Abstract：
:The mammalian kidney consumes a large amount of energy to support the reabsorptive work it needs to excrete metabolic wastes and to maintain homeostasis. Part of that energy is supplied via the metabolism of glucose. To gain insights into the transport and metabolic processes in the kidney, we have developed a detailed model of the renal medulla of the rat kidney. The model represents water and solute flows, transmural fluxes, and biochemical reactions in the luminal fluid of the nephrons and vessels. In particular, the model simulates the metabolism of oxygen and glucose. Using that model, we have identified parameters concerning glucose transport and basal metabolism that yield predicted blood glucose concentrations that are consistent with experimental measurements. The model predicts substantial axial gradients in blood glucose levels along various medullary structures. Furthermore, the model predicts that in the inner medulla, owing to the relatively limited blood flow and low tissue oxygen tension, anaerobic metabolism of glucose dominates.
journal_name
Bull Math Bioljournal_title
Bulletin of mathematical biologyauthors
Chen Y,Fry BC,Layton ATdoi
10.1007/s11538-016-0188-7subject
Has Abstractpub_date
2016-06-01 00:00:00pages
1318-36issue
6eissn
0092-8240issn
1522-9602pii
10.1007/s11538-016-0188-7journal_volume
78pub_type
杂志文章abstract：:The asymptotes and transition points of the net CO2 assimilation (A/Ci) rate curves of the steady-state Farquhar-von Caemmerer-Berry (FvCB) model for leaf photosynthesis of C3 plants are examined in a theoretical study, which begins from the exploration of the standard equations of hyperbolae after rotating the coordi...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-019-00676-z
更新日期：2019-12-23 00:00:00
abstract：:Collective dynamics of migrating cell populations drive key processes in tissue formation and maintenance under normal and diseased conditions. Collective cell behavior at the tissue level is typically characterized by considering cell density patterns such as clusters and moving cell fronts. However, there are also i...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-015-0079-3
更新日期：2015-04-01 00:00:00
abstract：:We study the global stability of a class of models for in-vivo virus dynamics that take into account the Cytotoxic T Lymphocyte immune response and display antigenic variation. This class includes a number of models that have been extensively used to model HIV dynamics. We show that models in this class are globally a...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-010-9543-2
更新日期：2011-03-01 00:00:00
abstract：:It has been postulated that fibroblast growth factor (FGF) treatment of cultured limb bud mesenchyme cells reinforces the lateral inhibitory effect, but the cells also show accelerated pattern appearance. In the present study, we analyze how a small change in a specific parameter affects the speed of pattern appearanc...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1016/j.bulm.2003.09.009
更新日期：2004-07-01 00:00:00
abstract：:We explore the dynamics of invasive weeds by partial differential equation (PDE) modelling and applying dynamical system and phase portrait techniques. We begin by applying the method of characteristics to a preexisting PDE model of the spreading of T. fluminensis, an invasive weed which has been responsible for nativ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-020-00825-9
更新日期：2021-01-07 00:00:00
abstract：:We present an improved mathematical model of population dynamics of mosquito-borne disease transmission. Our model considers the effect of mosquito repellent use and the mosquito's behavior or attraction to the infected human, which cause mosquitoes' biased distribution around the human population. Our analysis of the...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-019-00666-1
更新日期：2019-12-01 00:00:00
abstract：:This paper develops mathematical theory to determine the representativeness of clone libraries for various models, defined below in the text. In particular, the means and variances of fragment lengths and the mean of the length of a randomly selected fragment are determined, as well as the probability of the event tha...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1006/bulm.2001.0251
更新日期：2001-09-01 00:00:00
abstract：:We describe and analyze a periodically-forced difference equation model for malaria in mosquitoes that captures the effects of seasonality and allows the mosquitoes to feed on a heterogeneous population of hosts. We numerically show the existence of a unique globally asymptotically stable periodic orbit and calculate ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-011-9710-0
更新日期：2012-05-01 00:00:00
abstract：:Over the last 25 years, reforms in undergraduate biology education have transformed the way biology is taught at many institutions of higher education. This has been fueled in part by a burgeoning discipline-based education research community, which has advocated for evidence-based instructional practices based on fin...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-020-00739-6
更新日期：2020-05-13 00:00:00
abstract：:A stochastic analog to a deterministic model describing subpopulation emergence in heterogeneous tumors is developed. The resulting system is described by the Fokker-Planck or forward Kolmogorov equation. A finite element approach for the numerical solution to this equation is described. Four biological and clinical s...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/BF02459658
更新日期：1989-01-01 00:00:00
abstract：:We study crossflow filtration mechanisms in suspension-feeding fishes using computational fluid dynamics to model fluid flow and food particle movement in the vicinity of the gill rakers. During industrial and biological crossflow filtration, particles are retained when they remain suspended in the mainstream flow tra...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-011-9709-6
更新日期：2012-04-01 00:00:00
abstract：:A staged-progression HIV model is formulated and used to investigate the potential impact of an imperfect vaccine. The vaccine is assumed to have several desirable characteristics such as protecting against infection, causing bypass of the primary infection stage, and offering a disease-altering therapeutic effect (so...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-006-9095-7
更新日期：2006-11-01 00:00:00
abstract：:This paper investigates the dynamics of biomass in a marine ecosystem. A stochastic process is defined in which organisms undergo jumps in body size as they catch and eat smaller organisms. Using a systematic expansion of the master equation, we derive a deterministic equation for the macroscopic dynamics, which we ca...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-009-9496-5
更新日期：2010-08-01 00:00:00
abstract：:Although imatinib is an effective treatment for chronic myelogenous leukemia (CML), and nearly all patients treated with imatinib attain some form of remission, imatinib does not completely eliminate leukemia. Moreover, if the imatinib treatment is stopped, most patients eventually relapse (Cortes et al. in Clin. Canc...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-010-9553-0
更新日期：2011-05-01 00:00:00
abstract：:We study Eigen's quasispecies model in the asymptotic regime where the length of the genotypes goes to [Formula: see text] and the mutation probability goes to 0. A limiting infinite system of differential equations is obtained. We prove convergence of trajectories, as well as convergence of the equilibrium solutions....
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-018-0420-8
更新日期：2018-07-01 00:00:00
abstract：:This study investigates fluid flow and elastic deformation in tissues that are drained by the primary lymphatic system. A model is formulated based on the Rossi hypothesis that states that the primary lymphatic valves, which are formed by overlapping endothelial cells around the circumferential lining of lymphatic cap...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-015-0078-4
更新日期：2015-06-01 00:00:00
abstract：:The mechanical behavior of the actin cytoskeleton has previously been investigated using both experimental and computational techniques. However, these investigations have not elucidated the role the cytoskeleton plays in the compression resistance of cells. The present study combines experimental compression techniqu...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-013-9812-y
更新日期：2013-08-01 00:00:00
abstract：:In this work, we show that a one-dimensional model of the blood flow across the lungs can reproduce the evolution of a bolus versus the time. Solving the differential equation governing the bolus concentration in the framework of this model, we determine the solution which fulfills Gaussian initial boundary conditions...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/BF02458387
更新日期：1996-11-01 00:00:00
abstract：:Small populations at risk of extinction due to threshold or competitive exclusion have a vested interest in rapid growth. Taking chance of survival into account for diploid populations, Fisher's theorem predicts a sex ratio favoring females under certain circumstances. Theoretical consideration of competitive exclusio...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-009-9455-1
更新日期：2010-01-01 00:00:00
abstract：:A stochastic SIRS epidemic model with nonlinear incidence rate and varying population size is formulated to investigate the effect of stochastic environmental variability on inter-pandemic transmission dynamics of influenza A. Sufficient conditions for extinction and persistence of the disease are established. In the ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-015-0101-9
更新日期：2015-09-01 00:00:00
abstract：:We develop the mathematical machinery for the construction of an algebraic-combinatorial model using Petri nets to construct an oriented matroid representation of biochemical pathways. For demonstration purposes, we use a model metabolic pathway example from the literature to derive a general biochemical reaction netw...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1006/bulm.2001.0263
更新日期：2001-11-01 00:00:00
abstract：:This work aims to examine the global behavior of a Gause type predator-prey model considering two aspects: (i) the functional response is Holling type III and, (ii) the prey growth is affected by the Allee effect. We prove the origin of the system is an attractor equilibrium point for all parameter values. It has also...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-010-9577-5
更新日期：2011-06-01 00:00:00
abstract：:Many neurons in mammalian sensory systems exhibit On and Off responses when given appropriate excitatory and inhibitory stimuli. In some instances, such neurons can also exhibit a Mixed response where diminished On and Off responses are both present. In this manuscript, we present a simple single cell model for these ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-008-9358-6
更新日期：2009-01-01 00:00:00
abstract：:Human rabies is one of the major public health problems in China with an average of 1977 cases per year. It is estimated that 95% of these human rabies cases are due to dog bites. In recent years, the number of wildlife-associated human rabies cases has increased, particularly in the southeast and northeast regions of...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-018-00537-1
更新日期：2019-04-01 00:00:00
abstract：:In this paper we develop and extend a previous model of cell deformations, initially proposed to describe the dynamical behaviour of round-shaped cells such as keratinocytes or leukocytes, in order to take into account cell pseudopodial dynamics with large amplitude membrane deformations such as those observed in fibr...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1016/j.bulm.2003.11.004
更新日期：2004-09-01 00:00:00
abstract：:Pseudomonas aeruginosa is a Gram-negative bacterium that is responsible for a wide range of infections in humans. Colonies employ quorum sensing (QS) to coordinate gene expression, including for virulence factors, swarming motility and complex social traits. The QS signalling system of P. aeruginosa is known to involv...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-017-0288-z
更新日期：2017-06-01 00:00:00
abstract：:We describe a new model for laser-induced retinal damage. Our treatment is prompted by the failure of the traditional approach to accurately describe the image size dependence of laser-induced retinal injuries and by a recently reported study which demonstrated that laser injuries to the retina might not appear for up...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1016/S0092-8240(03)00028-4
更新日期：2003-07-01 00:00:00
abstract：:The tumour suppressor gene, p53, plays an important role in tumour development. Under low levels of oxygen (hypoxia), cells expressing wild-type p53 undergo programmed cell death (apoptosis), whereas cells expressing mutations in the p53 gene may survive and express angiogenic growth factors that stimulate tumour vasc...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1006/bulm.2000.0210
更新日期：2001-01-01 00:00:00
abstract：:The paper reviews the work of Kermack and McKendrick on the development of simple mathematical models of the transmission dynamics of viral and bacterial infectious agents within population of hosts. The focus of attention is centred on the notion of a threshold density of susceptible hosts to trigger an epidemic and ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章,评审
doi：10.1016/s0092-8240(05)80039-4
更新日期：1991-01-01 00:00:00
abstract：:Identifiability concerns finding which unknown parameters of a model can be estimated, uniquely or otherwise, from given input-output data. If some subset of the parameters of a model cannot be determined given input-output data, then we say the model is unidentifiable. In this work, we study linear compartment models...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-015-0098-0
更新日期：2015-08-01 00:00:00
