Estimation of the ischemic brain temperature with the particle filter method
In this work, a two-dimensional model was developed to analyze the transient temperature distribution in the head of a newborn, during local cooling promoted by the flow of cold water through a cap. The inverse problem dealt with the sequential estimation of the internal temperature of the head, by using non-invasive transient temperature measurements. A state estimation problem was solved with the Sampling Importance Resampling (SIR) algorithm of the Particle Filter method. Uncertainties in the evolution and observation models were assumed as additive, Gaussian, uncorrelated and with zero means. The uncertainties for the evolution model were obtained from Monte Carlo simulations, based on the uncertainties of the model parameters. The head temperature was accurately predicted with the Particle Filter method. Such a technique might be applied in the future to monitor the brain temperature of newborns and control the local cooling treatment of neonatal hypoxic-ischemic encephalopathy.
Keywordsneonatal hypoxic-ischemic encephalopathy ;, Sampling Importance Resampling (SIR) algorithm, particle filter, local brain cooling,
References J.E. Laszczyk, A.J. Nowak. The analysis of a newborn’s brain cooling process. LAP LAMBERT Academic Publishing, 2015, ISBN-13: 978-3-659-67932-2.
 J.E. Laszczyk, A. Maczko, W. Walas, A.J. Nowak. The numerical modeling of the heat transfer processes within neonate’s body based on the simplified geometric model. Information Technologies in Biomedicine, Lecture Notes in Computer Science, 7339: 310-318, 2012.
 F.C. Barone, G.Z. Feuerstein, R.E. White. Brain cooling during transient focal ischemia provides complete neuroprotection. Neuroscience and Biobehavioral Reviews, 21(1): 31-44, 1997.
 R.S.B. Clark, E.M. Kochanek, D.W. Marion, J.K. Schiding, M. White, A.M. Palmer, S.T. DeKosky. Mild post traumatic hypothermia reduces mortality after severe controlled cortical impact in rats. Journal of Cerebral Blood Flow and Metabolism, 16: 253-261, 1996.
 D.W. Marion, L.E. Penrod, S.F. Kelsey, W.D. Obrist, P.M. Kochanek, A.M. Palmer, S.R. Wisniewski, S.T. DeKosky. Treatment of traumatic brain injury with moderate hypothermia. The New England Journal of Medicine, 336: 540-546, 1997.
 P.D. Gluckman, J.S. Wyatt, D. Azzopardi, R. Ballard, A.D. Edwards, D.M. Ferriero, R.A. Polin, Ch.M. Robertson, M. Thoresen, A. Whitelaw, A.J. Gunn. Selective head cooling with mild systemic hypothermia after neonatal encephalopathy: multicentre randomised trial. The Lancet, 365(9460): 663-670, 2005.
 G. Kuhnen, N. Einer-Jensen, S.A. Tisherman. Cooling methods in Therapeutic hypothermia. Springer, United States of America, 2005.
 S.A. Zanelli, D.P. Stanley, D. Kaufman. Hypoxic-Ischemic Encephalopathy. Medscape, 2008
 C. Diao, L. Zhu, H. Wang. Cooling and rewarming for brain ischemia or injury: theoretical analysis. Annals of Biomedical Engineering, 31(3): 346-353, 2003.
 D. Bandola, A.J. Nowak, M. Rojczyk, Z. Ostrowski, W. Walas. Measurement and computational experiments within newborn’s brain cooling process. International Heat Transfer Conference Digital Library. Begell House Inc., 2018.
 B.H. Dennis, R.C. Eberhart, G.S. Dulikravich, S.W. Radons. Finite-element simulation of cooling of realistic 3-D human head and neck. Journal of Biomechanical Engineering, 125(6): 832-340, 2003.
 C. Pacheco, H.R.B. Orlande, M.J. Colaço, G.S. Dulikravich. State estimation problems in PRF-shift magnetic resonance thermometry. International Journal of Numerical Methods for Heat & Fluid Flow, 28: 315-335, 2018.
 A. Mohsen, H.R.B. Orlande, B. Lamien. Application of the photoacoustic technique for temperature measurements during hyperthermia. Inverse Problems in Science and Engineering, 10: 1-21, 2018.
 A. Mohsen, H.R.B. Orlande. Inverse photoacoustic technique for parameter and temperature estimation in tissues. Heat Transfer Engineering, 38: 1573-1594, 2016.
 A. Doucet, N. de Freitas, N. Gordon. Sequential Monte Carlo Methods in Practice. Springer, New York, 2001.
 J. Kaipio, E. Somersalo. Statistical and Computational Inverse Problems, Applied Mathematical Sciences. Springer-Verlag, 2004.
 B. Ristic, S. Arulampalam, N. Gordon. Beyond the Kalman Fliter. Artech House, Boston, 2004.
 S. Arulampalam, S. Maskell, N. Gordon, T. Clapp. A tutorial on particle filters for on-line non-linear/non-Gaussian bayesian tracking. IEEE Transactions on Signal Processing, 20: 174-188, 2001.
 C.P. Robert, A. Doucet, C. Andrieu. Computational advances for and from Bayesian analysis. Statistical Science, 19: 118-127, 2004.
 C. Andrieu, A. Doucet, S.S. Singh, V.B. Tadic. Particle methods for change detection, system identification and control. Proceedings of the IEEE, 92: 423-438, 2004.
 J. Carpenter, P. Clifford, P. Fearnhead. An improved particle filter for non-linear problems. IEE Proceedings - Radar, Sonar and Navigation, 146(1): 2-7, 1999.
 N. Kantas, A. Doucet, S.S. Singh, J. Maciejowski, N. Chopin. On particle filter methods for parameter estimation in state-space models. Statistical Science, 30: 328-351, 2015.
 P. Del Moral, A. Doucet, A. Jasra. Sequential Monte Carlo samplers. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 68(3): 411-426, 2006.
 H.F. Lopes, C.M. Carvalho. Online Bayesian Learning in Dynamic Models: An Illustrative Introduction to Particle Methods. In: P. Damien, P. Dellaportas, N.G. Polson, D.A. Stephens. Bayesian Theory and Applications, Oxford University, 2013.
 H.R.B. Orlande, M.J. Colaço, G.S. Dulikravich, F. Vianna, W.B. Silva, H.M. da Fonseca. O.
Fudym. State Estimation Problems in Heat Transfer. International Journal for Uncertainty
Quantification, 2: 239-258, 2012.
 C. Diao, L. Zhu. Theoretical simulation of temperature distribution in the brain during mild
hypothermia treatment for brain injury. Medical & Biological & Engineering & Computing, 39:
 H.H. Pennes. Analysis of tissue and arterial blood temperatures in the resting human forearm. Journal of Applied Physiology, 1(2): 93-122, 1948.
 X. Xu, R. Tikuisis, G. Giesbrecht. A mathematical model for human brain cooling during cold water near drowning. Journal of Applied Physiology, 86: 265-272, 1999.