Search results for: mathematical decomposition

Authors: Wiam El Kheir, Anais Dumais, Maude Beaudoin, Bernard Marcos, Nick Virgilio, Benoit Paquette, Nathalie Faucheux, Marc-Antoine Lauzon

Abstract:

The high infiltrative pattern of glioblastoma multiforme cells (GBM) is the main cause responsible for the actual standard treatments failure. The tumor high heterogeneity, the interstitial fluid flow (IFF) and chemokines guides GBM cells migration in the brain parenchyma resulting in tumor recurrence. Drug delivery systems emerged as an alternative approach to develop effective treatments for the disease. Some recent studies have proposed to harness the effect CXC-lchemokine-ligand-12 to direct and control the cancer cell migration through delivery system. However, the dynamics of the brain environment on the delivery system remains poorly understood. Nanoparticles (NPs) and hydrogels are known as good carriers for the encapsulation of different agents and control their release. We studied the release of CXCL12 (free or loaded into NPs) from an alginate-based hydrogel under static and indirect perfusion (IP) conditions. Under static conditions, the main phenomena driving CXCL12 release from the hydrogel was diffusion with the presence of strong interactions between the positively charged CXCL12 and the negatively charge alginate. CXCL12 release profiles were independent from the initial mass loadings. Afterwards, we demonstrated that the release could tuned by loading CXCL12 into Alginate/Chitosan-Nanoparticles (Alg/Chit-NPs) and embedded them into alginate-hydrogel. The initial burst release was substantially attenuated and the overall cumulative release percentages of 21%, 16% and 7% were observed for initial mass loadings of 0.07, 0.13 and 0.26 µg, respectively, suggesting stronger electrostatic interactions. Results were mathematically modeled based on Fick’s second law of diffusion framework developed previously to estimate the effective diffusion coefficient (Deff) and the mass transfer coefficient. Embedding the CXCL12 into NPs decreased the Deff an order of magnitude, which was coherent with experimental data. Thereafter, we developed an in-vitro 3D model that takes into consideration the convective contribution of the brain IFF to study CXCL12 release in an in-vitro microenvironment that mimics as faithfully as possible the human brain. From is unique design, the model also allowed us to understand the effect of IP on CXCL12 release in respect to time and space. Four flow rates (0.5, 3, 6.5 and 10 µL/min) which may increase CXCL12 release in-vivo depending on the tumor location were assessed. Under IP, cumulative percentages varying between 4.5-7.3%, 23-58.5%, 77.8-92.5% and 89.2-95.9% were released for the three initial mass loadings of 0.08, 0.16 and 0.33 µg, respectively. As the flow rate increase, IP culture conditions resulted in a higher release of CXCL12 compared to static conditions as the convection contribution became the main driving mass transport phenomena. Further, depending on the flow rate, IP had a direct impact on CXCL12 distribution within the simulated brain tissue, which illustrates the importance of developing such 3D in-vitro models to assess the efficiency of a delivery system targeting the brain. In future work, using this very model, we aim to understand the impact of the different phenomenon occurring on GBM cell behaviors in response to the resulting chemokine gradient subjected to various flow while allowing them to express their invasive characteristics in an in-vitro microenvironment that mimics the in-vivo brain parenchyma.

Keywords: 3D culture system, chemokines gradient, glioblastoma multiforme, kinetic release, mathematical modeling

Procedia PDF Downloads 84

Authors: Shuai Yuan, Minxia Shi, Xu Zhang, Jianzhi Yang, Kangqi Tian, Yuzheng Ma

Abstract:

The precise measurement of muscle activities is essential for understanding the function of various body movements. This work aims to develop a muscle magnetic field signal detection system based on mathematical analysis. Medical research has underscored that early detection of muscle atrophy, coupled with lifestyle adjustments such as dietary control and increased exercise, can significantly enhance muscle-related diseases. Currently, surface electromyography (sEMG) is widely employed in research as an early predictor of muscle atrophy. Nonetheless, the primary limitation of using sEMG to forecast muscle strength is its inability to directly measure the signals generated by muscles. Challenges arise from potential skin-electrode contact issues due to perspiration, leading to inaccurate signals or even signal loss. Additionally, resistance and phase are significantly impacted by adipose layers. The recent emergence of optically pumped magnetometers introduces a fresh avenue for bio-magnetic field measurement techniques. These magnetometers possess high sensitivity and obviate the need for a cryogenic environment unlike superconducting quantum interference devices (SQUIDs). They detect muscle magnetic field signals in the range of tens to thousands of femtoteslas (fT). The utilization of magnetometers for capturing muscle magnetic field signals remains unaffected by issues of perspiration and adipose layers. Since their introduction, optically pumped atomic magnetometers have found extensive application in exploring the magnetic fields of organs such as cardiac and brain magnetism. The optimal operation of these magnetometers necessitates an environment with an ultra-weak magnetic field. To achieve such an environment, researchers usually utilize a combination of active magnetic compensation technology with passive magnetic shielding technology. Passive magnetic shielding technology uses a magnetic shielding device built with high permeability materials to attenuate the external magnetic field to a few nT. Compared with more layers, the coils that can generate a reverse magnetic field to precisely compensate for the residual magnetic fields are cheaper and more flexible. To attain even lower magnetic fields, compensation coils designed by Biot-Savart law are involved to generate a counteractive magnetic field to eliminate residual magnetic fields. By solving the magnetic field expression of discrete points in the target region, the parameters that determine the current density distribution on the plane can be obtained through the conventional target field method. The current density is obtained from the partial derivative of the stream function, which can be represented by the combination of trigonometric functions. Optimization algorithms in mathematics are introduced into coil design to obtain the optimal current density distribution. A one-dimensional linear regression analysis was performed on the collected data, obtaining a coefficient of determination R2 of 0.9349 with a p-value of 0. This statistical result indicates a stable relationship between the peak-to-peak value (PPV) of the muscle magnetic field signal and the magnitude of grip strength. This system is expected to be a widely used tool for healthcare professionals to gain deeper insights into the muscle health of their patients.

Keywords: muscle magnetic signal, magnetic shielding, compensation coils, trigonometric functions.

Procedia PDF Downloads 56

Authors: Agboka Komi Mensah, John Odindi, Elfatih M. Abdel-Rahman, Onisimo Mutanga, Henri Ez Tonnang

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Ecosystems are networks of organisms and populations that form a community of various species interacting within their habitats. Such habitats are defined by abiotic and biotic conditions that establish the initial limits to a population's growth, development, and reproduction. The habitat’s conditions explain the context in which species interact to access resources such as food, water, space, shelter, and mates, allowing for feeding, dispersal, and reproduction. Dispersal is an essential life-history strategy that affects gene flow, resource competition, population dynamics, and species distributions. Despite the importance of dispersal in population dynamics and survival, understanding the mechanism underpinning the dispersal of organisms remains challenging. For instance, when an organism moves into an ecosystem for survival and resource competition, its progression is highly influenced by extrinsic factors such as its physiological state, climatic variables and ability to evade predation. Therefore, greater spatial detail is necessary to understand organism dispersal dynamics. Understanding organisms dispersal can be addressed using empirical and mechanistic modelling approaches, with the adopted approach depending on the study's purpose Cellular automata (CA) is an example of these approaches that have been successfully used in biological studies to analyze the dispersal of living organisms. Cellular automata can be briefly described as occupied cells by an individual that evolves based on proper decisions based on a set of neighbours' rules. However, in the ambit of modelling individual organisms dispersal at the landscape scale, we lack user friendly tools that do not require expertise in mathematical models and computing ability; such as a visual analytics framework for tracking and forecasting the dispersal behaviour of organisms. The term "visual analytics" (VA) describes a semiautomated approach to electronic data processing that is guided by users who can interact with data via an interface. Essentially, VA converts large amounts of quantitative or qualitative data into graphical formats that can be customized based on the operator's needs. Additionally, this approach can be used to enhance the ability of users from various backgrounds to understand data, communicate results, and disseminate information across a wide range of disciplines. To support effective analysis of the dispersal of organisms at the landscape scale, we therefore designed Pydisp which is a free visual data analytics tool for spatiotemporal dispersal modeling built in Python. Its user interface allows users to perform a quick and interactive spatiotemporal analysis of species dispersal using bioecological and climatic data. Pydisp enables reuse and upgrade through the use of simple principles such as Fuzzy cellular automata algorithms. The potential of dispersal modeling is demonstrated in a case study by predicting the dispersal of Fopius arisanus (Sonan), endoparasitoids to control Bactrocera dorsalis (Hendel) (Diptera: Tephritidae) in Kenya. The results obtained from our example clearly illustrate the parasitoid's dispersal process at the landscape level and confirm that dynamic processes in an agroecosystem are better understood when designed using mechanistic modelling approaches. Furthermore, as demonstrated in the example, the built software is highly effective in portraying the dispersal of organisms despite the unavailability of detailed data on the species dispersal mechanisms.

Keywords: cellular automata, fuzzy logic, landscape, spatiotemporal

Procedia PDF Downloads 77

Authors: Manavjit Singh Dhindsa, Ursula Das, Kshirasagar Naik, Marzia Zaman, Richard Purcell, Srinivas Sampalli, Abdul Mutakabbir, Chung-Horng Lung, Thambirajah Ravichandran

Abstract:

These days, wildland fires, also known as forest fires, are more prevalent than ever. Wildfires have major repercussions that affect ecosystems, communities, and the environment in several ways. Wildfires lead to habitat destruction and biodiversity loss, affecting ecosystems and causing soil erosion. They also contribute to poor air quality by releasing smoke and pollutants that pose health risks, especially for individuals with respiratory conditions. Wildfires can damage infrastructure, disrupt communities, and cause economic losses. The economic impact of firefighting efforts, combined with their direct effects on forestry and agriculture, causes significant financial difficulties for the areas impacted. This research explores different forest fire spread models and presents a comprehensive review of various techniques and methodologies used in the field. A forest fire spread model is a computational or mathematical representation that is used to simulate and predict the behavior of a forest fire. By applying scientific concepts and data from empirical studies, these models attempt to capture the intricate dynamics of how a fire spreads, taking into consideration a variety of factors like weather patterns, topography, fuel types, and environmental conditions. These models assist authorities in understanding and forecasting the potential trajectory and intensity of a wildfire. Emphasizing the need for a comprehensive understanding of wildfire dynamics, this research explores the approaches, assumptions, and findings derived from various models. By using a comparison approach, a critical analysis is provided by identifying patterns, strengths, and weaknesses among these models. The purpose of the survey is to further wildfire research and management techniques. Decision-makers, researchers, and practitioners can benefit from the useful insights that are provided by synthesizing established information. Fire spread models provide insights into potential fire behavior, facilitating authorities to make informed decisions about evacuation activities, allocating resources for fire-fighting efforts, and planning for preventive actions. Wildfire spread models are also useful in post-wildfire mitigation strategies as they help in assessing the fire's severity, determining high-risk regions for post-fire dangers, and forecasting soil erosion trends. The analysis highlights the importance of customized modeling approaches for various circumstances and promotes our understanding of the way forest fires spread. Some of the known models in this field are Rothermel’s wildland fuel model, FARSITE, WRF-SFIRE, FIRETEC, FlamMap, FSPro, cellular automata model, and others. The key characteristics that these models consider include weather (includes factors such as wind speed and direction), topography (includes factors like landscape elevation), and fuel availability (includes factors like types of vegetation) among other factors. The models discussed are physics-based, data-driven, or hybrid models, also utilizing ML techniques like attention-based neural networks to enhance the performance of the model. In order to lessen the destructive effects of forest fires, this initiative aims to promote the development of more precise prediction tools and effective management techniques. The survey expands its scope to address the practical needs of numerous stakeholders. Access to enhanced early warning systems enables decision-makers to take prompt action. Emergency responders benefit from improved resource allocation strategies, strengthening the efficacy of firefighting efforts.

Keywords: artificial intelligence, deep learning, forest fire management, fire risk assessment, fire simulation, machine learning, remote sensing, wildfire modeling

Procedia PDF Downloads 81