Mathematical models for the effects of hypertension and stress on kidney and their uncertainty.

Abstract:

:Determining the future state of individual patients, with regard to the susceptibility to life-threatening condition is a crucial problem in the public health. Chronic Kidney Disease (CKD) is a perilous disease, which is characterized by gradual loss of kidney function. This paper presents a set of mathematical models for CKD by applying both deterministic and stochastic approaches. Specifically, hypertension and stress are considered as the main causes of damaging and removing of nephrons thereby reducing the Glomerular Filtration Rate (GFR), which leads to irreparable damages to the kidney function and may result in renal failure, or even kidney loss. This paper analyzes the equilibria for both deterministic and stochastic models. In this regard, mathematical theorems related to stability and stochastic stability of the models are provided. The other important issue, which is discussed in the presented work, is the uncertainty problem for stochastic models. We have used simulations in MATLAB to calculate the uncertainty of the stochastic models. In addition, we have provided a framework for the future prediction of proposed models in specific cases. Finally, the models and the theoretical results are verified in application by applying them to the real clinical data.

journal_name

Math Biosci

journal_title

Mathematical biosciences

authors

Waezizadeh T,Mehrpooya A,Rezaeizadeh M,Yarahmadian S

doi

10.1016/j.mbs.2018.08.013

subject

Has Abstract

pub_date

2018-11-01 00:00:00

pages

77-95

eissn

0025-5564

issn

1879-3134

pii

S0025-5564(17)30533-3

journal_volume

305

pub_type

杂志文章
  • Analysis of logistic growth models.

    abstract::A variety of growth curves have been developed to model both unpredated, intraspecific population dynamics and more general biological growth. Most predictive models are shown to be based on variations of the classical Verhulst logistic growth equation. We review and compare several such models and analyse properties ...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/s0025-5564(02)00096-2

    authors: Tsoularis A,Wallace J

    更新日期:2002-07-01 00:00:00

  • Weber's law modeled by the mathematical description of a beam balance.

    abstract::A beam balance is analyzed as a model that describes Weber's law. The mathematical derivations of the torques on a beam balance produce a description that is strictly compatible with that law. The natural relationship of the beam balance model to Weber's law provides for an intuitive understanding of the relationship ...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(94)90083-3

    authors: Lanzara RG

    更新日期:1994-07-01 00:00:00

  • Spreading speeds as slowest wave speeds for cooperative systems.

    abstract::It is well known that in many scalar models for the spread of a fitter phenotype or species into the territory of a less fit one, the asymptotic spreading speed can be characterized as the lowest speed of a suitable family of traveling waves of the model. Despite a general belief that multi-species (vector) models hav...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2005.03.008

    authors: Li B,Weinberger HF,Lewis MA

    更新日期:2005-07-01 00:00:00

  • Optimal input design: case study of the metabolic process.

    abstract::An optimal input of nutrients into the metabolic process of the individual subject so as to effect desired therapeutic results is particularly important for the critically ill. A patient-related, individualized nutrients optimization procedure is proposed here. The procedure is applicable to any time-invariant and det...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(89)90004-7

    authors: Giladi R,Sideman S

    更新日期:1989-12-01 00:00:00

  • Numerical solution of inward solidification of a dilute ternary solution towards a semi-permeable spherical cell.

    abstract::Modeling a cell's response to encroaching ice has informed the development of cryopreservation protocols for four decades. It has been well documented that knowledge of the cellular state as a function of media and cooling rate faciliate informed cryopreservation protocol design and explain mechanisms of damage. Howev...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2019.108240

    authors: Anderson DM,Benson JD,Kearsley AJ

    更新日期:2019-10-01 00:00:00

  • Automatic learning of mortality in a CPN model of the systemic inflammatory response syndrome.

    abstract::The aim of this paper is to apply machine learning as a method to refine a manually constructed CPN for the assessment of the severity of the systemic inflammatory response syndrome (SIRS).The goal of tuning the CPN is to create a scoring system that uses only objective data, compares favourably with other severity-sc...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2016.11.004

    authors: Ward L,Paul M,Andreassen S

    更新日期:2017-02-01 00:00:00

  • Maximum sustainable yield with continuous age structure and density-dependent recruitment.

    abstract::The problem addressed is that of finding the harvesting policy that will maximize the yield and maintain a given population in a steady state. It is assumed that the equations describing the evolution of the population and the yield are linear but that the equation describing reproduction is nonlinear (density depende...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(94)90039-6

    authors: Dacorogna B,Weissbaum F,Arditi R

    更新日期:1994-03-01 00:00:00

  • Effect of Heterogeneous Oxygen Delivery on the Oxygen Distribution in Skeletal Muscle.

    abstract::Calculations of the oxygen distribution in resting and contracting skeletal muscle are presented, based on a mathematical model and experimental data obtained on the hamster cremaster muscle [Klitzman et al., Microvasc. Res. 25:108-131 (1983)]. The model considers a slab of tissue penetrated by a regular square array ...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(86)90164-1

    authors: Popel AS,Charny CK,Dvinsky AS

    更新日期:1986-09-01 00:00:00

  • Scaffold-mediated nucleation of protein signaling complexes: elementary principles.

    abstract::Proteins with multiple binding sites play important roles in cell signaling systems by nucleating protein complexes in which, for example, enzymes and substrates are co-localized. Proteins that specialize in this function are called by a variety names, including adapter, linker and scaffold. Scaffold-mediated nucleati...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2011.06.003

    authors: Yang J,Hlavacek WS

    更新日期:2011-08-01 00:00:00

  • A differential-delay model of pasture accumulation and loss in controlled grazing systems.

    abstract::A grazing population dynamics model is proposed where organisms in a grazed population have a fixed life span. The motivating context is that of ruminants grazing grass-dominant pasture. The model takes the form of a differential-delay equation in which the rate of loss of pasture due to senescence at some time depend...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(94)90031-0

    authors: Woodward SJ,Wake GC

    更新日期:1994-05-01 00:00:00

  • Age-density dependent population dispersal in RN.

    abstract::We discuss an N-dimensional model for diffusion of age dependent populations. Let rho(x, t, a) be the population density at time t, age a and spatial position x, and let u(x, t) = [formula: see text] rho(x, t, a) da be the total population at t and x. The directed dispersal model to be discussed, with diffusion depend...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/s0025-5564(97)10014-1

    authors: Hernández GE

    更新日期:1998-04-01 00:00:00

  • Stochastic differential equation models for spatially distributed neurons and propagation of chaos for interacting systems.

    abstract::Distribution or nuclear space-valued stochastic differential equations (SDEs) (diffusions as well as discontinuous equations) are discussed as stochastic models for the behavior of voltage potentials of spatially distributed neurons. A propagation of chaos result is obtained for an interacting system of Hilbert space-...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(92)90024-q

    authors: Kallianpur G

    更新日期:1992-12-01 00:00:00

  • Model parameter uncertainties in a dual-species biofilm competition model affect ecological output parameters much stronger than morphological ones.

    abstract::Bacterial biofilms are complex microbial depositions on immersed interfaces that form wherever the environmental conditions sustain microbial growth. Despite their name, biofilms can develop in highly irregular structures. Recently several mathematical concepts have been introduced to model these spatially structured ...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2011.05.006

    authors: Muhammad N,Eberl HJ

    更新日期:2011-09-01 00:00:00

  • Intrinsic coherence resonance in excitable membrane patches.

    abstract::The influence of intrinsic channel noise on the spiking activity of excitable membrane patches is studied by use of a stochastic generalization of the Hodgkin-Huxley model. Internal noise stemming from the stochastic dynamics of individual ion channels does affect the electric properties of the cell-membrane patches. ...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2006.08.024

    authors: Schmid G,Hänggi P

    更新日期:2007-06-01 00:00:00

  • New statistical tools for analyzing the structure of animal groups.

    abstract::The statistical characterization of the spatial structure of large animal groups has been very limited so far, mainly due to a lack of empirical data, especially in three dimensions (3D). Here we focus on the case of large flocks of starlings (Sturnus vulgaris) in the field. We reconstruct the 3D positions of individu...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2008.05.006

    authors: Cavagna A,Cimarelli A,Giardina I,Orlandi A,Parisi G,Procaccini A,Santagati R,Stefanini F

    更新日期:2008-07-01 00:00:00

  • Analyzing gene expression time-courses based on multi-resolution shape mixture model.

    abstract:OBJECTIVE:Biological processes actually are a dynamic molecular process over time. Time course gene expression experiments provide opportunities to explore patterns of gene expression change over a time and understand the dynamic behavior of gene expression, which is crucial for study on development and progression of ...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2016.08.012

    authors: Li Y,He Y,Zhang Y

    更新日期:2016-11-01 00:00:00

  • Spectra-based estimates of certain time-domain parameters of a bivariate stationary-point process.

    abstract::We consider estimates of certain time-domain parameters of a bivariate stationary-point process based on modified periodogram statistics. These estimates are shown to be asymptotically normal under regularity conditions. In the computations of the estimates, the advantage of using the FFT algorithm is demonstrated. Th...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(91)90061-m

    authors: Rigas AG

    更新日期:1991-05-01 00:00:00

  • Strategies for representing metabolic pathways within biochemical systems theory: reversible pathways.

    abstract::The search for systematic methods to deal with the integrated behavior of complex biochemical systems has over the past two decades led to the proposal of several theories of biochemical systems. Among the most promising is biochemical systems theory (BST). Recent comparisons of this theory with several others that ha...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章,评审

    doi:10.1016/0025-5564(89)90066-7

    authors: Sorribas A,Savageau MA

    更新日期:1989-06-01 00:00:00

  • A comprehensive mathematical framework for modeling intestinal smooth muscle cell contraction with applications to intestinal edema.

    abstract::The contraction of intestinal smooth muscle cells (ISMCs) involves many coordinated biochemical and mechanical processes. In this work, we present a framework for modeling ISMC contractility that begins with chemical models of calcium dynamics, continues with myosin light chain phosphorylation and force generation, an...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2014.12.009

    authors: Young J,Ozisik S,Riviere B,Shamim M

    更新日期:2015-04-01 00:00:00

  • A nonlinear numerical model of percutaneous drug absorption.

    abstract::A nonlinear mathematical model developed by Chandrasekaran et al. is examined to monitor pharmacokinetic profiles in percutaneous drug absorption and is addressed to several associated problems that could occur in the data analysis of in vitro experiments. The formulation of the model gives rise to a nonlinear partial...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(92)90054-z

    authors: Kubota K,Twizell EH

    更新日期:1992-03-01 00:00:00

  • Metabolic isotopomer labeling systems. Part III: path tracing.

    abstract::Isotope labeling systems (ILSs) are sets of balance equations that quantitatively describe the distribution of isotopic tracers in metabolic networks. The solution of ILSs, i.e., the calculation of isotopic labeling distributions (mostly in steady state) is the fundamental computational step of (13)C metabolic flux an...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2013.02.012

    authors: Wiechert W,Nöh K,Weitzel M

    更新日期:2013-07-01 00:00:00

  • Patient-specific modeling of the neuroendocrine HPA-axis and its relation to depression: Ultradian and circadian oscillations.

    abstract::In the Western world approximately 10% of the population experience severe depression at least once in their lifetime and many more experience a mild form of depression. Depression has been associated with malfunctions in the hypothalamus-pituitary-adrenal (HPA) axis. We suggest a novel mechanistic non-linear model ca...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2014.07.013

    authors: Gudmand-Hoeyer J,Timmermann S,Ottesen JT

    更新日期:2014-11-01 00:00:00

  • Formulating spread of species with habitat dependent growth and dispersal in heterogeneous landscapes.

    abstract::Habitat heterogeneity can have profound effects on the spreading dynamics of invasive species. Using integro-difference equations, we investigate the spreading dynamics in a one-dimensional heterogeneous landscape comprising alternating favourable and unfavourable habitat patches or randomly generated habitat patches ...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2016.02.013

    authors: Ramanantoanina A,Hui C

    更新日期:2016-05-01 00:00:00

  • Chemotherapy for tumors: an analysis of the dynamics and a study of quadratic and linear optimal controls.

    abstract::We investigate a mathematical model of tumor-immune interactions with chemotherapy, and strategies for optimally administering treatment. In this paper we analyze the dynamics of this model, characterize the optimal controls related to drug therapy, and discuss numerical results of the optimal strategies. The form of ...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2006.05.003

    authors: de Pillis LG,Gu W,Fister KR,Head T,Maples K,Murugan A,Neal T,Yoshida K

    更新日期:2007-09-01 00:00:00

  • Effective rate models for the analysis of transport-dependent biosensor data.

    abstract::Optical biosensors, including the BIACORE, provide an increasingly popular method for determining reaction rates of biomolecules. In a flow chamber, with one reactant immobilized on a chip on the sensor surface, a solution containing the other reactant (the analyte) flows through the chamber. The time course of bindin...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/s0025-5564(99)00023-1

    authors: Mason T,Pineda AR,Wofsy C,Goldstein B

    更新日期:1999-07-01 00:00:00

  • Comparison of mathematical frameworks for modeling erythropoiesis in the context of malaria infection.

    abstract::Malaria is an infectious disease present all around the globe and responsible for half a million deaths per year. A within-host model of this infection requires a framework capable of properly approximating not only the blood stage of the infection but also the erythropoietic process that is in charge of overcoming th...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2015.08.020

    authors: Fonseca LL,Voit EO

    更新日期:2015-12-01 00:00:00

  • Global dynamics of an SEIR epidemic model with saturating contact rate.

    abstract::Heesterbeek and Metz [J. Math. Biol. 31 (1993) 529] derived an expression for the saturating contact rate of individual contacts in an epidemiological model. In this paper, the SEIR model with this saturating contact rate is studied. The basic reproduction number R0 is proved to be a sharp threshold which completely d...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/s0025-5564(03)00087-7

    authors: Zhang J,Ma Z

    更新日期:2003-09-01 00:00:00

  • Optimal control of tumor size used to maximize survival time when cells are resistant to chemotherapy.

    abstract::The high failure rates encountered in the chemotherapy of some cancers suggest that drug resistance is a common phenomenon. In the current study, the tumor burden during therapy is used to slow the growth of the drug-resistant cells, thereby maximizing the survival time of the host. Three types of tumor growth model a...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(92)90038-x

    authors: Martin RB,Fisher ME,Minchin RF,Teo KL

    更新日期:1992-07-01 00:00:00

  • Lotka-Volterra representation of general nonlinear systems.

    abstract::In this article we elaborate on the structure of the generalized Lotka-Volterra (GLV) form for nonlinear differential equations. We discuss here the algebraic properties of the GLV family, such as the invariance under quasimonomial transformations and the underlying structure of classes of equivalence. Each class poss...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/s0025-5564(96)00131-9

    authors: Hernández-Bermejo B,Fairén V

    更新日期:1997-02-01 00:00:00

  • Kinetics of the formation of a protein corona around nanoparticles.

    abstract::Interaction of metal or oxide nanoparticles (NPs) with biological soft matter is one of the central phenomena in basic and applied biology-oriented nanoscience. Often, this interaction includes adsorption of suspended proteins on the NP surface, resulting in the formation of the protein corona around NPs. Structurally...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2016.09.018

    authors: Zhdanov VP,Cho NJ

    更新日期:2016-12-01 00:00:00