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Mathematical model

Wenrui Hao, Shihua Gong, Shuonan Wu, Jinchao Xu, Michael R Go, Avner Friedman, Dai Zhu
Abdominal aortic aneurysm (AAA) is a localized enlargement of the abdominal aorta, such that the diameter exceeds 3 cm. The natural history of AAA is progressive growth leading to rupture, an event that carries up to 90% risk of mortality. Hence there is a need to predict the growth of the diameter of the aorta based on the diameter of a patient's aneurysm at initial screening and aided by non-invasive biomarkers. IL-6 is overexpressed in AAA and was suggested as a prognostic marker for the risk in AAA. The present paper develops a mathematical model which relates the growth of the abdominal aorta to the serum concentration of IL-6...
2017: PloS One
Jeong-In Hwang, Sung-Eun Lee, Jang-Eok Kim
Pesticides that persist in soils may be taken up by the roots of plants. One way to assess plant uptake is to theoretically predict the extent of plant uptake using a mathematical model. In this study, a model was developed to predict plant uptake of pesticide residues in soils using various parameters, such as pesticide mobility within soil, plant transpiration stream, root-soil transfer rate, plant growth, and pesticide dissipation in either soils or plants. The accuracy of the model was evaluated by comparing the modeled concentrations with measured uptake concentrations of chlorpyrifos (CP) in lettuce, grown on treated soils with concentrations of approximately 10 and 20 mg kg-1 CP...
2017: PloS One
Yun Xia, Shuangqian Yan, Xian Zhang, Peng Ma, Wei Du, Xiaojun Feng, Bi-Feng Liu
Digital loop-mediated isothermal amplification (dLAMP) is an attractive approach for absolute quantification of nucleic acids with high sensitivity and selectivity. Theoretical and numerical analysis of dLAMP provides necessary guidance for the design and analysis of dLAMP devices. In this work, a mathematical model was proposed based on Monte Carlo method and the theories of Poisson statistics and chemometrics. To examine the established model, we fabricated a spiral chip with 1200 uniform and discrete reaction chambers (9...
February 17, 2017: Analytical Chemistry
Lu Peng, Dumitru Trucu, Ping Lin, Alastair Thompson, Mark A J Chaplain
Known as one of the hallmarks of cancer (Hanahan and Weinberg in Cell 100:57-70, 2000) cancer cell invasion of human body tissue is a complicated spatio-temporal multiscale process which enables a localised solid tumour to transform into a systemic, metastatic and fatal disease. This process explores and takes advantage of the reciprocal relation that solid tumours establish with the extracellular matrix (ECM) components and other multiple distinct cell types from the surrounding microenvironment. Through the secretion of various proteolytic enzymes such as matrix metalloproteinases or the urokinase plasminogen activator (uPA), the cancer cell population alters the configuration of the surrounding ECM composition and overcomes the physical barriers to ultimately achieve local cancer spread into the surrounding tissue...
February 16, 2017: Bulletin of Mathematical Biology
Thomas Millat, Klaus Winzer
Clostridial acetone-butanol-ethanol (ABE) fermentation features a remarkable shift in the cellular metabolic activity from acid formation, acidogenesis, to the production of industrial-relevant solvents, solventogensis. In recent decades, mathematical models have been employed to elucidate the complex interlinked regulation and conditions that determine these two distinct metabolic states and govern the transition between them. In this review, we discuss these models with a focus on the mechanisms controlling intra- and extracellular changes between acidogenesis and solventogenesis...
February 16, 2017: Applied Microbiology and Biotechnology
M Eusebia Guerrero-Sánchez, D Alberto Mercado-Ravell, Rogelio Lozano, C Daniel García-Beltrán
This paper presents the problem of safe and fast transportation of packages by an Unmanned Aerial Vehicle (UAV) kind quadrotor. A mathematical model and a control strategy for a special class of underactuated mechanical systems, composed of a quadrotor transporting a cable-suspended payload, are proposed. The Euler-Lagrange formulation is used to obtain the dynamic model of the system, where the integrated dynamics of the quadrotor, cable and payload are considered. An Interconnection and Damping Assignment-Passivity Based Control (IDA-PBC) is chosen because of its inherent robustness against parametric uncertainty and unmodeled dynamics...
February 13, 2017: ISA Transactions
Manuel Gehlen, Vartan Kurtcuoglu, Marianne Schmid Daners
BACKGROUND: Postural changes are related to changes in cerebrospinal fluid (CSF) dynamics. While sitting up leads to a decrease in cranial CSF pressure, it also causes shifts in the craniospinal CSF volume and compliance distribution. We hypothesized that jugular vein collapse in upright posture is a major contributor to these shifts in CSF volume and compliance. METHODS: To test this hypothesis, we implemented a mathematical lumped-parameter model of the CSF system and the relevant parts of the cardiovascular system...
February 16, 2017: Fluids and Barriers of the CNS
Arkadiusz Jędrzejewski
We investigate the q-voter model with stochastic noise arising from independence on complex networks. Using the pair approximation, we provide a comprehensive, mathematical description of its behavior and derive a formula for the critical point. The analytical results are validated by carrying out Monte Carlo experiments. The pair approximation prediction exhibits substantial agreement with simulations, especially for networks with weak clustering and large average degree. Nonetheless, for the average degree close to q, some discrepancies originate...
January 2017: Physical Review. E
Felix Droste, Benjamin Lindner
The response properties of excitable systems driven by colored noise are of great interest, but are usually mathematically only accessible via approximations. For this reason, dichotomous noise, a rare example of a colored noise leading often to analytically tractable problems, has been extensively used in the study of stochastic systems. Here, we calculate exact expressions for the power spectrum and the susceptibility of a leaky integrate-and-fire neuron driven by asymmetric dichotomous noise. While our results are in excellent agreement with simulations, they also highlight a limitation of using dichotomous noise as a simple model for more complex fluctuations: Both power spectrum and susceptibility exhibit an undamped periodic structure, the origin of which we discuss in detail...
January 2017: Physical Review. E
Irina Ginzburg
The effect of the heterogeneity in the soil structure or the nonuniformity of the velocity field on the modeled resident time distribution (RTD) and breakthrough curves is quantified by their moments. While the first moment provides the effective velocity, the second moment is related to the longitudinal dispersion coefficient (k_{T}) in the developed Taylor regime; the third and fourth moments are characterized by their normalized values skewness (Sk) and kurtosis (Ku), respectively. The purpose of this investigation is to examine the role of the truncation corrections of the numerical scheme in k_{T}, Sk, and Ku because of their interference with the second moment, in the form of the numerical dispersion, and in the higher-order moments, by their definition...
January 2017: Physical Review. E
Yong Zhuang, Alex Arenas, Osman Yağan
We present the mathematical analysis of generalized complex contagions in a class of clustered multiplex networks. The model is intended to understand spread of influence, or any other spreading process implying a threshold dynamics, in setups of interconnected networks with significant clustering. The contagion is assumed to be general enough to account for a content-dependent linear threshold model, where each link type has a different weight (for spreading influence) that may depend on the content (e.g., product, rumor, political view) that is being spread...
January 2017: Physical Review. E
E Mema, L Kondic, L J Cummings
We consider a mathematical model that consists of a nematic liquid crystal layer sandwiched between two parallel bounding plates, across which an external field is applied. We investigate how the number and type of solutions for the director orientation within the layer change as the field strength, anchoring conditions, and material properties of the nematic liquid crystal layer vary. In particular, we focus on how the inclusion of flexoelectric effects alters the Freedericksz and saturation thresholds.
January 2017: Physical Review. E
Maryam Taraji, Paul R Haddad, Ruth I J Amos, Mohammad Talebi, Roman Szucs, John W Dolan, Chris A Pohl
A design-of-experiment (DoE) model was developed, able to describe the retention times of a mixture of pharmaceutical compounds in hydrophilic interaction liquid chromatography (HILIC) under all possible combinations of acetonitrile content, salt concentration, and mobile-phase pH with R(2) > 0.95. Further, a quantitative structure-retention relationship (QSRR) model was developed to predict retention times for new analytes, based only on their chemical structures, with a root-mean-square error of prediction (RMSEP) as low as 0...
February 7, 2017: Analytical Chemistry
Gili Greenbaum, Nina H Fefferman
In populations occupying discrete habitat patches, gene flow between habitat patches may form an intricate population structure. In such structures, the evolutionary dynamics resulting from interaction of gene flow patterns with other evolutionary forces may be exceedingly complex. Several models describing gene flow between discrete habitat patches have been presented in the population genetics literature; however, these models have usually addressed relatively simple settings of habitable patches, and have stopped short of providing general methodologies for addressing non-trivial gene flow patterns...
February 16, 2017: Molecular Ecology
Asrul Akmal Shafie, Hui Yee Yeo, Laurent Coudeville, Lucas Steinberg, Balvinder Singh Gill, Rohani Jahis, Amar-Singh Hss
BACKGROUND: Dengue disease poses a great economic burden in Malaysia. METHODS: This study evaluated the cost effectiveness and impact of dengue vaccination in Malaysia from both provider and societal perspectives using a dynamic transmission mathematical model. The model incorporated sensitivity analyses, Malaysia-specific data, evidence from recent phase III studies and pooled efficacy and long-term safety data to refine the estimates from previous published studies...
February 15, 2017: PharmacoEconomics
Mario A Cypko, Matthaeus Stoehr, Marcin Kozniewski, Marek J Druzdzel, Andreas Dietz, Leonard Berliner, Heinz U Lemke
PURPOSE: Oncological treatment is being increasingly complex, and therefore, decision making in multidisciplinary teams is becoming the key activity in the clinical pathways. The increased complexity is related to the number and variability of possible treatment decisions that may be relevant to a patient. In this paper, we describe validation of a multidisciplinary cancer treatment decision in the clinical domain of head and neck oncology. METHOD: Probabilistic graphical models and corresponding inference algorithms, in the form of Bayesian networks, can support complex decision-making processes by providing a mathematically reproducible and transparent advice...
February 15, 2017: International Journal of Computer Assisted Radiology and Surgery
Stefan Kleinbeck, Michael Schäper, Anna Zimmermann, Meinolf Blaszkewicz, Thomas Brüning, Christoph van Thriel
Human data about the potency of ethyl acrylate to evoke sensory irritation is currently not available. Therefore, we conducted an experimental exposure study and the magnitude of chemosensory effects in healthy human volunteers was mathematically modeled by combining the factors current concentration (c) and duration/time (t). In a repeated-measures design, 19 subjects were exposed for 4 h to constant and varying concentrations (including peaks of 5 and 10 ppm) of ethyl acrylate with either a 2.5 or 5 ppm time-weighted average (TWA) concentration...
February 15, 2017: Archives of Toxicology
Justin C Hayes, David J M Kraemer
Characterizing the neural implementation of abstract conceptual representations has long been a contentious topic in cognitive science. At the heart of the debate is whether the "sensorimotor" machinery of the brain plays a central role in representing concepts, or whether the involvement of these perceptual and motor regions is merely peripheral or epiphenomenal. The domain of science, technology, engineering, and mathematics (STEM) learning provides an important proving ground for sensorimotor (or grounded) theories of cognition, as concepts in science and engineering courses are often taught through laboratory-based and other hands-on methodologies...
2017: Cogn Res Princ Implic
Catherine A A Beauchemin, Tomoyuki Miura, Shingo Iwami
The duration of the eclipse phase, from cell infection to the production and release of the first virion progeny, immediately followed by the virus-production phase, from the first to the last virion progeny, are important steps in a viral infection, by setting the pace of infection progression and modulating the response to antiviral therapy. Using a mathematical model (MM) and data for the infection of HSC-F cells with SHIV in vitro, we reconfirm our earlier finding that the eclipse phase duration follows a fat-tailed distribution, lasting 19 h (18-20 h)...
February 16, 2017: Scientific Reports
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