Mathematical computerized modeling of daily healthy thermal homeostasis

Associate Professor, PhD A.V. Tsyganov1
Dr.Sc.Phys.Math., Professor Y.V. Tsyganova2
Associate Professor, PhD I.V. Stolyarova1
1Ulyanovsk State Pedagogical University named after I.N. Ulyanov, Ulyanovsk
2Ulyanovsk State University, Ulyanovsk

Objective of the study was to revise the existing mathematical computerized models of daily thermal homeostasis in healthy individuals; and offer a new mathematical model classifiable with the discrete linear stochastic systems addressing the state space with unknown inputs and noisy measurements. The model state vector includes tests of the body temperatures in discrete moments, with mesor viewed as the unknown input. For the body temperature and mesor computations, we applied an optimal discrete filtering algorithm with the state vector and unknown input being estimated simultaneously. We developed application software in MATLAB for computerized modeling of the temperature curves and test process and for optimal estimates of parameters of the mathematical model. The study findings may be applied to analyze the daily thermal homeostasis in healthy individuals.

Keywords: thermometry, thermal homeostasis, discrete linear stochastic system, optimal discrete filtering, MATLAB.

References

  1. Krolivetskaya Yu.M., Petrova E.S. Postroenie stohasticheskih modeley teplovogo gomeostaza cheloveka [Stochastic models of human thermal homeostasis]. Vestnik Astrahan. gos. tekh. un-ta. Seriya: Upravlenie, vychisl. tekhn. inform, 2014, no. 1, pp. 140–152.
  2. Nefedov V.P., Yasaytis A.A., Novoseltsev V.N. Gomeostaz na razlichnyih urovnyah organizatsii biosistem [Homeostasis at different levels of organization of biosystems]. Novosibirsk: Nauka. Sib. branch, 1991. 232 p.
  3. Tsyganova Yu.V. Ob odnoy modeli sutochnoy termometrii teplovogo gomeostaza cheloveka [Model of daily thermometry of human thermal homeostasis]. Pervaya mezhdunar. zaoch. nauch.-prakt. konf. «Fundamentalnyie i prikladnyie issledovaniya po prioritetnyim napravleniyam bioekologii i biotehnologii», sektsiya 'Matematicheskoe modelirovanie v bioekologii i biotehnologii' [The 2st Intern. on-line res.-practical conf. 'Fundamental and applied research in priority areas of bioecology and biotechnology', section 'Mathematical modeling in bioecology and biotechnology'], February 2015. Ulyanovsk: Ulyanov UlSPU. pp. 167–170.
  4. Gillijns S., Moor B. de Unbiased minimum-variance input and state estimation for linear discrete-time systems with direct feedthrough. Automatica, vol. 43, 2007, pp. 934–937.
  5. Kelly G. Body temperature variability (Part 1): a review of the history of body temperature and its variability due to site selection, biological rhythms, fitness, and aging. Altern. Med. Rev. 2006. Vol. 11, no. 4. P. 278–93.
  6. Redfern P. , Minors D., Waterhouse J. Circadian rhythms, jet lag, and chronobiotics: an overview. Chronobiol. Intern. 1994. No. 11. Р. 253– 256.
  7. Semushin I.V., Tsyganova J.V., Skovikov A.G. Identification of a Simple Homeostasis Stochastic Model Based on Active Principle of Adaptation. Proceedings of International Conference 'Applied Stochastic Models and Data Analysis ASMDA 2013 & DEMOGRAPHICS 2013', 25–28 June 2013 Mataro (Barcelona), Spain. Barcelona, 2013. pp. 775–783.
  8. Semushin I.V., Tsyganova J.V., Kulikova M.V. et al. Identification of Human Body Daily Temperature Dynamics via Minimum State Prediction Error Method Proceedings of ECC2016, European Control Conference (Aalborg, Denmark. June 29–July 1, 2016). IEEE, 2016.pp. 2429–2434.