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  • 1
    Electronic Resource
    Electronic Resource
    Modification of the Effects of Ionizing Radiation by Differentiation-Induction (1989)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 567 (1989), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1989.tb16499.x
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  • 2
    Electronic Resource
    Electronic Resource
    Growth factors and growth control of heterogeneous cell populations (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 993-1011 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In an earlier work a model of the autocrine and paracrine pathways of tumor growth control was developed (Michelson and Leith. 1991. Autocrine and paracrine growth factors in tumor growth.Bull. math. Biol. 53, 639–656). The target population, a generic tumor, was modeled as a single, homogeneous population using the standard Verhulst equation of logistic growth. Mitogenic signals were represented by modifications to the Malthusian growth parameter and adaptational signals were represented by modifications to the carrying capacity. Three growth scenarios were described: (1) normal tissue wound healing, (2) unperturbed tumor growth, and (3) tumor growth in a radiation damaged environment, a phenomenon termed the Tumor Bed Effect (TBE). In this paper, we extend those results to include a “triad” of growth factor controls (autocrine, paracrine and endocrine) and heterogeneity of the target population. The heterogeneous factors in the model represent either intrinsic, epigenetic or environmental differences in both normally differentiating tissues and tumors. Three types of growth are modeled: (1) normal tissue differentiation or wound healing, assuming no communication between differentiated and undifferentiated cell compartments; (2) normal wound healing with feedback inhibition, due to signalling from the differentiated compartment; and (3) the development of hypoxia in a spherical tumor. The signal processing within the triad is discussed for each model and biologically reasonable constraints are defined for limits on growth control.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460696
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  • 3
    Electronic Resource
    Electronic Resource
    Interlocking triads of growth control in tumors (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 345-366 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A pair of growth control triads are used to describe coincident tumor growth and liver regeneration after partial hepatectomy. The models are extensions of previous growth control models which describe tumor growth in an unperturbed host (Michelson and Leith, 1991,Bull. math. Biol. 53, 639–656; idem, 1992, Proceedings of the Third International Conference on Communications and Control, Vol. 2, pp. 481–490; idem, 1992,Bull. math. Biol. 55, 993–1011; idem,J. theor. Biol. 169, 327–338). The linkage between the two triads depends upon systemic signals carried by soluble factors, and mathematical descriptors based upon biological first principals are proposed. The sources of the growth factors, their targets and the processing of their signals are investigated. Analyses of equilibrium in the constant coefficients case and simulated growth curves for the dynamic system are presented, and the effects of growth factor-induced mitogenesis and angiogenesis are discussed in particular. A case is made for early and late responses in the coupled control system. The biology of the signal processing paradigm is placed within a new theoretical context and discussed with regard to tumor adaptation, liver differentiation and the development of a tumor hypoxic fraction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460621
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  • 4
    Electronic Resource
    Electronic Resource
    Autocrine and paracrine growth factors in tumor growth: A mathematical model (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. 639-656 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical model of tumor growth including autocrine and paracrine control has been developed. The model starts with the logistic equation of Verhulst: dV/dt=rV(1−V/K). Autocrine controls are described as modifiers of the Malthusian growth rate (r), while paracrine controls modify the carrying capacity (K) of the system. The control mechanisms are expressed in terms of “candidate” functions, which are based upon the dynamic distribution of TGF-alpha and TGF-beta in the local tumor environment. Three paradigms of tissue growth have been modeled: normal tissue wound repair, unrestricted, unperturbed tumor growth, and tumor growth in a (radiation) damaged environment (the Tumor Bed Effect, TBE). These scenarios were used to test the dynamics of the system against known phenomena. Computer simulations are presented for each case. The model is being extended to include the description of heterogeneous tumors, within which subpopulations can express differential degrees of growth activity. Heterogeneous tumor models, with and without emergent subpopulations, and models of terminal differentiation are also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458633
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  • 5
    Electronic Resource
    Electronic Resource
    Time-dependent subpopulation induction in heterogeneous tumors (1988)
    Springer
    Bulletin of mathematical biology 50 (1988), S. 681-696 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Time-dependent induction of clonal heterogeneity in the neoplastic micro-environment is analysed within the context of a competitive ecology. A model that describes a constant source for clonal emergence was analysed by Michelsonet al. (1987) as an extension of a model proposed by Jansson and Revesz (1974). The extended model has been termed the JRE Model. This paper extends these analyses to time-dependent emergence rates which may represent induction in the presence of a cytotoxic agent. If the analysis is constrained to the tumor micro-environment, and if the emergent subpopulation is drug resistant, then the model may describe the induction and emergence of drug resistant subclones in a growing neoplasm. Asymptotic closed form solutions are derived for a class of emergence rate functions which decay asymptotically to a constant mutation rate. This underlying mutation rate may represent spontaneous mutation to the resistant phenotype, and has been analysed stochastically (Coldmanet al., 1985). The asymptotic solutions to the time-dependent model approach the steady state solution for the JRE Model which represents the dynamics observed in the presence of a constant, spontaneous mutation rate. The clinical and biological implications of these results are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460096
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  • 6
    Electronic Resource
    Electronic Resource
    A theoretical explanation of “Concomitant resistance” (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 733-747 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Concomitant resistance is a tumor growth dynamic which results when the growth of a second tumor implant is inhibited by the presence of the first. Recently, we modeled tumor growth in the presence of a regenerating liver after partial hepatectomy (Michelson and Leith,Bull. Math. Biol. 57, 345–366, 1995), with an interlocking pair of growth control triads to account for the accelerated growth observed in both tissues. We also modeled tumor dormancy and recurrence as a dynamic equilibrium achieved between proliferating and quiescent subpopulations. In this paper those studies are extended to initially model the concomitant resistance case. Two interlocking model systems are proposed. In one an interactive competition between the tumor implants is described, while in the other purely proportional growth inhibition is described. The equilibria and dynamics of each system when the coefficients are held constant are presented for three subcases of model parameters. We show that the dynamic called concomitant resistance can be real or apparent, and that if the model coefficients are held constant, the only way to truly achieve concomitant resistance is by forcing one of the tumors into total quiescence. If this is the true state of the inhibited implant, then a non-constant recruitment signal is required to insure regrowth when the inhibitor mass is excised. We compare these theoretical results to a potential explanation of the phenomenon provided by Prehn (Cancer Res. 53, 3266–3269, 1993).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461849
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  • 7
    Electronic Resource
    Electronic Resource
    Positive feedback and angiogenesis in tumor growth control (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 233-254 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In vivo tumor growth data from experiments performed in our laboratory suggest that basic fibroblast growth factor (bFGF) and vascular endothelial growth factor (VEGF) are angiogenic signals emerging from an up-regulated genetic message in the proliferating rim of a solid tumor in response to tumor-wide hypoxia. If these signals are generated in response to unfavorable environmental conditions, i.e. a decrease in oxygen tension, then the tumor may play an active role in manipulating its own environment. We have idealized this type of adaptive behavior in our mathematical model via a parameter which represents the carrying capacity of the host for the tumor. If that model parameter is held constant, then environmental control is limited to tumor shape and mitogenic signal processing. However, if we assume that the response of the local stroma to these signals is an increase in the host's ability to support an ever larger tumor, then our models describe a positive feedback control system. In this paper, we generalize our previous results to a model including a carrying capacity which depends on the size of the proliferating compartment in the tumor. Specific functional forms for the carrying capacity are discussed. Stability criteria of the system and steady state conditions for these candidate functions are analyzed. The dynamics needed to generate stable tumor growth, including countervailing negative feedback signals, are discussed in detail with respect to both their mathematical and biological properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462002
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  • 8
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    Dormancy, Regression, and Recurrence: Towards a Unifying Theory of Tumor Growth Control (1994)
    Elsevier
    Details
    Publication Date: 1994-08-01
    Print ISSN: 0022-5193
    Electronic ISSN: 1095-8541
    Topics: Biology
    Published by Elsevier
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  • 9
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    Tolerance of the spinal cord of rats to irradiation with cyclotron-accelerated helium ions (1975)
    Wiley
    Details
    Publication Date: 1975-06-01
    Print ISSN: 0008-543X
    Electronic ISSN: 1097-0142
    Topics: Biology , Medicine
    Published by Wiley on behalf of American Cancer Society.
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  • 10
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    Cellular radiosensitivity of a rat brain tumor (1975)
    Wiley
    Details
    Publication Date: 1975-06-01
    Print ISSN: 0008-543X
    Electronic ISSN: 1097-0142
    Topics: Biology , Medicine
    Published by Wiley on behalf of American Cancer Society.
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