Mechanistic Modelling of Biomass Growth, Glucose Consumption and Ethanol Production by Kluyveromyces marxianus in Batch Fermentation.

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., R+,03. Finally, the predictive ability of our mechanistic model was explored through several numerical simulations with expected results according to microbiology literature on batch fermentation.

Chemoimmunotherapy Administration Protocol Design for the Treatment of Leukemia through Mathematical Modeling and In Silico Experimentation.

Cancer with all its more than 200 variants continues to be a major health problem around the world with nearly 10 million deaths recorded in 2020, and leukemia accounted for more than 300,000 cases according to the Global Cancer Observatory. Although new treatment strategies are currently being developed in several ongoing clinical trials, the high complexity of cancer evolution and its survival mechanisms remain as an open problem that needs to be addressed to further enhanced the application of therapies. In this work, we aim to explore cancer growth, particularly chronic lymphocytic leukemia, under the combined application of CAR-T cells and chlorambucil as a nonlinear dynamical system in the form of first-order Ordinary Differential Equations. Therefore, by means of nonlinear theories, sufficient conditions are established for the eradication of leukemia cells, as well as necessary conditions for the long-term persistence of both CAR-T and cancer cells. Persistence conditions are important in treatment protocol design as these provide a threshold below which the dose will not be enough to produce a cytotoxic effect in the tumour population. In silico experimentations allowed us to design therapy administration protocols to ensure the complete eradication of leukemia cells in the system under study when considering only the infusion of CAR-T cells and for the combined application of chemoimmunotherapy. All results are illustrated through numerical simulations. Further, equations to estimate cytotoxicity of chlorambucil and CAR-T cells to leukemia cancer cells were formulated and thoroughly discussed with a 95% confidence interval for the parameters involved in each formula.

Force-Sensitive Mat for Vertical Jump Measurement to Assess Lower Limb Strength: Validity and Reliability Study.

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.

Tumor Clearance Analysis on a Cancer Chemo-Immunotherapy Mathematical Model.

Mathematical models may allow us to improve our knowledge on tumor evolution and to better comprehend the dynamics between cancer, the immune system and the application of treatments such as chemotherapy and immunotherapy in both short and long term. In this paper, we solve the tumor clearance problem for a six-dimensional mathematical model that describes tumor evolution under immune response and chemo-immunotherapy treatments. First, by means of the localization of compact invariant sets method, we determine lower and upper bounds for all cells populations considered by the model and we use these results to establish sufficient conditions for the existence of a bounded positively invariant domain in the nonnegative orthant by applying LaSalle's invariance principle. Then, by exploiting a candidate Lyapunov function we determine sufficient conditions on the chemotherapy treatment to ensure tumor clearance. Further, we investigate the local stability of the tumor-free equilibrium point and compute conditions for asymptotic stability and tumor persistence. All conditions are given by inequalities in terms of the system parameters, and we perform numerical simulations with different values on the chemotherapy treatment to illustrate our results. Finally, we discuss the biological implications of our work.

Changes in myocardial electrical impedance in human heart graft rejection.

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 degrees at 10 kHz to -3.8+/-2.1 degrees at 300 kHz, p<0.001). Rejection was associated with a significant decrease in myocardial impedance (Z) (15+/-6.6 Omega in grade 0, 13+/-6.0 Omega in grade 1A, and 3.3+/-0.9 Omega 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.

Effect of electrode locations and respiration in the characterization of myocardial tissue using a transcatheter impedance method.

Our objective is to evaluate whether it is possible to characterize the passive electrical properties of myocardial tissue in contact with the electrocatheters used in arrhythmia diagnosis or radio frequency ablation techniques. To characterize the tissue, we propose the use of electrical impedance spectroscopy to measure the impedance between the catheter tip and an external electrode, assuming a three-electrode method. We constructed a 3D finite-element model of the thorax to estimate the impedance as measured in different situations. We defined an area on the anterior wall of the left ventricle in which we simulated three tissue states: healthy, acute ischaemic and scar. We studied the effect of the following parameters on the measured impedance spectrum: the position of the external electrode, the position and orientation of the catheter tip and the overall effect of the subject's respiration. Results show that the highest frequency phase (around 300 kHz) yields the best differentiation of tissue states and that it is less sensitive to respiration than the impedance magnitude. The phase is also less influenced by the catheter tip position (either touching the wall or floating) and the orientation of the catheter inside the left ventricle. The best position for the external electrode is on the chest; this position is less affected by breathing and is more sensitive to tissue changes. One can still distinguish between tissue states if the external electrode is placed on the back, but the effect of respiration is higher.

Transmural versus nontransmural in situ electrical impedance spectrum for healthy, ischemic, and healed myocardium.

Electrical properties of myocardial tissue are anisotropic due to the complex structure of the myocardial fiber orientation and the distribution of gap junctions. For this reason, measured myocardial impedance may differ depending on the current distribution and direction with respect to myocardial fiber orientation and, consequently, according to the measurement method. The objective of this study is to compare the specific impedance spectra of the myocardium measured using two different methods. One method consisted of transmural measurements using an intracavitary catheter and the other method consisted of nontransmural measurements using a four-needle probe inserted into the epicardium. Using both methods, we provide the in situ specific impedance spectrum (magnitude and phase angle) of normal, ischemic, and infarcted pig myocardium tissue from 1 kHz to 1 MHz. Magnitude spectra showed no significant differences between the measurement techniques. However, the phase angle spectra showed significant differences for normal and ischemic tissues according to the measurement technique. The main difference is encountered after 60 min of acute ischeimia in the phase angle spectrum. Healed myocardial tissue showed a small and flat phase angle spectrum in both methods due tothe low content of cells in the transmural infarct scar. In conclusion, both transmural and nontransmural measurements of phase angle spectrum allow the differentiation among normal, ischemic, and infarcted tissue.