Operational stability study of lactate biosensors: modeling, parameter identification, and stability analysis.

Introduction: This paper investigates the operational stability of lactate biosensors, crucial devices in various biomedical and biotechnological applications. We detail the construction of an amperometric transducer tailored for lactate measurement and outline the experimental setup used for empirical validation. Methods: The modeling framework incorporates Brown and Michaelis-Menten kinetics, integrating both distributed and discrete delays to capture the intricate dynamics of lactate sensing. To ascertain model parameters, we propose a nonlinear optimization method, leveraging initial approximations from the Brown model's delay values for the subsequent model with discrete delays. Results: Stability analysis forms a cornerstone of our investigation, centering on linearization around equilibrium states and scrutinizing the real parts of quasi-polynomials. Notably, our findings reveal that the discrete delay model manifests marginal stability, occupying a delicate balance between asymptotic stability and instability. We introduce criteria for verifying marginal stability based on characteristic quasi-polynomial roots, offering practical insights into system behavior. Discussion: Qalitative examination of the model elucidates the influence of delay on dynamic behavior. We observe a transition from stable focus to limit cycle and period-doubling phenomena with increasing delay values, as evidenced by phase plots and bifurcation diagrams employing Poincaré sections. Additionally, we identify limitations in model applicability, notably the loss of solution positivity with growing delays, underscoring the necessity for cautious interpretation when employing delayed exponential function formulations. This comprehensive study provides valuable insights into the design and operational characteristics of lactate biosensors, offering a robust framework for understanding and optimizing their performance in diverse settings.

Approach to prediction and receiver operating characteristic analysis of a regression model for assessing the severity of the course Lyme borreliosis in children.

Introduction: Lyme borreliosis (LB) is a multisystemic zoonotic disease transmitted by the bite of infected tick vectors.The aim of the study is to develop a mathematical model for predicting the risk of severity of Lyme disease by the risk factor of the disseminated form of LB in children who have had a tick attack. To test the effectiveness of the formula for predicting the development of the disseminated stage of LB, we built a receiver operating characteristic (ROC) curve and determined the specificity and sensitivity of our model. The results of the examination of 122 patients with the confirmed local and disseminated stages of LB were taken as a basis. Material and methods: To build a prognostic model for prediction of the risk of the developing of the stage in LB predicting the risk of severity of course in Lyme borreliosis (PRSCLB), 122 children (aged 13 ±3 years) with LB were examined using multivariate regression analysis, including 52 boys and 70 girls. Groups of patients: 79 children with erythema migrans, 16 with Lyme arthritis, and 27 with nervous system involvement by LB. The quality of the prognostic model was checked by the Nagelkerke R Square (Nagelkerke R2) and the acceptability of this model was assessed using ROC analysis. Results: The method of multivariate regression analysis for predicting severe course and organ and system damage in LB in children, taking into account the factors and variants of the disease itself, makes it possible to develop a mathematical model for predicting the relative response factors (RRF) of severe forms of Lyme disease and will improve the effectiveness of treatment. This will create all the prerequisites for high-quality preventive measures and reduce the relative response factors rate.The initial data for predicting the severity of LB were 28 factors. According to the results of regression analysis, 24 factors were included in the model for predicting the severity of LB. Conclusions: The results of the study showed that the multifactorial model predicts the severity and organ and system damage in LB in children with an accuracy of 95%. The ROC curve, which was built on the basis of the results, has an area under the curve of 0.94, which indicates the high efficiency of the model.

MULTIFACTORIAL REGRESSION MODEL FOR PREDICTING THE LEVEL OF HEAT SENSITIVITY IN HEALTHY YOUNG PEOPLE IN THE CONTEXT OF GLOBAL WARMING.

OBJECTIVE: The aim: To create a mathematical model for predicting the level of heat sensitivity in healthy young people based on multivariate regression analysis. PATIENTS AND METHODS: Materials and methods: 150 healthy young people aged 17-20 years answered the questionnaire "Levels of heat sensitivity", underwent a heat test and mathematical analysis of the heart rate, after which the results were used to build a regression model of heat sensitivity. RESULTS: Results: The model of mathematical prediction of heat sensitivity (CHSL1/CHSL2), which we proposed for the first time, takes into account the most significant factors that influence the determination of higher and lower sensitivity to heat (Q1-Q6, %LF2, %HF1, %HF2, HR1, HR2), so its use will allow timely identi¬fication of individuals who are particularly susceptible to the effects of elevated ambient temperature and prevent the development of potential negative consequences of this exposure. CONCLUSION: Conclusions: Based on the results obtained, it is possible to use this prognostic model in the future to develop a diagnostic system for determining the level of heat sensitivity.

Prediction factors for the risk of diffuse non-toxic goiter development in type 2 diabetic patients.

Type 2 diabetes mellitus (T2DM) patient outcomes, treatment options, and corresponding healthcare expenses are affected by the presence of different comorbidities. AIM: The aim of this work was to develop an algorithm for predicting the risk of diffuse non-toxic goitre development in patients with T2DM according to a mathematical model obtained by regression analysis, for the timely implementation of appropriate preventive measures among T2DM patients. MATERIALS AND METHODS: We analyzed 541 medical records of T2DM patients. RESULTS: It was found the following risk factors influencing the occurrence of diffuse non-toxic goitre in patients with T2DM: age, gender, body mass index (BMI), glycosylated hemoglobin (HbA1c), homeostasis model assessment for insulin resistance (HOMA-IR), thyroid stimulating hormone (TSH), free thyroxine (fT4). Prognostic model of the risk of diffuse non-toxic goitre development in T2DM patients was built using multiple regression analysis. In order to stratify the risk of diffuse nontoxic goitre development in T2DM patients, the following criteria were proposed: no risk at RCG ≤ 5.0; low risk at 5.1≤ RCG ≤12,9; high risk at RCG ≥13.0.; where RCG - risk coefficient for the diffuse non-toxic goiter development in T2DM patients. CONCLUSIONS: Therefore, the developed algorithm and mathematical model for predicting the development of diffuse non-toxic goitre in T2DM patients are highly informative and allow to determine in advance the contingent of patients with a high probability of diffuse non-toxic goitre risk based both on routine laboratory data, such as HbA1c, HOMA-IR, TSH, fT4 levels and such factors as age, gender, and BMI.

Nonlinear Analytics for Electrochemical Biosensor Design Using Enzyme Aggregates and Delayed Mass Action.

The paper is devoted to the extension of Brown's model of enzyme kinetics to the case with distributed delays. Firstly, we construct a multi-substrate multi-inhibitor model using discrete and distributed delays. Furthermore, we consider simplified models including one substrate and one inhibitor, for which an experimental study has been performed. The algorithm of parameter identifications was developed which was tested on the experimental data of solution conductivity. Both the model and Kohlrausch's law parameters are obtained as a result of the optimization procedure. Comparison of plots constructed with the help of the estimated parameters has shown that in such case the model with distributed delays is more chemically adequate in comparison with the discrete one. The methods of generalization of the results to the multi-substrate multi-inhibitor cases are discussed.