Informationsteknologi Institutionen f¶r informationsteknologi | State estimation in endocrine systems with pulsatile hormone secretion Alexander

  • View
    214

  • Download
    0

Embed Size (px)

Text of Informationsteknologi Institutionen f¶r informationsteknologi | State estimation in endocrine...

  • Slide 1

Informationsteknologi Institutionen fr informationsteknologi | www.it.uu.se 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) Slide 2 Informationsteknologi Institutionen fr informationsteknologi | www.it.uu.se Outline Vocabulary Endocrine regulation Mathematical model Properties of the mathematical model State estimation Conclusions Slide 3 Informationsteknologi Institutionen fr informationsteknologi | www.it.uu.se 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 Slide 4 Informationsteknologi Institutionen fr informationsteknologi | www.it.uu.se 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 Slide 5 Informationsteknologi Institutionen fr informationsteknologi | www.it.uu.se Modeling, analysis and estimation of the testosterone regulation in the male GnRH LH Te 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 Slide 6 Informationsteknologi Institutionen fr informationsteknologi | www.it.uu.se Model: Pulsatile secretion x 1 GnRH x 2 LH x 3 - Te GnRH is released in a pulsatile manner: k and t k are evaluated by pulse modulation algorithm: when Te rises, the pulses of GnRH become sparser and their amplitude diminishes b 1, b 2, b 3 are positive and distinct Slide 7 Informationsteknologi Institutionen fr informationsteknologi | www.it.uu.se Pulse modulation in release hormone GnRH Pulse modulation (amplitude and frequency) Hormone kinetics Te The purpose of the feedback is to generate sequences of GnRH pulses where both the amplitudes and the frequency impart biological information Slide 8 Informationsteknologi Institutionen fr informationsteknologi | www.it.uu.se 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 Slide 9 Informationsteknologi Institutionen fr informationsteknologi | www.it.uu.se Chart of dynamic modes k k-cycle chaos N - - period doubling bifurcation curve Slide 10 Informationsteknologi Institutionen fr informationsteknologi | www.it.uu.se Validation on clinical data Slide 11 Informationsteknologi Institutionen fr informationsteknologi | www.it.uu.se 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 Slide 12 Informationsteknologi Institutionen fr informationsteknologi | www.it.uu.se Synchronous observer mode Slide 13 Informationsteknologi Institutionen fr informationsteknologi | www.it.uu.se Pointwise mapping Slide 14 Informationsteknologi Institutionen fr informationsteknologi | www.it.uu.se Pointwise mapping The mapping P(.) is continuous The derivatives of P(.) w. r. t. x and t are also continuous Slide 15 Informationsteknologi Institutionen fr informationsteknologi | www.it.uu.se Jacobian matrix Slide 16 Informationsteknologi Institutionen fr informationsteknologi | www.it.uu.se Local asymptotic stability Slide 17 Informationsteknologi Institutionen fr informationsteknologi | www.it.uu.se Simulation 2-cycle with non-zero initial conditions Chaotic solution in the plant Slide 18 Informationsteknologi Institutionen fr informationsteknologi | www.it.uu.se 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.