Modeling COVID-19 Pandemic with Hierarchical Quarantine and Time Delay

COVID-19 comes out as a sudden pandemic disease within human population. The pandemic dynamics of COVID-19 needs to be studied in detail. A pandemic model with hierarchical quarantine and time delay is proposed in this paper. In the COVID-19 case, the virus incubation period and the antibody failure will cause the time delay and reinfection, respectively, and the hierarchical quarantine strategy includes home isolation and quarantine in hospital. These factors that affect the spread of COVID-19 are well considered and analyzed in the model. The stability of the equilibrium and the nonlinear dynamics is studied as well. The threshold value τ k of the bifurcation is deduced and quantitatively analyzed. Numerical simulations are performed to establish the analytical results with suitable examples. The research reveals that the COVID-19 outbreak may recur over a period of time, which can be helpful to increase the number of tested people with or without symptoms in order to be able to early identify the clusters of infection. And before the effective vaccine is successfully developed, the hierarchical quarantine strategy is currently the best way to prevent the spread of this pandemic.

Dynamical analysis of a stochastic rumor-spreading model with Holling II functional response function and time delay

With the rapid development of information society, rumor plays an increasingly crucial part in social communication, and its spreading has a significant impact on human life. In this paper, a stochastic rumor-spreading model with Holling II functional response function considering the existence of time delay and the disturbance of white noise is proposed. Firstly, the existence of a unique global positive solution of the model is studied. Then the asymptotic behavior of the global solution around the rumor-free and rumor-local equilibrium nodes of the deterministic system is discussed. Finally, through some numerical results, the validity and availability of theoretical analysis is verified powerfully, and it shows that some factors such as the transmission rate, the intensity of white noise, and the time delay have significant relationship with the dynamical behavior of rumor spreading.

Exploring the complexity and chaotic behavior in plankton-fish system with mutual interference and time delay

Anti-predator defense is an important mechanism that preys use to reduce the stress of constant struggle in a high concentration of predator and commonly established through evolution that supports prey organisms against predators. In the current study, we explore a three-tier plankton-fish interaction model using two kinds of function form, Monod-Haldane and Beddington-DeAngelis type. We introduce a discrete-time delay in the top predator population due to gestation. Our main objective persuades in this article is to address the role of inhibitory effect, mutual interference and gestation delay on the system dynamics in the presence of intermediate and top predators population. We perform theoretical analyses such as positivity and boundedness along with the local stability conditions of the delayed plankton-fish system. We also derive the condition of stability and direction of Hopf-bifurcation by using normal form theory and center manifold theorem. Our numerical computation demonstrates the dynamical outcome such as periodic and chaotic solutions of the model system without and with time delay validates our analytical findings. We also draw bifurcation diagrams that show the complexity of different parameters of model system. Interestingly, extinction is noticed in the top predator owing to the defense of phytoplankton. Model system exhibits irregular behavior when the inhibitory effect of phytoplankton is high or the value of gestation period of fish is high. We explore the significance of time delay with defense in our study which promotes chaotic phenomena in plankton system. Further, we notice the occurrence of double Hopf-bifurcation in a certain range of predator's interference with variation in the coefficient of time delay.

COVID-19: Development of a robust mathematical model and simulation package with consideration for ageing population and time delay for control action and resusceptibility

The current global health emergency triggered by the pandemic COVID-19 is one of the greatest challenges we face in this generation. Computational simulations have played an important role to predict the development of the current pandemic. Such simulations enable early indications on the future projections of the pandemic and is useful to estimate the efficiency of control action in the battle against the SARS-CoV-2 virus. The SEIR model is a well-known method used in computational simulations of infectious viral diseases and it has been widely used to model other epidemics such as Ebola, SARS, MERS, and influenza A. This paper presents a modified SEIRS model with additional exit conditions in the form of death rates and resusceptibility, where we can tune the exit conditions in the model to extend prediction on the current projections of the pandemic into three possible outcomes; death, recovery, and recovery with a possibility of resusceptibility. The model also considers specific information such as ageing factor of the population, time delay on the development of the pandemic due to control action measures, as well as resusceptibility with temporal immune response. Owing to huge variations in clinical symptoms exhibited by COVID-19, the proposed model aims to reflect better on the current scenario and case data reported, such that the spread of the disease and the efficiency of the control action taken can be better understood. The model is verified using two case studies based on the real-world data in South Korea and Northern Ireland.

Investigation of the effect of a time delay on the characteristics and survival of dental pulp stem cells from extracted teeth

OBJECTIVES

This study investigates the post-extraction storage period of human dental pulp stem cells (hDPSCs) for stem cell banking by investigating the viability, function, mineralization, and gene expression of hDPSCs isolated from extracted teeth after 1 h, 6 h and 24 h post-tooth extraction.

DESIGN

hDPSCs were extracted from the pulp of impacted third molar teeth after 1 h, 6 h, and 24 h after extraction. The mesenchymal stem cell (MSCs) properties of three groups of cells were analyzed using flow cytometry. Cell morphology and proliferation were analyzed using a light microscope and an MTT assay. The viability, function, mineralization, and gene expression of hDPSCs of 1 h, 6 h, and 24 h groups were also assessed.

RESULTS

The delayed harvesting of hDPSCs for 1, 6 or 24 h caused a 31 % reduction in mineral nodule formation and a reduction in the gene expression of osteocalcin (OCN) and vascular endothelial growth factor-alpha (VEGFA). However, the 1, 6 or 24 h, time delay had little effect on MTT cell proliferation, cell viability or morphology. The delayed of harvesting of hDPSCs for 1, 6 or 24 h also had little effect on the expression of MSCs positive (CD44, CD106, CD90) or negative surface markers (CD45 and CD11b).

CONCLUSIONS

Our results suggest that a 24 h delay in harvesting hDPSCs from extracted teeth can reduce their mineralization and gene activity but does not markedly reduce survival. Quicker hDPSCs harvesting is likely to yield more useful hDPSCs for experimentation and clinical treatment.

The stability and accuracy analysis of automatic steering system with time delay

The paper presents a systematic method of stability analysis for automatic steering system involving a time delay and some external disturbances. The analysis focuses on the stability of automatic steering system with increase of the time delay from zero to infinity. Firstly, the structure and dynamic model of automatic steering system are briefly introduced, and PD control algorithm is adopted to further analysis the time delay mechanism of control system of automatic steering system. Then the time delay dynamic models of automatic steering system with PD control algorithm are derived, the time delay stability interval and critical time delay of automatic steering system are calculated by using the generalized Sturm criterion method. Finally, the accuracy of critical time delay calculation by proposed method, and the stability and accuracy of automatic steering system with time delay and external disturbance are illustrated by numerical simulations.

Finite-time stabilization and energy consumption estimation for delayed neural networks with bounded activation function

This paper concentrates on finite-time stabilization and energy consumption estimation for one type of delayed neural networks (DNNs) with bounded activation function. Under the bounded activation function condition and using the comparison theorem, a new switch controller is proposed to ensure the finite-time stability of the considered DNNs. Furthermore, the energy consumption produced in system controlling is estimated by inequality techniques. We generalize the previous results about the problem of finite-time stabilization and energy consumption estimation for neural networks. Ultimately, two numerical simulations are carried out to verify the validity of our results.

Expansion of off-site percutaneous coronary intervention centres significantly reduces ambulance driving time to primary PCI in the Netherlands

Introduction

In patients with ST-elevation myocardial infarction (STEMI), percutaneous coronary intervention (PCI)-mediated reperfusion is preferred over pharmacoinvasive reperfusion with fibrinolysis if transfer to a PCI centre can be ensured in ≤120 min. We evaluated the ambulance driving time to primary PCI centres in the Netherlands and assessed to what extent ambulance driving times were impacted by the expansion of off-site PCI centres.

Methods and results

We calculated the driving routes from every Dutch postal code to the nearest PCI centre with (on-site) or without (off-site) surgical back-up. We used data from ambulance records to estimate the ambulance driving time on each route. There were 16 on-site and 14 off-site PCI centres. The median (interquartile range) time to on-site PCI centres was 18.8 min (12.2–26.3) compared with 14.9 min (8.9–20.9) to any PCI centre (p < 0.001). In postal code areas that were impacted by the initiation of off-site PCI, the median driving time decreased from 25.4 (18.2–33.1) to 14.7 min (8.9–20.9) (p < 0.001). Ambulance driving times of >120 min were only seen in non-mainland areas.

Conclusion

Based on a computational model, timely ambulance transfer to a PCI centre within 120 min is available to almost all STEMI patients in the Netherlands. Expansion of off-site PCI has significantly reduced the driving time to PCI centres.

Accuracy of real-time respiratory motion tracking and time delay of gating radiotherapy based on optical surface imaging technique

Background

Surface-guided radiation therapy (SGRT) employs a non-invasive real-time optical surface imaging (OSI) technique for patient surface motion monitoring during radiotherapy. The main purpose of this study is to verify the real-time tracking accuracy of SGRT for respiratory motion and provide a fitting method to detect the time delay of gating.

Methods

A respiratory motion phantom was utilized to simulate respiratory motion using 17 cosine breathing pattern curves with various periods and amplitudes. The motion tracking of the phantom was performed by the Catalyst™ system. The tracking accuracy of the system (with period and amplitude variations) was evaluated by analyzing the adjusted coefficient of determination (A_R²) and root mean square error (RMSE). Furthermore, 13 actual respiratory curves, which were categorized into regular and irregular patterns, were selected and then simulated by the phantom. The Fourier transform was applied to the respiratory curves, and tracking accuracy was compared through the quantitative analyses of curve similarity using the Pearson correlation coefficient (PCC). In addition, the time delay of amplitude-based respiratory-gating radiotherapy based on the OSI system with various beam hold times was tested using film dosimetry for the Elekta Versa-HD and Varian Edge linacs. A dose convolution-fitting method was provided to accurately measure the beam-on and beam-off time delays.

Results

A_R² and RMSE for the cosine curves were 0.9990–0.9996 and 0.110–0.241 mm for periods ranging from 1 s to 10 s and 0.9990–0.9994 and 0.059–0.175 mm for amplitudes ranging from 3 mm to 15 mm. The PCC for the actual respiratory curves ranged from 0.9955 to 0.9994, which was not significantly affected by breathing patterns. For gating radiotherapy, the average beam-on and beam-off time delays were 1664 ± 72 and 25 ± 30 ms for Versa-HD and 303 ± 45 and 34 ± 25 ms for Edge, respectively. The time delay was relatively stable as the beam hold time increased.

Conclusions

The OSI technique provides high accuracy for respiratory motion tracking. The proposed dose convolution-fitting method can accurately measure the time delay of respiratory-gating radiotherapy. When the OSI technique is used for respiratory-gating radiotherapy, the time delay for the beam-on is considerably longer than the beam-off.

Stability of delayed inertial neural networks on time scales: A unified matrix-measure approach

This note introduces a unified matrix-measure concept to study the stability of a class of inertial neural networks with bounded time delays on time scales. The novel matrix-measure concept unifies the classic matrix-measure and the generalized matrix-measure concept. One sufficient global exponential stability criterion is obtained based on this key matrix-measure and no Lyapunov function is required. To make the stability performance better, another stability criterion in which more detailed information is involved has been acquired. The theoretical results in this note contain and extend some existing continuous-time and discrete-time works. A numerical example is given to show the validity of the results.

Delayed-Phase Enhancement for Evaluation of Malignant Pleural Mesothelioma on Computed Tomography: A Prospective Cohort Study

BACKGROUND

Radiologic assessment of malignant pleural mesothelioma (MPM) on computed tomography (CT) imaging can be limited by similar attenuations of MPM and adjacent tissues. This can result in inaccuracies in defining the presence and extent of pleural tumor burden. We hypothesized that increasing the time delay for pleural enhancement will optimize discrimination between MPM and noncancerous tissues on CT. Here we conduct a prospective observational study to determine the optimal time delay for imaging MPM on CT.

PATIENTS AND METHODS

Adult MPM patients (n = 15) were enrolled in this prospective exploratory imaging trial. Patients with < 1 cm MPM thickness, prior pleurectomy, pleurodesis, pleural radiotherapy, or antiangiogenic therapy were excluded. All patients underwent a dynamically-enhanced CT with multiple time delays (0 - 10 minutes) after intravenous contrast administration. Tumor tissue attenuation was measured at each phase of enhancement. A qualitative assessment of tumor enhancement kinetics was also performed. The optimal phase of enhancement based on qualitative lesion conspicuity and quantitative tumor enhancement was then compared.

RESULTS

MPM tumor enhancement was quantitatively and qualitatively increased at time delays beyond the conventional time delay for thoracic CT imaging (40-60 seconds). Patient tumor enhancement kinetics, displayed as the fraction of maximal tumor tissue attenuation as a function of time, revealed an optimal time delay of 230 to 300 seconds after intravenous contrast administration. There was an association between degree of tumor enhancement and subjective lesion conspicuity.

CONCLUSION

Optimal MPM contrast enhancement occurs at a later phase than typically acquired with conventional thoracic CT imaging.

Andronov-Hopf and Neimark-Sacker bifurcations in time-delay differential equations and difference equations with applications to models for diseases and animal populations

In many areas, researchers might think that a differential equation model is required, but one might be forced to use an approximate difference equation model if data is only available at discrete points in time. In this paper, a detailed comparison is given of the behavior of continuous and discrete models for two representative time-delay models, namely a model for HIV and an extended logistic growth model. For each model, there are seven different time-delay versions because there are seven different positions to include time delays. For the seven different time-delay versions of each model, proofs are given of necessary and sufficient conditions for the existence and stability of equilibrium points and for the existence of Andronov-Hopf bifurcations in the differential equations and Neimark-Sacker bifurcations in the difference equations. We show that only five of the seven time-delay versions have bifurcations and that all bifurcation versions have supercritical limit cycles with one having a repelling cycle and four having attracting cycles. Numerical simulations are used to illustrate the analytical results and to show that critical times for Neimark-Sacker bifurcations are less than critical times for Andronov-Hopf bifurcations but converge to them as the time step of the discretization tends to zero.

Controlling industrial dead-time systems: When to use a PID or an advanced controller

This work presents a comparative analysis of PID, DTC and MPC strategies when used to control SISO processes with dead time considering characteristics commonly found in industry, such as noisy measurements in the process output and modeling error. For unconstrained processes, it is shown that the performance improvement obtained by using a more advanced control strategy instead of a PID is small or nonexistent for cases which require high robustness. However, for cases with well-known process models it is shown that the improvement obtained by using a more complex control structure is justified even for small delays. For constrained processes it was demonstrated that a PID with anti-windup is able to provide similar or even better results than MPC when robust solutions are considered.

Towards the revival of oscillation from complete cessation in stochastic systems for application in molecular biology

Delay and noise are inevitable in complex systems that are common in biochemical networks. The system is often disturbed at various states irrespective of the size (small or large) of delay and noise. Therefore, it is of interest to describe the significance of delay and noise in stochastic Willamowski-Rossler chemical oscillator model using a delay stochastic (having random probability distribution) simulation algorithm. Oscillating dynamics moves to stable fixed point when delay at a fixed magnitude of noise drives the system from oscillating state to stochastic amplitude death state (complete cessation). However, the amplitude death state is induced to a revived oscillating state in stochastic system (which is far from equilibrium state) for noise with a fixed value of delay. Thus, significantly large and small noise induces the dynamics of the system to amplitude death state. Hence, we describe the interplay of delay and noise in stochastic systems for the proper and efficient functioning of the complex system that are frequent in biological networks.

Multiple bifurcations and coexistence in an inertial two-neuron system with multiple delays

In this paper, we construct an inertial two-neuron system with multiple delays, which is described by three first-order delayed differential equations. The neural system presents dynamical coexistence with equilibria, periodic orbits, and even quasi-periodic behavior by employing multiple types of bifurcations. To this end, the pitchfork bifurcation of trivial equilibrium is analyzed firstly by using center manifold reduction and normal form method. The system presents different sequences of supercritical and subcritical pitchfork bifurcations. Further, the nontrivial equilibrium bifurcated from trivial equilibrium presents a secondary pitchfork bifurcation. The system exhibits stable coexistence of multiple equilibria. Using the pitchfork bifurcation curves, we divide the parameter plane into different regions, corresponding to different number of equilibria. To obtain the effect of time delays on system dynamical behaviors, we analyze equilibrium stability employing characteristic equation of the system. By the Hopf bifurcation, the system illustrates a periodic orbit near the trivial equilibrium. We give the stability regions in the delayed plane to illustrate stability switching. The neural system is illustrated to have Hopf-Hopf bifurcation points. The coexistence with two periodic orbits is presented near these bifurcation points. Finally, we present some mixed dynamical coexistence. The system has a stable coexistence with periodic orbit and equilibrium near the pitchfork-Hopf bifurcation point. Moreover, multiple frequencies of the system induce the presentation of quasi-periodic behavior. The system presents stable coexistence with two periodic orbits and one quasi-periodic behavior.

Optimal design of CDM controller to frequency control of a realistic power system equipped with storage devices using grasshopper optimization algorithm

This paper presents a new robust load frequency control (LFC) technique based on an optimal design of the coefficient diagram method (CDM) in a three area thermal power system equipped with redox flow batteries (RFB). In order to emphasize on a realistic power system and obtain an accurate insight, important nonlinearities due to generation rate constraint (GRC), governor dead band (GDB) and time delay (TD) were considered. The innovation of the proposed controller in this paper is the use of a hybrid intelligent combination of a decentralized CDM technique and optimization throughout its algebraic equations. In addition, a new algorithm namely grasshopper optimization algorithm (GOA) was used to find the key parameters of the proposed controller in solving the LFC problem for the first time. Furthermore, this study applied a powerful modified objective function by considering the integral of time multiplied squared error (ITSE) criteria for both controller input signal (ACE), to minimize the area control error and output signal (Δu) to reduce the size of the actuator, settling time (Ts) to have a faster response and a function to increase the minimum damping ratio (MDR) among all eigen values. To demonstrate the effectiveness of the proposed scheme, the studied simulated power system was tested through different cases including a large step and sinusoidal load perturbations and wide uncertainty in dynamic parameters of a nonlinear power system. Comparative results have revealed the superiority of the optimal CDM technique, especially when it is equipped with RFB. In addition to graphical results, by taking into account the MDR of different control strategies, the preference of the proposed controller has become more validated. This newly developed strategy leads to a flexible and accurate controller with a powerful mathematical back up which can successfully cope with GRC, GDB and TD nonlinearities in perturbed uncertain power systems and provide fast, stable and robust dynamic responses. Thus, the proposed control strategy can be constructive and successfully applied to real world power system application.

Design of an optimal fractional fuzzy gain-scheduled Smith Predictor for a time-delay process with experimental application

This study addresses an experimental investigation of a novel modified Smith Predictor (SP) based fractional fuzzy gain-scheduled control scheme in control of a time-delayed thermal process. The control strategy employees a fuzzy algorithm to adjust convenient controller parameters based on the system's operating conditions. Performance enhancement of the closed-loop system enables more robust behavior in the presence of disturbance while reducing energy consumption by producing a smooth control signal in comparison with the traditional integer order SP structures. The proposed controller comprises self-tuning capabilities at runtime which makes it adaptive in nature. The motivation of the present paper is in both points of theory and experimental application. The theoretical contribution is to propose a new Smith Predictor based fractional order fuzzy dead-time compensation scheme that can handle uncertainties, parameter variations, and internal/external disturbances. The practical contribution is to apply the proposed control scheme to a real-time air-heating process. The performances of the elaborated control strategies are investigated in both computer simulation and experimental application under different operating conditions. The proposed fractional fuzzy control scheme is found superior to the classical PI-PD SP and integer fuzzy controllers for temperature profile tracking tasks. Moreover, complementary comments are highlighted on the advantages and drawbacks of each controller.

Nonlinear dynamics of a time-delayed epidemic model with two explicit aware classes, saturated incidences, and treatment

Whenever a disease emerges, awareness in susceptibles prompts them to take preventive measures, which influence individuals' behaviors. Therefore, we present and analyze a time-delayed epidemic model in which class of susceptible individuals is divided into three subclasses: unaware susceptibles, fully aware susceptibles, and partially aware susceptibles to the disease, respectively, which emphasizes to consider three explicit incidences. The saturated type of incidence rates and treatment rate of infectives are deliberated herein. The mathematical analysis shows that the model has two equilibria: disease-free and endemic. We derive the basic reproduction number R 0 of the model and study the stability behavior of the model at both disease-free and endemic equilibria. Through analysis, it is demonstrated that the disease-free equilibrium is locally asymptotically stable when R 0 < 1 , unstable when R 0 > 1 , and linearly neutrally stable when R 0 = 1 for the time delay ϱ > 0 . Further, an undelayed epidemic model is studied when R 0 = 1 , which reveals that the model exhibits forward and backward bifurcations under specific conditions, which also has important implications in the study of disease transmission dynamics. Moreover, we investigate the stability behavior of the endemic equilibrium and show that Hopf bifurcation occurs near endemic equilibrium when we choose time delay as a bifurcation parameter. Lastly, numerical simulations are performed in support of our analytical results.

Complete dimensional collapse in the continuum limit of a delayed SEIQR network model with separable distributed infectivity

We take up a recently proposed compartmental SEIQR model with delays, ignore loss of immunity in the context of a fast pandemic, extend the model to a network structured on infectivity and consider the continuum limit of the same with a simple separable interaction model for the infectivities β . Numerical simulations show that the evolving dynamics of the network is effectively captured by a single scalar function of time, regardless of the distribution of β in the population. The continuum limit of the network model allows a simple derivation of the simpler model, which is a single scalar delay differential equation (DDE), wherein the variation in β appears through an integral closely related to the moment generating function of u = β . If the first few moments of u exist, the governing DDE can be expanded in a series that shows a direct correspondence with the original compartmental DDE with a single β . Even otherwise, the new scalar DDE can be solved using either numerical integration over u at each time step, or with the analytical integral if available in some useful form. Our work provides a new academic example of complete dimensional collapse, ties up an underlying continuum model for a pandemic with a simpler-seeming compartmental model and will hopefully lead to new analysis of continuum models for epidemics.

Human-inspired stable bilateral teleoperation of mobile manipulators

This paper presents a novel strategy for delayed bilateral teleoperation of mobile manipulator robots. The strategy is based on the hypothesis that if the slave robot behaves similarly as the operator would do to the same task, the operator's perception of the system states improves, and therefore the performance of the task is better. The proposed scheme allows controlling in simultaneously the mobile platform and the manipulator robot employing a single master device and maintaining the stability of the system against variable and asymmetric communication time delays. Stability guidelines based on Lyapunov-Krasovskii method are provided for the adjustment of the delayed system. Besides, a new control allocation strategy is proposed founded on the study of human movement in a task of navigation-pick and place. Finally, the performance of the proposal is compared with the standard switched control using a real robotic platform. As a result in practice, the proposed scheme is easier and more intuitive for the operator, besides it allows to reduce significantly the time necessary to complete the task.

Basic reproduction ratios for periodic and time-delayed compartmental models with impulses

Much work has focused on the basic reproduction ratio [Formula: see text] for a variety of compartmental population models, but the theory of [Formula: see text] remains unsolved for periodic and time-delayed impulsive models. In this paper, we develop the theory of [Formula: see text] for a class of such impulsive models. We first introduce [Formula: see text] and show that it is a threshold parameter for the stability of the zero solution of an associated linear system. Then we apply this theory to a time-delayed computer virus model with impulse treatment and obtain a threshold result on its global dynamics in terms of [Formula: see text]. Numerically, it is found that the basic reproduction ratio of the time-averaged delayed impulsive system may overestimate the spread risk of the virus.

Output feedback H∞ control for active suspension of in-wheel motor driven electric vehicle with control faults and input delay

In this paper, an output feedback H_∞ controller is proposed for active suspension of an electric vehicle driven by in-wheel motors with actuator faults and time delay. The dynamic damping in-wheel motor driven system, in which the in-wheel motor is designed as a dynamic vibration absorber (DVA), is developed to improve ride quality and isolate the force transmitted to motor bearings. Furthermore, parameters of vehicle suspension and DVA are optimized based on the particle swarm optimization (PSO) to achieve better suspension performance. As some of the states such as the DVA velocity and unsprung mass velocity are difficult to measure, a robust H_∞ output feedback controller is developed to deal with the problem of active suspension control with actuator faults and time delay. The proposed controller could guarantee the system's asymptotic stability and H_∞ performance, simultaneously satisfying the performance constraints such as road holding, suspension stroke, and actuator limitation. Finally, the effectiveness of the proposed output feedback controllers is demonstrated based on the quarter vehicle suspension model under bump and random road excitations.

An affordable custom phantom for measurement of linac time delay in gated treatments with irregular breathing

Respiratory gated treatments are now common in order to reduce tumour motion uncertainties due to breathing. One issue associated with gated treatments is the time delay between the gating system and the linear accelerator. In this study we develop and characterise an affordable phantom to be used in routine and patient specific quality assurance (QA) of the Varian Real-Time Position Management™ (RPM) system. A photodiode has been incorporated into the phantom in order to estimate the time delay. A commercial Quasar phantom was customised to incorporate two stepper motors which independently control an anterior-posterior abdomen/thorax moving plate, and an inferior-superior moving lung insert. A photodiode placed in the path of the radiation is used to measure when beam on/off occurs. Two Arduino microcontroller boards have been utilised to control the motors, read the photodiode and write to an SD card. The measured beam on/off, correlated to the known positions of the phantom is compared to the gate window for RPM. The time delay was measured for sinusoidal movements with a period of 7.50 s and 3.75 s, and for three patient breathing traces. For the sinusoidal movements, time delays of 150 ± 34 ms and 39 ± 34 ms were measured, for 7.50 s and 3.75 s periods, respectively. In the case of the patients' breathing traces time delays of 135 ± 26 ms, 137 ± 34 ms and 129 ± 28 ms were measured. An affordable motion phantom has been developed for routine and patient specific QA of respiratory gating systems. It is capable of reproducing a patient's breathing waveform and performing time delay measurements with a photodiode. Results indicate a time delay of the order of 0.1-0.2 s for the RPM system.

[Evaluation of Bispectral Index time delay in response to anesthesia induction: an observational study]

BACKGROUND AND OBJECTIVES

According to the manufacturer, the Bispectral Index (BIS) has a processing time delay of 5-10s. Studies addressing this have suggested longer delays. We evaluated the time delay in the Bispectral Index response.

METHODS

Based on clinical data from 45 patients, using the difference between the predicted and the real BIS, calculated during a fixed 3minutes period after the moment the Bispectral Index dropped below 80 during the induction of general anesthesia with propofol and remifentanil.

RESULTS

The difference between the predicted and the real BIS was in average 30.09±18.73s.

CONCLUSION

Our results may be another indication that the delay in BIS processing may be much longer than stated by the manufacture, a fact with clinical implications.

Analytical fractional PID controller design based on Bode's ideal transfer function plus time delay

In this paper, a fractional order PID controller cascaded with a fractional filter is proposed for higher order processes. In this analytical design methodology, one or two reduced fractional orders plus time delay models are used to represent higher order system transfer functions. The controller parameters are determined so as to meet certain frequency domain specifications. A unity feedback reference model is employed where Bode's ideal loop transfer function plus time delay of the fractional order model is placed in the forward path. The addition of this time delay provides the exact determination of frequency domain specifications if the system either intrinsically owns a time delay or a time delay is injected by its reduced order model. The proposed methodology is compared with two other related methodologies and it has been observed that the proposed controller performs much better than the others. Moreover, some empirical formulas for time domain characteristics of the reference model are numerically derived in terms of certain frequency domain specifications and time delay of the fractional reduced order model. The accuracy of these formulas is tested by simulations. The iso-damping, noise attenuation and load disturbance suppression performances of the proposed controller are also considered and compared with those of other related controllers.