Conventional Compartmental Models Research Articles

Fuzzy-SIRD model: Forecasting COVID-19 death tolls considering governments intervention

Modeling the trend of contagious diseases has particular importance for managing them and reducing the side effects on society. In this regard, researchers have proposed compartmental models for modeling the spread of diseases. However, these models suffer from a lack of adaptability to variations of parameters over time. This paper introduces a new Fuzzy Susceptible–Infectious–Recovered–Deceased (Fuzzy-SIRD) model for covering the weaknesses of the simple compartmental models. Due to the uncertainty in forecasting diseases, the proposed Fuzzy-SIRD model represents the government intervention as an interval type 2 Mamdani fuzzy logic system. Also, since society’s response to government intervention is not a static reaction, the proposed model uses a first-order linear system to model its dynamics. In addition, this paper uses the Particle Swarm Optimization (PSO) algorithm for optimally selecting system parameters. The objective function of this optimization problem is the Root Mean Square Error (RMSE) of the system output for the deceased population in a specific time interval. This paper provides many simulations for modeling and predicting the death tolls caused by COVID-19 disease in seven countries and compares the results with the simple SIRD model. Based on the reported results, the proposed Fuzzy-SIRD model can reduce the root mean square error of predictions by more than 80% in the long-term scenarios, compared with the conventional SIRD model. The average reduction of RMSE for the short-term and long-term predictions are 45.83% and 72.56%, respectively. The results also show that the principle goal of the proposed modeling, i.e., creating a semantic relation between the basic reproduction number, government intervention, and society’s response to interventions, has been well achieved. As the results approve, the proposed model is a suitable and adaptable alternative for conventional compartmental models.

An Epidemic Model with Time Delay Determined by the Disease Duration

Immuno-epidemiological models with distributed recovery and death rates can describe the epidemic progression more precisely than conventional compartmental models. However, the required immunological data to estimate the distributed recovery and death rates are not easily available. An epidemic model with time delay is derived from the previously developed model with distributed recovery and death rates, which does not require precise immunological data. The resulting generic model describes epidemic progression using two parameters, disease transmission rate and disease duration. The disease duration is incorporated as a delay parameter. Various epidemic characteristics of the delay model, namely the basic reproduction number, the maximal number of infected, and the final size of the epidemic are derived. The estimation of disease duration is studied with the help of real data for COVID-19. The delay model gives a good approximation of the COVID-19 data and of the more detailed model with distributed parameters.

Kinetic Modeling of Dynamic PET-¹⁸F-FDG Atherosclerosis Without Blood Sampling

Atherosclerosis is a disease affecting the peripheral arteries characterized by a deposit of lipids and immune cells forming a plaque. The plaque can be calcified and be measured with CT, and it can be inflamed and be measured with PET and 18F-FDG. Since artery walls are too small and are dominated by blood activity, the conventional compartmental model becomes inadequate to provide artery metabolism especially when using an image derived input function from an artery. The purpose of this study was to quantitatively evaluate glucose metabolism in arteries with a more appropriate compartmental modeling. Kinetic modeling of arteries was conducted using the classical 18F-FDG compartmental model and a modification of this model without the need of blood sampling. The metabolic rate of glucose (MRG) was computed per artery segment in each image slice with both models. The ratio of calcification area (RCA) and Agatston calcification scores (ACSs) were automatically clustered with the automatic hierarchical $K$ -means algorithm. The rate constants showed significant variation between the two models ( $P ), however, $K_{i}$ was with good agreement in both models ( $P >0.05$ ). Both models found that MRG values in non-medication group were statistically significantly different from those in under-medication group.

A new compartmental model for describing the mixing behaviour in a multi-transversal jet reactor

The axial dispersion model (ADM) and tank-in-series model (TiSM) are conventionally used for determining mixing performance of a reactor, which is generated by transverse jets in many engineering applications. The effect of transverse jets on the mixing performance is not well determined by the ADM and TiSM when the Reynolds number of the mainstream flow is higher than ∼104. In this study, this problem was solved by a dispersive compartmental model (DCM). The DCM was a modification of the conventional compartmental model by adding a dispersive nature of plug flow compartment. The results of a series of tracer studies showed that the experimental data were better matched by the DCM than by the conventional models. The effect of transverse jets on the mixing characteristics was significant when the experimental data were modelled by the DCM. The DCM could be used for practical reactors where the E-curve shows a single peak.

Therapeutic drug monitoring and pharmacokinetic compartmental analysis of sulpiride double‐peak absorption profile after oral administration to human volunteers

The pharmacokinetics of oral drugs that exhibit double peaks cannot be described adequately by using conventional compartmental models. The aim of this study was to describe the double-peak plasma pharmacokinetic profile of sulpiride after oral administration to healthy volunteers based on physiological and biopharmaceutical considerations. A single 100 mg dose of sulpiride was given to 16 healthy volunteers. Blood samples were drawn at different times and analysed by a validated HPLC assay method. Plasma profiles were evaluated by non-compartmental and compartmental approaches. The non-compartmental parameters determined were k (0.079±0.008 h(-1)), t1/2 (9.0±2.9 h), Vd /F (330.5±87.3 L), Cl/F (38.2±9.8 L/h) and AUC0→∞ (1402.5±404.7 ng.h/mL). The compartmental analysis was described appropriately using a two-compartment body model, with first order absorption from two different sites in the gut. The parameters determined were k21 (0.68±0.2 h(-1)), ka1 (0.7±0.27 h(-1)), ka2 (2.7±1.8 h(-1)) Vc/F (45.1±15.7 L), α (33.3±1.5 h(-1)), β (0.11±0.03 h(-1)) and time for the beginning of the absorption from the second site (4.4±2.1 h). The developed analytical method was suitable for use in pharmacokinetic studies and therapeutic drug monitoring implementation. Sulpiride was well tolerated by the patients without any serious adverse events being observed. The double peaks in the serum concentration-time profiles could be due to differential rates of absorption along the gastrointestinal tract. The discontinuous absorption model with two sites of absorption was adequate to describe the double-peak of the sulpiride plasma profile. ClinicalTrials. gov identifiers: NCT01777685.

Validation of an axially distributed model for quantification of myocardial blood flow using 13N-ammonia PET

BackgroundEstimation of myocardial blood flow (MBF) with cardiac PET is often performed with conventional compartmental models. In this study, we developed and evaluated a physiologically and anatomically realistic axially distributed model. Unlike compartmental models, this axially distributed approach models both the temporal and the spatial gradients in uptake and retention along the capillary. MethodsWe validated PET-derived flow estimates with microsphere studies in 19 (9 rest, 10 stress) studies in five dogs. The radiotracer, 13N-ammonia, was injected intravenously while microspheres were administered into the left atrium. A regional reduction in hyperemic flow was forced by an external occluder in five of the stress studies. The flow estimates from the axially distributed model were compared with estimates from conventional compartmental models. ResultsThe mean difference between microspheres and the axially distributed blood flow estimates in each of the 17 segments was 0.03 mL/g/minute (95% CI [−0.05, 0.11]). The blood flow estimates were highly correlated with each regional microsphere value for the axially distributed model (y = 0.98x + 0.06 mL/g/minute; r = 0.74; P < .001), for the two-compartment (y = 0.64x + 0.34; r = 0.74; P < .001), and for three-compartment model (y = 0.69x + 0.54; r = 0.74; P < .001). The variance of the error of the estimates is higher with the axially distributed model than the compartmental models (1.7 [1.3, 2.1] times higher). ConclusionThe proposed axially distributed model provided accurate regional estimates of MBF. The axially distributed model estimated blood flow with more accuracy, but less precision, than the evaluated compartmental models.

Primary Colorectal Cancer: Use of Kinetic Modeling of Dynamic Contrast-enhanced CT Data to Predict Clinical Outcome

To compare four different tracer kinetic models for the analysis of dynamic contrast material-enhanced computed tomographic (CT) data with respect to the prediction of 5-year overall survival in primary colorectal cancer. This study was approved by the ethical review board. Archival dynamic contrast-enhanced CT data from 46 patients with colorectal cancer, obtained as part of a research study, were analyzed retrospectively by using the distributed parameter, conventional compartmental, adiabatic tissue homogeneity, and generalized kinetic models. Blood flow, blood volume, mean transit time (MTT), permeability-surface area product, extraction fraction, extravascular extracellular volume (v(e)), and volume transfer constant (K(trans)) were compared by using the Friedman test, with statistical significance at 5%. Following receiver operating characteristic analysis, parameters of the different kinetic models and tumor stage were compared with respect to overall survival discrimination, with use of Kaplan Meier analysis and a univariate Cox proportional hazard model, with additional cross-validation and permutation testing. Blood flow was lower with the distributed parameter model than with the conventional compartmental and adiabatic tissue homogeneity models (P < .0001), and blood flow values determined with the conventional compartmental and adiabatic tissue homogeneity models were similar. Conversely, MTT was longer with the distributed parameter model than with the conventional compartmental and adiabatic tissue homogeneity models (P < .0001). Blood volume, permeability-surface area product, and v(e) were higher with the conventional compartmental model than with the adiabatic tissue homogeneity, distributed parameter, or generalized kinetic models (P < .0001). The extraction fraction was higher with the distributed parameter model than with the adiabatic tissue homogeneity model. With respect to 5-year overall survival, only the distributed parameter model-derived v(e) was predictive of 5-year overall survival with a threshold value of 15.48 mL/100 mL after cross-validation and permutation testing. Parameter values differ significantly between models. Of the models investigated, the distributed parameter model was the best predictor of 5-year overall survival. http://radiology.rsna.org/lookup/suppl/doi:10.1148/radiol.12120186/-/DC1.

Dynamic contrast-enhanced MRI in breast cancer: A comparison between distributed and compartmental tracer kinetic models

Background/objectives: Dynamic Contrast Enhanced-Magnetic Resonance Imaging (DCE-MRI) is widely used in tumor diagnosis, staging and assessment of therapy response for different types of tumors, thanks to its capability to provide important functional information about tissue microvasculature. Tracer kinetic models used for estimating microcirculatory parameters can be broadly categorized as conventional compartmental (CC) or distributed- parameter (DP) models. While DP models seem to be more realistic, CC models (in particular the Tofts and the Brix models) have been widely used in clinical investigations over the past two decades. However, to date there is no direct comparison of CC vs DP models on real breast DCE-MRI data; moreover, a direct comparison between Tofts and Brix models, has not yet been reported on real breast data. Therefore, the purpose of this study was two-fold: on the one hand we analyzed the performance, on real breast DCE-MRI data, of CC vs DP models in terms of goodness-of-fit metrics; on the other hand we compared Tofts and Brix models on the basis of real breast DCE-MRI data. Methods: Three models were compared: two CC models (the Tofts and the Brix models) and one DP model (the ATH model). We gathered data in two different scenarios: DCE-MRI with high temporal resolution obtained by means of a k -space under-sampling and data sharing method known as Time-resolved angiography With Stochastic Trajectories (TWIST) and DCE-MRI with low temporal resolution obtained by means of the Spoiled Gradient-Echo k -space scheme known as Fast Low Angle Shot (FLASH). The performances of the three models were evaluated by means of three goodness-of-fit metrics: the Residual Sum of Squares, the Bayesian Information Criterion and the Akaike Information Criterion on four breast DCE-MRI examinations. Results: Although not conclusive, the results of this study suggest that the ATH model can achieve better fit in comparison to the Tofts and Brix models for TWIST data; and that the Brix model can achieve better fit with respect to the Tofts model for FLASH data. Conclusion: Given the current typical settings of clinical breast DCE-MRI examinations, there seems not to be a clear advantage, in terms of goodness-of-fit, of ATH with respect to Tofts and Brix models; moreover, at lower temporal resolution the Brix model can achieve better fit than the Tofts model.

Stereoselective pharmacokinetics of ibuprofen in rats: effect of enantiomer-enantiomer interaction in plasma protein binding.

Stereoselective pharmacokinetics of ibuprofen (IB) enantiomers were studied in rats. Unidirectional conversion from R-ibuprofen (R-IB) to S-ibuprofen (S-IB) was observed following intravenous administration. S-IB concentrations in plasma following racemate administration were simulated according to a conventional compartmental model using the parameters obtained after the administration of individual enantiomers, and resulted in overestimation of S-IB concentrations. Binding of IB enantiomers measured in rat plasma was stereoselective, the binding of R-IB being more favorable than that of S-IB. Moreover, there are interactions between IB enantiomers in binding, which may cause the increase of distribution volumes of IB enantiomers in the presence of their antipodes. Hence simulated S-IB concentrations according to a conventional compartment model were significantly greater than those observed. Indeed, when the enantiomer-enantiomer interactions were taken into account, simulation of S-IB concentrations in plasma following racemate administration was in good agreement with observed values. Therefore, interactions between stereoisomers as well as dispositional stereoselectivity have to be considered when pharmacokinetics of stereoisomers after administration of the racemate are compared to those after administration of individual isomers.

A Comparison of Three Computer Models for Prediction of Dose in Acute Amitriptyline Overdose

The pharmacokinetics of amitriptyline in overdose have been reported not to fit conventional compartmental models. In this study, the dose-concentration-time relationships of amitriptyline in overdose were modeled with discriminant analysis, with an evolutionary heuristic search program, and with a decision-tree model based on the entropy of uncertainty of classification. The computer models all used the same data from dogs administered treatment (80 mg/kg), toxic (250 mg/kg), or fatal (500 mg/kg) doses directly into the surgically isolated duodenum. All the models achieved a high degree of success (77 to 93%) in assigning records to the high-, low-, or middle-dose groups. Two of the models gave a probability of the assignment. Results of this analysis suggest that blood amitriptyline and nortriptyline concentrations are most useful in estimating dose in acute amitriptyline overdose.

Extended input-output flow analysis of ecosystems

The compartmental model of ecosystems open to their environments is extended by including self-loop ‘flows’ at compartments. According to this extension, the Markovian model corresponding to the conventional compartmental model is naturally generalized into the Markovian model with self-loops. By means of this generalized Markovian model, it is proved that the self-loop flow at each compartment in the extended compartmental model represents the storage at the compartment, which, together with the throughflow at the same compartment, constitutes the inclusive throughflow at that compartment. It is shown, on the basis of the maximum entropy principle, that the amount of storage (and thus, of inclusive throughflow) can be explicitly determined in terms of the turnover rate (thus, existing energy and throughflow) at each compartment. This makes it possible to generalize the flow analysis into the one which can analyze the cause-effect (causation) relationship among compartments in terms of not only throughflows but inclusive throughflows. Since the inclusive throughflow represents not only the throughflow but storage, and, in effect, the total energy existing at each compartment, the generalized flow analysis should reveal a more substantial aspect of the total interaction among subsystems (compartments). This account is applied to two significant issues in ecology: the issue of energy (or matter) cycling in ecosystems and the issue on direct influences versus indirect ones. A general measure of cycling efficiency of ecosystems with respect to both throughflow and inclusive throughflow is derived based on the generalized Markovian model, and studied in terms of natural ecosystem examples. The explicit expressions for the direct and indirect influences from one subsystem (compartment) to another are derived on the basis of the classification of paths into direct influence paths and indirect influence ones. It is shown that the relationship between direct and indirect influences is invariant for the throughflow and inclusive throughflow cases, and it is suggested that indirect influences tend to dominate over direct ones as the system connectance increases. Finally, a general method for evaluating the effects of storages on the cycling efficiency of ecosystems and the relationship between direct and indirect influences is developed, and these effects are studied analytically as well as in terms of natural ecosystem examples.

Endemic infections in growing populations

Most mathematical models for the transmission and maintenance of microparasitic infections take the host population to be unchanging in time. In recent years, however, populations of human hosts have been increasing relatively rapidly, especially in many developing countries. In this paper we indicate how the framework of conventional compartmental models for microparasitic infections may be extended to include the effects of host population growth. We give both analytic and numerical illustrations of the ways in which the age-specific incidence of infection, the average age at infection, and other epidemiological quantities are likely to change over time in response to such overall growth in host population density. In particular, we show that the basic reproductive rate of the microparasite, R 0, is to a good approximation given as R 0⋍ B/ A, where A is the average age at infection and B is the reciprocal of the birth rate.

Ecokinetics: A study of the fate and distribution of chemicals in laboratory ecosystems

AbstractThe anticipated kinetic behavior of different amounts or forms of a chemical in the environment can be studied by introducing the chemical into a laboratory ecosystem, collecting samples of the different components of the system at various times, and obtaining a sequence of concentrations of the chemical and/or its metabolites. Conventional compartmental models can be used to characterize this concentration‐time data in order to better predict the distribution and ultimate fate of a chemical introduced into the environment, to provide a quantitative measure for helping assess the environmental impact of different chemicals, and to reduce the cost of expensive laboratory testing and field work.

CIRCULATION-TIME MODELS OF THE UPTAKE OF INHALED ANAESTHETICS AND DATA FOR QUANTIFYING THEM

Conventional compartmental models of the uptake and distribution of inhaled anaesthetics assume that blood moves from lungs to tissues and from tissues back to lungs in zero time. Three new models which incorporate alternative representations of the finite time actually taken have been constructed in terms of Algol programs for a digital computer. It is shown that the conventional approach causes systematic errors in the computed uptake of low-solubility agents, in the arterial tension of high-solubility agents, and in the tissue tensions of all agents. The errors are important in the first minute or two of administration or recovery. The conventional distribution of blood volume between compartments is shown to be in error and to cause even greater systematic errors in computed results. Three different published distributions of tissue volume and cardiac output give different computed results and a preferred distribution is suggested.