OBSERVATION WITH BOUNDS OF BIOLOGICAL SYSTEMS - A Linear Programming Approach

Fernando Tadeo, Mustapha Ait Rami

Abstract

This paper presents a technique to estimate the states of biological systems that cannot be directly measured, by using available measurements of other states that affect them. More precisely, the proposed technique makes it possible to derive, at each moment, the possible range of variation of these unmeasured states. It is based on having a compartmental model of the system (which might include uncertain parameters), and then solving a Linear Programming problem. A practical example, based on the kinetic model of drug distribution through the human body, is provided to show its applicability.

References

  1. Ait Rami, M., Helmke, U., Tadeo, F. Positive Observation Problem For Linear Time-Lag Positive Systems IFAC Workshop on Systems, Structure and Control, Foz de Iguazu, Brazil, 2007.
  2. Ait Rami, M., Helmke, U., Tadeo, F. Positive observation problem for time-delays linear positive systems. IEEE Mediterranean Control Conference, Greece, 2007.
  3. Alamo, T., Bravo, J.M., Camacho, E.F., Guaranteed state estimation by zonotopes, Automatica, 41(6): 1035- 1043, 2005.
  4. Blake, G.M., Park-Holohan, S.-J., Fogelman, I., Quantitative Studies of Bone in Postmenopausal Women Using 18F-Fluoride and 99mTc-Methylene Diphosphonate. J of Nuclear Medicine, 43:338-345.
  5. Combastel, C.. A state bounding observer for uncertain nonlinear continuous-time systems based on zonotopes. 44th IEEE CDC, Seville, 2005.
  6. Cook, G.J.R., Lodge, M.A., Blake, G.M., Marsden, Pl.K., Fogelman, I. Differences in skeletal kinetics between vertebral and humeral bone measured by 18F-Fluoride positron emission tomography in postmenopausal women. J Bone Mineralization Research 15:763-769, 2000.
  7. Fogelman, I., Citrin, D.L., McKillop, J.H. et al., A clinical comparison of Tc-99m HEDP and Tc-99m MDP in the detection of bone metastases. J of Nuclear Medicine 20: 98-101, 1979.
  8. Gouze, J.L., Rapaport, A., Hadj-Sadok, Z.M.. Interval observers for uncertain biological systems. J of Ecological Modelling, 133:4556, 2000.
  9. Gover, R., Hwang, P.Y.C., Introduction to Random Signals and Applied Kalman Filtering. John Wiley & Sons, 1997.
  10. Hynne, F., Dano, S., Sorensen, P.G., Full-scale model of glycolysis in Saccharomyces cerevisiae. Biophysical Chemistry, 94: 12116, 2001.
  11. Jacquez, J.A., Compartmental Analysis in Biology and Medicine. Ann Arbor, MI: University of Michigan Press, 1985.
  12. Linninger, A.A., Xenos, M., Sweetman, B., Ponkshe, S., Guo, X., Penn, R. A mathematical model of blood, cerebrospinal fluid and brain dynamics. J of Mathematical Biology, 59(6): 729-759, 2009.
  13. Luenberger, D.G., An introduction to observers. IEEE Trans. Aut. Control, 16: 596-602, 1966.
  14. Luzyanina, T., Mrusek, S., Edwards, J.T., Roose, D., Ehl, S., Bocharov, G., Computational analysis of CFSE proliferation assay. J of Mathematical Biology 54(1): 57-89, 2007.
  15. Makler, P.T., Charkes, N.D. Studies of Skeletal Tracer Kinetics IV. Optimum Time Delay for Tc-99m(Sn) Methylene Disphosphonate Bone Imaging, J of Nuclear Medicine, 21: 641-645, 1980.
  16. Rapaport, A., Dochain, D., Interval observers for biochemical processes with uncertain kinetics and inputs, Mathematical Biosciences, 193(2) 235-253, 2005.
  17. Rosenthall, L., Arzoumanian, A., Lisbona, R., et al., A longitudinal comparison of the kinetics of 99mTc-MDP and 99mTc-EHDP in humans, Clin. Nucl. Med, 2: 232-234, 1997.
  18. Subramanian, G., McAfee, J.G., Blair R.J. et al., An evaluation of 99mTc-labeled phosphate compounds as bone imaging agents, Radiopharmaceuticals, 319- 328, 1975.
  19. Van Den Hof, J.M., Positive linear observers for linear compartmental systems. SIAM J on Control and Optimization, 36: 590-608, 1998.
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Paper Citation


in Harvard Style

Tadeo F. and Ait Rami M. (2010). OBSERVATION WITH BOUNDS OF BIOLOGICAL SYSTEMS - A Linear Programming Approach . In Proceedings of the Third International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2010) ISBN 978-989-674-018-4, pages 230-235. DOI: 10.5220/0002717602300235


in Bibtex Style

@conference{biosignals10,
author={Fernando Tadeo and Mustapha Ait Rami},
title={OBSERVATION WITH BOUNDS OF BIOLOGICAL SYSTEMS - A Linear Programming Approach},
booktitle={Proceedings of the Third International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2010)},
year={2010},
pages={230-235},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002717602300235},
isbn={978-989-674-018-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Third International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2010)
TI - OBSERVATION WITH BOUNDS OF BIOLOGICAL SYSTEMS - A Linear Programming Approach
SN - 978-989-674-018-4
AU - Tadeo F.
AU - Ait Rami M.
PY - 2010
SP - 230
EP - 235
DO - 10.5220/0002717602300235