterisation of kinetic models plays a central role in computational systems biology. Besides the lack of experimental data of high enough quality, some of the biggest challenges here are identification issues. Model parameters can be structurally non‐identifiable because of functional relationships. Noise in measured data is usually considered to be a nuisance for parameter estimation. However, it turns out that intrinsic fluctuations in particle numbers can make parameters identifiable that were previously non‐identifiable. The authors present a method to identify model parameters that are structurally non‐identifiable in a deterministic framework. The method takes time course recordings of biochemical systems in steady state or transient state as input. Often a functional relationship between parameters presents itself by a one‐dimensional manifold in parameter space containing parameter sets of optimal goodness. Although the system''s behaviour cannot be distinguished on this manifold in a deterministic framework it might be distinguishable in a stochastic modelling framework. Their method exploits this by using an objective function that includes a measure for fluctuations in particle numbers. They show on three example models, immigration‐death, gene expression and Epo‐EpoReceptor interaction, that this resolves the non‐identifiability even in the case of measurement noise with known amplitude. The method is applied to partially observed recordings of biochemical systems with measurement noise. It is simple to implement and it is usually very fast to compute. This optimisation can be realised in a classical or Bayesian fashion.Inspec keywords: biochemistry, physiological models, stochastic processes, measurement errors, fluctuations, parameter estimationOther keywords: model parameter identification, deterministic framework, biochemical system, steady state, transient state, stochastic modelling framework, objective function, immigration‐death model, gene expression, Epo–EpoReceptor interaction, stochastic fluctuations, measurement noise     

Optimal neuro‐fuzzy control of hepatitis C virus integrated by genetic algorithm

Hepatitis C blood born virus is a major cause of liver disease that more than three per cent of people in the world is dealing with, and the spread of hepatitis C virus (HCV) infection in different populations is one of the most important issues in epidemiology. In the present study, a new intelligent controller is developed and tested to control the hepatitis C infection in the population which the authors refer to as an optimal adaptive neuro‐fuzzy controller. To design the controller, some data is required for training the employed adaptive neuro‐fuzzy inference system (ANFIS) which is selected by the genetic algorithm. Using this algorithm, the best control signal for each state condition is chosen in order to minimise an objective function. Then, the prepared data is utilised to build and train the Takagi–Sugeno fuzzy structure of the ANFIS and this structure is used as the controller. Simulation results show that there is a significant decrease in the number of acute‐infected individuals by employing the proposed control method in comparison with the case of no intervention. Moreover, the authors proposed method improves the value of the objective function by 19% compared with the ordinary optimal control methods used previously for HCV epidemic.Inspec keywords: epidemics, diseases, blood, medical computing, microorganisms, genetic algorithms, fuzzy control, neurocontrollers, adaptive control, medical control systemsOther keywords: genetic algorithm, hepatitis C blood born virus, liver disease, hepatitis C virus infection, epidemiology, intelligent controller, optimal adaptive neuro‐fuzzy controller, adaptive neuro‐fuzzy inference system, ANFIS, genetic algorithm, control signal, state condition, objective function minimisation, Takagi‐Sugeno fuzzy structure, acute‐infected individuals, ordinary optimal control methods, HCV epidemic     

Deterministic inference for stochastic systems using multiple shooting and a linear noise approximation for the transition probabilities

Estimating model parameters from experimental data is a crucial technique for working with computational models in systems biology. Since stochastic models are increasingly important, parameter estimation methods for stochastic modelling are also of increasing interest. This study presents an extension to the ‘multiple shooting for stochastic systems (MSS)’ method for parameter estimation. The transition probabilities of the likelihood function are approximated with normal distributions. Means and variances are calculated with a linear noise approximation on the interval between succeeding measurements. The fact that the system is only approximated on intervals which are short in comparison with the total observation horizon allows to deal with effects of the intrinsic stochasticity. The study presents scenarios in which the extension is essential for successfully estimating the parameters and scenarios in which the extension is of modest benefit. Furthermore, it compares the estimation results with reversible jump techniques showing that the approximation does not lead to a loss of accuracy. Since the method is not based on stochastic simulations or approximative sampling of distributions, its computational speed is comparable with conventional least‐squares parameter estimation methods.Inspec keywords: stochastic systems, parameter estimation, probability, least squares approximationsOther keywords: deterministic inference, stochastic systems, multiple shooting, linear noise approximation, transition probabilities, systems biology, parameter estimation methods, likelihood function, normal distributions, intrinsic stochasticity effects, reversible jump techniques, approximative sampling, conventional least‐squares parameter estimation methods     

Evolutionary dynamics of morphological stability in a long‐term experiment with Escherichia coli

To investigate the questions in morphological evolution, some biologists seek to carry out evolution experiments owing to the incompleteness and uncontrollability of the fossil record and natural populations. To quantitatively analyse the morphology (cell size) evolution observed from a long‐term experiment with Escherichia coli, the authors present three mathematical approximations to the Wright–Fisher model of the morphological evolution. They firstly use a deterministic approximation, which fails to predict evolutionary dynamics of cell size and proves the importance of stochasticity in large populations. Then, they develop a stochastic approximation and derive an analytic expression for the anticipated waiting time to reach the stability of cell size. The results show that the calculation of this waiting time is in good agreement with the experimental data and that the selective advantage plays a prominent role in cell size evolution, with mutation rate and population size having less impact. Finally, they employ a multistep process to approximate the Wright–Fisher model of cell size evolution and acquire an analytical formula for the median waiting time until the stability of cell size. This median time supports the idea that the selective advantage is the dominant force for the morphological evolution in the long‐term experiment.Inspec keywords: microorganisms, cellular biophysics, evolution (biological), stochastic processesOther keywords: morphological stability, Escherichia coli, evolutionary dynamics, morphological evolution, Wright–Fisher model, deterministic approximation, stochastic approximation, mutation rate, population size, cell size evolution     

Dynamic optimal experimental design yields marginal improvement over steady‐state results for computational maximisation of regulatory T‐cell induction in ex vivo culture

The isolation of T cells, followed by differentiation into Regulatory T cells (Tregs), and re‐transplantation into the body has been proposed as a therapeutic option for inflammatory bowel disease. A key requirement for making this a viable therapeutic option is the generation of a large population of Tregs. However, cytokines in the local microenvironment can impact the yield of Tregs during differentiation. As such, experimental design is an essential part of evaluating the importance of different cytokine concentrations for Treg differentiation. However, currently only single, constant concentrations of the cytokines have been investigated. This work addresses this point by performing experimental design in silico which seeks to maximize the predicted induction of Tregs relative to Th17 cells, by selecting an optimal input function for the concentrations of TGF‐β, IL‐2, IL‐6, and IL‐23. While this approach sounds promising, the results show that only marginal improvements in the concentration of Tregs can be achieved for dynamic cytokine profiles as compared to optimal constant concentrations. Since constant concentrations are easier to implement in experiments, it is recommended for this particular system to keep the concentrations constant where IL‐6 should be kept low and high concentrations of TGF‐β, IL‐2, and IL‐23 should be used.Inspec keywords: patient treatment, molecular biophysics, proteins, cellular biophysics, diseasesOther keywords: Tregs relative, optimal input function, dynamic cytokine profiles, optimal constant concentrations, IL‐23, computational maximisation, regulatory T‐cell induction, inflammatory bowel disease, viable therapeutic option, local microenvironment, Treg differentiation, single concentrations, predicted induction, dynamic optimal experimental design, interleukin‐2, IL‐6, transforming growth factor‐β     

Analysis of healthy and tumour DNA methylation distributions in kidney‐renal‐clear‐cell‐carcinoma using Kullback–Leibler and Jensen–Shannon distance measures

DNA methylation is an epigenetic phenomenon in which methyl groups get bonded to the cytosines of the DNA molecule altering the expression of the associated genes. Cancer is linked with hypo or hyper‐methylation of specific genes as well as global changes in DNA methylation. In this study, the authors study the probability density function distribution of DNA methylation in various significant genes and across the genome in healthy and tumour samples. They propose a unique ‘average healthy methylation distribution’ based on the methylation values of several healthy samples. They then obtain the Kullback–Leibler and Jensen–Shannon distances between methylation distributions of the healthy and tumour samples and the average healthy methylation distribution. The distance measures of the healthy and tumour samples from the average healthy methylation distribution are compared and the differences in the distances are analysed as possible parameters for cancer. A classifier trained on these values was found to provide high values of sensitivity and specificity. They consider this to be a computationally efficient approach to predict tumour samples based on DNA methylation data. This technique can also be improvised to consider other differentially methylated genes significant in cancer or other epigenetic diseases.Inspec keywords: cancer, tumours, DNA, genetics, molecular biophysicsOther keywords: tumour DNA methylation distributions, kidney‐renal‐clear‐cell‐carcinoma, Kullback–Leibler distance measure, Jensen–Shannon distance measure, epigenetic phenomenon, methyl groups, cytosines, hyper‐methylation, probability density function distribution, average healthy methylation distribution     

Multi‐scale approach for simulating time‐delay biochemical reaction systems

This study presents a multi‐scale approach for simulating time‐delay biochemical reaction systems when there are wide ranges of molecular numbers. The authors construct a new efficient approach based on partitioning into slow and fast subsets in conjunction with predictor–corrector methods. This multi‐scale approach is shown to be much more efficient than existing methods such as the delay stochastic simulation algorithm and the modified next reaction method. Numerical testing on several important problems in systems biology confirms the accuracy and computational efficiency of this approach.Inspec keywords: biochemistry, delays, biological techniques, predictor‐corrector methodsOther keywords: multiscale approach, time‐delay biochemical reaction systems, predictor–corrector methods, delay stochastic simulation algorithm, modified next reaction method, numerical testing, systems biology, method accuracy, computational efficiency     

Competitive numerical analysis for stochastic HIV/AIDS epidemic model in a two‐sex population

This study is an attempt to explain a reliable numerical analysis of a stochastic HIV/AIDS model in a two‐sex population considering counselling and antiretroviral therapy (ART). The authors are comparing the solutions of the stochastic and deterministic HIV/AIDS epidemic model. Here, an endeavour has been made to explain the stochastic HIV/AIDS epidemic model is comparatively more pragmatic in contrast with the deterministic HIV/AIDS epidemic model. The effect of threshold number H ^* holds on the stochastic HIV/AIDS epidemic model. If H ^*  < 1 then condition helps us to control disease in a two‐sex human population while H ^*  > 1 explains the persistence of disease in the two‐sex human population. Lamentably, numerical methods such as Euler–Maruyama, stochastic Euler, and stochastic Runge–Kutta do not work for large time step sizes. The recommended structure preserving framework of the stochastic non‐standard finite difference (SNSFD) scheme conserve all vital characteristics such as positivity, boundedness, and dynamical consistency defined by Mickens. The effectiveness of counselling and ART may control HIV/AIDS in a two‐sex population.Inspec keywords: diseases, stochastic processes, epidemics, patient treatment, finite difference methodsOther keywords: two‐sex human population, antiretroviral therapy, competitive numerical analysis, stochastic HIV‐AIDS epidemic model, structure preserving framework, stochastic nonstandard finite difference scheme, SNSFD scheme, deterministic HIV‐AIDS epidemic model     

Architecture‐dependent robustness in a class of multiple positive feedback loops

Many types of multiple positive feedbacks with each having potentials to generate bistability exist extensively in natural, raising the question of why a particular architecture is present in a cell. In this study, the authors investigate multiple positive feedback loops across three classes: one‐loop class, two‐loop class and three‐loop class, where each class is composed of double positive feedback loop (DPFL) or double negative feedback loop (DNFL) or both. Through large‐scale sampling and robustness analysis, the authors find that for a given class, the homogeneous DPFL circuit (i.e. the coupled circuit that is composed of only DPFLs) is more robust than all the other circuits in generating bistable behaviour. In addition, stochastic simulation shows that the low stable state is more robust than the high stable state in homogeneous DPFL whereas the high‐stable state is more robust than the low‐stable state in homogeneous DNFL circuits. It was argued that this investigation provides insight into the relationship between robustness and network architecture.Inspec keywords: cellular biophysics, feedback, sampling methods, stochastic processesOther keywords: network architecture, low stable state, stochastic simulation, bistable behaviour, homogeneous DPFL circuit, robustness analysis, large‐scale sampling, DNFL, double negative feedback loop, double positive feedback loop, three‐loop class, two‐loop class, one‐loop class, cell architecture, bistability, multiple positive feedback loops, architecture‐dependent robustness     

Peripheral arterial disease screening for hemodialysis patients using a fractional‐order integrator and transition probability decision‐making model

Atherosclerosis and resultant peripheral arterial disease (PAD) are common complications in patients with type 2 diabetes mellitus or end‐stage renal disease and in elderly patients. The prevalence of PAD is higher in patients receiving haemodialysis therapy. For early assessment of arterial occlusion using bilateral photoplethysmography (PPG), such as changes in pulse transit time and pulse shape, bilateral timing differences could be used to identify the risk level of PAD. Hence, the authors propose a discrete fractional‐order integrator to calculate the bilateral area under the systolic peak (AUSP). These indices indicated the differences in both rise‐timing and amplitudes of PPG signals. The dexter and sinister AUSP ratios were preliminarily used to separate the normal condition from low/high risk of PAD. Then, transition probability‐based decision‐making model was employed to evaluate the risk levels. The joint probability could be specified as a critical threshold, < 0.81, to identify the true positive for screening low or high risk level of PAD, referring to the patients’ health records. In contrast to the bilateral timing differences and traditional methods, the proposed model showed better efficiency in PAD assessments and provided a promising strategy to be implemented in an embedded system.Inspec keywords: diseases, blood vessels, photoplethysmography, geriatrics, probability, decision makingOther keywords: peripheral arterial disease screening, hemodialysis patients, fractional‐order integrator, transition probability decision‐making model, diabetes mellitus, end‐stage renal disease, elderly patients, haemodialysis therapy, arterial occlusion, bilateral photoplethysmography, discrete fractional‐order integrator, systolic peak, bilateral area, PPG signals, dexter AUSP ratio, sinister AUSP ratio, transition probability‐based decision‐making model, joint probability, bilateral timing differences     

Small RNA‐mediated switch‐like regulation in bacterial quorum sensing

Quorum sensing (QS) is a signalling mechanism by which bacteria produce, release and then detect and respond to changes in their density and biosignals called autoinducers (AIs). There are multiple feedback loops in the QS system of Vibrio harveyi. However, how these feedback loops function to control signal processing remains unclear. In this study, the authors present a computational model for the switch‐like regulation of signal transduction by small regulatory RNA‐mediated QS based on intertwined network involving AIs, LuxO, LuxU, Qrr sRNAs and LuxR. In agreement with experimental observations, the model suggests that different feedbacks play critical roles in the switch‐like regulation. The authors results reveal that V. harveyi uses multiple feedbacks to precisely control signal transduction.Inspec keywords: biocommunications, biocontrol, biology computing, cellular biophysics, physiological models, RNAOther keywords: RNA‐mediated switch‐like regulation, bacterial quorum sensing, signaling mechanism, autoinducers, Vibrio harveyi, feedback loops function, signal processing control, switch‐like regulation     

Systems analysis utilising pathway interactions identifies sonic hedgehog pathway as a primary biomarker and oncogenic target in hepatocellular carcinoma

The development and progression of cancer is associated with disruption of biological networks. Historically studies have identified sets of signature genes involved in events ultimately leading to the development of cancer. Identification of such sets does not indicate which biologic processes are oncogenic drivers and makes it difficult to identify key networks to target for interventions. Using a comprehensive, integrated computational approach, the authors identify the sonic hedgehog (SHH) pathway as the gene network that most significantly distinguishes tumour and tumour‐adjacent samples in human hepatocellular carcinoma (HCC). The analysis reveals that the SHH pathway is commonly activated in the tumour samples and its activity most significantly differentiates tumour from the non‐tumour samples. The authors experimentally validate these in silico findings in the same biologic material using Western blot analysis. This analysis reveals that the expression levels of SHH, phosphorylated cyclin B1, and CDK7 levels are much higher in most tumour tissues as compared to normal tissue. It is also shown that siRNA‐mediated silencing of SHH gene expression resulted in a significant reduction of cell proliferation in a liver cancer cell line, SNU449 indicating that SHH plays a major role in promoting cell proliferation in liver cancer. The SHH pathway is a key network underpinning HCC aetiology which may guide the development of interventions for this most common form of human liver cancer.Inspec keywords: bioinformatics, cancer, cellular biophysics, genetics, liver, molecular biophysics, RNA, systems analysis, tumoursOther keywords: biomedical informatics, human liver cancer, network underpinning HCC aetiology, liver cancer cell line, cell proliferation, SHH gene expression, siRNA‐mediated silencing, CDK7 levels, phosphorylated cyclin B1, Western blot analysis, in silico findings, SHH pathway, human hepatocellular carcinoma, tumour‐adjacent samples, gene network, integrated computational approach, oncogenic drivers, biologic processes, cancer development, biological networks, cancer progression, oncogenic target, primary biomarker, sonic hedgehog pathway, pathway interactions, systems analysis     

Optimal sliding mode control of drug delivery in cancerous tumour chemotherapy considering the obesity effects

Different control strategies have been proposed for drug delivery in chemotherapy during recent years. These control algorithms are designed based on dynamic models of various orders. The order of the model depends on the number of effects considered in the model. In a recent model, the effect of obesity on the tumour progression and optimal control strategy in chemotherapy have been investigated in a fifth‐order state‐space model. However, the optimal controller is open loop and not robust to the common uncertainties of such biological system. Here, the sliding surface is obtained by the optimal trajectory and by considering uncertainties of some parameters, the robust‐sliding control law is formulated in a way to slid on the optimal surface. Then, a sliding mode controller is designed to determine the drug dose rate such that the system follows the optimal desired trajectory. The stability of the control system is proved and the simulation results indicate that three states track the trajectory and the remaining two states satisfy the constraints.Inspec keywords: drug delivery systems, drugs, tumours, cancer, optimal control, open loop systems, controllers, medical control systemsOther keywords: optimal sliding mode control, drug delivery, cancerous tumour chemotherapy, obesity effects, control algorithms, dynamic models, tumour progression, optimal control strategy, fifth‐order state‐space model, open loop, biological system, sliding surface, optimal trajectory, robust‐sliding control law, sliding mode controller, drug dose rate     

Blood glucose regulation in type 1 diabetic patients: an adaptive parametric compensation control‐based approach

Here, a direct adaptive control strategy with parametric compensation is adopted for an uncertain non‐linear model representing blood glucose regulation in type 1 diabetes mellitus patients. The uncertain parameters of the model are updated by appropriate design of adaptation laws using the Lyapunov method. The closed‐loop response of the plasma glucose concentration as well as external insulin infusion rate is analysed for a wide range of variation of the model parameters through extensive simulation studies. The result indicates that the proposed adaptive control scheme avoids severe hypoglycaemia and gives satisfactory performance under parametric uncertainty highlighting its ability to address the issue of inter‐patient variability.Inspec keywords: patient monitoring, adaptive control, diseases, Lyapunov methods, closed loop systems, medical control systems, patient treatment, medical computing, sugar, uncertain systems, blood, nonlinear control systems, physiological modelsOther keywords: blood glucose regulation, type 1 diabetic patients, adaptive parametric compensation control‐based approach, direct adaptive control strategy, nonlinear model, type 1 diabetes mellitus patients, uncertain parameters, appropriate design, adaptation laws, closed‐loop response, plasma glucose concentration, external insulin infusion rate, model parameters, adaptive control scheme, parametric uncertainty, inter‐patient variability     

Non‐fragile reliable control synthesis of the sugarcane borer

This study considers the problem of non‐fragile reliable control synthesis for mathematical model of interaction between the sugarcane borer (Diatraea saccharalis) and its egg parasitoid Trichogramma galloi. In particular, the control could be substituted by periodic releases of a small population of natural enemies and hence it is important to propose the time‐varying controller in sugarcane borer. The main aim of this study is to design a state feedback non‐fragile (time‐varying) reliable controller such that the states of the sugarcane borer system reach the equilibrium point within the desired period. A novel approach is proposed to deal with the uncertain matrices which appear in non‐fragile reliable control. Finally, simulations based on sugarcane borer systems are conducted to illustrate the advantages and effectiveness of the proposed design technique. The result reveals that the proposed non‐fragile control provides good performance in spite of periodic releases of a small population of natural enemies occurs.Inspec keywords: microorganisms, plant diseases, biology computing, state feedback, biocontrol, control system synthesisOther keywords: nonfragile reliable control synthesis, sugarcane borer, mathematical model, Diatraea saccharalis, egg parasitoid, Trichogramma galloi, periodic releases, natural enemies, state feedback nonfragile time‐varying reliable controller, equilibrium point, design technique     

Accuracy of the Maxwell–Wagner and the Bruggeman–Hanai mixture models for single cell dielectric spectroscopy

Dielectric spectroscopy (DS) is a non‐invasive, label‐free, and promising technique for measuring dielectric properties of biological cells. Recent developments in microfabrication techniques made it possible to perform DS measurements with minute volume of cell suspensions. However, when the cell size approaches the size of the measurement chamber, especially, for single cell measurements, the analytical models [Maxwell–Wagner and Bruggeman–Hanai (BH) mixture models] to extract cell parameters lose their accuracy. Moreover, variations in the cell position relative to the measurement electrodes decrease the accuracy of the analytical solutions. Impedance spectrum of a typical eukaryotic mammalian cell is generated for different geometrical configurations using finite element. The generated data are fitted to the analytical models and extracted cell parameters are compared with the original values. The results show that BH model works more effectively when chamber to cell radius ratio is <3.5 and chamber height to cell radius ratio is <3. Moreover, it is observed that analytical models estimate cell parameters with major errors when the cells are in the vicinity of the electrodes. However, for high‐volume fraction simulations, the BH model was able to predict cell parameters better even in the vicinity of the electrodes.Inspec keywords: cellular biophysics, bioelectric phenomena, dielectric properties, finite element analysis, biomedical measurement, biomedical electrodesOther keywords: Maxwell‐Wagner mixture model, Bruggeman‐Hanai mixture model, single cell dielectric spectroscopy, noninvasive label‐free technique, dielectric properties, biological cells, microfabrication techniques, cell suspensions, cell size, single cell measurements, cell position, measurement electrodes, impedance spectrum, eukaryotic mammalian cell, geometrical configurations, finite element, cell parameters, high‐volume fraction simulations, electrodes