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Extended model of impaired cerebral autoregulation in preterm infants: Heuristic feedback control

1 Department of Mathematics, Technical University of Munich, Boltzmannstr. 3, Garching, 85748, Germany
2 Research Unit for Cerebral Palsy and Children Neuro-Orthopedics of the Buhl-Strohmaier-Foundation, Orthopedic Department of the Clinic ‘rechts der Isar’, Technical University of Munich, Ismaninger Str. 22, Munchen, 81675, Germany

Cerebral autoregulation is the ability to keep almost constant cerebral blood flow (CBF) for some range of changing the mean arterial pressure (MAP). In preterm infants, this range is usually very small, even absent, and a passive (linear) dependence of CBF on MAP is observed. Also, variations of the partial CO2 pressure and intracranial/venous pressure result in fluctuations of CBF. The absence of cerebral autoregulation may be a cause of intracranial hemorrhages due to instability of cerebral blood vessels, especially in the so-called germinal matrix which exists in a developing brain from 22 to 32 weeks of gestation. In the current paper, a mathematical model of impaired cerebral autoregulation is extended compared with previous works of the authors, and a heuristic feedback control that is able to keep deviations from a nominal CBF within a reasonable range is proposed. Viability theory is used to prove that this control can successfully work against a wide range of disturbances.
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Keywords Cerebral autoregulation; feedback control; viability set; leadership kernel; discriminating kernel; grid method

Citation: Nikolai D. Botkin, Varvara L. Turova, Andrey E. Kovtanyuk, Irina N. Sidorenko, Renée Lampe. Extended model of impaired cerebral autoregulation in preterm infants: Heuristic feedback control. Mathematical Biosciences and Engineering, 2019, 16(4): 2334-2352. doi: 10.3934/mbe.2019117


  • 1. J. Donnelly, M. J. Aries and M. Czosnyka, Further understanding of cerebral autoregulation at the bedside: possible implications for future therapy, Expert Rev. Neurother., 15 (2015), 169–185.
  • 2. M. van de Bor and F. J. Walther, Cerebral blood flow velocity regulation in preterm infants, Biol. Neonate, 59 (1991), 329–335.
  • 3. J. R. Kaiser, C. H. Gauss and D. K.Williams, The effects of hypercapnia on cerebral autoregulation in ventilated very low birth weight infants, Pediatr. Res., 58 (2005), 931–935.
  • 4. J. J. Volpe, Intracranial hemorrhage: germinal matrix hemorrhage of the premature infant, in Neurology of the Newborn, 48 (2001), WB Saunders, Philadelphia, pp. 435.
  • 5. T. Lekic, D. Klebe, R. Poblete, et al., Neonatal brain hemorrhage (NBH) of prematurity: translational mechanisms of the vascular-neural network, Curr. Med. Chem., 22 (2015), 1214– 1238.
  • 6. O. Pryds and A. D. Edwards, Cerebral blood flow in the newborn infant, Arch. Dis. Child- Fetal, 74 (1996), F63–F69.
  • 7. P. Ballabh, Intraventricular hemorrhage in premature infants: mechanism of disease, Pediatr. Res., 67 (2010), 1–8.
  • 8. M. Ursino and C. A. Lodi, A simple mathematical model of the interaction between intracranial pressure and cerebral hemodynamics, J. Appl. Physiol., 82 (1997), 1256–1269.
  • 9. R. B. Panerai, S. L. Dawson and J. F. Potter, Linear and nonlinear analysis of human dynamic cerebral autoregulation, Am. J. Physiol.- Heart C, 277 (1999), H1089–H1099.
  • 10. M. S. Olufsen, A. Nadim and L. A. Lipsitz, Dynamics of cerebral blood flow regulation explained using a lumped parameter model, Am. J. Physiol.- Reg. I, 282 (2002), R611–R622.
  • 11. J. Alastruey, S. M. Moore, K.H. Parker, et al., Reduced modeling of blood flow in cerebral circulation: Coupling 1-D, 0-D and cerebral auto-regulation models, Int. J. Numer. Meth. Fl., 56 (2008), 1061–1067.
  • 12. V. Z. Marmarelis, D. C. Shin and R. Zhang, Linear and nonlinear modeling of cerebral flow autoregulation using principal dynamic modes, Open Biomed. Eng. J., 6 (2012), 42–55.
  • 13. B. Spronck, E. G. Martens, E. D. Gommer, et al., A lumped parameter model of cerebral blood flow control combining cerebral autoregulation and neurovascular coupling, Am. J. Physiol.- Heart C, 303 (2012), H1143–11H53.
  • 14. R. Lampe, N. Botkin, V. Turova, et al., Mathematical modelling of cerebral blood circulation and cerebral autoregulation: towards preventing intracranial hemorrhages in preterm newborns, Comput. Math. Method M., (2014), 1–9.
  • 15. S. Payne, Cerebral Autoregulation: Control of Blood Flow in the Brain, Springer, Berlin, 2016.
  • 16. N. Botkin, V. Turova and R. Lampe, Feedback control of impaired cerebral autoregulation in preterm infants: Mathematical modelling, in 25th Mediterranean Conference on Control and Automation (MED), IEEE, (2017), 229–234.
  • 17. S. K. Piechnik, P. A. Chiarelli and P. Jezzard, Modelling vascular reactivity to investigate the basis of the relationship between cerebral blood volume and flow under CO2 manipulation, NeuroImage, 39 (2008), 107–118.
  • 18. U. H. Thome and N. Ambalavanan, Permissive hypercapnia to decrease lung injury in ventilated preterm neonates, Semin. Fetal Neonat. M., 14 (2009), 21–27.
  • 19. J. P. Aubin, Viability Theory, Birkhäuser, Boston, 1991.
  • 20. N. N. Krasovskii and A. I. Subbotin, Game-theoretical control problems, Springer, New York, 1988.
  • 21. N. D. Botkin and V. L. Turova, Numerical construction of viable sets for autonomous conflict control systems, Mathematics, 2 (2014), 68–82.
  • 22. J. L. LeFlore and W. D. Engle, Clinical factors influencing blood pressure in the neonate, NeoReviews, 3 (2002), e145–e150.
  • 23. G. D. T. Inglis, K. R. Dunster and M. W. Davies, Establishing normal values of central venous pressure in very low birth weight infants, Physiol. Meas., 28 (2007), 1283.
  • 24. J. M. Perlman, Neurology: Neonatology questions and controversies, Saunders/Elsevier, Philadelphia, 2008.
  • 25. T.A. Polovova, Hemodynamics Features with Different Methods of Respiratory Support in Children with Extremely Low Body Weight, Ph.D thesis, Ural Scientific Research Institute of Maternity and Infancy Protection of the Ministry of Health of the Russian Federation in Ekaterinburg, 2014 (in Russian).
  • 26. R. Lampe, V. Turova, N. Botkin, et al., Postnatal paraclinical parameters associated to occurrence of intracerebral hemorrhage in preterm infants, Neuropediatrics, (2018).
  • 27. P. Cardaliaguet, A differential game with two players and one target, SIAM J. Control Optim., 34 (1996), 1441–1460.
  • 28. P. Cardaliaguet, M. Quincampoix and P. Saint-Pierre, Set valued numerical analysis for optimal control and differential games, in M. Bardi, T. E. S. Raghavan, T. Parthasarathy (eds.) Stochastic and Differential Games: Theory and Numerical Methods. Annals of the International Society of Dynamic Games 4 (1999), Birkhäuser, Boston, 177–274.
  • 29. N. Botkin, V. Turova, J. Diepolder, et al., Aircraft control during cruise flight in windshear conditions: viability approach, Dyn. Games Appl., (2017), 1–15.
  • 30. N. D. Botkin and V. L. Turova, Examples of computed viability kernels, Trudy Inst. Mat. i Mekh. UrO RAN, 21 (2015), 306–319.
  • 31. N. D. Botkin, K.-H. Hoffmann, N. Mayer, et al., Approximation schemes for solving disturbed control problems with non-terminal time and state constraints, Analysis, 31 (2011), 355–379.
  • 32. A. D. Edwards, J. S. Wyatt, C. Richardson, et al., Effects of indomethacin on cerebral haemodynamics in very preterm infants, The Lancet, 335 (1990), 1491–1495.
  • 33. N. D. Botkin, A. E. Kovtanyuk, V. L. Turova, et al., Direct modeling of blood flow through the vascular network of the germinal matrix, Comput. Biol. Med., 92 (2018), 147–155.


This article has been cited by

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