A Mathematical Model Based Study on Dynamic Changes of Chondrogenesis and Osteogenesis During Condylar Neck Fracture Healing / 华中科技大学学报(医学版)

Objective To explore the healing pattern of condylar neck fractures by using mathematical models to simulate the dynamic changes of osteogenesis and chondrogenesis in the process of rat condylar neck fracture healing.Methods A math-ematical model was constructed to simulate the healing process of rat condylar neck fractures.The values of various parameters(mb,mc,cb and cc)generated by the model at different time points within 28 days were statistically analyzed.Subsequently,den-sity maps and growth curves of bone,cartilage,osteoblasts,and chondrocytes were fitted and the osteogenesis mode was de-duced.Results The bone area ratio simulated by the mathematical model was similar to that measured in rat fracture experi-ments(P＞0.05).The simulated density maps showed that osteogenesis was concentrated around the periosteum from day 3 to day 7 after fracture,and then concentrated in the cartilage region and gradually replaced cartilage from day 7 to day 21.The bone growth curve and cartilage growth curve were positively correlated from day 5 to day 8 and from day 21 to day 28.However,the curves were negatively correlated from day 8 to day 14 after fracture.The growth curves of osteoblasts and chondrocytes both showed an increasing trend before decreasing,with chondrocyte density peaking at day 6 and osteoblast density peaking at day 13.Conclusion The mathematical model can effectively simulate the healing process of rat condylar neck fractures and display the dynamic changes of osteogenesis and chondrogenesis during the whole process.This provides a new idea for studying healing methods of condylar neck fractures.

Differences in pulse manifestations at Cunkou based on simplified modeling of tactile sensing / 数字中医药（英文）

Objective @#In the theories of pulse disgnosis in traditional Chinese medicine (TCM), it is emphasized that pulse manifestations at the radial artery within the wrist (called Cunkou) signify the physiological and pathological conditions of different internal organs in the human body. However, different opinions exist among researchers about the objectiveness of the pulse diagnosis technique. Some researchers mentioned that no significant differences were observed in pulse manifestations at various Cunkou areas, hence there might be some difficulty in evaluating the status of different organs through checking pulse manifestations at Cunkou. This research aims to analyze the pulse response at Cunkou from the aspect of the characteristics of tactile sensing, thus to give a preliminary explanation to the above question.@*Methods@#This research utilized the Weber-Fechner law to model the tactile sensing as a dynamic low-pass signal filter with varying bandwidths under different compression levels during pulse diagnosis. The model was applied to analyzing the clinical data collected previously by our group. The arterial pressures measured invasively with equipment from 14 patients with aorta coarctation were processed to simulate different pulse manifestations at Cun, Guan, and Chi positions of Cunkou when different compression levels were applied.@*Result@#Due to the characteristics of tactile sensing, significant variations were observed in pulse manifestations at different pulse-depths under the application of changing compression levels; while no such changes in pulse manifestations were observed from the employment of transducer only, without tactile sensing involved. The results explained why different understandings on pulse manifestations were formed between direct pulse-taking technique in TCM and modern sphygmography using transducers. The features of pulse manifestations at Cunkou, using direct pulse-taking technique but at different depths, superficial, middle, and deep positions, respectively, predicted by the developed tactile sensing model were in line with those described in TCM pulse theories.@*Conclusion@#Based on the developed tactile sensing model, this study preliminarily explains the phenomenon that pulse manifestation at Cunkou changes in response to the compression force applied during TCM pulse-taking. Integrating the tactile sensing model with the study of TCM pulse diagnosis opens a new chapter for visualizing and quantitatively interpreting pulse manifestations. This not only expands the scope of pulse diagnosis study effectively, but also provide a scientific basis for further technical upgrading and optimization of existing pulse diagnosis equipment.

Analysis on occupational health risk assessment methods / 中国职业医学

Occupational health risk assessment is a legal requirement. In legal terms, "occupational health risk assessment" is a means which focuses on occupational disease monitoring and special investigations, analyzing relevant information collected, and ultimately identifying high-risk industries and regions, and proposing reasonable, feasible, and scientific risk management and control recommendations to reduce occupational health risks in key industries and regions. The collection and selection of information are the foundation and core of occupational health risk assessment work. Causation determination is an important basis for information classification in occupational health risk assessment. The establishment and application of mathematical models are the prospects and directions for high-quality development of occupational health risk assessment work. However, the current research does not pay adequate attention on mathematical models for occupational health risk assessment methods, resulting in no substantial progression or improvement in occupational health risk assessment work. The key to future occupational health risk assessment work is to accurately grasp the definition of occupational health risk assessment in a legal term, to streamline and improve the indicator system of occupational health risk assessment, to actively explore and apply mathematical models for occupational health risk assessment, and to enhance the efficiency and accuracy of occupational health risk assessment work.

Dynamic Interactive Reasoning and Intelligent Dialectics of Chinese Medicine Based on Probability Graph / 世界科学技术-中医药现代化

This paper proposes a mathematical model based on probability graphs and an algorithm of iterative reasoning,which is an automatic interactive question-and-answer mathematical model based on the classic TCM syndrome differentiation system and the theory of prescription and syndrome correspondence.It is used for TCM online interactive consultation and automatic syndrome differentiation analysis to improve the effectiveness of remote TCM clinical consultation and help TCM artificial intelligence assist syndrome differentiation.This model can express the clinician's experience in syndrome differentiation,and reflect his ability to accumulate and apply knowledge of ancient Chinese books,which is conducive to the inheritance and development of TCM physicians'personal experience.The model is scalable and configurable,and can continuously accumulate experience in dialectics and knowledge of traditional Chinese medicine.The use of iterative reasoning algorithm can realize the automatic analysis and reasoning of more optimized syndrome analysis results through brief interactive question and answer,providing more efficient and convenient practical assistance for clinical diagnosis and treatment of traditional Chinese medicine,which is conducive to accelerating the inheritance and promotion of traditional Chinese medicine,and is conducive to the expansion of Chinese medicine.The mass basis and market supply of medical diagnosis and treatment services have far-reaching social benefits.

Research Progress on Disease Burden of Dengue in China / 中山大学学报(医学科学版)

The gradual relaxation of COVID-19 restrictions in China has increased the risk of imported dengue fever cases and may further prompt the outbreak. Systematic assessment of disease burden is crucial to improving prevention and control strategies， and resource allocation of dengue fever in China. After reviewing the definition， classification of disease burden， epidemiological evaluation methods such as potential years of life lost （PYLL） and disability adjusted of life years （DALY）， as well as economic evaluation methods such as step-by-step model method and human capital method， this article systematically summarizes the application of mixed models and catalytic models in quantifying the disease burden of latent dengue infected individuals， as well as the current research status and limitations of dengue disease burden in China， proposing suggestions for future assessment research on disease burden of dengue.

Effect of Tobacco Taxation on Smoking Prevalence and Smoking-Attributable Deaths in India

Background: Higher taxes are the single most effective way to encourage tobacco users to quit tobacco use and prevent youth from initiation. Objectives: The present study aims to estimate the effect of raising the tax on smoked tobacco products on its consumption and smoking‑attributable deaths in India. Materials and Methods: A mathematical model was developed which used the projected population of India, taxation rates on smoked tobacco products, smoking prevalence, and price elasticity of demand of cigarette and bidi from 2017 to 2025. Four scenarios of tax increment (0%, 25%, 50%, and 100%) on smoked tobacco products were created which were modeled to calculate smoking prevalence and smoking‑attributable deaths due to respiratory diseases, heart diseases, stroke tuberculosis, and cancer in country till 2025. Results: A relative decrease of 6.2% in the prevalence of smoking was observed between the existing tax rates and its increment to 100% over the last increment of 6%. Similarly, smoking‑attributable deaths (SAD) decreased by 6.04% on increasing the tax rates to 100% of the existing taxation rates. There has been a steady increase in SAD in scenario 1 which decreases effectively in scenario 4, which in turn leads to the saving of around 33,000 lives due to tobacco‑related diseases by 2025. Conclusion: The consumption of cigarettes and bidis can be reduced by raising the price of these products. The model will help policymakers in deciding to fix the tax and ultimately the price of cigarettes and bidi to reduce its consumption and smoking‑attributable mortality.

Research Progress in Computational Simulation of Thrombosis / 医用生物力学

Thrombosis is the process of platelet adhesion and aggregation or blood coagulation after the body is subjected to certain physical and chemical stimuli. At present, the use of basic experimental research and computational simulation to understand thrombosis has become a research hotspot. The complex process of thrombosis makes computational modeling very difficult, but the development of calculation models has still made great progress. At present, a variety of calculation models for thrombosis have been developed, including coagulation models based on ordinary differential equations, mathematical models based on finite element analysis, Lattice-Boltzmann method models, smooth particle dynamics method models, etc. Each model has its advantages and disadvantages.In this review, the physiological mechanism of thrombosis was explained, the models for simulating thrombosis were also systematically sorted out and evaluated, and the limitations of computational simulation and future application prospects were summarized as well.

Mathematical Model of Tumor Growth in Radiotherapy and Radiosensitivity Analysis / 医用生物力学

Objective To establish a mathematical model of tumor growth and invasion under radiotherapy, so as to numerically simulate the effect of radiotherapy on tumor growth and make sensitivity analysis.Methods The mathematical model of tumor growth and invasion with time evolution before and after radiotherapy was established. The model included four key variables in the process of tumor invasion: tumor cells, extracellular matrix (ECM), matrix-degradative enzymes (MDEs) and oxygen. The linear quadratic (LQ) model was used to simulate the survival probability of tumor cells after radiotherapy, and the effects of different radiotherapy schemes and radiotherapy coefficients on the treatment effect were discussed. Traditional radiotherapy and intraoperative targeted radiotherapy were compared.Results Under the premise of constant total dose, the results of radiotherapy were directly proportional to the radiotherapy coefficient, but not related to the radiotherapy frequency; the therapeutic effect of intraoperative targeted radiotherapy was better than that of standard treatment.Conclusions Simulation results are basically consistent with clinical experimental results. As a more efficient treatment method, intraoperative targeted radiotherapy can provide new ideas for clinical tumor treatment.

Simulación de la dinámica de la biomasa en plancton de un embalse colombiano tropical andino de alta montaña / Simulation of biomass dynamics in plankton of a high-altitude andean tropical reservoir in colombia

ABSTRACT The understanding of the relationships between the planktonic communities in a reservoir allows us to infer possible changes in the redistribution of matter and energy flows in these systems. This work proposes a dynamic model for the trophic network of the Riogrande II tropical reservoir, which integrates the planktonic trophic chains of detritus and grazing, limiting the prey-predator interactions by introducing the prey meeting factor (pmf). We built a dynamic model of mass balance supported by an extensive bibliographic search. The limitations of consumers and resources were represented simultaneously by means of the pmf. The data used to validate the model were compiled from previous investigations carried out in this reservoir from 2010 to 2013. The values of pmf that we found in each simulation suggest that the top predator can access its main prey in certain concentrations of total phosphorus, with a probability of encounter ranging from 9.3 % to 17.7 %. Our simulations indicate that most of the primary production is poorly used by the primary consumers in the photic zone, however, it enters in the flows of the detrital chain and supports the production of zooplankton almost entirely. According to this finding, the biomass densities obtained in the previous studies can be better explained by the causal relationships assumed in this model.

RESUMEN Entender las relaciones entre las comunidades planctónicas en un embalse nos permite inferir posibles cambios en la redistribución de los flujos de materia y energía en este sistema. Este trabajo propone un modelo dinámico para representar la red trófica del embalse tropical Riogrande II, donde se integran las cadenas tróficas de pastoreo y detritus y se limitan las interacciones entre predadores, presas y recursos al introducir un factor limitante de encuentro con la presa (pmf). El modelo dinámico se enfoca en el balance de masas sustentado en una amplia búsqueda bibliográfica. Los datos usados para validar el modelo se colectaron de datos previamente reportados para el embalse durante los años 2010 y 2013. Los valores de pmf obtenidos en cada simulación, sugieren que el predador dominante puede acceder a su presa principal a ciertas concentraciones de fósforo total, con una probabilidad de encuentro que va desde 9,3 % hasta 17,7 %. Nuestros resultados indican que la mayor parte de la producción primaria es poco aprovechada por los consumidores en la zona fótica, sin embargo, ingresa en el flujo de la cadena detrítica de manera que soporta la producción de zooplancton casi por completo. Las relaciones causales asumidas en este modelo explican en gran medida las densidades de biomasa reportadas en estudios previos.

Modelo matemático para estimar el índice de calidad de vida en adultos mayores usando la encuesta FUMAT

RESUMEN Son muchas las personas en el mundo actual que dedican su esfuerzo a lo que podría denominarse "la nueva cultura de la longevidad", que es el intento de vivir más y en mejores condiciones de vida. El objetivo de este trabajo es proponer un modelo matemático para estimar el índice de calidad de vida (ICV) en adultos mayores. El caso de estudio corresponde a ancianatos de la zona periurbana de Asunción, Paraguay. El estudio es observacional descriptivo de corte transversal. Participaron 33 adultos mayores de 60 años, de ambos sexos, para los cuales se estimó el ICV a través de la encuesta Evaluación del ICV en adultos mayores (FUMAT). Se aplicó una regresión múltiple lineal para estimar el ICV a través de un modelo matemático a partir de los parámetros de distintos indicadores. Respecto a los indicadores de la calidad de vida, se encontró que los promedios más bajos de los distintos indicadores corresponden a los relacionados al derecho (43±19), el bienestar material (45±30) y la autodeterminación (48±24). El modelo propuesto presenta un excelente acuerdo con los datos iniciales. Los valores de error estándar y RMSE son 0.22% y 0.10, respectivamente. Además, el modelo reproduce correctamente la dependencia de los distintos indicadores con el valor del ICV. Asimismo, permite identificar cuáles son los indicadores con más peso en la estimación del ICV, y permite predecir su valor en otras muestras.

ABSTRACT Many people nowadays dedicate their efforts to "the new culture of longevity", which is an attempt to live longer and in the best conditions of life. The objective is to propose a mathematical model to estimate the quality of life index (ICV) in older adults. The case study corresponds to nursing homes in the periurban area of ​​Asunción, Paraguay. This is a cross-sectional descriptive observational study. 33 adults over 60 years of age, of both sexes, participated, for whom the ICV was estimated through the ICV Assessment in Older Adults (FUMAT) survey. A multiple linear regression analysis was conducted to estimate the ICV using parameters of different indicators. Regarding the quality of life indicators, it was found that the lowest averages concerning the indicators correspond to those related to law (43 ± 19), material well-being (45 ± 30) and self-determination (48 ± 24). The proposed model presents an excellent agreement with the initial data. The standard error and RMSE values are 0.22% and 0.10, respectively. Furthermore, the model correctly reproduces the dependence of the different indicators on the ICV value. In addition, it allows us to identify the indicators with the most weight in estimating the ICV, and to predict its value in other samples.

Modelación matemática de los casos autóctonos de Covid-19. Municipio Bayamo. Febrero- Agosto 2021

El municipio Bayamo acumuló, 8162 casos positivos autóctonos de febrero a agosto en el año 2021, es el centro de la epidemia en la provincia de COVID-19 provocada por el SARS -CoV-2 determinado por el test de Proteína C Reactiva, representa el53,2 % del total de los casos en ese periodo en Granma, muy diferente a lo ocurrido en el año 2020 en el cual la provincia acumuló solamente 185personas contagiadas en nueve meses, con una tasa de 22.6 la más baja de Cuba. La provincia Granma acumuló 119 fallecidos en agosto/2021 que representa el 62,9 % de todos los muertos desde que comenzó la pandemia hasta agosto, lo que indica la alta incidencia de la epidemia que hay en estos momentos. Para la modelación matemática y el análisis de los casos positivos autóctonos de todos los ocurridos durante los meses de febrero a agosto en el año 2021 en Bayamo se obtuvieron polinomios de grado tres y cuatro que modelan el comportamiento de la epidemia durante los siete meses analizados, así como el de los fallecidos durante el mes de agosto en Granma con un carácter predictivo mayor al 98 % en todos los modelos.

The Bayamo municipality accumulated 8162 autochthonous positive cases from February to August in 2021, it is the center of the epidemic in the province of COVID-19 caused by SARS-CoV-2 determined by the C-Reactive Protein test, represents the 53.2% of the total cases in that period in Granma, very different from what happened in 2020 in which the province accumulated only 185 infected people in nine months, with a rate of 22.6, the lowest in Cuba. Granma province accumulated 119 deaths in August / 2021, which represents 62.9% of all deaths since the pandemic began until August, which indicates the high incidence of the epidemic that exists at the moment. For the mathematical modeling and analysis of the autochthonous positive cases of all those that occurred during the months of February to August in 2021 in Bayamo, polynomials of degree three and four were obtained that model the behavior of the epidemic during the seven months analyzed. as well as that of the deceased during the month of August in Granma with a predictive character greater than 98% in all models.

O município de Bayamo acumulou 8.162 casos autóctones positivos de fevereiro a agosto de 2021, é o centro da epidemia na província de COVID-19 causada pelo SARS-CoV-2 determinado pelo teste da Proteína C Reativa, representa 53,2% de o total de casos nesse período no Granma, muito diferente do que aconteceu em 2020 em que a província acumulou apenas 185 pessoas infectadas em nove meses, com uma taxa de 22,6, a mais baixa de Cuba. A província do Granma acumulou 119 mortes em agosto / 2021, o que representa 62,9% de todas as mortes desde o início da pandemia até agosto, o que indica a alta incidência da epidemia que existe no momento. Para a modelagem matemática e análise dos casos positivos autóctones de todos os ocorridos durante os meses de fevereiro a agosto de 2021 em Bayamo, foram obtidos polinômios de grau três e quatro que modelam o comportamento da epidemia durante os sete meses analisados. bem como o dos falecidos durante o mês de agosto no Granma com caráter preditivo superior a 98% em todos os modelos.

Modelo matemático para predecir la formación de agregados en el proceso de purificación de un anticuerpo monoclonal / Mathematical model for predicting the formation of aggregates in the purification process of a monoclonal antibody

El uso de anticuerpos monoclonales en la lucha contra el cáncer se convierte cada día más en la terapia de elección. Para la introducción de anticuerpos monoclonales en mercados internacionales de alta demanda y con elevados requerimientos de calidad se requiere su producción a gran escala. El incremento de la presencia de dímeros en el producto final afecta su calidad y, por tanto, la eficiencia y eficacia del proceso. El objetivo del presente trabajo fue obtener un modelo matemático que permita relacionar el porcentaje de dímeros con las variables de operación de mayor influencia. Se realizó el ajuste de un modelo de regresión lineal múltiple usando el programa Statgraphics Centurion XVII versión 17.2.00. El modelo se validó con lotes de producción, logrando errores relativos inferiores al 20 por ciento. Las variables significativas obtenidas fueron: masa de IgG en el sobrenadante; masa de IgG en el producto de salida del paso de captura de proteína A; pH en el producto de salida del paso de captura de proteína A; pH del producto ajustado y conductividad de salida en la membrana de intercambio aniónico. El modelo permitió encontrar un intervalo de trabajo de las variables de mayor influencia en la formación de dímeros para reducirlos hasta valores inferiores al 3 por ciento(AU)

The use of monoclonal antibodies in the fight against cancer is becoming more and more the selected therapy. The introduction of monoclonal antibodies highly demanded in international markets, with high quality requirements needs the production of monoclonal antibodies on a large scale. The increase of dimers in the final product affects its quality, therefore, the efficiency and effectiveness of the process. The objective of this work was to obtain a mathematical model to relate the percentage of dimers with the most influential operating variables. A multiple linear regression model was obtained using Statgraphics Centurion XVII version 17.2.00 software. The model was validated with new production data with a mean error of validation below 20 percent. The significant variables were: supernatant IgG mass; IgG mass in the effluent from Protein A capture column; pH of the effluent from Protein A capture column; pH of the adjusted product and conductivity of the effluent from anionic exchange membrane. A working interval for each of the influential variables were established, in order to reduce dimers below 3 percent(AU)

The Impact of Staying at Home on Controlling the Spread of COVID -19: Strategy of Control

Abstract In this paper, we present a new mathematical model to describe the evolution of the COVID-19 in countries under the state of emergency. Where the COVID-19 pandemic is sweeping country after country. The Italian and Moroccan authorities have declared a state of emergency in response to the growing threat of this novel coronavirus (COVID-19) outbreak by March 09 and 20, respectively. In-state of emergency, citizens cannot go out to public spaces without special authorization from local authorities. But after all these efforts exerted by these authorities, the number of new cases of the COVID-19 continues to rise significantly, which confirms the lack of commitment of some citizens. First, we aim to investigate the cause of new infections despite all strategies of control followed in these countries including media reports, awareness, and treatment, self-distancing and quarantine, by estimating the number of these people who underestimate the lives and safety of citizens and put them at risk. To do this, we use real data of the COVID-19 in Italy and Morocco to estimate the parameters of the model, and then we predict the number of these populations. Second, we propose an optimal control strategy that could be the optimal and the efficient way for the Moroccan and Italian authorities and other countries to make the state of emergency more efficient and to control the spread of the COVID-19. The model is analyzed for both countries and then to compare the implications of the obtained results. Numerical examples are provided to illustrate the efficiency of the strategy of control that we propose and to show what would have been happened in Morocco and Italy if this strategy of control was applied early.

Modelos matemáticos aplicados a la Epidemiología / Mathematical models applied to Epidemiology / Modelos matemáticos aplicados à Epidemiologia

RESUMEN Un modelo matemático es una descripción matemática (a menudo por medio de una función o una ecuación) de un fenómeno del mundo real, como el tamaño de una población, la expectativa de vida de una persona al nacer o la propagación de una epidemia. Para ver la importancia de estos en las Ciencias de la Salud, específicamente en la especialidad de Higiene y Epidemiología mostramos dos de ellos para predecir el comportamiento de epidemias. El primero lo exponemos mediante una ecuación diferencial de 1er orden y el segundo mediante un sistema de ecuaciones diferenciales.

ABSTRACT A mathematical model is a mathematical description (often by means of a function or an equation) of a real-world phenomenon, such as the size of a population, the life expectancy of a person at birth, or the spread of an epidemic. To see the importance of these in Health Sciences, specifically in the specialty of Hygiene and Epidemiology, we show two of them to predict the behavior of epidemics. We expose the first through a 1st order differential equation and the second through a system of differential equations.

RESUMO Um modelo matemático é uma descrição matemática (frequentemente por meio de uma função ouequação) de um fenômeno do mundo real, como o tamanho de uma população, a expectativa de vida de uma pessoaao nascer ou a propagação de uma epidemia. Para perceber a importância destesnas Ciências da Saúde, especificamente na especialidade Higiene e Epidemiologia, mostramos dois deles para prever o comportamento de epidemias. Expomos o primeiro por meio de uma equação diferencial de 1ª ordem e o segundo por meio de um sistema de equaçõ es diferenciais.

Mathematical modeling of the synergy between hyperthermia and radiotherapy in tumor treatment based on p53 signaling network / 中国药科大学学报

@#The aim of the current study was to investigate the synergistic effect between temperature and irradiation on p53 dynamics using mathematical model in p53 signaling pathway.Delayed differential equations were used to construct the dynamic p53 model. The accelerated τ-leap stochastic simulation algorithm was used to analyze the stochastic behavior.Loewe and Bliss combination indexes were used to calculate the synergy. Numerical simulations were performed in MATLAB software. Results showed that at relatively lower temperatures, the amplitude and characteristic pitch of p53 pulses varied with changing temperatures.The amplitude and duration of p53 pulses were highly variable. At temperatures below 39 °C, the amplitude of the first p53 pulse was increased when temperature was elevated, whereas the characteristic pitch of p53 pulses was decreased with increasing temperature.Under mild hyperthermia (≥ 41 °C), p53 pulses were disrupted and p53 proteins became steadily accumulated.The patterns of periodicity in auto-correlation plot gradually vanished when the temperature was increased. With the metrics of cumulative and maximal p53 levels, there existed notable synergistic effects between the temperature and irradiation doses. In addition, the effect of temperature on p53 dynamics was reversible.To sum up, temperature could significantly affect dynamic p53 patterns.Radiotherapy may also benefit from hyperthermia in tumor treatment.

Study on drug-target binding kinetics profiles of flavonoids in Chrysanthemum morifolium and xanthine oxidase / 中国中药杂志

Based on the target occupancy mathematical model, the binding kinetic process of potential active ingredients of lowering uric acid in Chrysanthemum morifolium with xanthine oxidase(XOD) was evaluated. The potential active ingredients of lowering uric acid in Ch. morifolium were screened by UPLC-Q-Exactivems MS technology, reference substance identification and in vitro enzymatic kinetics experiments. The binding kinetic parameters of xanthine oxidase and potential inhibitor in Ch. morifolium were determined by surface plasma resonance(SPR). The verified mathematical model of the XOD target occupancy evaluated the kinetic binding process of inhibitors and xanthine oxidase in vivo. According to UPLC-Q-Exactive MS and reference substance identification, 39 potential uric acid-lowering active ingredients in Ch. morifolium extracts were identified and the inhibitory activities of 23 compounds were determined. Three potential xanthine oxidase inhibitors were screened, namely genistein, luteolin, and apigenin. whose IC_(50 )were 1.23, 1.47 and 1.59 μmol·L~(-1), respectively. And the binding rate constants(K_(on)) were 1.26×10~6, 5.23×10~5 and 6.36×10~5 mol·L~(-1)·s~(-1), respectively. The dissociation rate constants(K_(off)) were 10.93×10~(-2), 1.59×10~(-2), and 5.3×10~(-2 )s~(-1), respectively. After evaluation by different administration methods, the three selected compounds can perform rapid and sustained inhibition of xanthine oxidase in vivo under combined administration. This study comprehensively evaluated the target occupancy process of three effective components in different ways of administration in vivo by UPLC-MS, concentration-response method, SPR technology and xanthine oxidase target occupancy model, which would provide a new research idea and method for screening active ingredients in traditional Chinese medicine.

Mathematical Model for Analyzing Five Flavor Compatibility-transformation Theory in Tangye Jingfatu / 中国实验方剂学杂志

Objective:<italic>Auxiliary Verse on Drugs and</italic> <italic>methods</italic> <italic>for Zang-Fu Organs （Fuxingjue Wuzangyongyao Fayao）</italic> written by TAO Hong-jing from the Liang dynasty covered many contents from<italic> </italic>a missing prescription book<italic> Classic of Decoction （Tangye Jingfa）</italic>， including a map revealing the compatibility principle of Chinese herbs， namely the Tangye Jingfatu. Represented by a centrosymmetric pentagon， the map describes a unique theoretical system for deficiency-excess syndrome differentiation of five Zang organs （liver， heart， spleen， lung and kidney） and the tonification-purgation and compatibility theory of five flavors （pungent， salt， sweet， sour and bitter）. Each Zang organ fixedly corresponds to one "property" flavor （purgation）， one "function" flavor （tonification） and one "transformation" flavor （harmonization） resulting from the combination of the former two. For example， the liver can be purged by sour， tonified by pungent， and moderated by sweet transformed by the combination of sour with pungent. The heart can be purged by bitter， tonified by salt， and astringed by sour transformed by the combination of bitter with salt. The spleen can be purged by pungent， tonified by sweet， and dried by bitter transformed by the interaction between pungent and sweet. The lung can be purged by salt， tonified by sour， and dispersed by pungent transformed by the combination of salt with sour. The kidney can be purged by sweet， tonified by bitter， and moistened by salt transformed by the combination of sweet with bitter. This study selected appropriate mathematical tools to analyze the fixed relationship between "property" flavor， "function" flavor and "transformation" flavor among the five Zang organs in “Tangye Jingfatu” and establish a mathematical model revealing the compatibility-transformation relationship among five flavors. Method:Based on the group representation of five elements （wood， fire， earth， metal， and water）， the correlations of "property" flavor， "function" flavor， and "transformation" flavor with five elements’ generation-restriction were deduced based on matrix calculation and group theory. The three-dimensional calculation method for vector product was expanded for establishing the mathematical operator of five flavors' compatibility-transformation. Result:<bold>and</bold> Conclusion:There is a mapping relationship of the purging， tonifying， and harmonizing functions represented by the "property" flavor， "function" flavor， and "transformation" flavor of the five zang organs in the "Tangye Jingfatu" with the five elements' generation-restriction. The established mathematical operator contributes to explaining the fixed collocations of five flavor transformation. Based on such algorithm， the tonifying and purging characteristics of five flavors in 10 representative classic prescriptions have been clearly expounded.

A mathematical model for quality evaluation of total saponins of Panax japonicas based on hypolipidemic activity / 中草药·英文版

Objective: The chemical finger printing-based methods for evaluating TCMs quality can report partial of TCMs quality without linking to effective constituents. In this study, a mathematical model was established for the quality evaluation of total saponins of Panax japonicus (TSPJ), a folk medicine in China and Japan for treating diseases, through coupling the dynamic changes of chemical constitutions with corresponding activities. Methods: High-performance liquid chromatography (HPLC) fingerprints were applied to establish the chromatographic database of TSPJ. The associated hypolipidemic activity database was determined by TG assay using HepG2 cell model. Correlation analyses of two databases were performed by partial least squares (PLS) for calculating regression coefficients, and the interval value of YZL value (the ratio of positive and negative peak-to-peak area coefficient) closely related to hypolipidemic activity was refined by the formula of Norminv function to value the quality of TSPJ. Results: In this study, the chromatographic data of 16 common peaks were obtained from 20 batches of TSPJ. After the estimate by this mathematical evaluation model, seven peaks were positively correlated with hypolipidemic activity, and nine peaks were negatively correlated with hypolipidemic activity. When the YZL value was less than 0.7861, the quality of sample was inferior, while YZL value was more than 6.6992, and the quality of samples was superior. The quality of another ten batches of TSPJ was further assessed to verify this method. Conclusion: These results indicated that the established model could be usefully applied to evaluate the quality of TSPJ in the hypolipidemic activity.

Modelling the impact of contact tracing of symptomatic individuals on the COVID-19 epidemic

OBJECTIVES: With the declining numbers of coronavirus disease 2019 (COVID-19) cases in the state of São Paulo, Brazil, social distancing measures have gradually been lifted. However, the risk of a surge in the number of cases cannot be overlooked. Even with the adoption of nonpharmaceutical interventions, such as restrictions on mass gatherings, wearing of masks, and complete or partial closure of schools, other public health measures may help control the epidemic. We aimed to evaluate the impact of the contact tracing of symptomatic individuals on the COVID-19 epidemic regardless of the use of diagnostic testing. METHODS: We developed a mathematical model that includes isolation of symptomatic individuals and tracing of contacts to assess the effects of the contact tracing of symptomatic individuals on the COVID-19 epidemic in the state of São Paulo. RESULTS: For a selection efficacy (proportion of isolated contacts who are infected) of 80%, cases and deaths may be reduced by 80% after 60 days when 5000 symptomatic individuals are isolated per day, each of them together with 10 contacts. On the other hand, for a selection efficacy of 20%, the number of cases and deaths may be reduced by approximately 40% and 50%, respectively, compared with the scenario in which no contact-tracing strategy is implemented. CONCLUSION: Contact tracing of symptomatic individuals may potentially be an alternative strategy when the number of diagnostic tests available is not sufficient for massive testing.

Modelo predictivo del riesgo de abandono escolar en educación media superior en México / Predictive model of high school students' dropout risk in Mexico

Resumen Los índices nacionales en materia de abandono escolar o deserción en la educación media superior en México fluctúan entre 14.5 % y 16.5 %, y la investigación empírica sugiere que el abandono se encuentra mayormente asociado a la reprobación, y esta, a su vez, a cuestiones como la falta de autorregulación en el aprendizaje y a los hábitos de estudio. La presente investigación tuvo como objetivo el establecimiento de un modelo para predecir el riesgo de abandono escolar en estudiantes de nivel medio superior en México. Se desarrolló una investigación cuantitativa, no experimental y transversal. La variable independiente, que fue el riesgo de abandono escolar, se valoró a través del Cuestionario de Abandono Escolar, mientras que las variables predictoras fueron los hábitos de estudio, la autorregulación del aprendizaje y los estilos de aprendizaje (por así convenir a la institución), valorados mediante el Cuestionario de Hábitos de Estudio, el Cuestionario de Estrategias de Aprendizaje y Motivación II (CEAM), y el Cuestionario Honey - Alonso de Estilos de Aprendizaje (CHAEA). Para determinar la ecuación predictiva, se utilizó el modelo de regresión logística binaria, mediante el método "pasos hacia atrás de Wald", con una muestra de 192 estudiantes del primer semestre de un bachillerato tecnológico agropecuario, en su mayoría con edades de entre 14 y 16 años. Se obtuvo un modelo que incluye las dimensiones de estrategias para la planificación del estudio y estrategias para la toma de apuntes, relacionadas con los hábitos de estudio; y autoeficacia para el aprendizaje, relacionada con la autorregulación, explicando el 37.0 % del fenómeno. Se concluye que con el establecimiento de mecanismos de predicción del riesgo de abandono escolar, se podrían mejorar o incrementar las dimensiones ya mencionadas, para reducir en cierta medida el riesgo de abandono escolar.

Abstract National high school dropout rates in Mexico, fluctuate between 14.5 % and 16.5 %, and empirical research suggests that dropout is mostly associated with failure, and that this in turn, is related to issues such as lack of learning self-regulation and study habits. The objective of this research was to establish a model that predicts the risk of high school students' drop in Mexico. A quantitative, non-experimental and cross-sectional research was developed. The independent variable, which was the risk of dropping out of school, was assessed through the School Dropout Questionnaire, while the predictive variables study habits, self-regulation learning and learning styles (as requested by the participating institution) were assessed through the Study Habits Questionnaire, the Learning Strategies and Motivation Questionnaire (CEAM II), and the Honey - Alonso Learning Styles Questionnaire (CHAEA). To determine the predictive equation, the binary logistic regression model was used using the "Wald backward elimination steps" method, with a sample of 192 first semester students of an agricultural technological baccalaureate, whose ages ranged between 14 and 16 years. A model that includes the dimensions of note taking study planning strategies related to study habits; and self-efficacy for learning, related to self-regulation was obtained. This model explained 37.0 % of the phenomenon. It is concluded the establishment of dropout risk prediction mechanisms could be improve or increase the development of the aforementioned dimensions in order to reduce to a certain extent the risk of dropping out.