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@ARTICLE{Bhler:10905,
      author       = {Bühler, J. and Huber, G. and Schmid, F. and Blümler, P.},
      title        = {{A}nalytical model for long-distance tracer-transport in
                      plants},
      journal      = {Journal of theoretical biology},
      volume       = {270},
      issn         = {0022-5193},
      address      = {London},
      publisher    = {Academic Press},
      reportid     = {PreJuSER-10905},
      pages        = {70 - 79},
      year         = {2011},
      note         = {We wish to thank Hanno Scharr, Wilfried Wolff, Michael
                      Thorpe and Peter Minchin for helpful discussions. Special
                      thanks go to Siegfried Jahnke for valuable comments and
                      access to the PET data. Jonas Buhler wants to thank Martin
                      Reissel for technical support. Friederike Schmid
                      acknowledges financial support from the MRL of UC Santa
                      Barbara during a sabbatical. This work was partially
                      supported by the MRSEC Program of the National Science
                      Foundation under Award no. DMR05-20415. Finally, Peter
                      Blumler wants to thank Helmut Soltner for an excursion into
                      Laplacian space! Last but not least continuous support from
                      Uli Schurr made this work possible.},
      comment      = {Journal of Theoretical Biology 270 (2011) 70–79},
      booktitle     = {Journal of Theoretical Biology 270
                       (2011) 70–79},
      abstract     = {Recent investigations of long-distance transport in plants
                      using non-invasive tracer techniques such as (11)C
                      radiolabeling monitored by positron emission tomography
                      (PET) combined with magnetic resonance imaging (MRI)
                      revealed the need of dedicated methods to allow a
                      quantitative data analysis and comparison of such
                      experiments. A mechanistic compartmental tracer transport
                      model is presented, defined by a linear system of partial
                      differential equations (PDEs). This model simplifies the
                      complexity of axial transport and lateral exchanges in the
                      transport pathways of plants (e.g. the phloem) by simulating
                      transport and reversible exchange within three compartments
                      using just a few parameters which are considered to be
                      constant in space and time. For this system of PDEs an
                      analytical solution in Fourier-space was found allowing a
                      fast and numerically precise evaluation. From the
                      steady-state behavior of the model, the system loss
                      (steadily fixed tracer along the transport conduits) was
                      derived as an additional parameter that can be readily
                      interpreted in a physiological way. The presented framework
                      allows the model to be fitted to spatio-temporal tracer
                      profiles including error and sensitivity analysis of the
                      estimated parameters. This is demonstrated for PET data sets
                      obtained from radish, sugar beet and maize plants.},
      keywords     = {Algorithms / Beta vulgaris: metabolism / Biological
                      Transport: physiology / Carbon Radioisotopes: metabolism /
                      Computer Simulation / Fourier Analysis / Magnetic Resonance
                      Imaging / Models, Biological / Phloem: metabolism / Plant
                      Roots: metabolism / Plant Structures: metabolism / Plants:
                      metabolism / Positron-Emission Tomography / Radioactive
                      Tracers / Raphanus: metabolism / Xylem: metabolism / Zea
                      mays: metabolism / Carbon Radioisotopes (NLM Chemicals) /
                      Radioactive Tracers (NLM Chemicals) / J (WoSType) / Phloem /
                      11C / Simulation / Data analysis / Positron
                      emissiontomography(PET)},
      cin          = {IBG-2},
      ddc          = {570},
      cid          = {I:(DE-Juel1)IBG-2-20101118},
      pnm          = {Terrestrische Umwelt},
      pid          = {G:(DE-Juel1)FUEK407},
      shelfmark    = {Biology / Mathematical $\&$ Computational Biology},
      typ          = {PUB:(DE-HGF)16},
      pubmed       = {pmid:21056579},
      UT           = {WOS:000286406700010},
      doi          = {10.1016/j.jtbi.2010.11.005},
      url          = {https://juser.fz-juelich.de/record/10905},
}