Modeling Of Stem Cells Differentiation

Communications in Applied and Industrial Mathematics, 2010

A mathematical model to describe the process of formation of bone tissue by replacement of cartilage tissue is presented and discussed. This model is based on an absorption-diffusion system which describes the interaction of two key signalling molecules. These molecules characterize the dynamics of the transition zone between the cartilage and the bone tissue. Some experimental data are needed to estimate some model parameters. We discuss how our results are essentially unaffected by small variations, and in a particular case, not necessarily small variations in the experimental values.

Stem cell therapies based on the differentiation of adult or embryonic cells into specialized ones appear to be effective for treating several human diseases. This work addresses the mathematical simulation of the proliferation kinetics of stem cells. Sheep bone marrow mesenchymal cells seeded at different initial concentrations in Petri dishes are expanded up to confluence. The sigmoidal temporal profiles of total counts obtained through classic hemocytometry are quantitatively interpreted by a novel model based on a 1-D, single-staged population balance approach capable to take into account the contact inhibition at confluence. The models' parameters have been determined by comparison with experimental data on population expansion starting from a single seeding concentration. The reliability of the model is tested by predicting the cell proliferation carried out starting from different seeding concentrations.

Bulletin of Mathematical Biology, 2008

been derived in an analytically rigorous fashion from a substantially more complex system involving multiple morphogens, extracellular matrix deposition, haptotaxis, and cell translocation. We identify regions in the parameter space of the reduced system where Turing-type pattern formation is possible, which we refer to as its "Turing space." Obtained values of the parameters are used in numerical simulations of the reduced system, using a new Galerkin finite element method, in tissue domains with nonstandard geometry. The reduced system exhibits patterns of spots and stripes like those seen in developing limbs, indicating its potential utility in hybrid continuum-discrete stochastic modeling of limb development. Lastly, we discuss the possible role in limb evolution of selection for increasingly morphostatic developmental mechanisms.

Journal of Biomedicine and Biotechnology, 2003

Stem cell activation and development is central to skeletal development, maintenance, and repair, as it is for all tissues. However, an integrated model of stem cell proliferation, differentiation, and transit between functional compartments has yet to evolve. In this paper, the authors review current concepts in stem cell biology and progenitor cell growth and differentiation kinetics in the context of bone formation. A cell-based modeling strategy is developed and offered as a tool for conceptual and quantitative exploration of the key kinetic variables and possible organizational hierarchies in bone tissue development and remodeling, as well as in tissue engineering strategies for bone repair.

Cell Proliferation, 2009

Objectives: Stem cell therapies based on differentiation of adult or embryonic stem cells into specialized ones appear to be effective for treating several human diseases. This work addresses the mathematical simulation of proliferation kinetics of stem cells.Materials and methods: Sheep bone marrow mesenchymal stem cells (phenotype characterized by flow cytometry analysis) seeded at different initial concentrations in Petri dishes were expanded to confluence. Sigmoid temporal profiles of total counts obtained through classic haemocytometry were quantitatively interpreted by both a phenomenological logistic equation and a novel model based on a one-dimensional, single-staged population balance approach capable of taking into account contact inhibition at confluence. The models’ parameters were determined by comparison with experimental data on population expansion starting from single seeding concentration. Reliability of the models was tested by predicting cell proliferation carried out starting from different seeding concentrations.Results and discussion: It was found that the proposed population balance modelling approach was successful in predicting the experimental data over the whole range of initial cell numbers investigated, while prediction capability of phenomenological logistic equation was more limited.

Physica A: Statistical Mechanics and its Applications, 2007

A central question in developmental biology is how cells interact to organize into tissues? In this paper, we study the role of mesenchyme-ectoderm interaction in the growing chick limb bud using Glazier and Graner's cellular Potts model, a grid-based stochastic framework designed to simulate cell interactions and movement. We simulate cellular mechanisms including cell adhesion, growth, and division and diffusion of morphogens, to show that differential adhesion between the cells, diffusion of growth factors through the extracellular matrix, and the elastic properties of the apical ectodermal ridge together can produce the proper shape of the limb bud.

Current stem cell research & therapy, 2015

Regenerative medicine is a multidisciplinary field where continued progress relies on the incorporation of a diverse set of technologies from a wide range of disciplines within medicine, science and engineering. This review describes how one such technique, mathematical modelling, can be utilised to improve the tissue engineering of organs and stem cell therapy. Several case studies, taken from research carried out by our group, ACTREM, demonstrate the utility of mechanistic mathematical models to help aid the design and optimisation of protocols in regenerative medicine.

Current Topics in Developmental Biology, 2008

Medical & Biological Engineering & Computing, 2010

The mathematical models prevalently used to represent stem cell proliferation do not have the level of accuracy that might be desired. The hyperbolastic growth models promise a greater degree of precision in representing data of stem cell proliferation. The hyperbolastic growth model H3 is applied to experimental data in both embryonic stem cells and adult mesenchymal stem cells. In the embryonic stem cells the results are compared with other popular models, including the Deasy model, which is used prevalently for stem cell growth. In the case of modelling adult mesenchymal stem cells, H3 is also successfully applied to describe the proliferative index. We demonstrated that H3 can accurately represent the dynamics of stem cell proliferation for both embryonic and adult mesenchymnal stem cells. We also recognize the importance of additional factors, such as cytokines, in determining the rate of growth. We propose the question of how to extend H3 to a multivariable model that can include the influence of growth factors.

Journal of Cellular Physiology, 2005

This study aimed at determining how kinetic parameters of adult human articular chondrocytes (AHAC) growth are modulated by the growth factor combination TGFb1, FGF-2, and PDGF BB (TFP), recently shown to stimulate AHAC proliferation. AHAC, isolated from cartilage biopsies of three individuals, were cultured in medium without (CTR) or with TFP. For growth curves, AHAC were seeded at 1,000 cells/cm 2 and cultured for 12 days, with cell numbers measured fluorimetrically in the same wells every 12 h. For microcolony tests, AHAC were seeded at 2.5 cells/cm 2 and cultured for 6 days, with cell numbers determined for each microcolony by phase contrast microscopy every 8 h. A mathematical model combining delay and logistic equations was developed to capture the growth kinetic parameters and to enable the description of the complete growth process of the cell culture. As compared to CTR medium, the presence of TFP increased the number of cells/well starting from the fifth day of culture, and a four-fold larger cell number was reached at confluency. For single microcolonies, TFP reduced the time for the first cell division by 26.6%, the time for subsequent cell divisions (generation time) by 16.8%, and the percentage of quiescent cells (Q c ) by 42.5%. The mathematical model fitted well the experimental data of the growth kinetic. Finally, using both microcolony tests and the mathematical model, we determined that prolonged cell expansion induces an enrichment of AHAC with shorter first division time, but not of those with shorter generation time.