Abstract
In this paper, a novel evolution equation for capillaries growth is proposed. An essential ingredient is given by the consideration of nutrient supply, for which a novel constitutive equation is also proposed. The biological and mechanical stimuli are assumed to depend in non-local way on relevant kinematical descriptors. The integro-differential equations governing the system evolution are extremely sensitive to parameter variations. However, it was possible to perform some meaningful numerical simulations in which osteophyte onset has been observed. While the choice of these parameters was judiciously driven by biomechanical “a priori” knowledge, the mathematical problems concerning well-posedness, stability and continuous dependence of solutions seem to be very challenging and will be object of future investigations. This effort seems motivated by the fact that proposed equations are, to our knowledge, the first ones allowing for the prediction of osteophytes onset.
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Bednarczyk, E., Lekszycki, T. A novel mathematical model for growth of capillaries and nutrient supply with application to prediction of osteophyte onset. Z. Angew. Math. Phys. 67, 94 (2016). https://doi.org/10.1007/s00033-016-0687-2
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DOI: https://doi.org/10.1007/s00033-016-0687-2