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

Nikolai D. Botkin; Varvara L. Turova; Andrey E. Kovtanyuk; Irina N. Sidorenko; Renée Lampe; Nikolai D. Botkin; Varvara L. Turova; Andrey E. Kovtanyuk; Irina N. Sidorenko; Renée Lampe

doi:10.3934/mbe.2019117

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 4: 2334-2352. doi: 10.3934/mbe.2019117

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Research article

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

Received: 07 June 2018 Accepted: 18 January 2019 Published: 15 March 2019

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.
- 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[J]. Mathematical Biosciences and Engineering, 2019, 16(4): 2334-2352. doi: 10.3934/mbe.2019117

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Abstract

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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