INDIRECT MEASUREMENT OF THE BRAIN TEMPERATURE DURING THE TREATMENT OF A NEUROLOGICAL DISORDER IN NEONATES

MOTIVATION

It is attributed to Hippocrates the quotation: “That which drugs fail to cure, the scalpel can cure. That which the scalpel fails to cure, heat can cure. If heat cannot cure, it must be deemed incurable.” (Hurwitz, 2013). Therefore, heat transfer applications in biomedicine date back to many years BC. Today’s bioheat transfer applications are innumerous, including thermal therapies of cancer. The literature on bioheat transfer is abundant, with more than 2600 documents that exhibit a steady increase in the Scopus database, since 1978 (keyword: “bioheat” – Scopus, 2024). The largest subject area of these documents is Engineering (26.3%), followed by Physics (14.3%) and Medicine (12%). Hence, engineers have been playing a fundamental role in scientific advancements related to the use of heat in biomedical applications.

In particular, this collaborative work involving the Silesian University of Technology (Poland) and the Federal University of Rio de Janeiro (Brazil) has been focused on the mild hypothermia treatment of the hypoxic-ischemic encephalopathy in neonates. The cooling of the brain by 2°C to 5°C below the normal body temperature can mitigate the effects of this neurological disorder, which is characterized by the lack of oxygen (hypoxia) and low blood flow (ischemia) in the brain (Clark et al., 1996; Barone et al., 1997; Marion, 1997; Hayashi and Dietrich, 2004; Gluckman et al., 2005; Łaszczyk et al., 2014; Silva et al., 2016, 2018; Łaszczyk and Nowak, 2016; Bandola et al., 2018). Commercial apparatuses are available for the systemic or the local cooling treatment of the hypoxic-ischemic encephalopathy in neonates. A blanket or a mattress at low temperatures can be used for systemic cooling, while local cooling can be achieved by surrounding the head of the newborn with a cool cap. The blanket, mattress or cap are maintained at low temperatures by the internal circulation of cold water, controlled by an external refrigeration system, while a radiant heater can also be jointly used to control de temperature of the neonate.

During the hypothermia treatment, temperature measurements are taken on the skins of the head and of the abdomen, while the internal body temperature is monitored through the rectum or nose. Although techniques are available for real-time measurements of the internal body temperature, such as magnetic resonance thermometry (Quesson et al., 2011), they demand dedicated equipment not generally found in clinics and/or that cannot be available during the whole hypothermia treatment. Therefore, accurate solutions of inverse problems are highly desirable for the indirect measurement of the brain temperature, based on the available measurements and mathematical modelling during the hypothermia treatment of the hypoxic-ischemic encephalopathy. The inverse problem solutions need to account for different sources of uncertainties.

INDIRECT MEASUREMENT OF THE BRAIN TEMPERATURE

The Sampling Importance Resampling (SIR) algorithm of the particle filter method (Ristic, 2004) was successfully applied in Nunes et al. (2019, 2022) for the estimation of the brain temperature during the mild hypothermia treatment of the hypoxic ischemic encephalopathy. Then, a stochastic model predictive control strategy based on the application of two nested particles filters was introduced to indirectly observe and control the body temperatures at specific positions (Nunes et al., 2023). While these previous works were based on simulated measurements containing additive Gaussian errors, the solution of the state estimation problem with the SIR algorithm was validated with actual measurements in Nunes et al. (2024). The agreement between estimated temperatures (obtained from the solution of the forward model with the inverse problem solution) and actual measurements was excellent, at a location where the measurements were not used in the inverse analysis (see Fig. 1).

Figure 1.  Comparison of estimated and actual measured temperatures at the front surface of the abdomen during the hypothermia treatment of the hypoxic ischemic encephalopathy [Reproduced from Nunes et al. (2024). Copyright © 2024 Elsevier Masson SAS. All rights reserved.].

A geometric model was also developed in Nunes et al. (2024) for the body of the neonate under treatment, based on dimensions measured after birth and on medical literature data about body proportions, as illustrated by Fig. 2. The body members were modelled by hemispheres and cylinders, consisting of concentric layers of different tissues. Fiala’s blood pool concept was considered for the circulatory system (Fiala et al., 1999) in Nunes et al. (2024).

Figure 2.  Geometric model developed in Nunes et al. (2024) to represent the neonate patient body (BSA – body surface area)

OUTLOOK

Customized medical treatments that comply with well-established protocols demand computational simulations under the effects of different sources of uncertainties. The solution of inverse problems can be used to account for uncertainties in mathematical models and measurements, particularly by using stochastic simulations within the Bayesian framework of statistics. The excellent results obtained with actual measurements revealed that the SIR algorithm of the particle filter can be a powerful and stable tool for the estimation of the brain temperature during the hypothermia treatment of the neonatal hypoxic-ischemic encephalopathy. The reduction of computational times of inverse problem solutions must be sought for real-time applications, including the use of low-fidelity models like those based on artificial intelligence.