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Differential equation

Nourridine Siewe, Abdul-Aziz Yakubu, Abhay R Satoskar, Avner Friedman
Leishmaniasis is a disease caused by the Leishmania parasites. The two common forms of leishmaniasis are cutaneous leishmaniasis (CL) and visceral leishmaniasis (VL). VL is the more severe of the two and, if untreated, may become fatal. The hallmark of VL is the formation of granuloma in the liver or the spleen. In this paper, we develop a mathematical model of the evolution of granuloma in the liver. The model is represented by a system of partial differential equations and it includes migration of cells from the adaptive immune system into the granuloma; the rate of the influx is determined by the strength of the immune response of the infected individual...
October 18, 2016: Journal of Theoretical Biology
Bram Thijssen, Tjeerd M H Dijkstra, Tom Heskes, Lodewyk F A Wessels
BACKGROUND: Computational models in biology are characterized by a large degree of uncertainty. This uncertainty can be analyzed with Bayesian statistics, however, the sampling algorithms that are frequently used for calculating Bayesian statistical estimates are computationally demanding, and each algorithm has unique advantages and disadvantages. It is typically unclear, before starting an analysis, which algorithm will perform well on a given computational model. RESULTS: We present BCM, a toolkit for the Bayesian analysis of Computational Models using samplers...
October 21, 2016: BMC Systems Biology
J Mushanyu, F Nyabadza, G Muchatibaya, A G R Stewart
The abuse of drugs is now an epidemic globally whose control has been mainly through rehabilitation. The demand for drug abuse rehabilitation has not been matched with the available capacity resulting in limited placement of addicts into rehabilitation. In this paper, we model limited rehabilitation through the Hill function incorporated into a system of nonlinear ordinary differential equations. Not every member of the community is equally likely to embark on drug use, risk structure is included to help differentiate those more likely (high risk) to abuse drugs and those less likely (low risk) to abuse drugs...
October 20, 2016: Bulletin of Mathematical Biology
Ahmad Ainurofiq, Syaiful Choiri, Muhamad Ali Azhari, Chaterin Romauli Siagian, Bambang Budi Suryadi, Fea Prihapsara, Sholichah Rohmani
Purpose: The aim of this research was to formulate and develop an orally disintegrating tablet (ODT) that incorporated a MEL/β-CD complex, using a quality by design (QbD) approach to enhance solubility and drug release. Methods: Multiple regression linear analysis was conducted to develop the kneading process and ODT formulation. Mixing time and amount of solvent were used as independent variables in kneading process optimisation, while the superdisintegrants were used to obtain the desired formulation. Fourier transform infrared spectroscopy and differential scanning calorimetry were performed for complex characterization...
September 2016: Advanced Pharmaceutical Bulletin
Qie He, Junfeng Zhu, David Dingli, Jasmine Foo, Kevin Zox Leder
Over the past decade, several targeted therapies (e.g. imatinib, dasatinib, nilotinib) have been developed to treat Chronic Myeloid Leukemia (CML). Despite an initial response to therapy, drug resistance remains a problem for some CML patients. Recent studies have shown that resistance mutations that preexist treatment can be detected in a substantial number of patients, and that this may be associated with eventual treatment failure. One proposed method to extend treatment efficacy is to use a combination of multiple targeted therapies...
October 2016: PLoS Computational Biology
Gary C-W Shyi, Chao-Chih Wang
The composite face task is one of the most popular research paradigms for measuring holistic processing of upright faces. The exact mechanism underlying holistic processing remains elusive and controversial, and some studies have suggested that holistic processing may not be evenly distributed, in that the top-half of a face might induce stronger holistic processing than its bottom-half counterpart. In two experiments, we further examined the possibility of asymmetric holistic processing. Prior to Experiment 1, we confirmed that perceptual discriminability was equated between top and bottom face halves; we found no differences in performance between top and bottom face halves when they were presented individually...
2016: Frontiers in Psychology
H Behar, N Brenner, G Ariel, Y Louzoun
Cooperative interactions between individuals in a population and their stability properties are central to population dynamics and evolution. We introduce a generic class of nonlinear dynamical systems describing such interactions between producers and non-producers of a rapidly equilibrating common resource extracted from a finite environment. In the deterministic mean field approximation, fast-growing non-producers drive the entire population to extinction. However, the presence of arbitrarily small perturbations destabilizes this fixed point into a stochastic attractor where both phenotypes can survive...
October 18, 2016: Physical Biology
Sheng Luo, Jodie L Lutkenhaus, Hadi Nasrabadi
For over a century, the phase behavior of bulk fluids has been described as PVT (pressure-volume-temperature) three-dimensional properties, but it has become increasingly clear that the liquid-vapor phase behavior in confined geometries is significantly altered from the bulk. Efforts have been devoted to accessing confined phase transitions using sorption, molecular simulations and theoretical methods. However, a comprehensive picture of PVT relationships for confined hydrocarbons remains uncertain. Herein, we introduce d (confining pore diameter) as a fourth dimension, and we present PVT-d behavior of confined fluids in nanopores...
October 18, 2016: Langmuir: the ACS Journal of Surfaces and Colloids
Jun Hwa Lee, Byong Chul Yoo, Yun Hwan Kim, Sun-A Ahn, Seung-Gu Yeo, Jae Youl Cho, Kyung-Hee Kim, Seung Cheol Kim
BACKGROUND: A low-mass-ion discriminant equation (LOME) was constructed to investigate whether systematic low-mass-ion (LMI) profiling could be applied to ovarian cancer (OVC) screening. RESULTS: Matrix-assisted laser desorption/ionization-time of flight (MALDI-TOF) mass spectrometry was performed to obtain mass spectral data on metabolites detected as LMIs up to a mass-to-charge ratio (m/z) of 2500 for 1184 serum samples collected from healthy individuals and patients with OVC, other types of cancer, or several types of benign tumor...
2016: BioData Mining
Christopher R Watts, Shaheen N Awan, Youri Maryn
PURPOSE: This study aimed to investigate the relationship and reliability of cepstral peak prominence (CPP) measures from two acoustic software applications, Analysis of Dysphonia in Speech and Voice (ADSV) and Praat. METHODOLOGY: Flemish and English recordings of sustained vowels and connected speech samples were analyzed using ADSV and Praat. Correlational analyses and measures of the standard error of the estimate were applied to the vowel and connected speech data obtained from the two programs...
October 14, 2016: Journal of Voice: Official Journal of the Voice Foundation
Qishui Zhong, Fuli Zhong, Jun Cheng, Hui Li, Shouming Zhong
This paper presents a state of charge (SOC) estimation method based on fractional order sliding mode observer (SMO) for lithium-ion batteries. A fractional order RC equivalent circuit model (FORCECM) is firstly constructed to describe the charging and discharging dynamic characteristics of the battery. Then, based on the differential equations of the FORCECM, fractional order SMOs for SOC, polarization voltage and terminal voltage estimation are designed. After that, convergence of the proposed observers is analyzed by Lyapunov's stability theory method...
October 14, 2016: ISA Transactions
Chunguang Piao, Jin Oh Kim
This paper considers the influence of the different thickness of the piezoelectric discs used in assembly of an ultrasonic sandwich transducer. The transducer consists of two piezoelectric discs with different thickness between 0 and 2.0mm and with same diameter 28mm. Its vibration characteristics of the radial and axial motions were investigated theoretically and experimentally in axisymmetric vibration modes. Theoretically, the differential equations of piezoelectric motions were solved to produce characteristic equations that provided natural frequencies and mode shapes...
September 28, 2016: Ultrasonics
Marco A Amaral, Lucas Wardil, Matjaž Perc, Jafferson K L da Silva
In times of plenty expectations rise, just as in times of crisis they fall. This can be mathematically described as a win-stay-lose-shift strategy with dynamic aspiration levels, where individuals aspire to be as wealthy as their average neighbor. Here we investigate this model in the realm of evolutionary social dilemmas on the square lattice and scale-free networks. By using the master equation and Monte Carlo simulations, we find that cooperators coexist with defectors in the whole phase diagram, even at high temptations to defect...
September 2016: Physical Review. E
Jingchen Feng, Stuart A Sevier, Bin Huang, Dongya Jia, Herbert Levine
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated with a delayed process but instead use an estimated average delay time. In an effort to examine the validity of this approach, we study systems with significant delays by explicitly incorporating intermediate steps. We show that such explicit models often yield significantly different equilibrium distributions and transition times as compared to DDEs with deterministic delay values...
September 2016: Physical Review. E
Alicia Martı Nez-González, Gabriel F Calvo, Jose M Ayuso, Ignacio Ochoa, Luis J Fernández, Víctor M Pérez-García
This chapter explores the use of mathematical models as promising and powerful tools to understand the complexity of tumors and their, frequently, hypoxic environment. We focus on gliomas, which are primary brain tumors derived from glial cells, mainly astrocytes and/or oligodendrocytes. A variety of mathematical models, based on ordinary and/or partial differential equations, have been developed both at the micro and macroscopic levels. The aim here is to describe in a quantitative way key physiopathological mechanisms relevant in these types of malignancies and to suggest optimal therapeutical strategies...
2016: Advances in Experimental Medicine and Biology
Xianghong Zhang, Sanyi Tang, Robert A Cheke, Huaiping Zhu
Dengue fever has rapidly become the world's most common vector-borne viral disease. Use of endosymbiotic Wolbachia is an innovative technology to prevent vector mosquitoes from reproducing and so break the cycle of dengue transmission. However, strategies such as population eradication and replacement will only succeed if appropriate augmentations with Wolbachia-infected mosquitoes that take account of a variety of factors are carried out. Here, we describe the spread of Wolbachia in mosquito populations using an impulsive differential system with four state variables, incorporating the effects of cytoplasmic incompatibility and the augmentation of Wolbachia-infected mosquitoes with different sex ratios...
October 12, 2016: Bulletin of Mathematical Biology
Vera Schützhold, Jens Hahn, Katja Tummler, Edda Klipp
Lipid metabolism is essential for all major cell functions and has recently gained increasing attention in research and health studies. However, mathematical modeling by means of classical approaches such as stoichiometric networks and ordinary differential equation systems has not yet provided satisfactory insights, due to the complexity of lipid metabolism characterized by many different species with only slight differences and by promiscuous multifunctional enzymes. Here, we present an object-oriented stochastic model approach as a way to cope with the complex lipid metabolic network...
2016: Frontiers in Molecular Biosciences
Andrew Abboud, Qi Mi, Ava Puccio, David Okonkwo, Marius Buliga, Gregory Constantine, Yoram Vodovotz
Inflammation induced by traumatic brain injury (TBI) is a complex mediator of morbidity and mortality. We have previously demonstrated the utility of both data-driven and mechanistic models in settings of traumatic injury. We hypothesized that differential dynamic inflammation programs characterize TBI survivors vs. non-survivors, and sought to leverage computational modeling to derive novel insights into this life/death bifurcation. Thirteen inflammatory cytokines and chemokines were determined using Luminex™ in serial cerebrospinal fluid (CSF) samples from 31 TBI patients over 5 days...
2016: Frontiers in Pharmacology
Georg Schreckenbach
Solvation effects influence reaction equilibria by preferentially stabilizing reactants or products (differential solvation). We propose using simple electrostatic concepts to qualitatively interpret and understand these effects, applying the Born and Kirkwood-Onsager equations. Scenarios include, for charged species, (a) redox potentials, (b) different total absolute charges between reactants and products, (c) size differences between reactants and products. In addition, for neutral species, they are (d) differences in total dipole moment, and (e) size differences...
October 11, 2016: Chemistry: a European Journal
L L Neves, L H A Monteiro
Let a neuronal population be composed of an excitatory group interconnected to an inhibitory group. In the Wilson-Cowan model, the activity of each group of neurons is described by a first-order nonlinear differential equation. The source of the nonlinearity is the interaction between these two groups, which is represented by a sigmoidal function. Such a nonlinearity makes difficult theoretical works. Here, we analytically investigate the dynamics of a pair of coupled populations described by the Wilson-Cowan model by using a linear approximation...
2016: Computational Intelligence and Neuroscience
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