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Peer Reviewed
See detailA mathematical model describing the biology of orthodontic tooth movement
Van Schepdael, A.; Vander Sloten, Jos; Geris, Liesbet ULg

in Goh Cho Hong, James; Teck Lim, Chwee (Eds.) proceedings of the 6th world congress on biomechanics (2010)

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See detailA MATHEMATICAL MODEL FOR CELL/MATRIX GROWTH ON 3D SURFACES USING THE LEVEL SET METHOD.
Guyot, Yann ULg; Papantoniou, Ioannis; Chai, Yoke Chin et al

Conference (2013, April 03)

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See detailA mathematical model of adult subventricular neurogenesis.
Ashbourn, JM; Miller, JJ; Reumers, V et al

in Journal of the Royal Society, Interface (2012)

Neurogenesis has been the subject of active research in recent years and many authors have explored the phenomenology of the process, its regulation and its purported purpose. Recent developments in ... [more ▼]

Neurogenesis has been the subject of active research in recent years and many authors have explored the phenomenology of the process, its regulation and its purported purpose. Recent developments in bioluminescent imaging (BLI) allow direct in vivo imaging of neurogenesis, and in order to interpret the experimental results, mathematical models are necessary. This study proposes such a mathematical model that describes adult mammalian neurogenesis occurring in the subventricular zone and the subsequent migration of cells through the rostral migratory stream to the olfactory bulb (OB). This model assumes that a single chemoattractant is responsible for cell migration, secreted both by the OB and in an endocrine fashion by the cells involved in neurogenesis. The solutions to the system of partial differential equations are compared with the physiological rodent process, as previously documented in the literature and quantified through the use of BLI, and a parameter space is described, the corresponding solution to which matches that of the rodent model. A sensitivity analysis shows that this parameter space is stable to perturbation and furthermore that the system as a whole is sloppy. A large number of parameter sets are stochastically generated, and it is found that parameter spaces corresponding to physiologically plausible solutions generally obey constraints similar to the conditions reported in vivo. This further corroborates the model and its underlying assumptions based on the current understanding of the investigated phenomenon. Concomitantly, this leaves room for further quantitative predictions pertinent to the design of future proposed experiments. [less ▲]

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See detailA mathematical model of bone regeneration including angiogenesis: relevance for tissue engineering strategies
Van Oosterwyck, Hans; Vander Sloten, Jos; Geris, Liesbet ULg

in European Cells and Materials (2008), Vol. 14(Suppl. 1,), 29

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See detailA mathematical model of calcium ion influence on the activity of osteogenic cells
Carlier, Aurélie ULg; Chai, Yoke Chin; Theys, Tina et al

Poster (2010, November 19)

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See detailA Mathematical Model of Rinderpest Infection in Cattle Populations
Tille, A.; Lefèvre, Claude; Pastoret, Paul-Pierre ULg et al

in Epidemiology & Infection (1991), 107(2), 441-52

A mathematical model for the epidemiology of rinderpest was developed, starting from a simplified descriptive analysis of the disease. A formula for the calculation of the probability of infection of a ... [more ▼]

A mathematical model for the epidemiology of rinderpest was developed, starting from a simplified descriptive analysis of the disease. A formula for the calculation of the probability of infection of a susceptible animal was first established. A deterministic failure threshold of the infection was then deduced. Deterministic and stochastic approaches were adopted using iterative methods on a computer. These allowed a description of the spread and the variability of an infection process in a population to be made. An illustration of the use of this model showed that, in some cases, variability effects due to stochastic factors were very important. In these particular conditions, the use of the deterministic model alone was not adequate for a good description of the infection. Consequently, improvements of the model were proposed in order to make it more realistic and to allow its use for the evaluation of the efficiency of field operations. [less ▲]

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See detailMathematical model of the acute inflammatory response to Escherichia coli in intramammary challenge
Detilleux, Johann ULg; Vangroenweghe, F.; Burvenich, C.

in Journal of Dairy Science (2006), 89(9), 3455-3465

We constructed a mathematical model of the early response to Escherichia coli infection of the mammary gland and explored the roles and interactions between inflammatory cells and bacteria. The model ... [more ▼]

We constructed a mathematical model of the early response to Escherichia coli infection of the mammary gland and explored the roles and interactions between inflammatory cells and bacteria. The model incorporates 3 equations that describe the interactions among bacteria, milk somatic cells, and blood leukocyte densities. These 3 equations were fitted to cell densities observed during acute inflammatory responses in unvaccinated and vaccinated heifers inoculated with 10(4) or 10(6) cfu of E. coli. The rates computed for the cellular transit from the storage sites to the blood and from the blood to the milk were lower in cows receiving 10(4) cfu but increased at approximately 6 x 10(-6) and 30 x 10(-6) microL/cfu per h in nonvaccinated or vaccinated cows inoculated with 10(6) cfu, respectively. The cellular rates of bacterial killing were highest in unvaccinated cows ( approximately 400 x 10(-6) microL/cell per h) when compared with vaccinated cows (200 to 300 x 10(-6) microL/cell per h). A critical density of milk somatic cells at which bacteria density is constant was computed from the model at 2 x 10(6) cells/mL, and a one-way sensitivity analysis revealed that the changes in milk cellular densities were mostly sensitive to variations in the rate of bacterial killing and in the rate of production of inflammatory cells. [less ▲]

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See detailMathematical model of the mitral valve and the cardiovascular system, application for studying, monitoring and in the diagnosis of valvular pathologies
Paeme, Sabine ULg; Moorhead, Katherine ULg; Chase, J. Geoffrey et al

in UKACC international Conference on Control 2010 : Coventry, 7-10 september 2010 (2010, September 07)

A cardiovascular and circulatory system (CVS) model has been validated in silico, and in several animal model studies. It accounts for valve dynamics using Heaviside functions to simulate a physiological ... [more ▼]

A cardiovascular and circulatory system (CVS) model has been validated in silico, and in several animal model studies. It accounts for valve dynamics using Heaviside functions to simulate a physiological accurate “open on pressure, close on flow” law. Thus, it does not consider the real time scale of the valve aperture dynamics and thus doesn’t fully capture valve dysfunction particularly where the dysfunction involves partial closure. This research describes a new closed-loop CVS model including a model describing the progressive aperture of the mitral valve and valid over the full cardiac cycle. This new model is solved for a healthy and diseased mitral valve. [less ▲]

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See detailMathematical model of the Northern Bering Sea.
Nihoul, Jacques ULg; Deleersnijder, Eric; Djenidi, Salim ULg

Book published by IRMA ed. (1990)

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See detailA mathematical model of the role of oxygen during normal and delayed fracture repair
Carlier, Aurélie ULg; Van Gastel, Nick; Carmeliet, Geert et al

Conference (2013, October 24)

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See detailMathematical model of the Western Scheldt Estuary
Djenidi, Salim ULg; Ronday, François ULg

in Proceedings of the IUGG General Assembly 1983 (1983)

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See detailMathematical Modeling in Wound Healing, Bone Regeneration and Tissue Engineering
Geris, Liesbet ULg; Gerisch, Alf; Schugart, Richard C.

in Acta Biotheoretica (2010), 58(4), 355-367

The processes of wound healing and bone regeneration and problems in tissue engineering have been an active area for mathematical modeling in the last decade. Here we review a selection of recent models ... [more ▼]

The processes of wound healing and bone regeneration and problems in tissue engineering have been an active area for mathematical modeling in the last decade. Here we review a selection of recent models which aim at deriving strategies for improved healing. In wound healing, the models have particularly focused on the inflammatory response in order to improve the healing of chronic wound. For bone regeneration, the mathematical models have been applied to design optimal and new treatment strategies for normal and specific cases of impaired fracture healing. For the field of tissue engineering, we focus on mathematical models that analyze the interplay between cells and their biochemical cues within the scaffold to ensure optimal nutrient transport and maximal tissue production. Finally, we briefly comment on numerical issues arising from simulations of these mathematical models. [less ▲]

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See detailMathematical modeling od the mitral valve. From local to global hemodynamics
Paeme, Sabine ULg

Doctoral thesis (2014)

Mitral valve dysfunction is a relatively common heart disease which typically requires mechanical valve replacement, with consequent high social and economic costs. More specifically, ischemic mitral ... [more ▼]

Mitral valve dysfunction is a relatively common heart disease which typically requires mechanical valve replacement, with consequent high social and economic costs. More specifically, ischemic mitral insufficiency following myocardial infarction has a dynamic behavior that can lead to failure in its detection in certain patients, creating a situation with increased risk of morbidity and mortality. Improving the tracking and the control of valvular pathologies is therefore crucial, as it offers significant opportunities to improve care, costs and prognosis for patients with this disease. To study heart and cardiac valve dysfunction, cardiologists need information about detailed pressure and flow dynamics around and through the valves, atria and ventricles. However, non-invasive information about pressure is currently limited to indices at specific times and invasive catheterization data, which is more traumatic for the patient, is not usually routinely available. One alternative to this involves mathematical modeling of the cardiovascular system which offers a non-invasive and inexpensive way of studying cardiac and circulatory dynamics. This is particularly beneficial where detailed, continuous measurements may not be practicable. This study consisted of the development of a multi-scale closed-loop model of the cardiovascular system that accounted for progressive mitral valve aperture area over the entire cardiac cycle. This multi-scale model, which included detailed mitral valve and left atrium models, was tested over a range of physiological situations and clinical data. The goal was to validate the model’s ability to reproduce clinically measured physiological and pathophysiological behavior in a manner that would enable a model to be made patient-specific using available data. The resulting model was designed to be made patient-specific, and thus capture and reproduce the patient’s unique hemodynamic state on both global and local scales. In particular, it was shown to provide significant information about the patient’s mitral valve dynamics and the detailed flow dynamics and pressure around it. These data are not currently available without extensive, invasive measurements, and this therefore represents a significant step forward in model-based sensing and diagnosis. It is hoped that the model and methods developed in this study will be a powerful tool in assisting medical teams in investigating, tracking, diagnosing and controlling the cardiovascular system. More specifically, the mitral valve, as well as other similar valves, could be directly monitored to improve the diagnosis, costs and prognosis of valvular dysfunction. Furthermore, the overall results justify detailed in vivo animal experiments to thoroughly validate these models and methods in advance of clinical trials. [less ▲]

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See detailMathematical modeling of biogeochemical processes associated to a coccolithophorid (Emiliania huxleyi) bloom - Study of the seasonal and long-term variability of biogeochemical properties in the Black Sea using a Data Interpolating Variational Analysis (DIVA)
Joassin, Pascal ULg

Doctoral thesis (2011)

A OD biogeochemical model has been developed to represent coccolithophorid physiological features concerned by carbon export (primary production, active DOC excretion, TEP formation, and calcification ... [more ▼]

A OD biogeochemical model has been developed to represent coccolithophorid physiological features concerned by carbon export (primary production, active DOC excretion, TEP formation, and calcification) and susceptible to be sensitive to varying pCO2. The model is initially calibrated and validated using a large set of biogeochemical data monitored during Emiliania huxleyi blooms induced in a mesocosm experiment, under present-day pCO2 conditions. Afterwards, impacts of varying pCO2 conditions on Emiliania huxleyi physiology are investigated using biogeochemical variables monitored in mesocosms under low and high pCO2 conditions. The methodology promotes a double approach: the recalibration model parameters’ that optimizes the representation of observations from low and high pCO2 treatments, and the utilization of a RM ANOVA procedure to indicate significant differences between biogeochemical variables monitored during blooms induced in low and high pCO2 treatments. Since the early 1970’s, the Black Sea ecosystem has suffered significant ecological alterations, essentially caused by anthropogenic impacts. Dam constructions on the Danube River in combination with heavy nutrients discharge via the riverine run-off lead to strong modifications of its physical and biogeochemical properties, with final consequences consisting in an enhancement of the typical anoxic state of the deep waters. The long-term evolution of key biogeochemical variables (oxygen, hydrogen sulfide, and chlorophyll) has been studied through the reconstruction of horizontal fields, using long time data series and the DIVA interpolating tool. In addition, the examination during the best sampled period (1986-1993) of these biogeochemical variables’ fields, completed with nitrates and phosphates fields, highlighted seasonal and horizontal variability within typical sections of their profiles. [less ▲]

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See detailMathematical modeling of bone regeneration during fracture healing
Geris, Liesbet ULg; Vander Sloten, Hans; Van Oosterwyck, Hans

in proceedings of the National Conference on Theoretical and Applied Mechanics (2009)

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See detailMathematical modeling of bone regeneration during fracture healing and implant osseointegration
Geris, Liesbet ULg

Doctoral thesis (2007)

Despite the extensive body of literature on bone regeneration, many questions remain on e.g. the regulatory mechanisms and potential treatment strategies of pathological regeneration cases. The hypothesis ... [more ▼]

Despite the extensive body of literature on bone regeneration, many questions remain on e.g. the regulatory mechanisms and potential treatment strategies of pathological regeneration cases. The hypothesis underlying this work states that mathematical models of bone regeneration can make a substantial contribution to this domain by proposing pathological regeneration mechanisms and designing therapies, which can subsequently be tested experimentally. In the first part of this work, existing mechanoregulatory and bioregulatory models of bone regeneration are implemented and applied to both implant osseointegration and fracture healing set-ups. A quantitative comparison with experimental results is performed. Thorough sensitivity analyses are carried out to assess the influence of various modelling aspects on the simulation outcome. Shortcomings of these models are identified and suggestions for improvements are made. In the second part of this work, a novel bioregulatory model of bone regeneration is developed in which several of the previously defined shortcomings are addressed. This model includes key aspects of the regeneration process such as intramembranous and endochondral ossification, angiogenesis and directed cell motion. The results obtained with this novel model are corroborated both qualitatively and quantitatively by comparison with experimental data for normal fracture healing. Cases of pathological fracture healing are simulated and experimentally testable therapeutic strategies are implemented. The last part of this work describes the establishment of a mathematical framework, based on the previously developed bioregulatory model, in which the regulatory influence of both biological and mechanical factors is combined. This is the first model of bone regeneration in which the coupling between mechanical loading and angiogenesis is made in an explicit and mechanistic manner. Several examples are given to illustrate the added value of this approach in simulating normal and pathological bone regeneration. In summary, this work demonstrates the potential of mathematical models in advancing the knowledge on bone regeneration and designing treatment strategies for pathological healing cases. [less ▲]

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See detailMathematical modeling of bone regeneration including the angiogenic process
Geris, Liesbet ULg; Vander Sloten, Jos; Van Oosterwyck, Hans

in Journal of Biomechanics (2006), 39(S1), 411-412

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See detailMathematical modeling of cell-cell and cell-matrix adhesion in tissue engineering using continuum models
Geris, Liesbet ULg; Gerisch, A.

in Geffen, A. (Ed.) Cellular and Biomolecular Mechanics and Mechanobiology (2011)

Key factors in the formation of cell aggregates in tissue engineering and other fields are the cell-cell and cell-matrix interactions. Other important factors are culture conditions such as nutrient and ... [more ▼]

Key factors in the formation of cell aggregates in tissue engineering and other fields are the cell-cell and cell-matrix interactions. Other important factors are culture conditions such as nutrient and oxygen supply and the characteristics of the environment (medium versus hydrogel). As mathematical models are increasingly used to investigate biological phenomena, it is important that processes such as cell adhesion are adequately described in the models. Recently a technique was developed to incorporate cell-cell and cell-matrix adhesion in continuum models through the use of non-local terms. In this study we apply this technique to model adhesion in a cell-in-gel culture set-up often found in tissue engineering applications. We briefly describe the biological issues underlying this study and the various modeling techniques used to capture adhesive behaviour. We furthermore elaborate on the numerical techniques that were developed in the course of this study. Finally, we consider a tissue engineering model that describes the spatiotemporal evolution of the concentration of cells, matrix, hydrogel, matrix degrading enzymes and oxygen/nutrients in a cell-in-gel culture system. Sensitivity analyses indicate a clear influence of the different adhesive processes on the final cell and collagen density and distribution, demonstrating the significance of cell adhesion in tissue engineering and the potential of the proposed mathematical technique. [less ▲]

Detailed reference viewed: 59 (17 ULg)