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  • 1. Banks-Sills, Leslie
    et al.
    Ståhle, Per
    Malmö högskola, School of Technology (TS).
    Svensson, Ingrid
    Eliaz, Noam
    Strain Driven Transport for Bone Modeling at the Periosteal Surface2011In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 230, no 1, p. 37-44Article in journal (Refereed)
    Abstract [en]

    Bone modeling and remodeling has been the subject of extensive experimental studies. There have been several mathematical models proposed to explain the observed behavior, as well. A different approach is taken here in which the bone is treated from a macroscopic view point. In this investigation, a one-dimensional analytical model is used to shed light on the factors which play the greatest role in modeling or growth of cortical bone at the periosteal surface. It is presumed that bone growth is promoted when increased amounts of bone nutrients, such as nitric oxide synthase (NOS) or messenger molecules, such as prostaglandin E2 (PGE2), seep out to the periosteal surface of cortical bone and are absorbed by osteoblasts. The transport of the bone nutrients is assumed to be a strain controlled process. Equations for the flux of these nutrients are written for a one-dimensional model of a long bone. The obtained partial differential equation is linearized and solved analytically. Based upon the seepage of nutrients out of the bone, the effect of loading frequency, number of cycles and strain level is examined for several experiments that were found in the literature. It is seen that bone nutrient seepage is greatest on the tensile side of the bone; this location coincides with the greatest amount of bone modeling

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  • 2.
    Masic, Alma
    et al.
    Malmö högskola, School of Technology (TS).
    Bengtsson, Jessica
    Christensson, Magnus
    Measuring and modeling the oxygen profile in a nitrifying Moving Bed Biofilm Reactor2010In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 227, no 1, p. 1-11Article in journal (Refereed)
    Abstract [en]

    In this paper we determine the oxygen profile in a biofilm on suspended carriers in two ways: firstly by microelectrode measurements and secondly by a simple mathematical model. The Moving Bed Biofilm Reactor is well-established for wastewater treatment where bacteria grow as a biofilm on the protective surfaces of suspended carriers. The flat shaped BiofilmChip P was developed to allow good conditions for transport of substrates into the biofilm. The oxygen profile was measured in situ the nitrifying biofilm with a microelectrode and it was simulated with a one-dimensional mathematical model. We extended the model by adding a CSTR equation, to connect the reactor to the biofilm through the boundary conditions. We showed the dependence of the thickness of the mass transfer boundary layer on the bulk flow rate. Finally, we estimated the erosion parameter λ to increase the concordance between the measured and simulated profiles. This lead to a simple empirical relationship between λ and the flow rate. The data gathered by in situ microelectrode measurements can, together with the mathematical model, be used in predictive modeling and give more insight in the design of new carriers, with the ambition of making process operation more energy efficient.

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