Capillary network formation and structure in a modified discrete mathematical model of angiogenesis

Angiogenesis, as part of cancer development, involves hierarchical complicated events and processes. Multiple studies have revealed the significance of the formation and structure of tumor-induced capillary networks. In this study, a discrete mathematical model of angiogenesis is studied and modified to capture the realistic physics of capillary network formation. Modifications are performed on the mathematical foundations of an existing discrete model of angiogenesis. The main modifications are the imposition of the matrix density effect, implementation of realistic boundary and initial conditions, and improvement of the method of governing equations based on physical observation. Results show that endothelial cells accelerate angiogenesis and capillary formation as they migrate toward the tumor and clearly exhibit the physical concept of haptotactic movement. On the other hand, consideration of blood flow-induced stress leads to a dynamic adaptive vascular network of capillaries which intelligibly reflects the brush border effect . The present modified model of capillary network formation is based on the physical rationale that defines a clear mathematical and physical interpretation of angiogenesis, which is likely to be used in cancer development modeling and anti-angiogenic therapies.

SIR Mathematical Model of Convalescent Plasma Transfusion Applied to the COVID-19 Pandemic Data in Indonesia to Control the Spread of the Disease

In this paper we develop a mathematical model of disease transmission dynamics. Although some vaccines for some infectious diseases are available, there are some cases where handling new emerging infectious diseases, such as COVID-19 pandemic, is still a difficult problem to handle. Preventive actions, such as wearing masks, distance guarding, frequent hand washing, and others are still the most important interventions in handling the transmission of this disease. Recently, several countries have allowed the use of convalescent plasma transfusion (CPT) in the management of moderate and severe COVID-19 patients. Several early studies of this use have yielded prospective results with reduced mortality rates. A recent work also shows that using a simple discrete mathematical model of CPT could reduce the outbreak of disease transmission, in the sense of reducing the peak number of active cases and the length of the outbreak itself. In this paper, we use a continuous SIR model applied to COVID-19 pandemic data in Indonesia to address an important question whether convalescent plasma transfusion may reduce the transmission of the disease.

Discrete Dynamic Model of the Mammalian Sperm Acrosome Reaction: The Influence of Acrosomal pH and Physiological Heterogeneity

The acrosome reaction (AR) is an exocytotic process essential for mammalian fertilization. It involves diverse physiological changes (biochemical, biophysical, and morphological) that culminate in the release of the acrosomal content to the extracellular medium as well as a reorganization of the plasma membrane (PM) that allows sperm to interact and fuse with the egg. In spite of many efforts, there are still important pending questions regarding the molecular mechanism regulating the AR. Particularly, the contribution of acrosomal alkalinization to AR triggering physiological conditions is not well understood. Also, the dependence of the proportion of sperm capable of undergoing AR on the physiological heterogeneity within a sperm population has not been studied. Here, we present a discrete mathematical model for the human sperm AR based on the physiological interactions among some of the main components of this complex exocytotic process. We show that this model can qualitatively reproduce diverse experimental results, and that it can be used to analyze how acrosomal pH (pHa) and cell heterogeneity regulate AR. Our results confirm that a pHa increase can on its own trigger AR in a subpopulation of sperm, and furthermore, it indicates that this is a necessary step to trigger acrosomal exocytosis through progesterone, a known natural inducer of AR. Most importantly, we show that the proportion of sperm undergoing AR is directly related to the detailed structure of the population physiological heterogeneity.

Evaluation of Urban Environmental and Economic Coordination Based on Discrete Mathematical Model

The urban ecological environment is the material basis and condition for human beings to engage in social and economic activities and the supporting system for the formation and sustainable development of cities. With the acceleration of urbanization and industrialization, urban living environments and economic development have become the focus of people’s attention. This leads to the necessity of studying how to improve the quality of the urban living environment and promote the harmonious coexistence of population, natural environment, and social economy. Traditional methods focus on multiple regression models to evaluate the urban environmental and economic harmony, but this method does not consider the weight of each index, resulting in poor accuracy of the evaluation results. This paper proposes a discrete mathematical model to design the evaluation index and evaluation system of urban environmental and economic coordination. It calculates the weight of each index; carrying capacity of the urban environment, the value of each environmental factor, and the comprehensive value of the environment is determined. The static evaluation and dynamic evaluation are used to evaluate the coordination of the urban environmental economy. The experimental results show that the designed evaluation method of urban environmental economic coordination has high accuracy and effectively improves the reliability and evaluation time.

Color perception and recognition method for Guangdong embroidery image based on discrete mathematical model

Aiming at the problem that the traditional color perception and recognition method for Guangdong embroidery image has poor color stereo restoring ability, a color perception, and recognition method for Guangdong embroidery image based on discrete mathematical model is proposed. Through histogram equalization, the input image with centralized gray distribution is transformed into the output image with approximate uniform distribution to enhance the dynamic range of the gray value of the pixels; the median filtering method is used to smooth the Guangdong embroidery image and remove the noise in the Guangdong embroidery image. The RGB spatial model and HSI spatial model of image color are constructed by normalizing the coordinates and color attributes of pixels. Using these two models to transform RGB color space and HSI color space, image color perception, and recognition model is established to realize color perception and recognition of Guangdong embroidery image. In order to verify the color stereo restoring ability of the method, the method is compared with the traditional method for color perception and recognition of Guangdong embroidery image, which proves that the color stereo restoring ability of the method is better than that of the traditional method.

Discrete dynamic model of the mammalian sperm acrosome reaction: the influence of acrosomal pH and biochemical heterogeneity

The acrosome reaction (AR) is an exocytotic process essential for mammalian fertilization. It involves diverse biochemical and physiological changes that culminate in the release of the acrosomal content to the extracellular medium as well as a reorganization of the plasma membrane (PM) that allows sperm to interact and fuse with the egg. In spite of many efforts, there are still important pending questions regarding the molecular mechanism regulating the AR. Particularly, the contribution of acrosomal alkalinization to AR triggering in physiological conditions is not well understood. Also, the dependence of the proportion of sperm capable of undergoing AR on the biochemical heterogeneity within a sperm population has not been studied. Here we present a discrete mathematical model for the human sperm AR, based on the biophysical and biochemical interactions among some of the main components of this complex exocytotic process. We show that this model can qualitatively reproduce diverse experimental results, and that it can be used to analyze how acrosomal pH (pHa) and cell heterogeneity regulate AR. Our results confirm that pHa increase can on its own trigger AR in a subpopulation of sperm, and furthermore, it indicates that this is a necessary step to trigger acrosomal exocytosis through progesterone, a known physiological inducer of AR. Most importantly, we show that the proportion of sperm undergoing AR is directly related to the detailed structure of the population biochemical heterogeneity.

STABILITY AND VIBRATIONS OF THE ELECTRONIC CLOSED SYSTEM STABILIZING THE COURSE OF A CAR WITH A TANK

To describe the disturbed movement of a car with a tank, a discrete mathematical model has been compiled, which allows one to take into account the oscillations of the free surface of the liquid and determine their effect on the directional stability of the car during uniform movement and during emergency braking. Linearization is carried out and an equation is obtained for the natural frequencies of oscillations of the electrohydromechanical system, which combines dynamic changes in the parameters of the movement of a car with a tank, partial layers of liquid in a tank and the operation of an electromagnetic drive of the control valve and an electronic PID controller for a two-circuit scheme to ensure directional stability. It is shown that low-frequency oscillations of the free surface of liquid lead to a significant reduction in the stability region, which indicates the need to take such oscillations into account when solving problems of analysis and synthesis of this system. It has been established that for a car with a tank, where low-frequency transverse oscillations of the liquid occur, which are accompanied by redistribution of mass and disturb the movement, an increase in the speed unambiguously leads to a deterioration in road-holding ability. This made it possible to exclude the speed from the variable parameters and significantly simplify the task. It was found that the liquid level in the tank, taking into account its connection with the maximum speed, has an ambiguous effect on the road-holding ability of the vehicle, and it is unacceptable to limit the research to calculations for 50 % of the load. Instead of this traditional simplification, it is necessary to find a line that bends from above those stability boundaries that correspond to many liquid levels from the entire range of their variation. It is shown that the dynamics of emergency braking weakly depends on the viscosity of the liquid in the tank, but with long-term continuous operation of the brake control system, self-oscillations appear in it. A method for tuning the parameters of an electronic regulator for low-amplitude self-oscillations is proposed.

CALCULATION OF THE CENTRIFULAL PUMP CRITICAL FREQUENCIES BASED ON ITS DISCRETE MATHEMATICAL MODEL

Calculations of the centrifugal machines critical frequencies of the rotors are currently carried out on the basis of the finite element method using multi-functional software as same as ANSYS and other similar, that work with finite elements of the three-dimensional type, as well as some specialized computer programs working with the beam-type finite elements. Anyway, the finite element method is used. But in this case an user needs a lot of time for prepation of the initial data. Therefore, this article presents a calculation of the critical frequencies of the rotor of a centrifugal fuel pump of a liquid-propellant engine based on its discrete model. This calculation also includes an algorithm of results clarification. This model has been verificated by comparing the critical frequencies obtained in calculations based on the finite element beam model and discrete model with using the algorithm of results clarification and without it.

The role of mechanical interactions in EMT

The detachment of cells from the boundary of an epithelial tissue and the subsequent invasion of these cells into surrounding tissues is important for cancer development and wound healing, and is strongly associated with the epithelial-mesenchymal transition (EMT). Chemical signals, such as TGF-beta, produced by surrounding tissue can be uptaken by cells and induce EMT. In this work, we present a novel cell-based discrete mathematical model of mechanical cellular relaxation, cell proliferation, and cell detachment driven by chemically-dependent EMT in an epithelial tissue. A continuum description of the model is then derived in the form of a novel nonlinear free boundary problem. Using the discrete and continuum models we explore how the coupling of chemical transport and mechanical interactions influences EMT, and postulate how this could be used to help control EMT in pathological situations.