Abstract：
:Mathematical models are essential tools to study how the cardiovascular system maintains homeostasis. The utility of such models is limited by the accuracy of their predictions, which can be determined by uncertainty quantification (UQ). A challenge associated with the use of UQ is that many published methods assume that the underlying model is identifiable (e.g. that a one-to-one mapping exists from the parameter space to the model output). In this study we present a novel workflow to calibrate a lumped-parameter model to left ventricular pressure and volume time series data. Key steps include using (1) literature and available data to determine nominal parameter values; (2) sensitivity analysis and subset selection to determine a set of identifiable parameters; (3) optimization to find a point estimate for identifiable parameters; and (4) frequentist and Bayesian UQ calculations to assess the predictive capability of the model. Our results show that it is possible to determine 5 identifiable model parameters that can be estimated to our experimental data from three rats, and that computed UQ intervals capture the measurement and model error.
journal_name
Math Bioscijournal_title
Mathematical biosciencesauthors
Marquis AD,Arnold A,Dean-Bernhoft C,Carlson BE,Olufsen MSdoi
10.1016/j.mbs.2018.07.001subject
Has Abstractpub_date
2018-10-01 00:00:00pages
9-24eissn
0025-5564issn
1879-3134pii
S0025-5564(17)30658-2journal_volume
304pub_type
杂志文章abstract：:A mathematical model for multispecies biofilm evolution based on continuum approach and mass conservation principles is presented. The model can describe biofilm growth dynamics including spatial distribution of microbial species, substrate concentrations, attachment, and detachment, and, in particular, is able to pre...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2014.10.009
更新日期：2015-01-01 00:00:00
abstract：:Reactivity (a.k.a initial growth) is necessary for diffusion driven instability (Turing instability). Using a notion of common Lyapunov function we show that this necessary condition is a special case of a more powerful (i.e. tighter) necessary condition. Specifically, we show that if the linearised reaction matrix an...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2012.04.006
更新日期：2012-09-01 00:00:00
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
更新日期：1994-03-01 00:00:00
abstract：:A model was developed for novel prediction of N-linked glycan branching pattern classification for CHO-derived N-linked glycoproteins. The model consists of 30 independent recurrent neural networks and uses predicted quantities of secondary structure elements and residue solvent accessibility as an input vector. The m...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2007.10.005
更新日期：2008-01-01 00:00:00
abstract：:A key feature of cell migration is how cell movement is affected by cell-cell interactions. Furthermore, many cell migratory processes such as neural crest stem cell migration [Thomas and Erickson, 2008; McLennan et al., 2012] occur on growing domains or in the presence of a chemoattractant. Therefore, it is important...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2015.04.002
更新日期：2015-06-01 00:00:00
abstract：:A mechanistic model of the Fitzhugh-Nagumo type is proposed for the pulse-like jasmonate response in plants. The model is composed of a bistable signaling pathway coupled to a negative feedback loop. The bistable signaling pathway describes a recently discovered positive feedback loop involving jasmonate and the MYC2 ...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2016.01.001
更新日期：2016-03-01 00:00:00
abstract：:In microarray data analysis, traditional methods that focus on single genes are increasingly replaced by methods that analyse functional units corresponding to biochemical pathways, as these are considered to offer more insight into gene expression and disease associations. However, the development of robust pipelines...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2014.09.005
更新日期：2015-02-01 00:00:00
abstract：:Classification of microarray data has always been a challenging task because of the enormous number of genes. In this study, a clustering method by integrating plant stress response gene expression data with biological knowledge is presented. Clustering is one of the promising tools for attribute reduction, but gene c...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2015.06.005
更新日期：2015-08-01 00:00:00
abstract：:Inflammation plays a critical role in the development and progression of cancer, evident in multiple patient populations manifesting increased, non-resolving inflammation, such as inflammatory bowel disease, viral hepatitis and obesity. Given the complexity of both the inflammatory response and the process of oncogene...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2014.07.009
更新日期：2015-02-01 00:00:00
abstract：:A stochastic model for hospital infection incorporating both direct transmission and indirect transmission via free-living bacteria in the environment is investigated. We examine the long term behavior of the model by calculating a stationary distribution and normal approximation of the distribution. The quasi-station...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2012.10.002
更新日期：2013-01-01 00:00:00
abstract：:In this paper, we first propose a prey-predator model with prey-stage structure and diffusion. Then we discuss the following three problems: (1) stability of non-negative constant steady states for the reduced ODE system and the corresponding reaction diffusion system with homogeneous Neumann boundary conditions; (2) ...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2007.08.008
更新日期：2008-04-01 00:00:00
abstract：:In this work, we derive and analyze a 2n+1-dimensional deterministic differential equation modeling the transmission and treatment of HIV (Human Immunodeficiency Virus) disease. The model is extended to a stochastic differential equation by introducing noise in the transmission rate of the disease. A theoretical treat...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2018.03.013
更新日期：2018-05-01 00:00:00
abstract：:We consider the spread of an epidemic through a population divided into n sub-populations, in which individuals move between populations according to a Markov transition matrix Σ and infectives can only make infectious contacts with members of their current population. Expressions for the basic reproduction number, R₀...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2012.01.002
更新日期：2012-03-01 00:00:00
abstract：:The acetone-butanol (AB) fermentation process in the anaerobic endospore-forming Gram-positive bacterium Clostridium acetobutylicum is useful as a producer of biofuels, particularly butanol. Recent work has concentrated on trying to improve the efficiency of the fermentation method, either through changes in the envir...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2012.11.004
更新日期：2013-02-01 00:00:00
abstract：:Chemokine receptor expression may vary dramatically among cell subsets. Therefore, the stage of differentiation and the lineage of CD4 cells may profoundly affect their susceptibility to infection by human immunodeficiency virus type 1 (HIV-1). However, the mechanisms of coreceptor competition for association with HIV...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2005.01.002
更新日期：2005-05-01 00:00:00
abstract：:During normal, voluntary movements, skeletal muscles typically contract in a highly dynamic manner; the length of the muscle and the speed of contraction change continuously. In this study, we present an approach to predict the accurate behavior of muscles for such dynamic contractions using Huxley's cross-bridge mode...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/s0025-5564(96)00115-0
更新日期：1997-01-01 00:00:00
abstract：:We numerically investigate the influence of intrinsic channel noise on the dynamical response of delay-coupling in neuronal systems. The stochastic dynamics of the spiking is modeled within a stochastic modification of the standard Hodgkin-Huxley model wherein the delay-coupling accounts for the finite propagation tim...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2013.02.007
更新日期：2013-09-01 00:00:00
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
更新日期：2016-11-01 00:00:00
abstract：:A number of recent research studies have focused on theoretical and experimental investigation of a bottleneck in a metabolic reaction network. However, there is no study on how the bottleneck affects the performance of a fermentation process when a product is highly toxic and remarkably influences the growth and deat...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2010.08.001
更新日期：2010-11-01 00:00:00
abstract：:In automatic feedback control of intravenous drug infusions, convergence to the setpoint is an important objective. This paper examines the stability of pharmacokinetic-pharmacodynamic models of patient response regulated with proportional integral feedback. The model consists of three components: linear compartmental...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/s0025-5564(97)00076-x
更新日期：1997-12-01 00:00:00
abstract：:According to metapopulation theory, the capacity of a habitat patch network to support the persistence of a species is measured by the metapopulation capacity of the patch network. Mathematically, metapopulation capacity is given by the leading eigenvalue lambda(M) of an appropriately constructed non-negative n x n ma...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/s0025-5564(02)00150-5
更新日期：2003-02-01 00:00:00
abstract：:This paper provides an introduction to and overview of the use of stochastic models and statistical analysis in the study of ion channels in cell membranes. An extensive bibliography is included. ...
journal_title：Mathematical biosciences
pub_type： 杂志文章,评审
doi：10.1016/0025-5564(92)90023-p
更新日期：1992-12-01 00:00:00
abstract：:Synthetic biology has shown its potential and promising applications in the last decade. However, many synthetic gene networks cannot work properly and maintain their desired behaviors due to intrinsic parameter variations and extrinsic disturbances. In this study, the intrinsic parameter uncertainties and external di...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2010.12.007
更新日期：2011-03-01 00:00:00
abstract：:We investigate an SIR epidemic model with discrete age groups to understand the transmission dynamics of an infectious disease in a host population with an age structure. We derive the basic reproduction number R0 and show that it is a sharp threshold parameter. If R0≤1, the disease-free equilibrium E0 is globally sta...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2018.12.003
更新日期：2019-02-01 00:00:00
abstract：:A new biological growth model is introduced. After random selection of possible growth sites, cells are added in an allowable random direction. Unlike the Eden model, the current model is grid independent and can be adapted to any curved surface. Growths of colonies of as many as 10(5) cells are simulated on planar, c...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/s0025-5564(97)00012-6
更新日期：1997-06-01 00:00:00
abstract：:We review a multiscale model of saliva secretion, describing in brief how the model is constructed and what we have so far learned from it. The model begins at the level of inositol trisphosphate receptors (IPR), and proceeds through the cellular level (with a model of acinar cell calcium dynamics) to the multicellula...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2014.06.017
更新日期：2014-11-01 00:00:00
abstract：:Cooperating behaviors abound across all domains of life, but are vulnerable to invasion by cheaters. An important evolutionary question is to determine mechanisms that stabilize and maintain cooperation levels and prevent population collapse. Policing is one strategy populations may employ to achieve this goal, and it...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2019.108257
更新日期：2019-10-01 00:00:00
abstract：:Multi-patch models - also known as metapopulation models - provide a simple framework within which the role of spatial processes in disease transmission can be examined. An n-patch model which distinguishes between k different classes of individuals is considered. The linear stability of spatially homogeneous solution...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2003.09.003
更新日期：2004-03-01 00:00:00
abstract：:In this paper, two cancer therapies are investigated through their mathematical models. Namely, angiogenesis inhibition (P. Hahndfeldt, D. Panigrahy, J. Folkman, L. Hlatky, Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy, Cancer Res. 59, 1...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2011.02.010
更新日期：2011-06-01 00:00:00
abstract：:The existence of cooperation in this world is a mysterious phenomenon. One of the mechanisms that explain the evolution of cooperation is repeated interaction. If interactions between the same individuals repeat and individuals cooperate conditionally, cooperation can evolve. A previous study pointed out that if indiv...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2017.04.002
更新日期：2017-07-01 00:00:00
