From biological and clinical experiments to mathematical models

Demongeot, Jacques; Françoise, Jean–Pierre; Nérini, David

doi:10.1098/rsta.2009.0187

Cited by 6 publications

(4 citation statements)

References 30 publications

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“…A. L. Goldberger and his colleagues' publications (Goldberger, West, 1987;Goldberger et al, 1988) were one of the first publications in which HR variability was determined by non-linear analysis methods. Mathematical point of view in the analysis of biological systems in question -using mathematical analysis techniques -helps to reveal new features of the system, which can be approved or denied by empirical experiments (Demongeot et al, 2009).…”

Section: Discussionmentioning

confidence: 99%

Dynamics of Concatenation between Cardiac Output and Indices of Arterial Blood Presure during Graded Exercise Stress in Endurance Cohort

Papievienė¹,

Trinkūnas²,

Buliuolis³

et al. 2018

BJSHS

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Research background and hypothesis. Potential mechanisms through which muscle perfusion is altered during prolonged exercise are not fully understood. The methods applied in the analysis of human data are very important because many crucial variables are not directly measureble or even identifiable.Research aim was to find out the peculiarities in concatenation between central and peripheral cardiovascular changes under conditions of increasing fatigue.Research methods. Well-trained endurance runners underwent a 50 W increase in workload (bicycle ergometry) every 6 minutes and they exercised until inability to continue the task. Dynamics of concatenation between cardiac output and systolic arterial blood pressure (ABP), diastolic ABP and total peripheral resistance were assessed using a method based on matrix theory proposed by Lithuanian scientists.Research results. The increase of cardiac output during exercising has the same tendency of stepwise increase of workload, but changes of systolic and diastolic ABP with accumulation of fatigue could be characterized as linear type dependent with the time of exercising. The concatenation between the changes in cardiac performance and behaviour of peripheral vasculature increased at onset of exercising and the decrease or loss of the concatenation led up to inability to continue exercising.Discussion and conclusions. The importance of peripheral factors, i. e. decrease of diastolic blood pressure, reduction of total peripheral vascular resistance plays an increasingly significant role for cardiac output during continuous exercising. The concatenations between the changes of these indices and cardiac output increase and in the case of high-grade fatigue concatenations begin to decline.

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Section: Discussionmentioning

confidence: 99%

Dynamics of Concatenation between Cardiac Output and Indices of Arterial Blood Presure during Graded Exercise Stress in Endurance Cohort

Papievienė¹,

Trinkūnas²,

Buliuolis³

et al. 2018

BJSHS

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“…The first ones are the processes and components (e.g. species, nutrients) to include, which are often a consensus between scientists from different ecology-related disciplines (animal and plant biology, microbiology, chemistry, physics, Demongeot et al, 2009). Those choices are assumptions that can be discussed, and testing their consequences on predictions helps to improve ecological theories.…”

Section: Introductionmentioning

confidence: 99%

Is structural sensitivity a problem of oversimplified biological models? Insights from nested Dynamic Energy Budget models

Aldebert

Kooi

Nérini

et al. 2018

Journal of Theoretical Biology

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Many current issues in ecology require predictions made by mathematical models, which are built on somewhat arbitrary choices. Their consequences are quantified by sensitivity analysis to quantify how changes in model parameters propagate into an uncertainty in model predictions. An extension called structural sensitivity analysis deals with changes in the mathematical description of complex processes like predation. Such processes are described at the population scale by a specific mathematical function taken among similar ones, a choice that can strongly drive model predictions. However, it has only been studied in simple theoretical models. Here, we ask whether structural sensitivity is a problem of oversimplified models. We found in predator-prey models describing chemostat experiments that these models are less structurally sensitive to the choice of a specific functional response if they include mass balance resource dynamics and individual maintenance. Neglecting these processes in an ecological model (for instance by using the well-known logistic growth equation) is not only an inappropriate description of the ecological system, but also a source of more uncertain predictions.

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“…Because they describe physical, chemical and biological processes at different time and space scales, such models are at the interface of different disciplines. Consequently, they often result from a consensus among the various specialists involved in their development [1]. Such a consensual nature generally explains this increasing number of parameters and state variables, because each implied process is relevant from the specialist point of view.…”

Section: Introductionmentioning

confidence: 99%

Towards a simplification of models using regression trees

Eynaud

Nérini

Baklouti

et al. 2013

J. R. Soc. Interface.

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Over-parametrization in modelling is a well-known issue that makes it hard to identify which part of a model is responsible for a given behaviour. In line with that ascertainment, this work presents the outline of an empirical method to simplify models by decreasing the number of parameters. By using regression trees to classify outputs according to related input parameters, the method provides the modeller with an objective tool to reduce the range of the used parameters and, under certain conditions, to establish relations between them. Thereby, the complexity of the model is reduced on the basis of mathematical arguments. As an example, a dynamic energy budget-based model of a mesopelagic bacterial ecosystem is simplified using the presented method. The main benefits of such a method are thus highlighted: (i) more robust parameter estimations; (ii) less complex formulations; and (iii) fewer modelling assumptions. To conclude, the difficulties encountered are discussed, and several solutions are proposed to deal with them.

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From biological and clinical experiments to mathematical models

Cited by 6 publications

References 30 publications

Dynamics of Concatenation between Cardiac Output and Indices of Arterial Blood Presure during Graded Exercise Stress in Endurance Cohort

Dynamics of Concatenation between Cardiac Output and Indices of Arterial Blood Presure during Graded Exercise Stress in Endurance Cohort

Is structural sensitivity a problem of oversimplified biological models? Insights from nested Dynamic Energy Budget models

Towards a simplification of models using regression trees

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