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  • 1
    Electronic Resource
    Electronic Resource
    Mathematical oncology: Cancer summed up (2003)
    [s.l.] : Nature Publishing Group
    Nature 421 (2003), S. 321-321 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] ...Experimental oncology is awash with data. In 2001 alone, over 21,000 articles on characterizing, diagnosing and treating malignancies were published. The powerful techniques of molecular biology have demonstrated innumerable cancer-related alterations in the structure and function of ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/421321a
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  • 2
    Electronic Resource
    Electronic Resource
    Turing patterns in fish skin? (1996)
    [s.l.] : Nature Publishing Group
    Nature 380 (1996), S. 678-678 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] SIR - Kondo and Asai1 interpret observ-ations on the time evolution of skin patterns of the angelfish (Pomacanthus) as the first instance of a Turing (reac-tion-diffusion) pattern in biology. But we believe that reaction-diffusion systems per se cannot provide a mechanistic basis for one of the ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/380678a0
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  • 3
    Electronic Resource
    Electronic Resource
    Diffusion driven instability in an inhomogeneous domain (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 365-384 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Diffusion driven instability in reaction-diffusion systems has been proposed as a mechanism for pattern formation in numerous embryological and ecological contexts. However, the possible effects of environmental inhomogeneities has received relatively little attention. We consider a general two species reaction-diffusion model in one space dimension, with one diffusion coefficient a step function of the spatial coordinate. We derive the dispersion relation and the solution of the linearized system. We apply our results to Turing-type models for both embryogenesis and predator-prey interactions. In the former case we derive conditions for pattern to be isolated in one part of the domain, and in the latter we introduce the concept of “environmental instability”. Our results suggest that environmental inhomogeneity could be an important regulator of biological pattern formation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460888
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  • 4
    Electronic Resource
    Electronic Resource
    Book reviews (1994)
    Springer
    Bulletin of mathematical biology 56 (1994), S. 1163-1172 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460291
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  • 5
    Electronic Resource
    Electronic Resource
    A mathematical model for fibro-proliferative wound healing disorders (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 787-808 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The normal process of dermal wound healing fails in some cases, due to fibro-proliferative disorders such as keloid and hypertrophic scars. These types of abnormal healing may be regarded as pathologically excessive responses to wounding in terms of fibroblastic cell profiles and their inflammatory growth-factor mediators. Biologically, these conditions are poorly understood and current medical treatments are thus unreliable. In this paper, the authors apply an existing deterministic mathematical model for fibroplasia and wound contraction in adult mammalian dermis (Olsenet al., J. theor. Biol. 177, 113–128, 1995) to investigate key clinical problems concerning these healing disorders. A caricature model is proposed which retains the fundamental cellular and chemical components of the full model, in order to analyse the spatiotemporal dynamics of the initiation, progression, cessation and regression of fibro-contractive diseases in relation to normal healing. This model accounts for fibroblastic cell migration, proliferation and death and growth-factor diffusion, production by cells and tissue removal/decay. Explicit results are obtained in terms of the model processes and parameters. The rate of cellular production of the chemical is shown to be critical to the development of a stable pathological state. Further, cessation and/or regression of the disease depend on appropriate spatiotemporally varying forms for this production rate, which can be understood in terms of the bistability of the normal dermal and pathological steady states—a central property of the model, which is evident from stability and bifurcation analyses. The work predicts novel, biologically realistic and testable pathogenic and control mechanisms, the understanding of which will lead toward more effective strategies for clinical therapy of fibro-proliferative disorders.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459482
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  • 6
    Electronic Resource
    Electronic Resource
    Role of fibroblast migration in collagen fiber formation during fetal and adult dermal wound healing (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 1077-1100 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Adult dermal wounds, in contrast to fetal wounds, heal with the formation of scar tissue. A crucial factor in determining the degree of scarring is the ratio of types I and III collagen, which regulates the diameter of the combined fibers. We developed a reaction-diffusion model which focuses on the control of collagen synthesis by different isoforms of the polypeptide transforming growth factor-β (TGFβ). We used the model to investigate the current controversy as to whether the fibroblasts migrate into the wound from the surrounding unwounded dermis or from the underlying subcutaneous tissue. Numerical simulations of a spatially independent, temporal model led to a value of the collagen ratio consistent with that of healthy tissue for the fetus, but corresponding to scarring in the adult. We investigated the effect of topical application of TGFβ and show that addition of isoform 3 reduces scar tissue formation, in agreement with the experiment. However, numerical solutions of the reaction-diffusion system do not exhibit this sensitivity to growth factor application. Mathematically, this corresponds to the observation that behind healing wavefront solutions, a particular healed state is always selected independent of transients, even though there is a continuum of possible positive steady states. We explain this phenomenon using a caricature system of equations, which reflects the key qualitative features of the full model but has a much simpler mathematical form. Biologically, our results suggest that the migration into a wound of fibroblasts and TGFβ from the surrounding dermis alone cannot account for the essential features of the healing process, and that fibroblasts entering from the underlying subcutaneous tissue are crucial to the healing process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460102
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  • 7
    Electronic Resource
    Electronic Resource
    Reaction and diffusion on growing domains: Scenarios for robust pattern formation (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 1093-1120 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We investigate the sequence of patterns generated by a reaction—diffusion system on a growing domain. We derive a general evolution equation to incorporate domain growth in reaction—diffusion models and consider the case of slow and isotropic domain growth in one spatial dimension. We use a self-similarity argument to predict a frequency-doubling sequence of patterns for exponential domain growth and we find numerically that frequency-doubling is realized for a finite range of exponential growth rate. We consider pattern formation under different forms for the growth and show that in one dimension domain growth may be a mechanism for increased robustness of pattern formation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0131
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  • 8
    Electronic Resource
    Electronic Resource
    Hierarchically coupled ultradian oscillators generating robust circadian rhythms (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 517-532 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Ensembles of mutually coupled ultradian cellular oscillators have been proposed by a number of authors to explain the generation of circadian rhythms in mammals. Most mathematical models using many coupled oscillators predict that the output period should vary as the square root of the number of participating units, thus being inconsistent with the well-established experimental result that ablation of substantial parts of the suprachiasmatic nuclei (SCN), the main circadian pacemaker in mammals, does not eliminate the overt circadian functions, which show no changes in the phases or periods of the rhythms. From these observations, we have developed a theoretical model that exhibits the robustness of the circadian clock to changes in the number of cells in the SCN, and that is readily adaptable to include the successful features of other known models of circadian regulation, such as the phase response curves and light resetting of the phase.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459463
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  • 9
    Electronic Resource
    Electronic Resource
    Pattern formation of scale cells in lepidoptera by differential origin-dependent cell adhesion (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 807-828 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We present a model for the formation of parallel rows of scale cells in the developing adult wing of moths and butterflies. Precursors of scale cells differentiate throughout each epithelial monolayer and migrate into rows that are roughly parallel to the body axis. Grafting experiments have revealed what appears to be a gradient of adhesivity along the wing. What is more, cell adhesivity character is maintained after grafting. Thus we suggest that it is a cell’s location prior to migration that determines its interactions during migration. We use nonlinear bifurcation analysis to show that differential origin-dependent cell adhesion can result in the stabilization of rows over spots.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1998.0062
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  • 10
    Electronic Resource
    Electronic Resource
    Modelling a new angle on understanding cancer (2002)
    [s.l.] : Nature Publishing Group
    Nature 420 (2002), S. 462-462 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Sir There was a striking absence of discussion of quantitative methods in the recent interesting theoretical debate on the timing and nature of mutations controlling acquisition of the metastatic phenotype in invasive cancers (R. Bernards and R. A. Weinberg Nature ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/420462b
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