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State estimation in endocrine systems with pulsatile hormone secretion

State estimation in endocrine systems with pulsatile hormone secretion. Alexander Medvedev Information Technology Uppsala University 752 37 Uppsala SWEDEN alexander.medvedev@it.uu.se.

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State estimation in endocrine systems with pulsatile hormone secretion

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  1. State estimation in endocrine systems with pulsatile hormone secretion Alexander Medvedev Information Technology Uppsala University 752 37 Uppsala SWEDEN alexander.medvedev@it.uu.se Joint work with A. Churilov (S:t Petersburg State University and Zh.Zhasubaliyev (South-West State University of Russia)

  2. Outline • Vocabulary • Endocrine regulation • Mathematical model • Properties of the mathematical model • State estimation • Conclusions

  3. Why going biomedical? • New challenging control and estimation problems • Multifactoral diseases (diabetes, cancer, heart diseases, epilepsy, ect) need system approach • Many unsolved problems of life science are due to dynamical phenomena • Abundance of experimental data • High societal impact Citing Hiroaki Kitano: ”Although the road ahead is long and winding, it leads to a future where biology and medicine are transformed into precision engineering”

  4. Endocrinology • A hormone is a chemical messenger from one cell (or group of cells) to another. • Hormones are produced by nearly every organ and tissue type in a multicellular organism. • Hormones can be secreted in continuous (basal) or pulsatile (non-basal) manner. • Endocrinology deals with disorders of the endocrine system and hormones. • The use of dynamical mathematical models and methods in endocrinology is widespread • Analysis of feedback phenomena • Estimation of immeasurable hormone concentrations • Control: artificial pancreas, fertility therapies

  5. GnRH LH Te Modeling, analysis and estimation of the testosterone regulation in the male • Problems addressed: • Mathematical modeling • Kinetic parameter estimation • Estimation of GnRH pulses • Why? • Pulsatile secretion – general mechanism in endocrinology • Treatment of reproductive failure • Contraceptives for men • Treatment of prostate cancer • Changes in GnRH pulse frequency are related to, e. g. obesity, aging GnRH – gonadotropin releasing hormone (hypothalamus) LH – luteinizing hormone (hypophysis) Te – testosterone (testes) Te and LH serum concentration measured at 10 min sampling time in a young male

  6. Model: Pulsatile secretion x1 – GnRH x2 – LH x3 - Te b1, b2, b3 are positive and distinct GnRH is released in a pulsatile manner: gk and tk are evaluated by pulse modulation algorithm: when Te rises, the pulses of GnRH become sparser and their amplitude diminishes

  7. Pulse modulation in release hormone GnRH The purpose of the feedback is to generate sequences of GnRH pulses where both the amplitudes and the frequency impart biological information Te x Pulse modulation (amplitude and frequency) Hormone kinetics

  8. Complex dynamics • The model has no equilibria • Homeostasis – biological self-regulation • All the solutions are bounded • Difficult to achieve in stochastic formulations • The model exhibits multiple cycles • 1-cycle always exists and unique • Chaos • Only one attractor is discovered so far

  9. Chart of dynamic modes • Pk – k-cycle • P∞ – chaos • N- - period doubling bifurcation curve

  10. Validation on clinical data

  11. Release hormone observer • Pulsatile release of GnRH is of high interest but not measured in the human • An observer is used for model-based estimation of GnRH concentration

  12. Synchronous observer mode

  13. Pointwise mapping

  14. Pointwise mapping • The mapping P(.) is continuous • The derivatives of P(.) w. r. t. x and t are • also continuous

  15. Jacobian matrix

  16. Local asymptotic stability

  17. Simulation Chaotic solution in the plant 2-cycle with non-zero initial conditions

  18. Conclusions • A hybrid model of hormone regulation with intrinsic impulse-modulated feedback is shown to possess complex dynamics. • An observer with a static output estimation error feedback for the closed-loop endocrine regulation model is suggested. • A condition for the state estimation error stabilizability is obtained. • Conditions for local asymptotic stability of the state estimation error under m-cycle in the endocrine plant are derived.

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