Physicochemical characterization and phase II metabolic profiling of echinochrome A, a bioactive constituent from sea urchin, and its physiologically based pharmacokinetic modeling in rats and humans.

Echinochrome A, a natural naphthoquinone pigment found in sea urchins, is increasingly being investigated for its nutritional and therapeutic value associated with antioxidant, anticancer, antiviral, antidiabetic, and cardioprotective activities. Although several studies have demonstrated the biological effects and therapeutic potential of echinochrome A, little is known regarding its biopharmaceutical behaviors. Here, we aimed to investigate the physicochemical properties and metabolic profiles of echinochrome A and establish a physiologically-based pharmacokinetic (PBPK) model as a useful tool to support its clinical applications. We found that the lipophilicity, color variability, ultraviolet/visible spectrometry, and stability of echinochrome A were markedly affected by pH conditions. Moreover, metabolic and pharmacokinetic profiling studies demonstrated that echinochrome A is eliminated primarily by hepatic metabolism and that four possible metabolites, i.e., two glucuronidated and two methylated conjugates, are formed in rat and human liver preparations. A whole-body PBPK model incorporating the newly identified hepatic phase II metabolic process was constructed and optimized with respect to chemical-specific parameters. Furthermore, model simulations suggested that echinochrome A could exhibit linear disposition profiles without systemic and local tissue accumulation in clinical settings. Our proposed PBPK model of echinochrome A could be a valuable tool for predicting drug interactions in previously unexplored scenarios and for optimizing dosage regimens and drug formulations.

Fractional transit compartment model for describing drug delayed response to tumors using Mittag-Leffler distribution on age-structured PKPD model.

The response of a cell population is often delayed relative to drug injection, and individual cells in a population of cells have a specific age distribution. The application of transit compartment models (TCMs) is a common approach for describing this delay. In this paper, we propose a TCM in which damaged cells caused by a drug are given by a single fractional derivative equation. This model describes the delay as a single equation composed of fractional and ordinary derivatives, instead of a system of ODEs expressed in multiple compartments, applicable to the use of the PK concentration in the model. This model tunes the number of compartments in the existing model and expresses the delay in detail by estimating an appropriate fractional order. We perform model robustness, sensitivity analysis, and change of parameters based on the amount of data. Additionally, we resolve the difficulty in parameter estimation and model simulation using a semigroup property, consisting of a system with a mixture of fractional and ordinary derivatives. This model provides an alternative way to express the delays by estimating an appropriate fractional order without determining the pre-specified number of compartments.

Designing isolation guidelines for COVID-19 patients with rapid antigen tests.

Appropriate isolation guidelines for COVID-19 patients are warranted. Currently, isolating for fixed time is adopted in most countries. However, given the variability in viral dynamics between patients, some patients may no longer be infectious by the end of isolation, whereas others may still be infectious. Utilizing viral test results to determine isolation length would minimize both the risk of prematurely ending isolation of infectious patients and the unnecessary individual burden of redundant isolation of noninfectious patients. In this study, we develop a data-driven computational framework to compute the population-level risk and the burden of different isolation guidelines with rapid antigen tests (i.e., lateral flow tests). Here, we show that when the detection limit is higher than the infectiousness threshold values, additional consecutive negative results are needed to ascertain infectiousness status. Further, rapid antigen tests should be designed to have lower detection limits than infectiousness threshold values to minimize the length of prolonged isolation.

Lag Synchronization of Noisy and Nonnoisy Multiple Neurobiological Coupled FitzHugh-Nagumo Networks with and without Delayed Coupling.

This paper presents a methodology for synchronizing noisy and nonnoisy multiple coupled neurobiological FitzHugh-Nagumo (FHN) drive and slave neural networks with and without delayed coupling, under external electrical stimulation (EES), external disturbance, and variable parameters for each state of both FHN networks. Each network of neurons was configured by considering all aspects of real neurons communications in the brain, i.e., synapse and gap junctions. Novel adaptive control laws were developed and proposed that guarantee the synchronization of FHN neural networks in different configurations. The Lyapunov stability theory was utilized to analytically derive the sufficient conditions that ensure the synchronization of the FHN networks. The effectiveness and robustness of the proposed control laws were shown through different numerical simulations.

Extended transit compartment model to describe tumor delay using Coxian distribution.

The measured response of cell population is often delayed relative to drug injection, and individuals in a population have a specific age distribution. Common approaches for describing the delay are to apply transit compartment models (TCMs). This model reflects that all damaged cells caused by drugs suffer transition processes, resulting in death. In this study, we present an extended TCM using Coxian distribution, one of the phase-type distributions. The cell population attacked by a drug is described via age-structured models. The mortality rate of the damaged cells is expressed by a convolution of drug rate and age density. Then applying to Erlang and Coxian distribution, we derive Erlang TCM, representing the existing model, and Coxian TCMs, reflecting sudden death at all ages. From published data of drug and tumor, delays are compared after parameter estimations in both models. We investigate the dynamical changes according to the number of the compartments. Model robustness and equilibrium analysis are also performed for model validation. Coxian TCM is an extended model considering a realistic case and captures more diverse delays.

Designing isolation guidelines for COVID-19 patients utilizing rapid antigen tests: a simulation study using viral dynamics models.

Appropriate isolation guidelines for COVID-19 patients are warranted. Currently, isolating for fixed time is adapted in most countries. However, given the variability in viral dynamics between patients, some patients may no longer be infectious by the end of isolation (thus they are redundantly isolated), whereas others may still be infectious. Utilizing viral test results to determine ending isolation would minimize both the risk of ending isolation of infectious patients and the burden due to redundant isolation of noninfectious patients. In our previous study, we proposed a computational framework using SARS-CoV-2 viral dynamics models to compute the risk and the burden of different isolation guidelines with PCR tests. In this study, we extend the computational framework to design isolation guidelines for COVID-19 patients utilizing rapid antigen tests. Time interval of tests and number of consecutive negative tests to minimize the risk and the burden of isolation were explored. Furthermore, the approach was extended for asymptomatic cases. We found the guideline should be designed considering various factors: the infectiousness threshold values, the detection limit of antigen tests, symptom presence, and an acceptable level of releasing infectious patients. Especially, when detection limit is higher than the infectiousness threshold values, more consecutive negative results are needed to ascertain loss of infectiousness. To control the risk of releasing of infectious individuals under certain levels, rapid antigen tests should be designed to have lower detection limits than infectiousness threshold values to minimize the length of prolonged isolation, and the length of prolonged isolation increases when the detection limit is higher than the infectiousness threshold values, even though the guidelines are optimized for given conditions.

Development and application of a physiologically based pharmacokinetic model for entrectinib in rats and scale-up to humans: Route-dependent gut wall metabolism.

Entrectinib (Rozlytrek®) is an oral antineoplastic agent approved by the U.S. Food and Drug Administration in 2019 for the treatment of c-ros oncogene 1 (ROS1)-positive non-small cell lung cancer and neurotrophic tyrosine receptor kinase (NTRK) fusion-positive solid tumors. Although there have been a few studies on the pharmacokinetics of entrectinib, the relative contributions of several kinetic factors determining the oral bioavailability and systemic exposure of entrectinib are still worthy of investigation. Experimental data on the intestinal absorption and disposition of entrectinib in rats were acquired from studies on in vitro protein binding/tissue S9 metabolism, in situ intestinal perfusion, and in vivo dose-escalation/hepatic extraction. Using these datasets, an in-house whole-body physiologically based pharmacokinetic (PBPK) model incorporating the QGut model concepts and segregated blood flow in the gut was constructed and optimized with respect to drug-specific parameters. The established rat PBPK model was further extrapolated to humans through relevant physiological scale-up and parameter optimization processes. The optimized rat and human PBPK models adequately captured the impact of route-dependent gut metabolism on the systemic exposure to entrectinib and closely mirrored various preclinical and clinical observations. Our proposed PBPK model could be useful in optimizing dosage regimens and predicting drug interaction potential in various clinical conditions, after partial modification and validation.

Revisiting the guidelines for ending isolation for COVID-19 patients.

Since the start of the COVID-19 pandemic, two mainstream guidelines for defining when to end the isolation of SARS-CoV-2-infected individuals have been in use: the one-size-fits-all approach (i.e. patients are isolated for a fixed number of days) and the personalized approach (i.e. based on repeated testing of isolated patients). We use a mathematical framework to model within-host viral dynamics and test different criteria for ending isolation. By considering a fixed time of 10 days since symptom onset as the criterion for ending isolation, we estimated that the risk of releasing an individual who is still infectious is low (0-6.6%). However, this policy entails lengthy unnecessary isolations (4.8-8.3 days). In contrast, by using a personalized strategy, similar low risks can be reached with shorter prolonged isolations. The obtained findings provide a scientific rationale for policies on ending the isolation of SARS-CoV-2-infected individuals.

Lag synchronization of coupled time-delayed FitzHugh-Nagumo neural networks via feedback control.

Synchronization plays a significant role in information transfer and decision-making by neurons and brain neural networks. The development of control strategies for synchronizing a network of chaotic neurons with time delays, different direction-dependent coupling (unidirectional and bidirectional), and noise, particularly under external disturbances, is an essential and very challenging task. Researchers have extensively studied the synchronization mechanism of two coupled time-delayed neurons with bidirectional coupling and without incorporating the effect of noise, but not for time-delayed neural networks. To overcome these limitations, this study investigates the synchronization problem in a network of coupled FitzHugh-Nagumo (FHN) neurons by incorporating time delays, different direction-dependent coupling (unidirectional and bidirectional), noise, and ionic and external disturbances in the mathematical models. More specifically, this study investigates the synchronization of time-delayed unidirectional and bidirectional ring-structured FHN neuronal systems with and without external noise. Different gap junctions and delay parameters are used to incorporate time-delay dynamics in both neuronal networks. We also investigate the influence of the time delays between connected neurons on synchronization conditions. Further, to ensure the synchronization of the time-delayed FHN neuronal networks, different adaptive control laws are proposed for both unidirectional and bidirectional neuronal networks. In addition, necessary and sufficient conditions to achieve synchronization are provided by employing the Lyapunov stability theory. The results of numerical simulations conducted for different-sized multiple networks of time-delayed FHN neurons verify the effectiveness of the proposed adaptive control schemes.

A Tumor-Immune Interaction Model for Synergistic Combinations of Anti PD-L1 and Ionizing Irradiation Treatment.

Combination therapy with immune checkpoint blockade and ionizing irradiation therapy (IR) generates a synergistic effect to inhibit tumor growth better than either therapy does alone. We modeled the tumor-immune interactions occurring during combined IT and IR based on the published data from Deng et al. The mathematical model considered programmed cell death protein 1 and programmed death ligand 1, to quantify data fitting and global sensitivity of critical parameters. Fitting of data from control, IR and IT samples was conducted to verify the synergistic effect of a combination therapy consisting of IR and IT. Our approach using the model showed that an increase in the expression level of PD-1 and PD-L1 was proportional to tumor growth before therapy, but not after initiating therapy. The high expression level of PD-L1 in T cells may inhibit IT efficacy. After combination therapy begins, the tumor size was also influenced by the ratio of PD-1 to PD-L1. These results highlight that the ratio of PD-1 to PD-L1 in T cells could be considered in combination therapy.

An immune therapy model for effective treatment on inflammatory bowel disease.

Inflammatory bowel disease (IBD) is a disease that causes inflammation throughout the digestive tract. Repeated inflammation and frequent relapses cause intestinal damage and expose the patient to a higher risk. In this work, we proposed an immune therapy model for effective treatment strategy through mathematical modeling for patients with IBD. We evaluated the ability of the patient's immune system to recover during treatment. For this, we defined the interval of healthy individual, and examined the frequency of compartments such as T cells and cytokines considered in the model maintain the normal state. Based on the fact that each patient has a unique immune system, we have shown at the same drug works differently, depending on the individual immune system characteristics for every patient. It is known that IBD is related to an imbalance between pro- and anti- inflammatory cytokines as the cause of the disease. So the ratios of pro- to anti- inflammatory cytokines are used as an indicator of patient's condition and inflammation status in various diseases. We compared the ratios of pro- to anti- inflammatory cytokine according to patient's individual immune system and drugs. Since the effects of biological drugs are highly dependent on the patient's own immune system, it is essential to define the immune system status before selecting and using a biological drug.

Evaluation of COVID-19 epidemic outbreak caused by temporal contact-increase in South Korea.

OBJECTIVES: On March 15, 2020, 61.3% of the confirmed cases of COVID-19 infection in South Korea are associated with the worship service that was organized on February 9 in the Shincheonji Church of Jesus in Daegu. We aim to evaluate the effects of mass infection in South Korea and assess the preventive control intervention. METHOD: Using openly available data of daily cumulative confirmed cases and deaths, the basic and effective reproduction numbers was estimated using a modified susceptible-exposed-infected-recovered-type epidemic model. RESULTS: The basic reproduction number was estimated to be R0=1.77. The effective reproduction number increased approximately 20 times after the mass infections from the 31 st patient, which was confirmed on February 9 in the Shincheonji Church of Jesus, Daegu. However, the effective reproduction number decreased to less than unity after February 28 owing to the implementation of high-level preventive control interventions in South Korea, coupled with voluntary prevention actions by citizens. CONCLUSION: Preventive action and control intervention were successfully established in South Korea.

A mathematical model for assessing the effectiveness of controlling relapse in Plasmodium vivax malaria endemic in the Republic of Korea.

Malaria has persisted as an endemic near the Demilitarized Zone in the Republic of Korea since the re-emergence of Plasmodium vivax malaria in 1993. The number of patients affected by malaria has increased recently despite many controls tools, one of the reasons behind which is the relapse of malaria via liver hypnozoites. Tafenoquine, a new drug approved by the United States Food and Drug Administration in 2018, is expected to reduce the rate of relapse of malaria hypnozoites and thereby decrease the prevalence of malaria among the population. In this work, we have developed a new transmission model for Plasmodium vivax that takes into account a more realistic intrinsic distribution from existing literature to quantify the current values of relapse parameters and to evaluate the effectiveness of the anti-relapse therapy. The model is especially suitable for estimating parameters near the Demilitarized Zone in Korea, in which the disease follows a distinguishable seasonality. Results were shown that radical cure could significantly reduce the prevalence level of malaria. However, eradication would still take a long time (over 10 years) even if the high-level treatment were to persist. In addition, considering that the vector's behavior is manipulated by the malaria parasite, relapse repression through vector control at the current level may result in a negative effect in containing the disease. We conclude that the use of effective drugs should be considered together with the increased level of the vector control to reduce malaria prevalence.

Recent advances in physiologically based pharmacokinetic and pharmacodynamic models for anticancer nanomedicines.

Nanoparticles (NPs) have distinct pharmacokinetic (PK) properties and can potentially improve the absorption, distribution, metabolism, and elimination (ADME) of small-molecule drugs loaded therein. Owing to the unwanted toxicities of anticancer agents in healthy organs and tissues, their precise delivery to the tumor is an essential requirement. There have been numerous advancements in the development of nanomedicines for cancer therapy. Physiologically based PK (PBPK) models serve as excellent tools for describing and predicting the ADME properties and the efficacy and toxicity of drugs, in combination with pharmacodynamic (PD) models. The recent preliminary application of these modeling approaches to NPs demonstrated their potential benefits in research and development processes relevant to the ADME and pharmacodynamics of NPs and nanomedicines. Here, we comprehensively review the pharmacokinetics of NPs, the developed PBPK models for anticancer NPs, and the developed PD model for anticancer agents.

Modeling to capture bystander-killing effect by released payload in target positive tumor cells.

BACKGROUND: Antibody-drug conjugates (ADCs) are intended to bind to specific positive target antigens and eradicate only tumor cells from an intracellular released payload through the lysosomal protease. Payloads, such as MMAE, have the capacity to kill adjacent antigen-negative (Ag-) tumor cells, which is called the bystander-killing effect, as well as directly kill antigen-positive (Ag+) tumor cells. We propose that a dose-response curve should be independently considered to account for target antigen-positive/negative tumor cells. METHODS: A model was developed to account for the payload in Ag+/Ag- cells and the associated parameters were applied. A tumor growth inhibition (TGI) effect was explored based on an ordinary differential equation (ODE) after substituting the payload concentration in Ag+/Ag- cells into an Emax model, which accounts for the dose-response curve. To observe the bystander-killing effects based on the amount of Ag+/Ag- cells, the Emax model is used independently. TGI models based on ODE are unsuitable for describing the initial delay through a tumor-drug interaction. This was solved using an age-structured model based on the stochastic process. RESULTS: ß∈(0,1] is a fraction parameter that determines the proportion of cells that consist of Ag+/Ag- cells. The payload concentration decreases when the ratio of efflux to influx increases. The bystander-killing effect differs with varying amounts of Ag+ cells. The larger ß is, the less bystander-killing effect. The decrease of the bystander-killing effect becomes stronger as Ag+ cells become larger than the Ag- cells. Overall, the ratio of efflux to influx, the amount of released payload, and the proportion of Ag+ cells determine the efficacy of the ADC. The tumor inhibition delay through a payload-tumor interaction, which goes through several stages, may be solved using an age-structured model. CONCLUSIONS: The bystander-killing effect, one of the most important topics of ADCs, has been explored in several studies without the use of modeling. We propose that the bystander-killing effect can be captured through a mathematical model when considering the Ag+ and Ag- cells. In addition, the TGI model based on the age-structure can capture the initial delay through a drug interaction as well as the bystander-killing effect.

Qualitative and Sensitivity Analysis of the Effect of Electronic Cigarettes on Smoking Cessation.

Recently, the role of the electronic cigarettes (e-cigarettes) in a way to reduce smoking is increasing. E-cigarettes are a device that delivers only the nicotine, and its use is considered less harmful to health compared with tobacco cigarettes. Smokers frequently make use of e-cigarettes as one of the nonsmoking aid devices. In this work, we propose a mathematical model to analyze the effect of e-cigarettes on smoking cessation. The stability and the bifurcation of the model have been discussed. The parameter estimations from the observed data are drawn, and using the parameters, a reasonable smoking model has been designed. Moreover, by considering the sensitivity results depending on the basic reproduction number R0, the effective strategies that reduce the smokers are investigated. Numerical simulations of the model show that e-cigarettes may somewhat diminish the numbers of smokers, but it does not reduce the number of quitters ultimately.

Mathematical modeling of antibody drug conjugates with the target and tubulin dynamics to predict AUC.

Antibody drug conjugates (ADCs)are one of the most recently developed chemotherapeutics to treat some types of tumor cells. They consist of monoclonal antibodies (mAbs), linkers, and potent cytotoxic drugs. Unlike common chemotherapies, ADCs combine selectively with a target at the surface of the tumor cell, and a potent cytotoxic drug (payload) effectively prevents microtubule polymerization. In this work, we construct an ADC model that considers both the target of antibodies and the receptor (tubulin) of the cytotoxic payloads. The model is simulated with brentuximab vedotin, one of ADCs, and used to investigate the pharmacokinetic (PK) characteristics of ADCs in vivo. It also predicts area under the curve (AUC) of ADCs and the payloads by identifying the half-life. The results show that dynamical behaviors fairly coincide with the observed data and half-life and capture AUC. Thus, the model can be used for estimating some parameters, fitting experimental observations, predicting AUC, and exploring various dynamical behaviors of the target and the receptor.

Classification and sensitivity analysis of the transmission dynamic of hepatitis B.

BACKGROUND: Hepatitis B infection caused by the hepatitis B virus is one of the most serious viral infections and a global health problem. In the transmission of hepatitis B infection, three different phases, i.e. acute infected, chronically infected, and carrier individuals, play important roles. Carrier individuals are especially significant, because they do not exhibit any symptoms and are able to transmit the infection. Here we assessed the transmissibility associated with different infection stages of hepatitis B and generated an epidemic model. METHODS: To demonstrate the transmission dynamic of hepatitis B, we investigate an epidemic model by dividing the infectious class into three subclasses, namely acute infected, chronically infected, and carrier individuals with both horizontal and vertical transmission. RESULTS: Numerical results and sensitivity analysis of some important parameters are presented to show that the proportion of births without successful vaccination, perinatally infected individuals, and direct contact rate are highest risk factors for the spread of hepatitis B in the community. CONCLUSION: Our work provides a coherent platform for studying the full dynamics of hepatitis B and an effective direction for theoretical work.

Analysis of a vector-bias effect in the spread of malaria between two different incidence areas.

In 2005, Lacroix et al. demonstrated that infected humans are more attractive to mosquitoes, a phenomenon known as the vector-bias effect. The aim of this study was to determine how a vector-bias effect affects the changes in the dynamics of malaria transmission, and the changes in control strategies and cost-effectiveness for optimal control considering the regional characteristics or force of infections for different transmission rates. We used a vector-bias mathematical model and considered two different incidence areas: a high transmission area and a low transmission area. Our results showed that the dynamics in the two areas differed; as bias exists and the strategy for optimal control could be changed in the different areas. Thus, this work may give that considering the vector-bias effect in different areas facilitates prediction of the future dynamics and make decisions for establishing controls. We also mention the evolution of malaria parasites in this study.

Optimal treatment strategy for a tumor model under immune suppression.

We propose a mathematical model describing tumor-immune interactions under immune suppression. These days evidences indicate that the immune suppression related to cancer contributes to its progression. The mathematical model for tumor-immune interactions would provide a new methodology for more sophisticated treatment options of cancer. To do this we have developed a system of 11 ordinary differential equations including the movement, interaction, and activation of NK cells, CD8(+)T-cells, CD4(+)T cells, regulatory T cells, and dendritic cells under the presence of tumor and cytokines and the immune interactions. In addition, we apply two control therapies, immunotherapy and chemotherapy to the model in order to control growth of tumor. Using optimal control theory and numerical simulations, we obtain appropriate treatment strategies according to the ratio of the cost for two therapies, which suggest an optimal timing of each administration for the two types of models, without and with immunosuppressive effects. These results mean that the immune suppression can have an influence on treatment strategies for cancer.