Abstract：
:In this work, we present a pedagogical tumour growth example, in which we apply calibration and validation techniques to an uncertain, Gompertzian model of tumour spheroid growth. The key contribution of this article is the discussion and application of these methods (that are not commonly employed in the field of cancer modelling) in the context of a simple model, whose deterministic analogue is widely known within the community. In the course of the example, we calibrate the model against experimental data that are subject to measurement errors, and then validate the resulting uncertain model predictions. We then analyse the sensitivity of the model predictions to the underlying measurement model. Finally, we propose an elementary learning approach for tuning a threshold parameter in the validation procedure in order to maximize predictive accuracy of our validated model.
journal_name
Bull Math Bioljournal_title
Bulletin of mathematical biologyauthors
Collis J,Connor AJ,Paczkowski M,Kannan P,Pitt-Francis J,Byrne HM,Hubbard MEdoi
10.1007/s11538-017-0258-5subject
Has Abstractpub_date
2017-04-01 00:00:00pages
939-974issue
4eissn
0092-8240issn
1522-9602pii
10.1007/s11538-017-0258-5journal_volume
79pub_type
杂志文章abstract：:It has been recently observed that the dynamical properties of mass action systems arising from many models of biochemical reaction networks can be characterized by considering the corresponding properties of a related generalized mass action system. The correspondence process known as network translation in particula...
journal_title：Bulletin of mathematical biology
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doi：10.1007/s11538-015-0077-5
更新日期：2015-06-01 00:00:00
abstract：:Analysis schemes for the classification of synergism and antagonism for mixed agents operate on the discrepancies between observed and calculated results. As such they cannot be confirmed by experiments and therefore have to be tested in terms of mathematical and logical self-consistency. The concept of independent ac...
journal_title：Bulletin of mathematical biology
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doi：10.1007/BF02458276
更新日期：1994-09-01 00:00:00
abstract：:This paper investigates cell proliferation dynamics in small tumor cell aggregates using an individual-based model (IBM). The simulation model is designed to study the morphology of the cell population and of the cell lineages as well as the impact of the orientation of the division plane on this morphology. Our IBM m...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-017-0333-y
更新日期：2017-10-01 00:00:00
abstract：:Moment closure methods are widely used to analyze mathematical models. They are specifically geared toward derivation of approximations of moments of stochastic models, and of similar quantities in other models. The methods possess several weaknesses: Conditions for validity of the approximations are not known, magnit...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-017-0321-2
更新日期：2017-09-01 00:00:00
abstract：:A stochastic evolutionary dynamics of two strategies given by 2x 2 matrix games is studied in finite populations. We focus on stochastic properties of fixation: how a strategy represented by a single individual wins over the entire population. The process is discussed in the framework of a random walk with site depend...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-006-9061-4
更新日期：2006-11-01 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：:Alcohol consumption and abuse is widespread in sub-Saharan Africa where most HIV infections occur and has been associated with risky sexual behaviors. It may therefore be one of the most common, potentially modifiable HIV risk factors in this region. A deterministic system of ordinary differential equations incorporat...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-012-9747-8
更新日期：2012-09-01 00:00:00
abstract：:The paper presents results on the asymptotic properties of the least-squares estimates (LSEs) of the reaction constants in mass-action, stochastic, biochemical network models. LSEs are assumed to be based on the longitudinal data from partially observed trajectories of a stochastic dynamical system, modeled as a conti...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-012-9744-y
更新日期：2012-08-01 00:00:00
abstract：:We study the emergence of collective spatio-temporal objects in biological systems by representing individually the elementary interactions between their microscopic components. We use the immune system as a prototype for such interactions. The results of this detailed explicit analysis are compared with the tradition...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1016/S0092-8240(03)00007-7
更新日期：2003-05-01 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：: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 detaile...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-016-0188-7
更新日期：2016-06-01 00:00:00
abstract：:In this paper, we use multiple scale homogenisation to derive a set of averaged macroscale equations that describe the movement of nutrients in partially saturated soil that contains growing potato tubers. The soil is modelled as a poroelastic material, which is deformed by the growth of the tubers, where the growth o...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-019-00656-3
更新日期：2019-10-01 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：:We develop a numerical method for estimating optimal parameters in a mathematical model of the within-host dynamics of malaria infection. The model consists of a quasilinear system of partial differential equations. Convergence theory for the computed parameters is provided. Following this analysis, we present several...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-011-9650-8
更新日期：2011-11-01 00:00:00
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：:The culmination of the morphogenesis of the cellular slime mould Dictyostelium discoideum involves complex cell movements which transform a mound of cells into a globule of spores on a slender stalk. We show that cyclic AMP signalling and differential adhesion, combined with cell differentiation and slime production, ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1006/bulm.2001.0277
更新日期：2002-03-01 00:00:00
abstract：:A system of differential equations for the control of tumor cells growth in a cycle nonspecific chemotherapy is presented. Spontaneously acquired drug resistance is accounted for, as well as the evolution in time of normal cells. In addition, optimization of conflicting objectives forms the aim of the chemotherapeutic...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/BF02458426
更新日期：1997-07-01 00:00:00
abstract：:A semi-empirical model applicable to the flow of blood and other particulate suspensions through narrow tubes has been developed. It envisages a central core of blood surrounded by a wall layer of reduced hematocrit. With the help of this model the wall layer thickness and extent of plug flow may be calculated using p...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/BF02459514
更新日期：1975-10-01 00:00:00
abstract：:Molecular motors such as kinesin and dynein are responsible for transporting material along microtubule networks in cells. In many contexts, motor dynamics can be modelled by a system of reaction-advection-diffusion partial differential equations (PDEs). Recently, quasi-steady-state (QSS) methods have been applied to ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-017-0314-1
更新日期：2017-09-01 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 construct a population dynamics model of the competition among immune system cells and generic tumor cells. Then, we apply the theory of optimal control to find the optimal schedule of injection of autologous dendritic cells used as immunotherapeutic agent. The optimization method works for a general ODE system and...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-005-9014-3
更新日期：2006-02-01 00:00:00
abstract：:We introduce here a gene evolution model which is an extension of the time-continuous stochastic IDIS model (Lèbre and Michel in J. Comput. Biol. Chem. 34:259-267, 2010) to sequence length. This new IDISL (Insertion Deletion Independent of Substitution based on sequence Length) model gives an analytical expression of ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-012-9735-z
更新日期：2012-08-01 00:00:00
abstract：:Advances in fluorescent labeling of cells as measured by flow cytometry have allowed for quantitative studies of proliferating populations of cells. The investigations (Luzyanina et al. in J. Math. Biol. 54:57-89, 2007; J. Math. Biol., 2009; Theor. Biol. Med. Model. 4:1-26, 2007) contain a mathematical model with fluo...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-010-9524-5
更新日期：2011-01-01 00:00:00
abstract：:The coexistence of a large number of phytoplankton species on a seemingly limited variety of resources is a classical problem in ecology, known as 'the paradox of the plankton'. Strong fluctuations in species abundance due to the external factors or competitive interactions leading to oscillations, chaos and short-ter...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-006-9109-5
更新日期：2006-11-01 00:00:00
abstract：:The multifractal analysis of binary images of DNA is studied in order to define a methodological approach to the classification of DNA sequences. This method is based on the computation of some multifractality parameters on a suitable binary image of DNA, which takes into account the nucleotide distribution. The binar...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-013-9859-9
更新日期：2013-09-01 00:00:00
abstract：:Preserving a system's viability in the presence of diversity erosion is critical if the goal is to sustainably support biodiversity. Reduction in population heterogeneity, whether inter- or intraspecies, may increase population fragility, either decreasing its ability to adapt effectively to environmental changes or f...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章,评审
doi：10.1007/s11538-014-9983-1
更新日期：2015-02-01 00:00:00
abstract：:Whilst the human body expends energy constantly, the human diet consists of a mix of carbohydrates and fats delivered in a discontinuous manner. To deal with this sporadic supply of energy, there are transport, storage and utilisation mechanisms, for both carbohydrates and fats, around all tissues of the body. Insulin...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-016-0181-1
更新日期：2016-06-01 00:00:00
abstract：:Dengue is a growing public health problem in tropical and subtropical cities. It is transmitted by mosquitoes, and the main strategy for epidemic prevention and control is insecticide fumigation. Effective management is, however, proving elusive. People's day-to-day movement about the city is believed to be an importa...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-016-0209-6
更新日期：2016-10-01 00:00:00
abstract：:This paper considers plant-pollinator systems in which plants are divided into two categories: The plants that secret a substantial volume of nectar in their flowers are called secretors, while those without secreting nectar are called nonsecretors (cheaters). The interaction between pollinators and secretors is mutua...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-013-9846-1
更新日期：2013-07-01 00:00:00
abstract：:Farmers frequently decide where to locate the colonies of their domesticated eusocial bees, especially given the following mutually exclusive scenarios: (i) there are limited nectar and pollen sources within the vicinity of the apiary that cause competition among foragers; and (ii) there are fewer pollinators compared...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-014-9943-9
更新日期：2014-05-01 00:00:00
