A compartment and metapopulation model of Rocky Mountain spotted fever in southwestern United States and northern Mexico

Rocky Mountain spotted fever (RMSF) is a fatal tick-borne zoonotic disease that has emerged as an epidemic in western North America since the turn of the 21st century. Along the US south-western border and across northern Mexico, the brown dog tick, Rhipicephalus sanguineus, is responsible for spreading the disease between dogs and humans. The widespread nature of the disease and the ongoing epidemics contrast with historically sporadic patterns of the disease. Because dogs are amplifying hosts for the Rickettsia rickettsii bacteria, transmission dynamics between dogs and ticks are critical for understanding the epidemic. In this paper, we developed a compartment metapopulation model and used it to explore the dynamics and drivers of RMSF in dogs and brown dog ticks in a theoretical region in western North America. We discovered that there is an extended lag-as much as two years-between introduction of the pathogen to a naïve population and epidemic-level transmission, suggesting that infected ticks could disseminate extensively before disease is detected. A single large city-size population of dogs was sufficient to maintain the disease over a decade and serve as a source for disease in surrounding smaller towns. This model is a novel tool that can be used to identify high risk areas and key intervention points for epidemic RMSF spread by brown dog ticks.

Improved data analysis techniques for calculating more accurate radon and thoron exhalation rates from building interior solid walls

The impacts of mathematical models and associated parameters on radon (222Rn) and thoron (220Rn) exhalation rates based on in-situ testing at building interior solid walls were demonstrated to improve data analysis techniques. The results showed that the heterogeneity of their activity concentrations within the measurement system was more significant for thoron than radon. The diurnal variation in indoor radon should be considered for better data quality. In conclusion, a model should be appropriately made and selected under the purposes and accuracy requirements of the exhalation test.

Estimating averted illnesses from influenza vaccination for children and pregnant women - El Salvador, Panama, and Peru, 2011-2018

BACKGROUND

Estimating the burden of disease averted by vaccination can assist policymakers to implement, adjust, and communicate the value of vaccination programs. Demonstrating the use of a newly available modeling tool, we estimated the burden of influenza illnesses averted by seasonal influenza vaccination in El Salvador, Panama, and Peru during 2011-2017 among two influenza vaccine target populations: children aged 6-23 months and pregnant women.

METHODS

We derived model inputs, including incidence, vaccine coverage, vaccine effectiveness, and multipliers from publicly available country-level influenza surveillance data and cohort studies. We also estimated changes in illnesses averted when countries' vaccine coverage was achieved using four different vaccine deployment strategies.

RESULTS

Among children aged 6-23 months, influenza vaccination averted an estimated cumulative 2,161 hospitalizations, 81,907 medically-attended illnesses, and 126,987 overall illnesses during the study period, with a prevented fraction ranging from 0.3 % to 12.5 %. Among pregnant women, influenza vaccination averted an estimated cumulative 173 hospitalizations, 6,122 medically attended illnesses, and 16,412 overall illnesses, with a prevented fraction ranging from 0.2 % to 10.9 %. Compared to an influenza vaccine campaign with equal vaccine distribution during March-June, scenarios in which total cumulative coverage was achieved in March and April consistently resulted in the greatest increase in averted illness (23 %-3,129 % increase among young children and 22 %-3,260 % increase among pregnant women).

DISCUSSION

Influenza vaccination campaigns in El Salvador, Panama, and Peru conducted between 2011 and 2018 prevented hundreds to thousands of influenza-associated hospitalizations and illnesses in young children and pregnant women. Existing vaccination programs could prevent additional illnesses, using the same number of vaccines, by achieving the highest possible coverage within the first two months of an influenza vaccine campaign.

A compartment model for subcutaneous injection of monoclonal antibodies

Despite the growing popularity of subcutaneous (SC) administration for monoclonal antibodies (mAbs), there remains a limited understanding of the significance of mAb transport rate constants within the interstitial space and the lymphatic system on their pharmacokinetics. To bridge this knowledge gap, we introduce a compartmental model for subcutaneously administered mAbs. Our model differentiates FcRn-expressing cells across various sites, and the model predictions agree with experimental data from both human and rat studies. Our findings indicate that the time to reach the maximum mAb concentration in the plasma, denoted by Tmax, displays a weak positive correlation with mAb half-life and a negligible correlation with bioavailability. In contrast, the half-life of mAbs exhibits a strong positive correlation with bioavailability. Moreover, the rate of mAb transport from lymph to plasma significantly affects the mAb half-life. Increasing the transport rates of mAbs from the injection site to the lymph or from lymph to plasma enhances bioavailability. These insights, combined with our compartmental model, contribute to a deeper understanding of the pharmacokinetics of subcutaneously administered mAbs.

Estimating the instantaneous reproduction number (Rt) by using particle filter

Background

Monitoring the transmission of coronavirus disease 2019 (COVID-19) requires accurate estimation of the effective reproduction number (R t ). However, existing methods for calculating R t may yield biased estimates if important real-world factors, such as delays in confirmation, pre-symptomatic transmissions, or imperfect data observation, are not considered.

Method

To include real-world factors, we expanded the susceptible-exposed-infectious-recovered (SEIR) model by incorporating pre-symptomatic (P) and asymptomatic (A) states, creating the SEPIAR model. By utilizing both stochastic and deterministic versions of the model, and incorporating predetermined time series of R t , we generated simulated datasets that simulate real-world challenges in estimating R t . We then compared the performance of our proposed particle filtering method for estimating R t with the existing EpiEstim approach based on renewal equations.

Results

The particle filtering method accurately estimated R t even in the presence of data with delays, pre-symptomatic transmission, and imperfect observation. When evaluating via the root mean square error (RMSE) metric, the performance of the particle filtering method was better in general and was comparable to the EpiEstim approach if perfectly deconvolved infection time series were provided, and substantially better when R t exhibited short-term fluctuations and the data was right truncated.

Conclusions

The SEPIAR model, in conjunction with the particle filtering method, offers a reliable tool for predicting the transmission trend of COVID-19 and assessing the impact of intervention strategies. This approach enables enhanced monitoring of COVID-19 transmission and can inform public health policies aimed at controlling the spread of the disease.

Coupled disease-vaccination behavior dynamic analysis and its application in COVID-19 pandemic

Predicting the evolutionary dynamics of the COVID-19 pandemic is a complex challenge. The complexity increases when the vaccination process dynamic is also considered. In addition, when applying a voluntary vaccination policy, the simultaneous behavioral evolution of individuals who decide whether and when to vaccinate must be included. In this paper, a coupled disease-vaccination behavior dynamic model is introduced to study the coevolution of individual vaccination strategies and infection spreading. We study disease transmission by a mean-field compartment model and introduce a non-linear infection rate that takes into account the simultaneity of interactions. Besides, the evolutionary game theory is used to investigate the contemporary evolution of vaccination strategies. Our findings suggest that sharing information with the entire population about the negative and positive consequences of infection and vaccination is beneficial as it boosts behaviors that can reduce the final epidemic size. Finally, we validate our transmission mechanism on real data from the COVID-19 pandemic in France.

A systematic procedure for incorporating separable static heterogeneity into compartmental epidemic models

In this paper, we show how to modify a compartmental epidemic model, without changing the dimension, such that separable static heterogeneity is taken into account. The derivation is based on the Kermack-McKendrick renewal equation.

Attention based parameter estimation and states forecasting of COVID-19 pandemic using modified SIQRD Model

In this work, we propose a new mathematical modeling of the spread of COVID-19 infection in an arbitrary population, by modifying the SIQRD model as m-SIQRD model, while taking into consideration the eight governmental interventions such as cancellation of events, closure of public places etc., as well as the influence of the asymptomatic cases on the states of the model. We introduce robustness and improved accuracy in predictions of these models by utilizing a novel deep learning scheme. This scheme comprises of attention based architecture, alongside with Generative Adversarial Network (GAN) based data augmentation, for robust estimation of time varying parameters of m-SIQRD model. In this regard, we also utilized a novel feature extraction methodology by employing noise removal operation by Spline interpolation and Savitzky-Golay filter, followed by Principal Component Analysis (PCA). These parameters are later directed towards two main tasks: forecasting of states to the next 15 days, and estimation of best policy encodings to control the infected and deceased number within the framework of data driven synergetic control theory. We validated the superiority of the forecasting performance of the proposed scheme over countries of South Korea and Germany and compared this performance with 7 benchmark forecasting models. We also showed the potential of this scheme to determine best policy encodings in South Korea for 15 day forecast horizon.

Exo-SIR: an epidemiological model to analyze the impact of exogenous spread of infection

Epidemics like Covid-19 and Ebola have impacted people's lives significantly. The impact of mobility of people across the countries or states in the spread of epidemics has been significant. The spread of disease due to factors local to the population under consideration is termed the endogenous spread. The spread due to external factors like migration, mobility, etc., is called the exogenous spread. In this paper, we introduce the Exo-SIR model, an extension of the popular SIR model and a few variants of the model. The novelty in our model is that it captures both the exogenous and endogenous spread of the virus. First, we present an analytical study. Second, we simulate the Exo-SIR model with and without assuming contact network for the population. Third, we implement the Exo-SIR model on real datasets regarding Covid-19 and Ebola. We found that endogenous infection is influenced by exogenous infection. Furthermore, we found that the Exo-SIR model predicts the peak time better than the SIR model. Hence, the Exo-SIR model would be helpful for governments to plan policy interventions at the time of a pandemic.

Exploration of the Plausible Mechanism of Ethambutol Induced Ocular Toxicity by Using Proteomics Informed Physiologically Based Pharmacokinetic (PBPK) Modeling

PURPOSE

Ethambutol (EMB) is a first-line anti-tubercular drug that is known to cause optic neuropathy. The exact mechanism of its eye toxicity is unknown; however, proposition is metal chelating effect of both EMB and its metabolite 2,2'-(ethylenediamino)-dibutyric acid (EDBA). The latter is formed by sequential metabolism of EMB by alcohol dehydrogenases (ADHs) and aldehyde dehydrogenases (ALDHs). The purpose of this study was to predict the levels of drug and EDBA in the eye using physiologically based pharmacokinetic (PBPK) modeling.

METHODS

The PBPK model of EMB was developed using GastroPlus. The intrinsic hepatic clearance of ALDH, calculated by the model, was scaled down using proteomics data to estimate the rate of formation of EDBA in the eye. Additionally, the comparative permeability of EMB and EDBA was assessed by employing in silico and in vitro approaches. The rate of formation of EDBA in the eye and permeability data were then incorporated in a compartmental model to predict the ocular levels of EMB and EDBA.

RESULTS

The simulation results of compartmental model highlighted that there was an on-site formation of EDBA upon metabolism of EMB. Furthermore, in silico and in vitro studies revealed that EDBA possessed much lower permeability than EMB. These observations meant that once EDBA was formed in the eye, it was not permeated out and hence achieved higher ocular concentration.

CONCLUSION

The on-site formation of EDBA in the eye, its higher local concentration due to lower ocular clearance and its pre-known characteristic to chelate metal species better explains the ocular toxicity shown by EMB.

Evaluating the sensitivity of SARS-CoV-2 infection rates on college campuses to wastewater surveillance

As college campuses reopened in fall 2020, we saw a large-scale experiment unfold on the efficacy of various strategies to contain the SARS-CoV-2 virus. Traditional individual surveillance testing via nasal swabs and/or saliva is among the measures that colleges are pursuing to reduce the spread of the virus on campus. Additionally, some colleges are testing wastewater on their campuses for signs of infection, which can provide an early warning signal for campuses to locate COVID-positive individuals. However, a representation of wastewater surveillance has not yet been incorporated into epidemiological models for college campuses, nor has the efficacy of wastewater screening been evaluated relative to traditional individual surveillance testing, within the structure of these models. Here, we implement a new model component for wastewater surveillance within an established epidemiological model for college campuses. We use a hypothetical residential university to evaluate the efficacy of wastewater surveillance for maintaining low infection rates. We find that wastewater sampling with a 1-day lag to initiate individual screening tests, plus completing the subsequent tests within a 4-day period can keep overall infections within 5% of the infection rates seen with traditional individual surveillance testing. Our results also indicate that wastewater surveillance can effectively reduce the number of false positive cases by identifying subpopulations for surveillance testing where infectious individuals are more likely to be found. Through a Monte Carlo risk analysis, we find that surveillance testing that relies solely on wastewater sampling can be fragile against scenarios with high viral reproductive numbers and high rates of infection of campus community members by outside sources. These results point to the practical importance of additional surveillance measures to limit the spread of the virus on campus and the necessity of a proactive response to the initial signs of outbreak.

Evaluating medical capacity for hospitalization and intensive care unit of COVID-19: A queue model approach

BACKGROUND

The surge of COVID-19 pandemic has caused severe respiratory conditions and a large number of deaths due to the shortage of intensive care unit (ICU) in many countries.

METHODS

We developed a compartment queue model to describe the process from case confirmation, home-based isolation, hospitalization, ICU, recovery, and death. By using public assessed data in Lombardy, Italy, we estimated two congestion indices for isolation wards and ICU. The excess ICU needs were estimated in Lombardy, Italy, and other countries when data were available, including France, Spain, Belgium, New York State in the USA, South Korea, and Japan.

RESULTS

In Lombardy, Italy, the congestion of isolation beds had increased from 2.2 to the peak of 6.0 in March and started to decline to 3.9 as of 9^th May, whereas the demand for ICU during the same period has not decreased yet with an increasing trend from 2.9 to 8.0. The results showed the unmet ICU need from the second week in March as of 9^th May. The same situation was shown in France, Spain, Belgium, and New York State, USA but not for South Korea and Japan. The results with data until December 2020 for Lombardy, Italy were also estimated to reflect the demand for hospitalization and ICU after the occurrence of viral variants.

CONCLUSION

Two congestion indices for isolation wards and ICU beds using open assessed tabulated data with a compartment queue model underpinning were developed to monitor the clinical capacity in hospitals in response to the COVID-19 pandemic.

Conditional particle filters with diffuse initial distributions

Conditional particle filters (CPFs) are powerful smoothing algorithms for general nonlinear/non-Gaussian hidden Markov models. However, CPFs can be inefficient or difficult to apply with diffuse initial distributions, which are common in statistical applications. We propose a simple but generally applicable auxiliary variable method, which can be used together with the CPF in order to perform efficient inference with diffuse initial distributions. The method only requires simulatable Markov transitions that are reversible with respect to the initial distribution, which can be improper. We focus in particular on random walk type transitions which are reversible with respect to a uniform initial distribution (on some domain), and autoregressive kernels for Gaussian initial distributions. We propose to use online adaptations within the methods. In the case of random walk transition, our adaptations use the estimated covariance and acceptance rate adaptation, and we detail their theoretical validity. We tested our methods with a linear Gaussian random walk model, a stochastic volatility model, and a stochastic epidemic compartment model with time-varying transmission rate. The experimental findings demonstrate that our method works reliably with little user specification and can be substantially better mixing than a direct particle Gibbs algorithm that treats initial states as parameters.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s11222-020-09975-1.

COVID-19 outbreak in Wuhan demonstrates the limitations of publicly available case numbers for epidemiological modeling

Epidemiological models are widely used to analyze the spread of diseases such as the global COVID-19 pandemic caused by SARS-CoV-2. However, all models are based on simplifying assumptions and often on sparse data. This limits the reliability of parameter estimates and predictions. In this manuscript, we demonstrate the relevance of these limitations and the pitfalls associated with the use of overly simplistic models. We considered the data for the early phase of the COVID-19 outbreak in Wuhan, China, as an example, and perform parameter estimation, uncertainty analysis and model selection for a range of established epidemiological models. Amongst others, we employ Markov chain Monte Carlo sampling, parameter and prediction profile calculation algorithms. Our results show that parameter estimates and predictions obtained for several established models on the basis of reported case numbers can be subject to substantial uncertainty. More importantly, estimates were often unrealistic and the confidence/credibility intervals did not cover plausible values of critical parameters obtained using different approaches. These findings suggest, amongst others, that standard compartmental models can be overly simplistic and that the reported case numbers provide often insufficient information for obtaining reliable and realistic parameter values, and for forecasting the evolution of epidemics.

Analysis of second outbreak of COVID-19 after relaxation of control measures in India

At present, more and more countries have entered the parallel stage of fighting the epidemic and restoring the economy after reaching the inflection point. Due to economic pressure, the government of India had to implement a policy of relaxing control during the rising period of the epidemic. This paper proposes a compartment model to study the development of COVID-19 in India after relaxing control. The Sigmoid function reflecting the cumulative effect is used to characterize the model-based diagnosis rate, cure rate and mortality rate. Considering the influence of the lockdown on the model parameters, the data are fitted using the method of least squares before and after the lockdown. According to numerical simulation and model analysis, the impact of India's relaxation of control before and after the inflection point is studied. Research shows that adopting a relaxation policy prematurely will have disastrous consequences. Even if the degree of relaxation is only 5% before the inflection point, it will increase the number of deaths by 15.03%. If the control is relaxed after the inflection point, the higher degree of relaxation, the more likely a secondary outbreak will occur, which will extend the duration of the pandemic, leading to more deaths and put more pressure on the health care system. It is found that after the implementation of the relaxation policy, medical quarantine capability and public cooperation are two vital indicators. The results show that if the supply of kits and detection speed can be increased after the control is relaxed, the secondary outbreak can be effectively avoided. Meanwhile, the increase in public cooperation can significantly reduce the spread of the virus, suppress the second outbreak of the pandemic and reduce the death toll. It is of reference significance to the government's policy formulation.

Understanding gradients in industrial bioreactors

Gradients in industrial bioreactors have attracted substantial research attention since exposure to fluctuating environmental conditions has been shown to lead to changes in the metabolome, transcriptome as well as population heterogeneity in industrially relevant microorganisms. Such changes have also been found to impact key process parameters like the yield on substrate and the productivity. Hence, understanding gradients is important from both the academic and industrial perspectives. In this review the causes of gradients are outlined, along with their impact on microbial physiology. Quantifying the impact of gradients requires a detailed understanding of both fluid flow inside industrial equipment and microbial physiology. This review critically examines approaches used to investigate gradients including large-scale experimental work, computational methods and scale-down approaches. Avenues for future work have been highlighted, particularly the need for further coordinated development of both in silico and experimental tools which can be used to further the current understanding of gradients in industrial equipment.

A novel variant of the 13C-methacetin liver function breath test that eliminates the confounding effect of individual differences in systemic CO2 kinetics

The principle of dynamic liver function breath tests is founded on the administration of a ¹³C-labeled drug and subsequent monitoring of ¹³CO₂ in the breath, quantified as time series delta over natural baseline ¹³CO₂ (DOB) liberated from the drug during hepatic CYP-dependent detoxification. One confounding factor limiting the diagnostic value of such tests is that only a fraction of the liberated ¹³CO₂ is immediately exhaled, while another fraction is taken up by body compartments from which it returns with delay to the plasma. The aims of this study were to establish a novel variant of the methacetin-based breath test LiMAx that allows to estimate and to eliminate the confounding effect of systemic ¹³CO₂ distribution on the DOB curve and thus enables a more reliable assessment of the hepatic detoxification capacity compared with the conventional LiMAx test. We designed a new test variant (named "2DOB") consisting of two consecutive phases. Phase 1 is initiated by the intravenous administration of ¹³C-bicarbonate. Phase 2 starts about 30 min later with the intravenous administration of the ¹³C-labelled test drug. Using compartment modelling, the resulting 2-phasic DOB curve yields the rate constants for the irreversible elimination and the reversible exchange of plasma ¹³CO₂ with body compartments (phase 1) and for the detoxification and exchange of the drug with body compartments (phase 2). We carried out the 2DOB test with the test drug ¹³C-methacetin in 16 subjects with chronic liver pathologies and 22 normal subjects, who also underwent the conventional LiMAx test. Individual differences in the systemic CO₂ kinetics can lead to deviations up to a factor of 2 in the maximum of DOB curves (coefficient of variation CV ≈ 0.2) which, in particular, may hamper the discrimination between subjects with normal or mildly impaired detoxification capacities. The novel test revealed that a significant portion of the drug is not immediately metabolized, but transiently taken up into a storage compartment. Intriguingly, not only the hepatic detoxification rate but also the storage capacity of the drug, turned out to be indicative for a normal liver function. We thus used both parameters to define a scoring function which yielded an excellent disease classification (AUC = 0.95) and a high correlation with the MELD score (R_Spearman = 0.92). The novel test variant 2DOB promises a significant improvement in the assessment of impaired hepatic detoxification capacity. The suitability of the test for the reliable characterization of the natural history of chronic liver diseases (fatty liver-fibrosis-cirrhosis) has to be assessed in further studies.

Temporal distribution of Fukushima-derived 137Cs in coniferous forest soil evaluated based on compartment-exponential model

Based on the compartment and exponential models, the distribution of Fukushima-derived ¹³⁷Cs was evaluated at four sampling dates in undisturbed coniferous forest soil. The compartment model was employed to evaluate the dynamic of ¹³⁷Cs in the three sub-sections of the forest floor (FF), namely undergrowth (UG), litter layer (OL), and fragmented litter layer (OF), while the exponential model was administrated to describe its distribution below the FF. According to the compartment model, the derived ecological half-life of ¹³⁷Cs in the UG, OL, and OF layers was 0.97, 1.1, and 4.9 years, respectively, indicating ¹³⁷Cs resides much longer in the OF layer. Hence, this soil section remains a potential source of radiation dose mainly due to its high ¹³⁷Cs content associated with low attenuation effect. Below the OF layer, the ¹³⁷Cs distribution was well described by exponential model and its derived relaxation lengths were in the range of 0.8-1.4 cm, implying the migration of ¹³⁷Cs in mineral soil is very slow and almost intact during the observation time. Collectively, our results highlighted that the compartment model for the FF and the exponential model for the soil below the FF are adequate enough to generate essential information. Thus, the potential decontamination measures should have to be chosen on their effect on the FF's ¹³⁷Cs. Graphical abstract.

Analysing detection of chronic diseases with prolonged sub-clinical periods: modelling and application to hypertension in the U.S

Background

We recently introduced a system of partial differential equations (PDEs) to model the prevalence of chronic diseases with a possibly prolonged state of asymptomatic, undiagnosed disease preceding a diagnosis. Common examples for such diseases include coronary heart disease, type 2 diabetes or cancer. Widespread application of the new method depends upon mathematical treatment of the system of PDEs.

Methods

In this article, we study the existence and the uniqueness of the solution of the system of PDEs. To demonstrate the usefulness and importance of the system, we model the age-specific prevalence of hypertension in the US 1999–2010.

Results

The examinations of mathematical properties provide a way to solve the systems of PDEs by the method of characteristics. In the application to hypertension, we obtain a good agreement between modeled and surveyed age-specific prevalences.

Conclusions

The described system of PDEs provides a practical way to examine the epidemiology of chronic diseases with a state of undiagnosed disease preceding a diagnosis.

Numerical analysis of apparent decitabine uptake in HCT116 cells: Incorporation of a bidirectional first-order kinetic parameter for ENT1 transport and Michaelis-Menten parameters for subsequent phosphorylation

Decitabine (DAC), a DNA methylation inhibitor, is transported into cancer cells mainly via equilibrative nucleoside transporter 1 (ENT1) and subsequently phosphorylated by deoxycytidine kinase (dCK). We previously reported that apparent DAC uptake into cells may be described using a simple compartment model with clearance for facilitated diffusion (PS) and subsequent phosphorylation (CL_met). In the present study, time course of apparent intracellular [³H]-DAC uptake was analyzed numerically, and PS and CL_met values were calculated using the compartment model in human colon cancer HCT116 cells. PS at 0.1 μM [³H]-DAC was markedly decreased in the presence of 100 μM irinotecan or etoposide, while CL_met was markedly decreased in the presence of 100 μM cytarabine or gemcitabine. CL_met at 0.1-10 μM [³H]-DAC varied in a concentration-dependent manner and was described by Michaelis-Menten parameters K_m,met and V_max,met. In conclusion, DAC uptake mainly via ENT1 may be described by a bidirectional first-order kinetic parameter, while phosphorylation by dCK may be described by Michaelis-Menten parameters.

Reference region extraction by clustering for the pharmacokinetic analysis of dynamic contrast-enhanced MRI in prostate cancer

PURPOSE

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) measures changes in the concentration of an administered contrast agent to quantitatively evaluate blood circulation in a tumor or normal tissues. This method uses a pharmacokinetic analysis based on the time course of a reference region, such as muscle, rather than arterial input function. However, it is difficult to manually define a homogeneous reference region. In the present study, we developed a method for automatic extraction of the reference region using a clustering algorithm based on a time course pattern for DCE-MRI studies of patients with prostate cancer.

METHODS

Two feature values related to the shape of the time course were extracted from the time course of all voxels in the DCE-MRI images. Each voxel value of T1-weighted images acquired before administration were also added as anatomical data. Using this three-dimensional feature vector, all voxels were segmented into five clusters by the Gaussian mixture model, and one of these clusters that included the gluteus muscle was selected as the reference region.

RESULTS

Each region of arterial vessel, muscle, and fat was segmented as a different cluster from the tumor and normal tissues in the prostate. In the extracted reference region, other tissue elements including scattered fat and blood vessels were removed from the muscle region.

CONCLUSIONS

Our proposed method can automatically extract the reference region using the clustering algorithm with three types of features based on the time course pattern and anatomical data. This method may be useful for evaluating tumor circulatory function in DCE-MRI studies.

A subcutaneous insulin pharmacokinetic model for insulin Detemir

BACKGROUND AND OBJECTIVE

Type 2 diabetes (T2D) is rapidly increasing in incidence and has significant social and economic costs. Given the increasing cost of complications, even relatively short delays in the onset of T2D can significantly reduce long-term complications and costs. Equally, recent studies have shown the onset of T2D can be delayed by use of long-acting insulin, despite the risk and concomitant low adherence. Thus, there is a strong potential motivation to develop models of long-acting insulin analogues to enable safe, effective use in model-based dosing systems. In particular, there are no current models of long-acting insulin Detemir and its unique action for model-based control. The objective of this work is to develop a first model of insulin Detemir and its unique action, and validate it against existing data in the literature.

METHODS

This study develops a detailed compartment model for insulin Detemir. Model specific parameters are identified using data from a range of published clinical studies on the pharmacokinetic of insulin Detemir. Model validity and robustness are assessed by identifying the model for each study and using average identified parameters over several dose sizes and study cohorts. Comparisons to peak concentration, time of peak concentration and overall error versus measured plasma concentrations are used to assess model accuracy and validity.

RESULTS

Almost all studies and cohorts fit literature data to within one standard deviation of error, even when using averaged identified model parameters. However, there appears to be a noticeable dose dependent dynamic not included in this first model, nor reported in the literature studies.

CONCLUSIONS

A first model of insulin Detemir including its unique albumin binding kinetics is derived and provisionally validated against clinical pharmacokinetic data. The pharmacokinetic curves are suitable for model-based control and general enough for use. While there are limitations in the studies used for validation that prevent a more complete understanding, the results provide an effective first model and justify the design and implementation of further, more precise human trials.

Simple pharmacokinetic models accounting for drug monitoring results of atomoxetine and its 4-hydroxylated metabolites in Japanese pediatric patients genotyped for cytochrome P450 2D6

Atomoxetine is an approved medicine for attention-deficit/hyperactivity disorder and a cytochrome P450 2D6 (CYP2D6) probe substrate. Simple physiologically based pharmacokinetic (PBPK) models and compartment models were set up to account for drug monitoring results of 33 Japanese patients (6-15 years of age) to help establish the correct dosage for the evaluation of clinical outcomes. The steady-state one-point drug monitoring data for the most participants indicated the extensive biotransformation of atomoxetine to 4-hydroxyatomoxetine under individually prescribed doses of atomoxetine. However, 5 participants (with impaired CYP2D6 activity scores based on the CYP2D6 genotypes) showed high plasma concentrations of atomoxetine (0.53-1.5 μM) compared with those of total 4-hydroxyatomoxetine (0.49-1.4 μM). Results from full PBPK models using the in-built Japanese pediatric system of software Simcyp, one-compartment models, and new simple PBPK models (using parameters that reflected the subjects' small body size and normal/reduced CYP2D6-dependent clearance) could overlay one-point measured drug/metabolite plasma concentrations from almost common 28 participants within threefold ranges. Validated one-compartment or simple PBPK models can be used to predict steady-state plasma concentrations of atomoxetine and/or its primary metabolites in Japanese pediatric patients (>6 years) who took a variety of individualized doses in a clinical setting.

Derivation and presentation of formulas for drug concentrations in two-, three- and four-compartment pharmacokinetic models

Although compartment models are frequently used in pharmacokinetics, it is difficult to find complete analytical formulas describing the behaviour of drugs in universal simpler compartment models in the accessible literature. The paper presents derivations of formulas for general two- and three-compartment models, including the possibilities of original non-zero quantity in all compartments and elimination from all compartments. Formulas for four-compartment models are also derived with the restriction that original quantity is non-zero in only one compartment. Derivation uses Laplace transformation but does not require prior knowledge of the technique. The derived analytical formulas are verified numerically. These formulas can be easily simplified to less complex cases.

A Short-Term Population Model of the Suicide Risk: The Case of Spain

A relevant proportion of deaths by suicide have been attributed to other causes that produce the number of suicides remains hidden. The existence of a hidden number of cases is explained by the nature of the problem. Problems like this involve violence, and produce fear and social shame in victims' families. The existence of violence, fear and social shame experienced by victims favours a considerable number of suicides, identified as accidents or natural deaths. This paper proposes a short time discrete compartmental mathematical model to measure the suicidal risk for the case of Spain. The compartment model classifies and quantifies the amount of the Spanish population within the age intervals (16, 78) by their degree of suicide risk and their changes over time. Intercompartmental transits are due to the combination of quantitative and qualitative factors. Results are computed and simulations are performed to analyze the sensitivity of the model under uncertain coefficients.

Distinctive distributions and migrations of 239+240Pu and 241Am in Chinese forest, grassland and desert soils

The vertical distributions and downward migrations of the global fallout derived ^239+240Pu and ²⁴¹Am in diverse types of Chinese soils (forest, grassland and desert) were studied. The mean ^239+240Pu and ²⁴¹Am activity concentrations in the investigated soil cores were 0.28-0.69 mBq/g and 0.13-0.37 mBq/g, respectively, while the accumulative inventories were 61.53-138.99 Bq/m² for ^239+240Pu and 28.29-61.05 Bq/m² for ²⁴¹Am. The convection-dispersion equation (CDE) was used to calculate the migration parameters of ^239+240Pu and higher apparent dispersion coefficients (D) were observed for the acidic forest soils compared with the alkaline grassland and desert soils; meanwhile a compartment model was employed to compare the migration of ^239+240Pu and ²⁴¹Am in successive soil layers which showed that the migration behaviors of ^239+240Pu and ²⁴¹Am were rather similar; both velocities were less than 0.3 cm/y in diverse types of soils and these findings were compatible with those of short-term laboratory simulation experiments in China.

An evaluation and update of methods for estimating the number of influenza cases averted by vaccination in the United States

INTRODUCTION

To evaluate the public health benefit of yearly influenza vaccinations, CDC estimates the number of influenza cases and hospitalizations averted by vaccine. Available input data on cases and vaccinations is aggregated by month and the estimation model is intentionally simple, raising concerns about the accuracy of estimates.

METHODS

We created a synthetic dataset with daily counts of influenza cases and vaccinations, calculated "true" averted cases using a reference model applied to the daily data, aggregated the data by month to simulate data that would actually be available, and evaluated the month-level data with seven test methods (including the current method). Methods with averted case estimates closest to the reference model were considered most accurate. To examine their performance under varying conditions, we re-evaluated the test methods when synthetic data parameters (timing of vaccination relative to cases, vaccination coverage, infection rate, and vaccine effectiveness) were varied over wide ranges. Finally, we analyzed real (i.e., collected by surveillance) data from 2010 to 2017 comparing the current method used by CDC with the best-performing test methods.

RESULTS

In the synthetic dataset (population 1 million persons, vaccination uptake 55%, seasonal infection risk without vaccination 12%, vaccine effectiveness 48%) the reference model estimated 28,768 averted cases. The current method underestimated averted cases by 9%. The two best test methods estimated averted cases with <1% error. These two methods also worked well when synthetic data parameters were varied over wide ranges (≤6.2% error). With the real data, these two methods estimated numbers of averted cases that are a median 8% higher than the currently-used method.

CONCLUSIONS

We identified two methods for estimating numbers of influenza cases averted by vaccine that are more accurate than the currently-used algorithm. These methods will help us to better assess the benefits of influenza vaccination.

Numerical simulation for treatment of hypothermia based on vascular interventional direct heating system

The treatment of hypothermia suffered by naval fighters owing to seawater immersion has been a focus of research in recent years. Currently, the treatment of hypothermia in China is limited to external rewarming, which is of low efficiency and is not effective for patients suffering moderate to severe hypothermia. We thus proposed a vascular interventional heating method which directly heats the blood flow via a minimally invasive heating needle for rewarming. And a numerical simulation using a compartment model based on finite difference method was conducted. A set of whole body heating treatment simulation was also developed. Appropriate treatment parameters and procedures can be set and adjusted based on patient physical parameters. Here temperature response curves of different heating modes were obtained and analyzed. It was demonstrated that the desired thermal response can be achieved by adjusting the heating power and heating time, ensuring controllable accuracy in the treatment of patients with severe hypothermia. The proposed treatment for hypothermia is a new and effective alternative, and further progress is expected in clinical trials.

Analysis on the influence of forest soil characteristics on radioactive Cs infiltration and evaluation of residual radioactive Cs on surfaces

We investigated the depth profiles of radioactive Cs, ignition loss, and cation exchange capacity (CEC) in five types of forest soils sampled using scraper plates. We then simulated the monitored depth profiles in a compartment model, taking ignition loss as a parameter based on experimental results showing a positive correlation between ignition loss and the CEC. The calculated values were comparable with the monitored values, though some discrepancy was observed in the middle of the soil layer. Based on decontamination data on the surface dose rate and surface contamination concentration, we newly defined a surface residual index (SRI) to evaluate the residual radioactive Cs on surfaces. The SRI value tended to gradually decrease in forests and unpaved roads and was much smaller in forests and on unpaved roads than on paved roads. The radioactive Cs was assumed to have already infiltrated underground 18 months after the nuclear power plant accident, and the sinking was assumed to be ongoing. The SRI values measured on paved roads suggested that radioactive Cs remained on the surfaces, though a gradual infiltration was observed towards the end of the monitoring term. The SRI value is thought to be effective in grasping the rough condition of residual radioactive Cs quickly at sites of decontamination activity in the field. The SRI value may be serviceable for actual contamination works after further research is done to elucidate points such as the relation between the SRI and the infiltration of radioactive Cs in various types of objects.

Comparison of surveillance-based metrics for the assessment and monitoring of disease detection: simulation study about type 2 diabetes

Background

Screening and detection of cases are a common public health priority for treatable chronic conditions with long subclinical periods. However, the validity of commonly-used metrics from surveillance systems for rates of detection (or case-finding) have not been evaluated.

Methods

Using data from a Danish diabetes register and a recently developed illness-death model of chronic diseases with subclinical conditions, we simulate two scenarios of different performance of case-finding. We report different epidemiological indices to assess case-finding in both scenarios and compare the validity of the results.

Results

The commonly used ratio of detected cases over total cases may lead to misleading conclusions. Instead, the ratio of undetected cases over persons without a diagnosis is a more valid index to distinguish the quality of case-finding. However, incidence-based measures are preferable to prevalence based indicators.

Conclusion

Prevalence-based indices for assessing case-finding should be interpreted with caution. If possible, incidence-based indices should be preferred.

Electronic supplementary material

The online version of this article (doi:10.1186/s12874-017-0328-2) contains supplementary material, which is available to authorized users.

Modelling the cardiovascular system for assessing the blood pressure curve

A four compartment model of the cardiovascular system is developed. To allow for easy interpretation and to minimise the number of parameters, an effort was made to keep the model as simple as possible. Using a standard method (Matlab function fminsearch) to calculate the parameter values led to unacceptable run times or non-convergence. Consequently we developed an algorithm which first finds the most important model parameters and uses these as a basis for a four stage process which accurately determines all parameter values. This process is then applied to data from three ICU patients. Good agreement between the model and measured arterial pressure is demonstrated in all cases.

Beyond conventional antibiotics - New directions for combination products to combat biofilm

Medical device related infections are a significant and growing source of morbidity and mortality. Biofilm formation is a common feature of medical device infections that is not effectively prevented or treated by systemic antibiotics. Antimicrobial medical device combination products provide a pathway for local delivery of antimicrobial therapeutics with the ability to achieve high local concentrations while minimizing systemic side effects. In this review, we present considerations for the design of local antimicrobial delivery systems, which can be facilitated by modeling local pharmacokinetics in the context of the target device application. In addition to the need for local delivery, a critical barrier to progress in the field is the need to incorporate agents effective against biofilm. This article aims to review key properties of antimicrobial peptides that make them well suited to meet the demands of the next generation of antimicrobial medical devices, including broad spectrum activity, rapid and biocidal mechanisms of action, and efficacy against biofilm.

Incorporating bolus and infusion pharmacokinetics into the ICING insulin model

The ICING model has been successfully used to guide clinical decisions on insulin administration in critical illness. However, insulin pharmacokinetics in the ICING model can be improved to better describe both intravenous (IV) bolus and infusion insulin administration. Patient data from 217 Dynamic Insulin Sensitivity and Secretion Tests (DISST) and 36 Intravenous Glucose Tolerance Tests (IVGTT) from independent dietary intervention studies was used to fit model parameters to a model structure that conforms to known behaviour. The DISST tests measured both endogenous and exogenous IV insulin bolus responses, while the IVGTT measured exogenous IV insulin infusion dynamics. Unidentifiable parameters were given physiologically justified values, with knowledge on relative insulin clearance rates used to constrain parameter values. The resulting whole-cohort description was able to simultaneously describe both IV bolus and infusion dynamics, and improves ICING model descriptive capability. Improved infusion dynamics will allow better description of subcutaneous insulin, the insulin administration route favoured in outpatient care of diabetes.

Quantitative aspects of drug permeation across in vitro and in vivo barriers

The kinetics of permeation across epithelial and endothelial cell sheets and across cell membranes is determinant for the pharmacokinetics of a drug. In vitro transport experiments with cultured cells or artificial barriers have tremendously improved the predictability of the in vivo behaviour of tested compounds. This article focuses on the parameters and calculation methods that are used to describe permeation quantitatively, with a focus on in vitro experiments and the prediction of intestinal absorption and blood-brain barrier passage. It shows under which in vitro experimental conditions standard calculations are adequate and under which conditions equations should be adapted to the experimental details. The impact of volume differences between donor and receiver compartments, pH gradients, addition of albumin, accumulation in the barrier and unidirectional transport by an efflux transporter on the results is shown in simulations. The article should make researchers aware of experimental factors that affect the outcome of a permeation experiment and how to account for this during data analysis. Finally, strategies to predict the in vivo behaviour of a compound based on the in vitro data are discussed. The goal of the article is to support researchers in choosing experimental conditions and calculation methods that deliver appropriate and reproducible results in permeation studies in vitro.

Improved simultaneous estimation of tracer kinetic models with artificial immune network based optimization method

Tracer kinetic modeling (TKM) is a promising quantitative method for physiological and biochemical processes in vivo. In this paper, we investigated the applications of an immune-inspired method to better address the issues of Simultaneous Estimation (SIME) of TKM with multimodal optimization. Experiments of dynamic FDG PET imaging experiments and simulation studies were carried out. The proposed artificial immune network (TKM_AIN) shows more scalable and effective when compared with the gradient-based Marquardt-Levenberg algorithm and the scholastic-based simulated annealing method.

Modeling the response of ON and OFF retinal bipolar cells during electric stimulation

Retinal implants allowing blind people suffering from diseases like retinitis pigmentosa and macular degeneration to regain rudimentary vision are struggling with several obstacles. One of the main problems during external electric stimulation is the co-activation of the ON and OFF pathways which results in mutual impairment. In this study the response of ON and OFF cone retinal bipolar cells during extracellular electric stimulation from the subretinal space was examined. To gain deeper insight into the behavior of these cells sustained L-type and transient T-type calcium channels were integrated in the synaptic terminals of reconstructed 3D morphologies of ON and OFF cone bipolar cells. Intracellular calcium concentration in the synaptic regions of the model neurons was investigated as well since calcium influx is a crucial parameter for cell-to-cell activity between bipolar cells and retinal ganglion cells. It was shown that monophasic stimulation results in significant different calcium concentrations in the synaptic terminals of ON and OFF bipolar cells. Intracellular calcium increased to values up to fourfold higher in the OFF bipolar model neuron in comparison to the ON bipolar cell. Furthermore, geometric properties strongly influence the activation of bipolar cells. Monophasic, biphasic, single and repetitive pulses with similar lengths, amplitudes and polarities were applied to the two model neurons.

Dose-dependent clearance kinetics of intratracheally administered titanium dioxide nanoparticles in rat lung

AEROSIL(®) P25 titanium dioxide (TiO2) nanoparticles dispersed in 0.2% disodium phosphate solution were intratracheally administered to male F344 rats at doses of 0 (control), 0.375, 0.75, 1.5, 3.0, and 6.0 mg/kg. The rats were sacrificed under anesthesia at 1 day, 3 days, 7 days, 4 weeks, 13 weeks, and 26 weeks after administration. Ti levels in various pulmonary and extrapulmonary organs were determined using sensitive inductively coupled plasma sector field mass spectrometry. One day after administration, the lungs contained 62-83% of TiO2 administered dose. Twenty-six weeks after administration, the lungs retained 6.6-8.9% of the TiO2 administered at the 0.375, 0.75, and 1.5 mg/kg doses, and 13% and 31% of the TiO2 administered at the 3.0 and 6.0 mg/kg doses, respectively. The pulmonary clearance rate constants from compartment 1, k1, were estimated using a 2-compartment model and were found to be higher for the 0.375 and 0.75 mg/kg doses of TiO2 (0.030/day for both) than for TiO2 doses of 1.5-6.0 mg/kg (0.014-0.022/day). The translocation rate constants from compartment 1 to 2, k12, were estimated to be 0.015 and 0.018/day for the 0.375 and 0.75 mg/kg doses, and 0.0025-0.0092/day for doses of 1.5-6.0mg/kg. The pulmonary clearance rate constants from compartment 2, k2, were estimated to be 0.0086 and 0.0093/day for doses of 0.375 and 0.75 mg/kg, and 0-0.00082/day for 1.5-6.0 mg/kg doses. Translocation of TiO2 from the lungs to the thoracic lymph nodes increased in a time- and dose-dependent manner, accounting for 0.10-3.4% of the administered dose at 26 weeks. The measured thoracic lymph node burdens were a much better fit to the thoracic lymph node burdens estimated assuming translocation from compartment 1 to the thoracic lymph nodes, rather than those estimated assuming translocation from compartment 2 to the thoracic lymph nodes. The translocation rate constants from the lungs to the thoracic lymph nodes, kLung→Lym, were 0.000037-0.00081/day, and these also increased with increasing doses of TiO2. Although a small amount of TiO2 had translocated to the liver by 3 days after the administration (0.0023-0.012% of the highest dose administered, 6.0 mg/kg), translocation to the other extrapulmonary organs was not detected.

Ionic mechanisms in peripheral pain

Chronic pain constitutes an important and growing problem in society with large unmet needs with respect to treatment and clear implications for quality of life. Computational modeling is used to complement experimental studies to elucidate mechanisms involved in pain states. Models representing the peripheral nerve ending often address questions related to sensitization or reduction in pain detection threshold. In models of the axon or the cell body of the unmyelinated C-fiber, a large body of work concerns the role of particular sodium channels and mutations of these. Furthermore, in central structures: spinal cord or higher structures, sensitization often refers not only to enhanced synaptic efficacy but also to elevated intrinsic neuronal excitability. One of the recent developments in computational neuroscience is the emergence of computational neuropharmacology. In this area, computational modeling is used to study mechanisms of pathology with the objective of finding the means of restoring healthy function. This research has received increased attention from the pharmaceutical industry as ion channels have gained increased interest as drug targets. Computational modeling has several advantages, notably the ability to provide mechanistic links between molecular and cellular levels on the one hand and functions at the systems level on the other hand. These characteristics make computational modeling an additional tool to be used in the process of selecting pharmaceutical targets. Furthermore, large-scale simulations can provide a framework to systematically study the effects of several interacting disease parameters or effects from combinations of drugs.