Biophysical compartment models for single-shell diffusion MRI in the human brain: a model fitting comparison

Clinically oriented studies commonly acquire diffusion MRI (dMRI) data with a single non-zero b-value (i.e. single-shell) and diffusion weighting of b=1000 s/mm2. To produce microstructural parameter maps, the tensor model is usually used, despite known limitations. Although compartment models have demonstrated improved fits in multi-shell dMRI data, they are rarely used for single-shell parameter maps, where their effectiveness is unclear from the literature. Here, various compartment models combining isotropic balls and symmetric tensors were fitted to single-shell dMRI data to investigate model fitting optimization and extract the most information possible. Full testing was performed in 5 subjects, and 3 subjects with multi-shell data were included for comparison. The results were tested and confirmed in a further 50 subjects. The Markov chain Monte Carlo (MCMC) model fitting technique outperformed non-linear least squares. Using MCMC, the 2-fibre-orientation mono-exponential ball & stick model (BSME 2) provided artifact-free, stable results, in little processing time. The analogous ball & zeppelin model (BZ2) also produced stable, low-noise parameter maps, though it required much greater computing resources (50 000 burn-in steps). In single-shell data, the gamma-distributed diffusivity ball & stick model (BSGD 2) underperformed relative to other models, despite being an often-used software default. It produced artifacts in the diffusivity maps even with extremely long processing times. Neither increased diffusion weighting nor a greater number of gradient orientations improved BSGD 2 fits. In white matter (WM), the tensor produced the best fit as measured by Bayesian information criterion. This result contrasts with studies using multi-shell data. However, in crossing fibre regions the tensor confounded geometric effects with fractional anisotropy (FA): the planar/linear WM FA ratio was 49%, while BZ2 and BSME 2 retained 76% and 83% of restricted fraction, respectively. As a result, the BZ2 and BSME 2 models are strong candidates to optimize information extraction from single-shell dMRI studies.

Advancement of pharmacokinetic models of iohexol in patients aged 70 years or older with impaired kidney function

Plasma clearance of iohexol is a pivotal metric to quantify glomerular filtration rate (GFR), but the optimal timing and frequency of plasma sampling remain to be assessed. In this study, we evaluated the impact of a Bayesian estimation procedure on iohexol clearance estimates, and we identified an optimal sampling strategy based on data in individuals aged 70+. Assuming a varying number of random effects, we re-estimated previously developed population pharmacokinetic two- and three-compartment models in a model development group comprising 546 patients with iohexol concentration data up to 300 min post injection. Model performance and optimal sampling times were assessed in an evaluation group comprising 104 patients with reduced GFR and concentration data up to 1440 min post injection. Two- and three-compartment models with random effects for all parameters overestimated clearance values (bias 5.07 and 4.40 mL/min, respectively) and underpredicted 24-h concentrations (bias − 14.5 and − 12.0 µg/ml, respectively). Clearance estimates improved distinctly when limiting random effects of the three-compartment model to clearance and central volume of distribution. Two blood samples, one early and one 300 min post injection, were sufficient to estimate iohexol clearance. A simplified three-compartment model is optimal to estimate iohexol clearance in elderly patients with reduced GFR.

Comparative study of linear regression and SIR models of COVID-19 propagation in Ukraine before vaccination

The global COVID-19 pandemic began in December 2019 and spread rapidly around the world. Worldwide, more than 230 million people fell ill, 4.75 million cases were fatal. In addition to the threat to health, the pandemic resulted in social problems, an economic crisis and the transition of an ordinary life to a "new reality". Mathematical modeling is an effective tool for controlling the epidemic process of COVID-19 in specified territories. Modeling makes it possible to predict the future dynamics of the epidemic process and to identify the factors that affect the increase in incidence in the greatest way. The simulation results enable public health professionals to take effective evidence-based responses to contain the epidemic. The study aims to develop machine learning and compartment models of COVID-19 epidemic process and to investigate experimental results of simulation. The object of research is COVID-19 epidemic process and its dynamics in territory of Ukraine. The research subjects are methods and models of epidemic process simulation, which include machine learning methods and compartment models. To achieve this aim of the research, we have used machine learning forecasting methods and have built COVID-19 epidemic process linear regression model and COVID-19 epidemic process compartment model. Because of experiments with the developed models, the predictive dynamics of the epidemic process of COVID-19 for 30 days were obtained for confirmed cases, recovered and death. For ‘Confirmed’, ‘Recovered’ and ‘Death’ cases mean errors have almost 1.15, 0.037 and 1.39 percent deviant, respectively, with a linear regression model. For ‘Confirmed’, ‘Recovered’ and ‘Death’ cases mean errors have almost 3.29, 1.08, and 0.71 percent deviant, respectively, for the SIR model. Conclusions. At this stage in the development of the epidemic process of COVID-19, it is more expedient to use a linear model to predict the incidence rate, which has shown higher accuracy and efficiency, the reason for that lies on the fact that the used linear regression model for this research was implemented on merely 30 days (from fifteen days before 2nd of March) and not the whole dataset of COVID-19. Also, it is expected that if we try to forecast in longer time ranges, the linear regression model will lose precision. Alternatively, since SIR model is more comprised in including more factors, the model is expected to perform better in fore-casting longer time ranges.

Development of Compartment Models for Diagnostic Purposes

The importance of recognizing the presence of process faults and resolving these faults is continuously increasing parallel to the development of industrial processes. Fault detection methods which are both robust and sensitive help to recognize the presence of faults in time to avoid malfunctions, financial loss, environmental damage or loss of human life. In the literature, the use of various model-based fault detection methods has gained a considerable degree of popularity. Methods usually based on black-box models, data-based techniques or models using symbolic logic, e.g.\ expert systems, have become widespread. White-box models, on the other hand, have been applied less despite their considerable robustness because of multiple reasons. Firstly, their complexity and the relatively vast amount of technological and modelling knowledge needed to construct them for industrial systems. Secondly, their large computational demand which makes them less suitable for online fault detection. In this study, the aim was to resolve these problems by developing a method to simplify the complex Computational Fluid Dynamics models employed to describe the equipment used in the chemical industry into less complex model structures. These simpler structures are Compartment Models, a type of white-box model which breaks down a complex system into smaller units with idealized behaviour. In the case of a small number of compartments, the computational load of such models is not significant, therefore, they can be employed for the purposes of online fault detection while providing an accurate representation of the system. For the purpose of identifying the compartmental structure, fuzzy logic was employed to create a model which approximates the real behaviour of the system as accurately as possible. Our future objective is to explore the possibility of combining this model with various diagnostic methods (expert systems, Bayesian networks, parity relations, etc.) and derive robust tools for the purpose of fault detection.

Automated Compartment Model Development Based on Data from Flow-Following Sensor Devices

Due to the heterogeneous nature of large-scale fermentation processes they cannot be modelled as ideally mixed reactors, and therefore flow models are necessary to accurately represent the processes. Computational fluid dynamics (CFD) is used more and more to derive flow fields for the modelling of bioprocesses, but the computational demands associated with simulation of multiphase systems with biokinetics still limits their wide applicability. Hence, a demand for simpler flow models persists. In this study, an approach to develop data-based flow models in the form of compartment models is presented, which utilizes axial-flow rates obtained from flow-following sensor devices in combination with a proposed procedure for automatic zoning of volume. The approach requires little experimental effort and eliminates the necessity for computational determination of inter-compartmental flow rates and manual zoning. The concept has been demonstrated in a 580 L stirred vessel, of which models have been developed for two types of impellers with varying agitation intensities. The sensor device measurements were corroborated by CFD simulations, and the performance of the developed compartment models was evaluated by comparing predicted mixing times with experimentally determined mixing times. The data-based compartment models predicted the mixing times for all examined conditions with relative errors in the range of 3–27%. The deviations were ascribed to limitations in the flow-following behavior of the sensor devices, whose sizes were relatively large compared to the examined system. The approach provides a versatile and automated flow modelling platform which can be applied to large-scale bioreactors.

Nonlinear Compartment Models with Time-Dependent Parameters

A nonlinear compartment model generates a semi-process on a simplex and may have an arbitrarily complex dynamical behaviour in the interior of the simplex. Nonetheless, in applications nonlinear compartment models often have a unique asymptotically stable equilibrium attracting all interior points. Further, the convergence to this equilibrium is often wave-like and related to slow dynamics near a second hyperbolic equilibrium on the boundary. We discuss a generic two-parameter bifurcation of this equilibrium at a corner of the simplex, which leads to such dynamics, and explain the wave-like convergence as an artifact of a non-smooth nearby system in C0-topology, where the second equilibrium on the boundary attracts an open interior set of the simplex. As such nearby idealized systems have two disjoint basins of attraction, they are able to show rate-induced tipping in the non-autonomous case of time-dependent parameters, and induce phenomena in the original systems like, e.g., avoiding a wave by quickly varying parameters. Thus, this article reports a quite unexpected path, how rate-induced tipping can occur in nonlinear compartment models.

RESEARCH OF APPROACHES TO CONSTRUCTING PREDICTIVE MODELS OF THE SPREAD OF VIRAL DISEASES

The article is devoted to the analysis of the available mathematical models in epidemiology and the possibility of their modification. We note that the situation with the COVID-19 virus pandemic is characterized by several features not comprehensively studied in the existing models. For a rational response to existing challenges, it is necessary to have a predictive and analytical apparatus in the complex (national and regional scale) mathematical models with a planning horizon of 2 years (the expected period of mass production of vaccines). The article discusses the existing approaches to predicting the spread of the COVID-19 virus in Russia based on mathematical models of epidemics. The possibilities and limitations of the proposed approaches are considered. In the conditions of the Russian Federation, transport connectivity at the interregional and intraregional levels plays an important role, and for megalopolises - transport flows within large agglomerations and the age structure of the population. In contrast to previous pandemics and epidemics, public policy plays a significant role. The approach, which consist in building multi-agent models that combine the advantages of compartment models and models based on the Monte Carlo method (individually oriented) is proposed by the authors. It is planned to use compartment models to assess the dynamics of the process and individually-oriented models - at the level of individual territories and districts.

Multi-Tissue Multi-Compartment Models of Diffusion MRI

State-of-the-art multi-compartment microstructural models of diffusion MRI (dMRI) in the human brain have limited capability to model multiple tissues at the same time. In particular, the available techniques that allow this multi-tissue modelling are based on multi-TE acquisitions. In this work we propose a novel multi-tissue formulation of classical multi-compartment models that relies on more common single-TE acquisitions and can be employed in the analysis of previously acquired datasets. We show how modelling multiple tissues provides a new interpretation of the concepts of signal fraction and volume fraction in the context of multi-compartment modelling. The software that allows to inspect single-TE diffusion MRI data with multi-tissue multi-compartment models is included in the publicly available Dmipy Python package.

An Optimal Lockdown Relaxation Strategy for Minimizing the Economic Effects of COVID-19 Outbreak

In order to recover the damage to the economy by the ongoing COVID-19 pandemic, many countries consider the transition from strict lockdowns to partial lockdowns through relaxation of preventive measures. In this work, we propose an optimal lockdown relaxation strategy, which is aimed at minimizing the damage to the economy, while confining the COVID-19 incidence to a level endurable by the available healthcare facilities in the country. In order to capture the transmission dynamics, we adopt the compartment models and develop the relevant optimization model, which turns out to be nonlinear. We generate approximate solutions to the problem, whereas our experimentation is based on the data on the COVID-19 outbreak in Sri Lanka.