Predictive models may be considered a tool to ensure food quality as they provide insights that support decision making on the design of processes, such as fermentation. Objective: To formulate a mathematical model that describes the growth of lactic acid bacteria (LAB) in batch fermentation. Methodology: Based on real-life experimental data from eight LAB strains, we formulated a primary model in the form of a third-degree polynomial function that successfully describes the four phases observed in LAB growth, i.e., lag, exponential, stationary, and death. Our cubic mathematical model allows us to understand the fundamental nonlinear dynamics of LAB as well as its time-variant dependencies. Parameters of the model are written in terms of initial biomass, maximum biomass, maximum growth rate, and lag phase duration. Further, a statistical analysis was performed to compare our cubic primary model with the ones proposed by Gompertz, Baranyi, and Vázquez-Murado by computing the coefficient of determination $\left(R^2\right)$, the residual sum of squares $\left(R,S,S\right)$, and the Akaike Information Criterion $\left(A,I,C\right)$. Results: The average statistical results from the cubic model are as follows: $R^2=0.820$ providing a better fit than the other three models, $RSS=0.658$ and $AIC=-6.499$, where both values are lower than the other models considered in this study. Conclusion: The cubic primary model formulated in this work describes the behavior of biomass as it accurately represents the four phases of biomass growth in batch fermentation process.

In this paper, we explore the application of Chimeric Antigen Receptor (CAR) T cell therapy for the treatment of Acute Lymphocytic Leukaemia (ALL) by means of in silico experimentation, mathematical modelling through first-order Ordinary Differential Equations and nonlinear systems theory. By combining the latter with systems biology on cancer evolution we were able to establish a sufficient condition on the therapy dose to ensure complete response. The latter is illustrated across multiple numerical simulations when comparing three mathematically formulated administration protocols with one of a phase 1 dose-escalation trial on CAR-T cells for the treatment of ALL on children and young adults. Therefore, both our analytical and in silico results are consistent with real-life scenarios. Finally, our research indicates that tumour cells growth rate and the killing efficacy of the therapy are key factors in the designing of personalised strategies for cancer treatment.

This paper presents results concerning mechanistic modeling to describe the dynamics and interactions between biomass growth, glucose consumption and ethanol production in batch culture fermentation by Kluyveromyces marxianus (K. marxianus). The mathematical model was formulated based on the biological assumptions underlying each variable and is given by a set of three coupled nonlinear first-order Ordinary Differential Equations. The model has ten parameters, and their values were fitted from the experimental data of 17 K. marxianus strains by means of a computational algorithm design in Matlab. The latter allowed us to determine that seven of these parameters share the same value among all the strains, while three parameters concerning biomass maximum growth rate, and ethanol production due to biomass and glucose had specific values for each strain. These values are presented with their corresponding standard error and $95\%$ confidence interval. The goodness of fit of our system was evaluated both qualitatively by in silico experimentation and quantitative by means of the coefficient of determination and the Akaike Information Criterion. Results regarding the fitting capabilities were compared with the classic model given by the logistic, Pirt, and Luedeking–Piret Equations. Further, nonlinear theories were applied to investigate local and global dynamics of the system, the Localization of Compact Invariant Sets Method was applied to determine the so-called localizing domain, i.e., lower and upper bounds for each variable; whilst Lyapunov’s stability theories allowed to establish sufficient conditions to ensure asymptotic stability in the nonnegative octant, i.e., ${\mathbf{R}}_{+,0}^3$. Finally, the predictive ability of our mechanistic model was explored through several numerical simulations with expected results according to microbiology literature on batch fermentation.

Background: Monitoring of post-transplant heart rejection is currently based on endomyocardial biopsy analysis. This study aimed to assess the effects of heart graft rejection on myocardial electrical impedance. Methods and results: Twenty-nine cardiac transplant patients and 9 controls underwent measurement of myocardial electrical impedance using a specifically designed amplifying system. The module and phase angle of myocardial impedance were measured. Histopathological rejection grading was performed according to ISHLT classification. Fifty impedance tests were performed in transplanted patients. Myocardial impedance (Z) was higher in controls than in transplanted patients (p<0.001) and followed a progressive decline at increasing current frequencies (p<0.001). Likewise, the phase angle of impedance in controls ranged from positive values at low frequencies to negative values at higher frequencies (from 2.5±0.9° at 10 kHz to − 3.8±2.1° at 300 kHz, p<0.001). Rejection was associated with a significant decrease in myocardial impedance (Z) (15±6.6 Ω in grade 0, 13±6.0 Ω in grade 1A, and 3.3±0.9 Ω in grade 3A at 10 kHz, p<0.003). Conclusions: Mild degrees of cardiac graft rejection are associated with significant changes in myocardial electrical impedance in transplant patients. Further clinical investigation is warranted to assess the potential of cardiac impedance to detect heart graft rejection.

Background: Vertical jump height is widely used in health care and sports fields to assess muscle strength and power from lower limb muscle groups. Different approaches have been proposed for vertical jump height measurement. Some commonly used approaches need no sensor at all; however, these methods tend to overestimate the height reached by the subjects. There are also novel systems using different kind of sensors like force-sensitive resistors, capacitive sensors, and inertial measurement units, among others, to achieve more accurate measurements. Objective: The objective of this study is twofold. The first objective is to validate the functioning of a developed low-cost system able to measure vertical jump height. The second objective is to assess the effects on obtained measurements when the sampling frequency of the system is modified. Methods: The system developed in this study consists of a matrix of force-sensitive resistor sensors embedded in a mat with electronics that allow a full scan of the mat. This mat detects pressure exerted on it. The system calculates the jump height by using the flight-time formula, and the result is sent through Bluetooth to any mobile device or PC. Two different experiments were performed. In the first experiment, a total of 38 volunteers participated with the objective of validating the performance of the system against a high-speed camera used as reference (120 fps). In the second experiment, a total of 15 volunteers participated. Raw data were obtained in order to assess the effects of different sampling frequencies on the performance of the system with the same reference device. Different sampling frequencies were obtained by performing offline downsampling of the raw data. In both experiments, countermovement jump and countermovement jump with arm swing techniques were performed. Results: In the first experiment an overall mean relative error (MRE) of 1.98% and a mean absolute error of 0.38 cm were obtained. Bland-Altman and correlation analyses were performed, obtaining a coefficient of determination equal to R2=.996. In the second experiment, sampling frequencies of 200 Hz, 100 Hz, and 66.6 Hz show similar performance with MRE below 3%. Slower sampling frequencies show an exponential increase in MRE. On both experiments, when dividing jump trials in different heights reached, a decrease in MRE with higher height trials suggests that the precision of the proposed system increases as height reached increases. Conclusions: In the first experiment, we concluded that results between the proposed system and the reference are systematically the same. In the second experiment, the relevance of a sufficiently high sampling frequency is emphasized, especially for jump trials whose height is below 10 cm. For trials with heights above 30 cm, MRE decreases in general for all sampling frequencies, suggesting that at higher heights reached, the impact of high sampling frequencies is lesser.