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Differential equation

Laurence A Hutton-Smith, Eamonn A Gaffney, Helen M Byrne, Philip K Maini, Kapil Gadkar, Norman Alan Mazer
Intravitreally (IVT) injected macromolecules for the treatment of age-related macular degeneration must permeate through the inner limiting membrane (ILM) into the retina and through the retinal pigment epithelium (RPE) to enter the choroid. A quantitative understanding of intraocular transport mechanisms, elimination pathways and the effect of molecular size, is currently incomplete. We present a semi-mechanistic, 3-compartment (retina, vitreous and aqueous) pharmacokinetic (PK) model, expressed using linear ordinary differential equations (ODEs), to describe the molecular concentrations following a single IVT injection...
June 20, 2017: Molecular Pharmaceutics
M I Betti, L M Wahl, M Zamir
A system of partial differential equations is derived as a model for the dynamics of a honey bee colony with a continuous age distribution, and the system is then extended to include the effects of a simplified infectious disease. In the disease-free case, we analytically derive the equilibrium age distribution within the colony and propose a novel approach for determining the global asymptotic stability of a reduced model. Furthermore, we present a method for determining the basic reproduction number [Formula: see text] of the infection; the method can be applied to other age-structured disease models with interacting susceptible classes...
June 19, 2017: Bulletin of Mathematical Biology
O K Richard, D Codron, K B Hagen, K-H Südekum, M Clauss
Carnivores do not vary markedly in their digestive efficiency for protein and fat, but whether they resemble other trophic guilds (omnivores and herbivores) in this respect has not been evaluated. We collated data on apparent crude protein (CP) and crude fat (ether extracts, EE) digestibility in 157 mammal species, applying the Lucas principle of regressing digestible nutrient content against nutrient content, where the slope of the regression equation represents the true digestibility and the intercept the metabolic losses per unit dry matter intake...
June 2017: Journal of Animal Physiology and Animal Nutrition
Michael Brenner, Sakineh Esmaeili Mohsen Abadi, Ramin Balouchzadeh, H Felix Lee, Hoo Sang Ko, Michael Johns, Nehal Malik, Joshua J Lee, Guim Kwon
Destruction of the insulin-producing β-cells is the key determinant of diabetes mellitus regardless of their types. Due to their anatomical location within the islets of Langerhans scattered throughout the pancreas, it is difficult to monitor β-cell function and mass clinically. To this end, we propose to use a mathematical model of glucose-insulin homeostasis to estimate insulin secretion, glucose uptake by tissues, and hepatic handling of glucose. We applied the mathematical model by Lombarte et al. (2013) to compare various rate constants representing glucose-insulin homeostasis between lean (11% fat)- and high fat diet (HFD; 45% fat)-fed mice...
June 2017: Heliyon
S Visser, R Nicks, O Faugeras, S Coombes
The Nunez model for the generation of electroencephalogram (EEG) signals is naturally described as a neural field model on a sphere with space-dependent delays. For simplicity, dynamical realisations of this model either as a damped wave equation or an integro-differential equation, have typically been studied in idealised one dimensional or planar settings. Here we revisit the original Nunez model to specifically address the role of spherical topology on spatio-temporal pattern generation. We do this using a mixture of Turing instability analysis, symmetric bifurcation theory, centre manifold reduction and direct simulations with a bespoke numerical scheme...
June 15, 2017: Physica D. Nonlinear Phenomena
Virgilio Vázquez, Ignacio Barradas
In this paper we propose and discuss a simple two-dimensional model describing the interaction between two species: a plant population that gets pollinated by an insect population. The plants attract the insects deceiving them and not delivering any reward. We are interested in analysing the effect of learning by the insect population due to unsuccessfully visiting the deceiving plants. We are especially interested in three elements: conditions for the simultaneous coexistence of both species, their extinction as a function of the biological cost of the deceptiveness for the pollinator, and the appearance of oscillations in the dynamics...
December 2017: Journal of Biological Dynamics
Christopher J Rhodes, John Wharton, Pavandeep Ghataorhe, Geoffrey Watson, Barbara Girerd, Luke S Howard, J Simon R Gibbs, Robin Condliffe, Charles A Elliot, David G Kiely, Gerald Simonneau, David Montani, Olivier Sitbon, Henning Gall, Ralph T Schermuly, H Ardeschir Ghofrani, Allan Lawrie, Marc Humbert, Martin R Wilkins
BACKGROUND: Idiopathic and heritable pulmonary arterial hypertension form a rare but molecularly heterogeneous disease group. We aimed to measure and validate differences in plasma concentrations of proteins that are associated with survival in patients with idiopathic or heritable pulmonary arterial hypertension to improve risk stratification. METHODS: In this observational cohort study, we enrolled patients with idiopathic or heritable pulmonary arterial hypertension from London (UK; cohorts 1 and 2), Giessen (Germany; cohort 3), and Paris (France; cohort 4)...
June 14, 2017: Lancet Respiratory Medicine
Radu Mihaila, Dipali Ruhela, Edward Keough, Elena Cherkaev, Silvia Chang, Beverly Galinski, René Bartz, Duncan Brown, Bonnie Howell, James J Cunningham
Lipid nanoparticles (LNPs) have been used to successfully deliver small interfering RNAs (siRNAs) to target cells in both preclinical and clinical studies and currently are the leading systems for in vivo delivery. Here, we propose the use of an ordinary differential equation (ODE)-based model as a tool for optimizing LNP-mediated delivery of siRNAs. As a first step, we have used a combination of experimental and computational approaches to develop and validate a mathematical model that captures the critical features for efficient siRNA-LNP delivery in vitro...
June 16, 2017: Molecular Therapy. Nucleic Acids
Daniel D Seaton
Transcriptional regulatory circuits are often complex, consisting of many components and regulatory interactions. Mathematical modeling is an important tool for understanding the behavior of these circuits, and identifying gaps in our understanding of gene regulation. Ordinary differential equations (ODEs) are a commonly used formalism for constructing mathematical models of complex regulatory networks. Here, I outline the steps involved in developing, parameterizing, and testing an ODE model of a gene regulatory network...
2017: Methods in Molecular Biology
Julia Hippisley-Cox, Carol Coupland
Objective To develop and externally validate risk prediction equations to estimate absolute and conditional survival in patients with colorectal cancer. Design Cohort study.Setting General practices in England providing data for the QResearch database linked to the national cancer registry.Participants 44 145 patients aged 15-99 with colorectal cancer from 947 practices to derive the equations. The equations were validated in 15 214 patients with colorectal cancer from 305 different QResearch practices and 437 821 patients with colorectal cancer from the national cancer registry...
June 15, 2017: BMJ: British Medical Journal
Amit K Chattopadhyay, Elias C Aifantis
The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths...
May 2017: Physical Review. E
Claudia Cianci, Stephen Smith, Ramon Grima
Conventional master equation approaches approximate the diffusion of molecules in continuum space by the process of particles hopping on a spatial lattice. The hopping probability from one voxel (spatial lattice point) to its neighbor is usually considered to be constant throughout space. Such an assumption is only consistent with pointlike molecules and thus neglects volume-exclusion effects due to finite particle size. A few studies have attempted to introduce volume-exclusion effects by choosing the hopping probability from one voxel to a neighboring one to be a linear function of the number density...
May 2017: Physical Review. E
George Backus, Michel Rieutord
Inertial modes are the eigenmodes of contained rotating fluids restored by the Coriolis force. When the fluid is incompressible, inviscid, and contained in a rigid container, these modes satisfy Poincaré's equation that has the peculiarity of being hyperbolic with boundary conditions. Inertial modes are, therefore, solutions of an ill-posed boundary-value problem. In this paper, we investigate the mathematical side of this problem. We first show that the Poincaré problem can be formulated in the Hilbert space of square-integrable functions, with no hypothesis on the continuity or the differentiability of velocity fields...
May 2017: Physical Review. E
Christopher Griffin, Andrew Belmonte
We study the problem of stabilized coexistence in a three-species public goods game in which each species simultaneously contributes to one public good while freeloading off another public good ("cheating"). The proportional population growth is governed by an appropriately modified replicator equation, depending on the returns from the public goods and the cost. We show that the replicator dynamic has at most one interior unstable fixed point and that the population becomes dominated by a single species. We then show that by applying an externally imposed penalty, or "tax" on success can stabilize the interior fixed point, allowing for the symbiotic coexistence of all species...
May 2017: Physical Review. E
Xinxian Shao, Bruce Levin, Ilya Nemenman
There is an abundance of information about the genetic basis, physiological and molecular mechanisms of bacterial pathogenesis. In contrast, relatively little is known about population dynamic processes, by which bacteria colonize hosts and invade tissues and cells and thereby cause disease. In an article published in 1978, Moxon and Murphy presented evidence that, when inoculated intranasally with a mixture streptomycin sensitive and resistant (Sm (S) and Sm (R) ) and otherwise isogenic strains of Haemophilus influenzae type b (Hib), neonatal rats develop a bacteremic infection that often is dominated by only one strain, Sm (S) or Sm (R) ...
June 15, 2017: Physical Biology
Benjamin Engelhardt, Maik Kschischo, Holger Fröhlich
Ordinary differential equations (ODEs) are a popular approach to quantitatively model molecular networks based on biological knowledge. However, such knowledge is typically restricted. Wrongly modelled biological mechanisms as well as relevant external influence factors that are not included into the model are likely to manifest in major discrepancies between model predictions and experimental data. Finding the exact reasons for such observed discrepancies can be quite challenging in practice. In order to address this issue, we suggest a Bayesian approach to estimate hidden influences in ODE-based models...
June 2017: Journal of the Royal Society, Interface
Stephen Smith, Claudia Cianci, Ramon Grima
It is now well established that cell interiors are significantly crowded by macromolecules, which impede diffusion and enhance binding rates. However, it is not fully appreciated that levels of crowding are heterogeneous, and can vary substantially between subcellular regions. In this article, starting from a microscopic model, we derive coupled nonlinear partial differential equations for the concentrations of two populations of large and small spherical particles with steric volume exclusion. By performing an expansion in the ratio of the particle sizes, we find that the diffusion of a small particle in the presence of large particles obeys an advection-diffusion equation, with a reduced diffusion coefficient and a velocity directed towards less crowded regions...
June 2017: Journal of the Royal Society, Interface
Jie Hou, Jianji Dong, Xinliang Zhang
Systems of ordinary differential equations (SODEs) are crucial for describing the dynamic behaviors in various systems such as modern control systems which require observability and controllability. In this Letter, we propose and experimentally demonstrate an all-optical SODE solver based on the silicon-on-insulator platform. We use an add/drop microring resonator to construct two different ordinary differential equations (ODEs) and then introduce two external feedback waveguides to realize the coupling between these ODEs, thus forming the SODE solver...
June 15, 2017: Optics Letters
Getachew Teshome Tilahun, Oluwole Daniel Makinde, David Malonza
We propose and analyse a nonlinear mathematical model for the transmission dynamics of pneumonia disease in a population of varying size. The deterministic compartmental model is studied using stability theory of differential equations. The effective reproduction number is obtained and also the asymptotic stability conditions for the disease free and as well as for the endemic equilibria are established. The possibility of bifurcation of the model and the sensitivity indices of the basic reproduction number to the key parameters are determined...
June 14, 2017: Journal of Biological Dynamics
Ren Bai, Jun-Tao Wang, Ye Deng, Ji-Zheng He, Kai Feng, Li-Mei Zhang
Paddy rice fields occupy broad agricultural area in China and cover diverse soil types. Microbial community in paddy soils is of great interest since many microorganisms are involved in soil functional processes. In the present study, Illumina Mi-Seq sequencing and functional gene array (GeoChip 4.2) techniques were combined to investigate soil microbial communities and functional gene patterns across the three soil types including an Inceptisol (Binhai), an Oxisol (Leizhou), and an Ultisol (Taoyuan) along four profile depths (up to 70 cm in depth) in mesocosm incubation columns...
2017: Frontiers in Microbiology
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