Mathematical Biosciences and Engineering最新文献

This study investigated how permanent charges influence the dynamics of ionic channels. Using a quasi-one-dimensional classical Poisson-Nernst-Planck (PNP) model, we investigated the behavior of two distinct ion species-one positively charged and the other negatively charged. The spatial distribution of permanent charges was characterized by zero values at the channel ends and a constant charge $ Q_0 $ within the central region. By treating the classical PNP model as a boundary value problem (BVP) for a singularly perturbed system, the singular orbit of the BVP depended on $ Q_0 $ in a regular way. We therefore explored the solution space in the presence of a small permanent charge, uncovering a systematic dependence on this parameter. Our analysis employed a rigorous perturbation approach to reveal higher-order effects originating from the permanent charges. Through this investigation, we shed light on the intricate interplay among boundary conditions and permanent charges, providing insights into their impact on the behavior of ionic current, fluxes, and flux ratios. We derived the quadratic solutions in terms of permanent charge, which were notably more intricate compared to the linear solutions. Through computational tools, we investigated the impact of these quadratic solutions on fluxes, current-voltage relations, and flux ratios, conducting a thorough analysis of the results. These novel findings contributed to a deeper comprehension of ionic flow dynamics and hold potential implications for enhancing the design and optimization of ion channel-based technologies.

This article considered the sampled-data control issue for a dynamic positioning ship (DPS) with the Takagi-Sugeno (T-S) fuzzy model. By introducing new useful terms such as second-order term of time, an improved Lyapunov-Krasovskii function (LKF) was constructed. Additionally, the reciprocally convex method is introduced to bound the derivative of LKF. According to the constructed LKF, the sampling information during the whole sampling period was fully utilized, and less conservatism was obtained. Then, the stability condition, robust performance, mode uncertainty and sampled-data controller design were analyzed by means of the linear matrix inequality (LMI). Finally, an example was given to demonstrate the effectiveness of the proposed method.

Severe acute respiratory syndrome coronavirus 2 (SARS‑CoV‑2) has been evolving rapidly after causing havoc worldwide in 2020. Since then, it has been very hard to contain the virus owing to its frequently mutating nature. Changes in its genome lead to viral evolution, rendering it more resistant to existing vaccines and drugs. Predicting viral mutations beforehand will help in gearing up against more infectious and virulent versions of the virus in turn decreasing the damage caused by them. In this paper, we have proposed different NMT (neural machine translation) architectures based on RNNs (recurrent neural networks) to predict mutations in the SARS-CoV-2-selected non-structural proteins (NSP), i.e., NSP1, NSP3, NSP5, NSP8, NSP9, NSP13, and NSP15. First, we created and pre-processed the pairs of sequences from two languages using k-means clustering and nearest neighbors for training a neural translation machine. We also provided insights for training NMTs on long biological sequences. In addition, we evaluated and benchmarked our models to demonstrate their efficiency and reliability.

We developed a mathematical model to simulate dynamics associated with the proliferation of Geobacter and ultimately optimize cellular operation by analyzing the interaction of its components. The model comprises two segments: an initial part comprising a logistic form and a subsequent segment that incorporates acetate oxidation as a saturation term for the microbial nutrient medium. Given that four parameters can be obtained by minimizing the square root of the mean square error between experimental Geobacter growth and the mathematical model, the model underscores the importance of incorporating nonlinear terms. The determined parameter values closely align with experimental data, providing insights into the mechanisms that govern Geobacter proliferation. Furthermore, the model has been transformed into a scaleless equation with only two parameters to simplify the exploration of qualitative properties. This allowed us to conduct stability analysis of the fixed point and construct a co-dimension two bifurcation diagram.

The technology of robot-assisted prostate seed implantation has developed rapidly. However, during the process, there are some problems to be solved, such as non-intuitive visualization effects and complicated robot control. To improve the intelligence and visualization of the operation process, a voice control technology of prostate seed implantation robot in augmented reality environment was proposed. Initially, the MRI image of the prostate was denoised and segmented. The three-dimensional model of prostate and its surrounding tissues was reconstructed by surface rendering technology. Combined with holographic application program, the augmented reality system of prostate seed implantation was built. An improved singular value decomposition three-dimensional registration algorithm based on iterative closest point was proposed, and the results of three-dimensional registration experiments verified that the algorithm could effectively improve the three-dimensional registration accuracy. A fusion algorithm based on spectral subtraction and BP neural network was proposed. The experimental results showed that the average delay of the fusion algorithm was 1.314 s, and the overall response time of the integrated system was 1.5 s. The fusion algorithm could effectively improve the reliability of the voice control system, and the integrated system could meet the responsiveness requirements of prostate seed implantation.

Resistance to treatment poses a major challenge for cancer therapy, and oncoviral treatment encounters the issue of viral resistance as well. In this investigation, we introduce deterministic differential equation models to explore the effect of resistance on oncolytic viral therapy. Specifically, we classify tumor cells into resistant, sensitive, or infected with respect to oncolytic viruses for our analysis. Immune cells can eliminate both tumor cells and viruses. Our research shows that the introduction of immune cells into the tumor-virus interaction prevents all tumor cells from becoming resistant in the absence of conversion from resistance to sensitivity, given that the proliferation rate of immune cells exceeds their death rate. The inclusion of immune cells leads to an additional virus-free equilibrium when the immune cell recruitment rate is sufficiently high. The total tumor burden at this virus-free equilibrium is smaller than that at the virus-free and immune-free equilibrium. Therefore, immune cells are capable of reducing the tumor load under the condition of sufficient immune strength. Numerical investigations reveal that the virus transmission rate and parameters related to the immune response significantly impact treatment outcomes. However, monotherapy alone is insufficient for eradicating tumor cells, necessitating the implementation of additional therapies. Further numerical simulation shows that combination therapy with chimeric antigen receptor (CAR T-cell) therapy can enhance the success of treatment.

In this article, we have constructed a stochastic SIR model with healthcare resources and logistic growth, aiming to explore the effect of random environment and healthcare resources on disease transmission dynamics. We have showed that under mild extra conditions, there exists a critical parameter, i.e., the basic reproduction number $ R_0^s $, which completely determines the dynamics of disease: when $ R_0^s < 1 $, the disease is eradicated; while when $ R_0^s > 1 $, the disease is persistent. To validate our theoretical findings, we conducted some numerical simulations using actual parameter values of COVID-19. Both our theoretical and simulation results indicated that (1) the white noise can significantly affect the dynamics of a disease, and importantly, it can shift the stability of the disease-free equilibrium; (2) infectious disease resurgence may be caused by random switching of the environment; and (3) it is vital to maintain adequate healthcare resources to control the spread of disease.

Within the domain of cardiovascular diseases, arrhythmia is one of the leading anomalies causing sudden deaths. These anomalies, including arrhythmia, are detectable through the electrocardiogram, a pivotal component in the analysis of heart diseases. However, conventional methods like electrocardiography encounter challenges such as subjective analysis and limited monitoring duration. In this work, a novel hybrid model, AttBiLFNet, was proposed for precise arrhythmia detection in ECG signals, including imbalanced class distributions. AttBiLFNet integrates a Bidirectional Long Short-Term Memory (BiLSTM) network with a convolutional neural network (CNN) and incorporates an attention mechanism using the focal loss function. This architecture is capable of autonomously extracting features by harnessing BiLSTM's bidirectional information flow, which proves advantageous in capturing long-range dependencies. The attention mechanism enhances the model's focus on pertinent segments of the input sequence, which is particularly beneficial in class imbalance classification scenarios where minority class samples tend to be overshadowed. The focal loss function effectively addresses the impact of class imbalance, thereby improving overall classification performance. The proposed AttBiLFNet model achieved 99.55% accuracy and 98.52% precision. Moreover, performance metrics such as MF1, K score, and sensitivity were calculated, and the model was compared with various methods in the literature. Empirical evidence showed that AttBiLFNet outperformed other methods in terms of both accuracy and computational efficiency. The introduced model serves as a reliable tool for the timely identification of arrhythmias.

The coronary artery constitutes a vital vascular system that sustains cardiac function, with its primary role being the conveyance of indispensable nutrients to the myocardial tissue. When coronary artery disease occurs, it will affect the blood supply of the heart and induce myocardial ischemia. Therefore, it is of great significance to numerically simulate the coronary artery and evaluate its blood supply capacity. In this article, the coronary artery lumped parameter model was derived based on the relationship between circuit system parameters and cardiovascular system parameters, and the blood supply capacity of the coronary artery in healthy and stenosis states was studied. The aortic root pressure calculated by the aortic valve fluid-structure interaction (AV FSI) simulator was employed as the inlet boundary condition. To emulate the physiological phenomenon of sudden pressure drops resulting from an abrupt reduction in blood vessel radius, a head loss model was connected at the coronary artery's entrance. For each coronary artery outlet, the symmetric structured tree model was appended to simulate the terminal impedance of the missing downstream coronary arteries. The particle swarm optimization (PSO) algorithm was used to optimize the blood flow viscous resistance, blood flow inertia, and vascular compliance of the coronary artery model. In the stenosis states, the relative flow and fractional flow reserve (FFR) calculated by numerical simulation corresponded to the published literature data. It was anticipated that the proposed model can be readily adapted for clinical application, serving as a valuable reference for diagnosing and treating patients.

Attention deficit hyperactivity disorder (ADHD) is a common childhood developmental disorder. In recent years, pattern recognition methods have been increasingly applied to neuroimaging studies of ADHD. However, these methods often suffer from limited accuracy and interpretability, impeding their contribution to the identification of ADHD-related biomarkers. To address these limitations, we applied the amplitude of low-frequency fluctuation (ALFF) results for the limbic system and cerebellar network as input data and conducted a binary hypothesis testing framework for ADHD biomarker detection. Our study on the ADHD-200 dataset at multiple sites resulted in an average classification accuracy of 93%, indicating strong discriminative power of the input brain regions between the ADHD and control groups. Moreover, our approach identified critical brain regions, including the thalamus, hippocampal gyrus, and cerebellum Crus 2, as biomarkers. Overall, this investigation uncovered potential ADHD biomarkers in the limbic system and cerebellar network through the use of ALFF realizing highly credible results, which can provide new insights for ADHD diagnosis and treatment.