The relationship between compartment models and their stochastic counterparts: A comparative study with examples of the COVID-19 epidemic modeling

Deterministic compartment models (CMs) and stochastic models, including stochastic CMs and agent-based models, are widely utilized in epidemic modeling. However, the relationship between CMs and their corresponding stochastic models is not well understood. The present study aimed to address this gap by conducting a comparative study using the susceptible, exposed, infectious, and recovered (SEIR) model and its extended CMs from the coronavirus disease 2019 modeling literature. We demonstrated the equivalence of the numerical solution of CMs using the Euler scheme and their stochastic counterparts through theoretical analysis and simulations. Based on this equivalence, we proposed an efficient model calibration method that could replicate the exact solution of CMs in the corresponding stochastic models through parameter adjustment. The advancement in calibration techniques enhanced the accuracy of stochastic modeling in capturing the dynamics of epidemics. However, it should be noted that discrete-time stochastic models cannot perfectly reproduce the exact solution of continuous-time CMs. Additionally, we proposed a new stochastic compartment and agent mixed model as an alternative to agent-based models for large-scale population simulations with a limited number of agents. This model offered a balance between computational efficiency and accuracy. The results of this research contributed to the comparison and unification of deterministic CMs and stochastic models in epidemic modeling. Furthermore, the results had implications for the development of hybrid models that integrated the strengths of both frameworks. Overall, the present study has provided valuable epidemic modeling techniques and their practical applications for understanding and controlling the spread of infectious diseases.

Using seconds-resolved pharmacokinetic datasets to assess pharmacokinetic models encompassing time-varying physiology

AIM

Pharmacokinetics have historically been assessed using drug concentration data obtained via blood draws and bench-top analysis. The cumbersome nature of these typically constrains studies to at most a dozen concentration measurements per dosing event. This, in turn, limits our statistical power in the detection of hours-scale, time-varying physiological processes. Given the recent advent of in vivo electrochemical aptamer-based (EAB) sensors, however, we can now obtain hundreds of concentration measurements per administration. Our aim in this paper was to assess the ability of these time-dense datasets to describe time-varying pharmacokinetic models with good statistical significance.

METHODS

We used seconds-resolved measurements of plasma tobramycin concentrations in rats to statistically compare traditional one- and two-compartmental pharmacokinetic models to new models in which the proportional relationship between a drug's plasma concentration and its elimination rate varies in response to changing kidney function.

RESULTS

We found that a modified one-compartment model in which the proportionality between the plasma concentration of tobramycin and its elimination rate falls reciprocally with time either meets or is preferred over the standard two-compartment pharmacokinetic model for half of the datasets characterized. When we reduced the impact of the drug's rapid distribution phase on the model, this one-compartment, time-varying model was statistically preferred over the standard one-compartment model for 80% of our datasets.

CONCLUSIONS

Our results highlight both the impact that simple physiological changes (such as varying kidney function) can have on drug pharmacokinetics and the ability of high-time resolution EAB sensor measurements to identify such impacts.

Spherical harmonics representation of the steady-state membrane potential shift induced by tDCS in realistic neuron models

Objective.We provide a systematic framework for quantifying the effect of externally applied weak electric fields on realistic neuron compartment models as captured by physiologically relevant quantities such as the membrane potential or transmembrane current as a function of the orientation of the field.Approach.We define a response function as the steady-state change of the membrane potential induced by a canonical external field of 1 V m^-1as a function of its orientation. We estimate the function values through simulations employing reconstructions of the rat somatosensory cortex from the Blue Brain Project. The response of different cell types is simulated using the NEURON simulation environment. We represent and analyze the angular response as an expansion in spherical harmonics.Main results.We report membrane perturbation values comparable to those in the literature, extend them to different cell types, and provide their profiles as spherical harmonic coefficients. We show that at rest, responses are dominated by their dipole terms (ℓ=1), in agreement with experimental findings and compartment theory. Indeed, we show analytically that for a passive cell, only the dipole term is nonzero. However, while minor, other terms are relevant for states different from resting. In particular, we show howℓ=0andℓ=2terms can modify the function to induce asymmetries in the response.Significance.This work provides a practical framework for the representation of the effects of weak electric fields on different neuron types and their main regions-an important milestone for developing micro- and mesoscale models and optimizing brain stimulation solutions.

Assessing transmission risks and control strategy for monkeypox as an emerging zoonosis in a metropolitan area

To model the spread of monkeypox (MPX) in a metropolitan area for assessing the risk of possible outbreaks, and identifying essential public health measures to contain the virus spread. The animal reservoir is the key element in the modeling of zoonotic disease. Using a One Health approach, we model the spread of the MPX virus in humans considering potential animal hosts such as rodents (e.g., rats, mice, squirrels, chipmunks, etc.) and emphasize their role and transmission of the virus in a high-risk group, including gay and bisexual men-who-have-sex-with-men (gbMSM). From model and sensitivity analysis, we identify key public health factors and present scenarios under different transmission assumptions. We find that the MPX virus may spill over from gbMSM high-risk groups to broader populations if the efficiency of transmission increases in the higher-risk group. However, the risk of outbreak can be greatly reduced if at least 65% of symptomatic cases can be isolated and their contacts traced and quarantined. In addition, infections in an animal reservoir will exacerbate MPX transmission risk in the human population. Regions or communities with a higher proportion of gbMSM individuals need greater public health attention. Tracing and quarantine (or "effective quarantine" by postexposure vaccination) of contacts with MPX cases in high-risk groups would have a significant effect on controlling the spreading. Also, monitoring for animal infections would be prudent.

Inferring Insulin Secretion Rate from Sparse Patient Glucose and Insulin Measures

The insulin secretion rate (ISR) contains information that can provide a personal, quantitative understanding of endocrine function. If the ISR can be reliably inferred from measurements, it could be used for understanding and clinically diagnosing problems with the glucose regulation system. Objective: This study aims to develop a model-based method for inferring a parametrization of the ISR and related physiological information among people with different glycemic conditions in a robust manner. The developed algorithm is applicable for both dense or sparsely sampled plasma glucose/insulin measurements, where sparseness is defined in terms of sampling time with respect to the fastest time scale of the dynamics. Methods: An algorithm for parametrizing and validating a functional form of the ISR for different compartmental models with unknown but estimable ISR function and absorption/decay rates describing the dynamics of insulin accumulation was developed. The method and modeling applies equally to c-peptide secretion rate (CSR) when c-peptide is measured. Accuracy of fit is reliant on reconstruction error of the measured trajectories, and when c-peptide is measured the relationship between CSR and ISR. The algorithm was applied to data from 17 subjects with normal glucose regulatory systems and 9 subjects with cystic fibrosis related diabetes (CFRD) in which glucose, insulin and c-peptide were measured in course of oral glucose tolerance tests (OGTT). Results: This model-based algorithm inferred parametrization of the ISR and CSR functional with relatively low reconstruction error for 12 of 17 control and 7 of 9 CFRD subjects. We demonstrate that when there are suspect measurements points, the validity of excluding them may be interrogated with this method. Significance: A new estimation method is available to infer the ISR and CSR functional profile along with plasma insulin and c-peptide absorption rates from sparse measurements of insulin, c-peptide, and plasma glucose concentrations. We propose a method to interrogate and exclude potentially erroneous OGTT measurement points based on reconstruction errors.

Models for plasma kinetics during simultaneous therapeutic plasma exchange and extracorporeal membrane oxygenation

This paper focuses on the derivation and simulation of mathematical models describing new plasma fraction in blood for patients undergoing simultaneous extracorporeal membrane oxygenation and therapeutic plasma exchange. Models for plasma exchange with either veno-arterial or veno-venous extracorporeal membrane oxygenation are considered. Two classes of models are derived for each case, one in the form of an algebraic delay equation and another in the form of a system of delay differential equations. In special cases, our models reduce to single compartment ones for plasma exchange that have been validated with experimental data (Randerson et al., 1982, Artif. Organs, 6, 43-49). We also show that the algebraic differential equations are forward Euler discretizations of the delay differential equations, with timesteps equal to transit times through model compartments. Numerical simulations are performed to compare different model types, to investigate the impact of plasma device port switching on the efficiency of the exchange process, and to study the sensitivity of the models to their parameters.

Higher-order diffusion MRI characterization of mesorectal lymph nodes in rectal cancer

PURPOSE

Mesorectal lymph node staging plays an important role in treatment decision making. Here, we explore the benefit of higher-order diffusion MRI models accounting for non-Gaussian diffusion effects to classify mesorectal lymph nodes both 1) ex vivo at ultrahigh field correlated with histology and 2) in vivo in a clinical scanner upon patient staging.

METHODS

The preclinical investigation included 54 mesorectal lymph nodes, which were scanned at 16.4 T with an extensive diffusion MRI acquisition. Eight diffusion models were compared in terms of goodness of fit, lymph node classification ability, and histology correlation. In the clinical part of this study, 10 rectal cancer patients were scanned with diffusion MRI at 1.5 T, and 72 lymph nodes were analyzed with Apparent Diffusion Coefficient (ADC), Intravoxel Incoherent Motion (IVIM), Kurtosis, and IVIM-Kurtosis.

RESULTS

Compartment models including restricted and anisotropic diffusion improved the preclinical data fit, as well as the lymph node classification, compared to standard ADC. The comparison with histology revealed only moderate correlations, and the highest values were observed between diffusion anisotropy metrics and cell area fraction. In the clinical study, the diffusivity from IVIM-Kurtosis was the only metric showing significant differences between benign (0.80 ± 0.30 μm² /ms) and malignant (1.02 ± 0.41 μm² /ms, P = .03) nodes. IVIM-Kurtosis also yielded the largest area under the receiver operating characteristic curve (0.73) and significantly improved the node differentiation when added to the standard visual analysis by experts based on T₂ -weighted imaging.

CONCLUSION

Higher-order diffusion MRI models perform better than standard ADC and may be of added value for mesorectal lymph node classification in rectal cancer patients.

Modeling the pharmacokinetics and pharmacodynamics of sevoflurane using compartment models in children and adults

BACKGROUND

Sevoflurane pharmacokinetics have been traditionally described using physiological models, while pharmacodynamics employed the use of minimal alveolar concentration.

AIMS

The integrated pharmacokinetic-pharmacodynamic relationship of sevoflurane in both adults and children was reviewed using compartment models. We wished to delineate age-related changes in both pharmacokinetics and pharmacodynamics.

METHODS

The bispectral index and sevoflurane endtidal concentration were continuously measured in 50 patients, aged 3-71 years, scheduled for minor surgery. During maintenance of anesthesia and after stable bispectral index values of 60-65 were obtained, the inspired concentration of sevoflurane was increased to 5 vol % for 5 minutes or until BIS 40 and then decreased. Data were analyzed using mammillary compartments with nonlinear mixed effects population modeling. The covariate effects of age and size were investigated.

RESULTS

A three-compartment PK model adequately described sevoflurane pharmacokinetics. Size standardization using allometry explained clearance and volume changes with age. The equilibration half-time (1.48 minutes) increased with age, but could be predicted using allometry in those under 40 years. The effect site concentration eliciting half the maximum response at age 40 years was 1.3% (95%CI 1.22, 1.42) decreased with age from 1.6% at 3 years to 1.1% at 70 years.

CONCLUSION

Pharmacokinetic compartment models offer an alternative method to describe inhalation anesthetic drug disposition and effects.

The muddle of ages, turnover, transit, and residence times in the carbon cycle

Comparisons among ecosystem models or ecosystem dynamics along environmental gradients commonly rely on metrics that integrate different processes into a useful diagnostic. Terms such as age, turnover, residence, and transit times are often used for this purpose; however, these terms are variably defined in the literature and in many cases, calculations ignore assumptions implicit in their formulas. The aim of this opinion piece was i) to make evident these discrepancies and the incorrect use of formulas, ii) highlight recent results that simplify calculations and may help to avoid confusion, and iii) propose the adoption of simple and less ambiguous terms.

The usage of a three-compartment model to investigate the metabolic differences between hepatic reductase null and wild-type mice

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The Cytochrome P450 (CYP) system is involved in 90% of the human body's interactions with xenobiotics and due to this, it has become an area of avid research including the creation of transgenic mice. This paper proposes a three-compartment model which is used to explain the drug metabolism in the Hepatic Reductase Null (HRN) mouse developed by the University of Dundee (Henderson, C. J., Otto, D. M. E., Carrie, D., Magnuson, M. A., McLaren, A. W., Rosewell, I. and Wolf, C. R. (2003) Inactivation of the hepatic cytochrome p450 system by conditional deletion of hepatic cytochrome p450 reductase. J. Biol. Chem. , 13480-13486). The model is compared with a two-compartment model using experimental data from studies using wild-type and HRN mice. This comparison allowed for metabolic differences between the two types of mice to be isolated. The three sets of drug data (Gefitinib, Midazolam and Thalidomide) showed that the transgenic mouse has a decreased rate of metabolism.

Model-based estimation of microscopic anisotropy using diffusion MRI: a simulation study

Non-invasive estimation of cell size and shape is a key challenge in diffusion MRI. This article presents a model-based approach that provides independent estimates of pore size and eccentricity from diffusion MRI data. The technique uses a geometric model of finite cylinders with gamma-distributed radii to represent pores of various sizes and elongations. We consider both macroscopically isotropic substrates and substrates of semi-coherently oriented anisotropic pores and we use Monte Carlo simulations to generate synthetic data. We compare the sensitivity of single and double diffusion encoding (SDE and DDE) sequences to the size distribution and eccentricity, and further analyse different protocols of DDE sequences with parallel and/or perpendicular pairs of gradients. We show that explicitly accounting for size distribution is necessary for accurate microstructural parameter estimates, and a model that assumes a single size yields biased eccentricity values. We also find that SDE sequences support estimates, although DDE sequences with mixed parallel and perpendicular gradients enhance accuracy. In the case of macroscopically anisotropic substrates, this model-based approach can be extended to a rotationally invariant framework to provide features of pore shape (specifically eccentricity) in the presence of size distribution and orientation dispersion.

Information-based ranking of 10 compartment models of diffusion-weighted signal attenuation in fixed prostate tissue

This study compares the theoretical information content of single- and multi-compartment models of diffusion-weighted signal attenuation in prostate tissue. Diffusion-weighted imaging (DWI) was performed at 9.4 T with multiple diffusion times and an extended range of b values in four whole formalin-fixed prostates. Ten models, including different combinations of isotropic, anisotropic and restricted components, were tested. Models were ranked using the Akaike information criterion. In all four prostates, two-component models, comprising an anisotropic Gaussian component and an isotropic restricted component, ranked highest in the majority of voxels. Single-component models, whether isotropic (apparent diffusion coefficient, ADC) or anisotropic (diffusion tensor imaging, DTI), consistently ranked lower than multi-component models. Model ranking trends were independent of voxel size and maximum b value in the range tested (1.6-16 mm(3) and 3000-10,000 s/mm(2)). This study characterizes the two major water components previously identified by biexponential models and shows that models incorporating both anisotropic and restricted components provide more information-rich descriptions of DWI signals in prostate tissue than single- or multi-component anisotropic models and models that do not account for restricted diffusion.

Fiber Orientation and Compartment Parameter Estimation From Multi-Shell Diffusion Imaging

Diffusion MRI offers the unique opportunity of assessing the structural connections of human brains in vivo. With the advance of diffusion MRI technology, multi-shell imaging methods are becoming increasingly practical for large scale studies and clinical application. In this work, we propose a novel method for the analysis of multi-shell diffusion imaging data by incorporating compartment models into a spherical deconvolution framework for fiber orientation distribution (FOD) reconstruction. For numerical implementation, we develop an adaptively constrained energy minimization approach to efficiently compute the solution. On simulated and real data from Human Connectome Project (HCP), we show that our method not only reconstructs sharp and clean FODs for the modeling of fiber crossings, but also generates reliable estimation of compartment parameters with great potential for clinical research of neurological diseases. In comparisons with publicly available DSI-Studio and BEDPOSTX of FSL, we demonstrate that our method reconstructs sharper FODs with more precise estimation of fiber directions. By applying probabilistic tractography to the FODs computed by our method, we show that more complete reconstruction of the corpus callosum bundle can be achieved. On a clinical, two-shell diffusion imaging data, we also demonstrate the feasibility of our method in analyzing white matter lesions.

A new relation between prevalence and incidence of a chronic disease

In 1991 Keiding published a relation between the age-specific prevalence and incidence of a chronic disease (in Age-specific incidence and prevalence: a statistical perspective. J. Roy. Stat. Soc. A, 154, 371-412). For special cases alternative formulations by differential equations were given recently in Brinks et al. (2013, Deriving age-specific incidence from prevalence with an ordinary differential equation. Statist. Med., 32, 2070-2078) and in Brinks & Landwehr (2014, Age- and time-dependent model of the prevalence of non-communicable diseases and application to dementia in Germany, Theor. Popul. Biol., 92, 62-68). From these works, we generalize formulations and discuss the advantages of the novel approach. As an implication, we obtain a new way of estimating the incidence rate of a chronic disease from prevalence data. This enables us to employ cross-sectional studies where otherwise expensive and lengthy follow-up studies are needed. This article illustrates and validates the novel method in a simulation study about dementia in Germany.

Modeling considerations for in vivo quantification of the dopamine transporter using [(11)C]PE2I and positron emission tomography

The dopamine transporter (DAT) is an important imaging target as changes in DAT have been implicated in a variety of neurologic and psychiatric disorders and can result from certain classes of medications. [(11)C]N-(3-iodoprop-2E-enyl)-2beta-carbomethoxy-3beta-(4-methylphenyl)nortropane ([(11)C]PE2I), a radioligand with high specificity for DAT, has been shown to exhibit favorable kinetics and to produce high contrast positron emission tomography (PET) images. To better characterize this ligand and to assess its measurement reliability, PET images of seven subjects were acquired in a test-retest paradigm. For optimal model performance, each subject was scanned for 120 mins, ensuring that high binding regions could reach equilibrium, a validated coregistration method was performed for accurate anatomic delineations and an exhaustive search for a reference region having one-tissue compartment kinetics was undertaken. Eleven modeling methods were tested and six metrics were used for method evaluation. A noniterative two-tissue compartment method with 100 mins of scanning time was found to be optimal for characterizing [(11)C]PE2I.