Brain temperature is a fundamental physiological variable that can affect numerous neural processes, from basic properties such as nerve conduction velocity, passive membrane potential, and synaptic transmission, to global regulation of brain activity (Wang et al., 2014). Specifically, fluctuations within the physiological temperature range (33–37°C in rodents) have been shown to modify channel kinetics (Rosen, 2001), reuptake of neurotransmitters by transporters (Xie et al., 2000), miniature postsynaptic currents (Simkus and Stricker, 2002), the neuronal firing rates of single neurons (Tryba and Ramirez, 2004; Guatteo et al., 2005), and neuronal synchronization (Csernai et al., 2019). Conversely, neuronal activity is one of the main determinants of brain temperature (Kiyatkin et al., 2002). Thus, brain activity both affects and is affected by fluctuations in temperature. In clinical settings, brain temperature increases in common pathological conditions such as stroke or head injury (Mrozek et al., 2012), and temperature is deliberately lowered in interventions to protect the brain from hypoxic events (Faridar et al., 2011). Since heat plays a crucial role in neuronal functioning (Kiyatkin, 2010; Alonso and Marder, 2020) and brain tissue is very sensitive to thermal damage (Yarmolenko et al., 2011), it is crucial to understand which factors contribute to changes in brain temperature under normal circumstances.

Generally, brain temperature is considered to be the net result of heat production, which is determined by brain metabolism, and heat dissipation, which is determined by brain blood flow and the brain-to-blood temperature gradient (Hayward and Baker, 1969). The sleep–wake states, non–rapid-eye-movement (NREM) sleep, rapid-eye-movement (REM) sleep, and wakefulness, define brain states associated with specific neuronal activities, oxygen consumption, and metabolism (Nir et al., 2013). The latter two (active) brain states are accompanied by increases in brain temperature, whereas NREM sleep evidences a decrease (Hayward and Baker, 1969; Obál et al., 1985; Franken et al., 1992a; Hoekstra et al., 2019). Besides decreased heat production, increased heat dissipation further contributes to the decreases in brain temperature during NREM sleep: (i) although the global blood flow to the brain decreases in absolute terms, it increases when taking the considerable drop in oxygen consumption during NREM sleep into account (McAvoy et al., 2019), and (ii) since body temperature is actively down-regulated through peripheral vasodilation (and perspiration in humans) after sleep onset, the brain-to-blood temperature gradient increases (Szymusiak, 2018).

By quantifying the relationship between sleep–wake state and brain temperature we reported that the sleep–wake distribution explains 84% of the variance in brain temperature in the rat (Franken et al., 1992b), a finding we recently replicated in the mouse (Hoekstra et al., 2019). However, the 1992 analysis has been criticized for overestimating the impact of sleep–wake state by having averaged over hourly intervals and ignoring other contributing factors such as locomotion (Heller et al., 2011), and the sequential nature of assessing the contribution of sleep–wake and circadian-related factors (Witting and Mirmiran, 1997). Although recent studies have found the contribution of locomotor activity to brain temperature to be negligible (Shirey et al., 2015; Hoekstra et al., 2019) and confirmed that circadian factors do not contribute significantly to brain temperature (Baker et al., 2005), the concerns underlying the use of hourly values and a fixed order of assessing the contributing factors have not been directly addressed.

To resolve these outstanding issues, we drew on a recent dataset (Hoekstra et al., 2019) to develop a mathematical model that simulates changes in brain temperature at the high time resolution required to account for its rapid fluctuations during sleep–wake state transitions. This new model explained 91% of the variance in brain temperature and reduced the model error to 0.26°C down from an observed dynamic range of 3.13°C. In addition to accurately capturing the short-term dynamics associated with sleep–wake transitions, the model revealed prior wake prevalence as a novel, longer-term factor altering the range of values within which brain temperature is regulated. The circadian factor explained 9.3% of the overall variance in brain temperature, of which 7.6% was redundant with the contribution of the other two factors. Finally, we show that the model can accurately predict brain temperature dynamics in an independent cohort of mice using the parameter settings obtained in the main experiment. This model thus, contributes to better documenting and quantifying the fundamental dependence of brain temperature on the sleep–wake state.

Wakefulness and REM sleep can be considered to be the opposite of NREM sleep in brain temperature dynamics. In the cortical activated states of wakefulness and REM sleep, brain temperature increases, whereas during NREM sleep when cortical input is reduced and neuronal activity becomes synchronized, temperature decreases (Obál et al., 1985; Franken et al., 1992a). Therefore, based on a previously described model in the rat (Franken et al., 1992b), we used the following exponential equations to iteratively simulate changes of brain temperature in the mouse:

With a time step (${\displaystyle \mathrm{\Delta }t}$) of 0.0011 hr (i.e., the 4-s epochs at which sleep–wake states were scored), the current temperature (${\displaystyle T_t}$) was calculated based on the preceding temperature (${\displaystyle T_{t-1}}$) according to the distance from an upper asymptote (U) and time constant ${\displaystyle {\tau }_{WR}}$ when the mouse was awake or in REM sleep at time t or, when in NREM sleep, according to the distance from the lower asymptote (L) and time constant ${\displaystyle {\tau }_N}$. The four free parameters of this basic model were the two time constants (in hours) and the values of the two asymptotes (in °C) between which brain temperature could vary. Drawing on previous results and assumptions (Franken et al., 1992b), we initially set the values for both time constants to 0.47 hr, the lower and upper asymptotes to the minimum and maximum temperatures reached in each animal during the 96-hr recording, respectively, and the initial temperature (${\displaystyle T_0}$) to the average temperature in the first 5 min of the recording. However, the following features were further developed to improve the simulation: (1) as already mentioned above, we defined 2 different time constants to represent the increase and decrease in temperature, instead of just 1 for both processes, (2) the asymptote values were free parameters, (3) all free parameters were simultaneously optimized for each mouse, (4) optimization took into consideration the entire recording, including sleep deprivation and recovery, instead of the baseline period alone, and (5) performance was assessed at a sub-minute time scale; that is, the 4-s resolution at which the sleep–wake states were determined, rather than at an hourly resolution.

Based on this more refined model, referred to as Model 0, we simulated the temperature recordings based on the individual sleep–wake state sequence data (Figure 1), with an average correlation coefficient (r) of 0.91, and a median root mean square (RMS) error of 0.36°C across animals. Generally, the time constant of wakefulness was higher than the one of NREM sleep (i.e., in 9 out of 11 mice; with median of 0.33 vs. 0.23 hr), indicating that the rate of increase of cortical temperature during wakefulness was slower than its decrease in NREM sleep. The difference between the upper and lower asymptotes varied by roughly 3°C, with the upper asymptotes consistently near the temperature values observed during SD (Supplementary file 1).

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However, the simulation presented deviations from the measured cortical temperature, especially when higher temperatures were reached during the light phase and sometimes around lower values during the dark phase (see arrows in Figure 1A). When we examined the time course of the average hourly residuals of the model across animals (Figure 1B), we found a systematic fluctuation in the fit; during the baseline light periods simulated values were too high and during the dark periods too low, compared to the recorded temperature values. The residual RMS (i.e., the RMS of the averaged hourly residuals) amounted to 0.19°C. However, the residuals during sleep deprivation (SD) which occurred during the light period resembled those observed during the dark period, which argues against a simple circadian modulation. Although incorporating a circadian modulation of both asymptotes as previously done in the rat (Franken et al., 1992b) somewhat improved the overall fit (RMS error = 0.32°C; residual RMS = 0.15°C), it did not abolish the apparent periodicity in the baseline residuals in mice and resulted in an even poorer fit during SD (Figure 1—figure supplement 1). Given the time-of-day independent similarity between the residuals during the SD and the dark phase, an alternative factor that could contribute to a temporary upregulation of brain temperature (beyond the sleep–wake state- driven changes already captured by the simulation) could be the prior periods of sustained wakefulness (Obermeyer et al., 1991). To explore this possibility, instead of a circadian modulation, we changed the asymptotes according to the prevalence of wakefulness (and REM sleep, for consistency) prior to each data point. We refer to this factor as ‘prior wake prevalence’. The window size over which prior wake prevalence was calculated, as well as the time lag for affecting the asymptotes, were kept as free parameters. Modulation of the asymptotes according to prior wake prevalence considerably improved the fit (r = 0.95; RMS error = 0.28°C; Figure 2) and removed most of the excessive overestimations during light periods, as well as the underestimation of temperature during the dark periods (see arrows in Figure 2A). We found that the optimal window size was 4.0 hr, with a shift of 1.5 hr prior to the time point under consideration, and a scaling factor of 1.2°C. The latter parameter represents the maximum possible modulation of either asymptote (i.e., 100% wakefulness or 100% NREM sleep during a given 4.0 hr window; Supplementary file 2). We optimized all the parameters simultaneously in this new model (i.e., Model 1) and found that all of the values obtained with Model 0 changed significantly (p≤0.002; F(2,10) ≥ 9.98, one-way repeated measures analysis of variance [rANOVA]): the lower asymptote increased, leading to a substantial reduction in the inter-asymptote temperature range from 3.1°C to 2.0°C, which might have contributed to the substantial shortening of the time constants (0.18 and 0.13 hr for wake/REM sleep and NREM sleep, respectively), as they need to be faster to compensate for the reduced distance from the asymptote so that a similar increase/decrease temperature rate can be achieved.

Figure 2

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Interestingly, after incorporating the prior wake-prevalence factor, the residuals of the new model showed a consistent light–dark (circadian) modulation (Figure 2B), with an over-estimation of the temperatures in the light periods, including the SD (residual RMS = 0.12°C). To account for this modulation, we again applied a 24 hr sine-wave modulation onto the asymptotes. The combined effect of modulating the asymptotes according to prior wake-prevalence and circadian time (i.e., Model 2) almost flattened the residuals (residual RMS = 0.09°C; Figure 2C) and further improved the fit (r = 0.96; RMS error = 0.26°C). The amplitude of the sine wave was 0.19°C with a phase of −0.63 hr, placing the trough of the circadian influence at ZT5.37. The window size over which the prior wake- prevalence was calculated shortened to 3.0 hr and the difference between the asymptotes decreased to 1.85°C (Table 1). Relative to Model 1, the only free parameter that exhibited a significant change was the scaling factor of the prior wake prevalence window (which dropped from 1.2 to 1.0°C, paired t-test, T(10) = 5.4; p=0.0003). Figure 3 shows the final fit of Model 2 to the temperature data for each of the 11 animals. Note that mouse #616 displayed exceptionally long waking periods (see periods of uninterrupted high temperature levels in the dark periods) that likely contributed to the exceptionally long prior wake prevalence window (5.5 hr) and the large scale factor relative to the circadian influence (1.05 vs. 0.11°C), modulating the asymptotes in this animal. These aberrant parameters, might in turn, explain the exceptional phase of the trough of the circadian factor (ZT15.6).

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Since Model 2 explained roughly 91% of the variance in the data, we next examined the contribution of each of the three factors. To do so, we decomposed the simulated temperature signal into its three constituent factors by removing the circadian and/or prior wake-prevalence factors, and subtracting the respective result from the Model 2 output (see 'Materials and methods'). Consistent with the R² value of 83% achieved in Model 0, the factor sleep–wake state accounted for the largest portion of the variance, that is, 74% (Figure 3—figure supplement 1). Some of this explained variance was, however, shared with the other two factors in the model, that is, prior wake prevalence (27%) and circadian time (4%), leaving 42% as the unique contribution of the sleep–wake state. In comparison, the uniquely explained variance contributed by the prior wake prevalence and the circadian process were considerably smaller (12% and 2%, respectively). In total, the overall explained variance contributed by prior wake prevalence was 43% and by the circadian process 9%, of which 3% was shared.

In 5 of these 11 mice, we ran additional experiments with a similar design but shorter SD (2 and/or 4 hr, starting at ZT0) and only one day of recovery. To verify whether the parameters found in the main experiment were not overfitted to the specific experiment, we tested the performance of Model 2 in each of the additional recordings, using the individually optimized parameters from the 6 hr SD experiment (Table 1). The simulation proved to be robust for all the new recordings (all r values ≥0.91, and RMS errors ≤0.37), thus convincingly demonstrating the generalization of parameters within animals over time and across different experiments (Supplementary file 3).

Finally, given the high precision of the simulations, we inquired whether the algorithm could go beyond the simulations based on parameters adjusted specifically to an individual mouse. To this end, we used the median parameter values found previously (Table 1) to predict brain temperature in a different cohort of mice (n = 5) recorded in the context of another study. The experiment had the same 96 hr design as the current study, and none of those data were used to optimize the model parameters. To test the model without providing temperature data, and because the model is iterative, we needed to estimate the initial temperature (T₀) to start the first iteration. We first used the main dataset to associate the average temperature and the percentage of Wake/REM state in the first 7 min of recording by linear regression, and then estimated the T₀ values in the current dataset based on wake/REM prevalence in the first 7 min (see 'Materials and methods', and Figure 4—figure supplement 1). After obtaining T₀, we used Model 2 to simulate the brain temperature of the independent cohort. Remarkably, all the correlation coefficients were between 0.93 and 0.95, although the median of the RMS error was 0.48°C since some recordings had consistent differences in absolute temperatures from physiological values, as was also observed in the main dataset (see columns 2-3 in Table 1). When we brought the empirical temperature data to the same average level as the predicted temperature traces (without changing scale), the median of the RMS error was reduced to 0.34°C and the fine overlap between predicted and observed temperature measures was again revealed (Figure 4, and Figure 4—figure supplement 2). Repeating this process for the test group with the medians of the more basic models 0 and 1, yielded correlation coefficients in the 0.86–0.89 and 0.91–0.93 ranges, respectively.

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We developed and made available a tool to predict brain temperature dynamics based on the sleep–wake state sequence. The model showed a very accurate fit with data obtained under undisturbed baseline conditions, and during and following SD of varying lengths. It equally well predicted the global temperature dynamics on a time scale of hours and the changes following sleep–wake transitions on the order of seconds. In addition to two known factors modulating brain temperature, that is, the sleep–wake state and circadian influences, we identified a novel contributing factor involving the prior wake prevalence, which accounted for the up-regulation of brain temperature observed during periods of sustained wakefulness.

The two core Matlab scripts for brain temperature simulation and parameters optimization, are provided as supplementary material, together with an example of the data and running scripts. In addition, the recorded temperatures, sleep scoring, and simulated temperatures of the three models are available for each of the 11 animals in the main experiment, as an Excel file.

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Author details

1. Yaniv Sela

   Sagol School of Neuroscience, Tel Aviv University, Tel Aviv, Israel

   Contribution

   Software, Formal analysis, Investigation, Visualization, Writing - original draft, Writing - review and editing

   For correspondence

   YanivDoar@gmail.com

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-2244-2067

2. Marieke MB Hoekstra

   Center for Integrative Genomics, University of Lausanne, Lausanne, Switzerland

   Present address

   UK Dementia Research Institute at Imperial College London, Department of Brain Sciences, London, United Kingdom

   Contribution

   Conceptualization, Investigation, Methodology, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-0723-2026

3. Paul Franken

   Center for Integrative Genomics, University of Lausanne, Lausanne, Switzerland

   Contribution

   Conceptualization, Resources, Supervision, Funding acquisition, Writing - original draft, Writing - review and editing

   For correspondence

   paul.franken@unil.ch

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-2500-2921

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