Modelling the time‐resolved modulations of cardiac activity in rats: A study on pharmacological autonomic stimulation

Abstract

Abstract

Assessing cardiac dynamics over time is essential for understanding cardiovascular health and its parallel patterns of activity with the brain. We present a methodology to estimate the time‐resolved sympathetic and parasympathetic modulations of cardiac dynamics, specifically tailored for the rat heart. To evaluate the performance of our method, we study a dataset comprising spontaneously hypertensive rats (SHR) and Wistar–Kyoto (WKY) rats. These rats were administered dobutamine to elicit autonomic dynamics. The results obtained from our method demonstrated accurate time‐resolved depiction of sympathetic reactivity induced by dobutamine administration. These responses closely resembled the expected autonomic alterations observed during physical exercise conditions, albeit emulated pharmacologically. We further compared our method with standard measures of low‐frequency (LF) and high‐frequency (HF) components, which are commonly used, although debated, for sympathetic and parasympathetic activity estimation. The comparisons with LF and HF measures further confirmed the effectiveness of our method in better capturing autonomic changes in rat cardiac dynamics. Our findings highlight the potential of our adapted method for time‐resolved analysis in future clinical and translational studies involving rodent models. The validation of our approach in animal models opens new avenues for investigating the relationship between ongoing changes in cardiac activity and parallel changes in brain dynamics. Such investigations are crucial for advancing our understanding of the brain–heart connection, particularly in cases involving neurodegeneration, brain injuries and cardiovascular conditions.

Key points

• We developed a method for time‐resolved estimation of sympathetic and parasympathetic modulations in rat cardiac dynamics, validated against standard low‐frequency and high‐frequency measures.

• We used a cohort of spontaneously hypertensive rats and Wistar–Kyoto rats, with dobutamine administration to induce autonomic responses.

• Our method accurately depicted time‐resolved sympathetic reactivity similar to autonomic changes during physical exercise.

• Our findings suggest potential for future clinical and translational studies on the brain–heart connection, particularly in cardiovascular conditions.

Abstract figure legend Time‐resolved estimation of cardiac rhythmicity parameters. A pipeline is shown for the estimation of the fluctuating cardiac parameters, based on the Poincaré plot. The Poincaré plot illustrates the successive changes in interbeat intervals (IBI). The parameters computation includes the distance from the ellipse centre to the origin (baseline cardiac cycle duration, CCD), as well as the minor (SD1) and major ratios (SD2), representing the short‐ and long‐term cardiac rhythmicity changes within the defined time window.

Introduction

Cardiac activity is regulated in the short term through two synergistic pathways: the sympathetic system, which acts as a positive ionotropic, and the parasympathetic system, with a negative ionotropic effect (Mahoney et al., 2016; Ruffolo, 1987; Spyer, 1990), with these disruptions typically being manifested in the heart rate and rhythm (or heart rate variability; HRV) (Macpherson et al., 2009). Standard HRV analysis in rats typically relies on 2–3 min time‐averaged measures, such as mean heart rate or SD of RR intervals (Kuwahara et al., 1994; Rowan et al., 2007). However, this approach overlooks the rich oscillatory nature of cardiac dynamics, which could provide further insights about the sympathetic and parasympathetic modulations of cardiac dynamics.

Recent advancements in humans have shown that time‐resolved analysis of cardiac rhythmicity is a valuable tool for understanding concurrent changes in brain activity (Candia‐Rivera et al., 2022; Sargent et al., 2024), highlighting the advantages of the time‐resolved analysis over time‐averaged measures. Animal models have provided important insights into brain–heart interactions (Hsueh et al., 2023; Jammal Salameh et al., 2024), but the exploration of cardiac changes has largely been limited to simple increases or decreases in heart rate, overlooking the contextual shifts in cardiac rhythmicity.

We recently proposed a time‐resolved measurements of sympathetic and parasympathetic modulations of cardiac dynamics in humans, which was validated in different experimental conditions demonstrating its robustness (Candia‐Rivera et al., 2025). Our method addressed a recurrent debate about the specificity of different cardiac rhythms with respect to sympathetic or parasympathetic mechanisms. The frequency domain analysis of HRV, typically relying on the estimation of low‐frequency (LF) and high‐frequency (HF) ranges, has been challenged because of the inaccurate estimation of sympathetic activity within the LF range (Goldstein et al., 2011). To address this issue, the proposed method performs an individual‐specific separation of the slow and fast HRV oscillations in combination with concurrent changes in the baseline heart rate, enabling a more precise estimation of sympathetic and parasympathetic modulations of cardiac dynamics.

The present study aimed to demonstrate the effectiveness of our individual‐specific approach in rats. We hypothesized that adapting the cardiac sympathetic and parasympathetic indices could accurately track short‐term changes in cardiac rhythmicity during autonomic elicitation, outperforming standard spectral measures such as LF and HF. We validate the efficacy of our method using a dataset of rats exposed to dobutamine (Hazari et al., 2017, 2012), where dobutamine emulates a non‐resting state condition similar to the physiological responses as a result of exercise because of sympathetic activations and parasympathetic deactivations (Sharma et al., 2015). We applied our method to spontaneously hypertensive rats (SHR), known for their rapid sympathetic reactivity (Shanks et al., 2013), and then tested on a group of Wistar–Kyoto (WKY) rats. The validation of our approach in a rat model opens new avenues for advancing our understanding of cardiovascular dynamics and their relationships with ongoing neural dynamics in different clinical conditions.

Methods

Dataset description

Open access datasets were used in this study (Hazari et al., 2017, 2012), comprising 22 rats from two different strains: WKY and SHR (Charles River, Wilmington, MA, USA). The rats were aged 12 weeks, all males, and they weighed between 300 and 400 g. All rats were aseptically implanted with radiotelemeters (Model TA11CTA‐F40; Data Sciences International, St Paul, MN, USA) for continuous measurement of the ECG. ECGAuto software (EMKA Technologies USA, Falls Church, VA, USA) was used to visualize individual ECG signals and measure interbeat interval (IBI) or R‐to‐R peak segment durations (RR series).

The rats were catheterized i.v. in the left jugular vein for the administration of dobutamine. Dobutamine (Sigma‐Aldrich, St Louis, MO, USA) was infused 0.2 mL min⁻¹ for 2 min in awake rats, after a 5 min baseline period (Hazari et al., 2017, 2012). Administered doses were 20, 40, 80, 160 and 320 µg kg⁻¹.

Half of the cohort consisted of rats exposed to diesel exhaust, while the other half was exposed to purified air. However, our primary focus was not on comparing these two conditions. Instead, we concentrated on the instantaneous changes triggered by dobutamine administration. The effects of diesel exhaust on cardiovascular physiology remain inconclusive in the literature. Research suggests that significant effects are generally observed with long‐term exposure (Bradley et al., 2013) or in individuals with pre‐existing conditions (Carll et al., 2013). Diesel exhaust exposure has been linked to an increased risk of cardiac arrhythmias (Hazari et al., 2017; Rossi et al., 2021). However, these findings have not been consistently replicated in other models (Mills et al., 2011; Peretz et al., 2008).

For simplicity, the various doses of dobutamine administration were combined in the statistical analyses. As a result of the substantial variability in the duration of both pre‐ and post‐infusion periods, we established a minimum duration of 30 s for each. This criterion led to 41 trials for all SHR and 52 trials for all WKY rats.

The experimental protocols were approved by and in accordance with the guidelines of the Institutional Animal Care and Use Committee of the United States Environmental Protection Agency, Research Triangle Park, North Carolina.

Estimation of cardiac sympathetic and parasympathetic indices

The estimation of cardiac sympathetic and parasympathetic indices was based on a previously developed model for humans (Candia‐Rivera et al., 2025). The model is based on the Poincaré plot, a method that depicts the fluctuations on the duration of successive IBI or RR series (Woo et al., 1992), as shown in Fig. 1A . Notably, this method eliminates the need to resample the IBI series, unlike traditional HRV approaches, such as spectral estimations.

Figure 1. Pipeline for the estimation of the fluctuating parameters of the Poincaré plot.

A, the Poincaré plot illustrates the successive changes in interbeat intervals (IBI). The parameters computation includes the distance from the ellipse centre to the origin (CCD), and the minor (SD1) and major ratios (SD2). B, group median and median absolute deviation in bold curve and shaded areas of CCD, SD1 and SD2.

Three features are extracted from the Poincaré plot: the cardiac cycle duration measured as the distance to the origin (CCD), and the minor (SD1) and major (SD2) ratios of the ellipse that quantify the short‐ and long‐term fluctuations of HRV, respectively (Sassi et al., 2015).

The time‐varying fluctuations of the distance to the origin and the ellipse ratios were computed with a sliding‐time window, as follows:

$$\begin{array}{ccc}& & \mathrm{CCD}\left(t\right)\hfill \\ & & =\sqrt{\mathrm{mean}{\left(\mathrm{IB}{\mathrm{I}}_{i,\text{…},n-1}\right)}^2+\mathrm{mean}{\left(\mathrm{IB}{\mathrm{I}}_{i+1,\text{…},n}\right)}^2}\hfill \end{array}$$ (1)

$$\mathrm{S}{\mathrm{D}}_1\left(t\right)=\sqrt{{\lambda }_{{\mathrm{\Omega }}_t}\left(1\right)}$$ (2)

$$\mathrm{S}{\mathrm{D}}_2\left(t\right)=\sqrt{{\lambda }_{{\mathrm{\Omega }}_t}\left(2\right)}$$ (3)

where ${\lambda }_{{\mathrm{\Omega }}_t}(i)$ denotes the i ^th the eigenvalue of the covariance matrix of $\mathrm{IB}{\mathrm{I}}_{i,\text{…},n-1}$ and $\mathrm{IB}{\mathrm{I}}_{i+1,\text{…},n}$, with ${\mathrm{\Omega }}_t:t-T\le t_i\le t$, and $n$ is the length of IBI in the time window ${\mathrm{\Omega }}_t.$

The original method included the implementation of four different approaches to compute the covariance matrices: ‘exact’, ‘robust’, ‘95%’ and ‘approximate’ (Candia‐Rivera et al., 2025). In this study, the robust approach was used, which computes the covariance matrix using a shrinkage covariance estimator based on the Ledoit–Wolf lemma for analytic calculation of the optimal shrinkage intensity (Schäfer & Strimmer, 2005). The sliding time window to compute the indices (T) was fixed in 3 s, which takes into account that typical IBI of the rat is around 100 ms and slow fluctuations occur in the range 0.1–1 Hz (Rowan et al., 2007).

The distance to the origin $CC{D}_0$ and ellipse ratios $S{D}_{01}$ and $S{D}_{02}$ for the whole experimental duration are computed to re‐centre the time‐resolved estimations of CCD, SD1 and SD2. The Cardiac Parasympathetic Index ($\mathrm{CPI}$) and the Cardiac Sympathetic Index ($\mathrm{CSI}$) are computed as follows:

$$D\left(t\right)=\overline{\mathrm{CCD}}\left(t\right)+\mathrm{CC}{\mathrm{D}}_0$$ (4)

$$\mathrm{CPI}\left(t\right)={\mathrm{k}}_p·\left(\overline{\mathrm{S}{\mathrm{D}}_1}\left(t\right)+\mathrm{S}{\mathrm{D}}_{01}\right)+\stackrel{\sim }{D}\left(t\right)$$ (5)

$$\mathrm{CSI}\left(t\right)={\mathrm{k}}_s·\left(\overline{\mathrm{S}{\mathrm{D}}_2}\left(t\right)+\mathrm{S}{\mathrm{D}}_{02}\right)+D\left(t\right)$$ (6)

where $\overline{\mathrm{S}{\mathrm{D}}_x}$ is the demeaned $\mathrm{S}{\mathrm{D}}_x$ and $\stackrel{\sim }{D}$ is the flipped $D$ with respect the mean.

The coefficients $k_p$ and $k_s$ determine the influence of fast and slow HRV oscillations relative to changes in the baseline heart rate. In this study, these values were experimentally determined using the SHR dataset and subsequently validated in the WKY dataset. The coefficients were established by comparing the experimental conditions (rest vs. dobutamine) across a range of $k_p$ and $k_s$ values (from 1 to 20). Statistical differences were assessed based on paired comparisons using the Wilcoxon test.

Estimation of sympathetic and parasympathetic indices using spectral components

The spectral HRV analysis was computed following the adapted Wigner–Ville method, for estimating the LF and HF time series (Orini et al., 2012). First, the IBI series were evenly re‐sampled using spline interpolation and demeaned. The re‐sampling frequency was set to 20 Hz, which is commonly set at 10 Hz or higher in rodents (Aubert et al., 1999). The pseudo‐Wigner–Ville algorithm consists of a two‐dimensional Fourier transform with an ambiguity function kernel to perform two‐dimensional filtering (Orini et al., 2012). It is important to note that in rats, the IBI can be as short as 100 ms, compared to the typical range of 600–1000 ms in humans (Konopelski & Ufnal, 2016). As a result, the LF and HF bands in rat studies have been redefined multiple times, typically as 0.1–1 Hz and 1–3.5 Hz (or alternatively 0.1–1.5 Hz and 1.5–5 Hz), respectively (Rowan et al., 2007). In this study, the frequency bands were defined as LF: 0.1–1 Hz and HF: 1–3.5 Hz.

Statistical analysis

To statistically evaluate the performance of the two methods (time‐frequency and Poincaré plot) in discerning the experimental conditions, we used a two‐sided non‐parametric Wilcoxon signed‐rank test for paired samples. The time‐resolved information for all the estimated features was condensed as the average value for each experimental session (30 s duration each condition), and the group‐wise descriptive measures are expressed as medians and median absolute deviations. Multiple comparisons were corrected using the Bonferroni rule.

Post hoc exploratory analyses were conducted to assess the contribution of each variable, including rat type (SHR or WKY), exposure (purified air or diesel exhaust) and dobutamine dose (20, 40, 80, 160 and 320 µg kg⁻¹), as well as their potential interaction effects on the differences in CSI and CPI values. These differences were calculated as the change in values 30 s after dobutamine administration compared to 30 s before. Model performance was evaluated using the Akaike information criterion (AIC), assessing both the individual contributions of the variables and their interactions in fitting the model. The model with the lowest AIC value was considered the best in each case.

Results

We investigated cardiac dynamics in two rat strains subjected to autonomic elicitation through dobutamine infusion. Our method, based on Poincaré plot descriptors of RR intervals, computed cardiac sympathetic and parasympathetic indices (CSI and CPI). Using the SHR strain, we determined parameters $k_p$ and $k_s$, which define the weight of HRV components with respect to the changes in baseline heart rate. Parameter definition involved testing $k_p$ and $k_s$ values to effectively distinguish between rest and dobutamine conditions for CSI and CPI estimation, respectively. The Z‐value from the Wilcoxon test comparing both conditions served as an indicator for optimal parameters. The inflection point for CSI was identified at $k_s$ = 3, and, for CPI, it was at $k_p$= 12, as illustrated in Fig. 2A . Figure 2B provides an example of a single rat, depicting the estimation of CSI and CPI for various values of $k_p$ and $k_s$.

Figure 2. Estimation of the parameters ${\mathit{k}}_{\mathit{p}}$ and ${\mathit{k}}_{\mathit{s}}$ for the estimation of CSI and CPI in the SHR strain.

A, the Z‐value from the Wilcoxon test comparing CSI and CPI for the conditions rest vs. dobutamine, as a function of $k_p$ and $k_s$ values. The star indicates the inflection point from which $k_s$ = 3 and $k_p$= 12 were used for the rest of the study. B, changes in R, SD1 and SD2 for one rat in the transition from rest to dobutamine infusion, and their respective CSI and CPI estimation based on different values of $k_p$ and $k_s$.

Using the optimal parameters identified in Fig. 2, we present the results of the statistical comparison between rest and dobutamine conditions for the two rat strains in Fig. 3. Furthermore, we include comparisons of their spectral counterparts, LF and HF. Our findings indicate a consistently higher distinguishability of conditions for CSI and CPI compared to LF and HF.

Figure 3. Cardiac autonomic indices CSI and CPI, and their spectral counterparts LF and HF under the rest to dobutamine transition.

A, time course of the computed indices between −30 to 30 s with respect to the condition change onset. The plot indicates the group median and the shaded areas the median absolute deviation. Time series were Z‐score normalized per subject before averaging for visualization purposes. B, statistical comparison using a signed rank Wilcoxon test, comparing the mean 30 s after the condition change with respect to the 30 s before. Dashed lines indicate the group median. All signal amplitude units are arbitrary units.

Figure 3 also illustrates time‐resolved transitions for all autonomic markers, segmented by rat strain. In Fig. 3A , the SHR strain exhibits a distinct increase in sympathetic markers following dobutamine infusion, with CSI surpassing LF. Simultaneously, there is a reduction in parasympathetic activity, where CPI proves to be more pronounced than HF. Similar sympathetic trends are observed in the WKY strain, whereas the WKY strain displays no significant change in HF after dobutamine infusion, with CPI emerging as an effective marker in this scenario. The distribution of averaged autonomic markers during rest and dobutamine periods in Fig. 3B further underscores the robustness of CSI and CPI in comparison to their spectral estimates’ counterparts.

As part of the exploratory analysis, various linear mixed models were fitted to examine CSI and CPI values as functions of rat type (SHR or WKY), exposure (purified air or diesel exhaust) and dobutamine dose (20, 40, 80, 160 and 320 µg kg⁻¹).

For CSI (Table 1), in two‐factor models (N = 1, 2, 3), the lowest AIC value was observed when the dose variable was excluded, indicating that CSI is primarily influenced by diesel exhaust exposure and rat type. In three‐factor models (N = 4 to 8), the best fit was achieved when dose was treated as an independent variable alongside the interaction between diesel exhaust exposure and rat type. This suggests that dose does not significantly interact with the other variables regarding its effects on CSI.

Table 1.

Linear mixed model fitting Cardiac Sympathetic Index (CSI)

N model	Formula	AIC
1	CSI ∼ 1 + Exposure + RatType + (1|ID)	−406.7596
2	CSI ∼ 1 + Exposure + Dose + (1|ID)	−368.4319
3	CSI ∼ 1 + RatType + Dose + (1|ID)	−366.8458
4	CSI ∼ 1 + Exposure + RatType + Dose + (1|ID)	−376.7366
5	CSI ∼ 1 + Dose + Exposure*RatType + (1|ID)	−498.3792
6	CSI ∼ 1 + RatType + Exposure*Dose + (1|ID)	−346.9463
7	CSI ∼ 1 + Exposure + RatType*Dose + (1|ID)	−341.2821
8	CSI ∼ 1 + Exposure * RatType * Dose + (1|ID)	−403.9011

ID = {1, …, 22}, Exposure = {Air, Diesel}, Rat Type = {SHR, WKY}, Dose = {20, 40, 80, 160 and 320 µg kg⁻¹}. AIC, Akaike information criterion (lowest value indicates best fitting).

For CPI (Table 2), in two‐factor models (N = 1, 2, 3), diesel exhaust exposure and dose appeared to have a stronger influence on CPI values. In three‐factor models (N = 4 to 8), CPI was best explained by considering the interaction among all three factors. These findings, although limited by the number of data points, suggest that CSI and CPI are influenced differently by the analysed factors. Further studies with larger datasets are needed to confirm these observations.

Table 2.

Linear mixed model fitting Cardiac Parasympathetic Index (CPI)

N model	Formula	AIC
1	CPI ∼ 1 + Exposure + RatType + (1|ID)	85.0815
2	CPI ∼ 1 + Exposure + Dose + (1|ID)	84.1944
3	CPI ∼ 1 + RatType + Dose + (1|ID)	85.9075
4	CPI ∼ 1 + Exposure + RatType + Dose + (1|ID)	78.1941
5	CPI ∼ 1 + Dose + Exposure*RatType + (1|ID)	62.9700
6	CPI ∼ 1 + RatType + Exposure*Dose + (1|ID)	59.6205
7	CPI ∼ 1 + Exposure + RatType*Dose + (1|ID)	63.8296
8	CPI ∼ 1 + Exposure * RatType * Dose + (1|ID)	−44.6750

ID = {1, …, 22}, Exposure = {Air, Diesel}, Rat Type = {SHR, WKY}, Dose = {20, 40, 80, 160 and 320 µg kg⁻¹}. AIC, Akaike information criterion (lowest value indicates best fitting).

Discussion

Heart rhythmicity analysis has the potential to be a valuable non‐invasive technique for assessing autonomic nervous activity in rats (Kuwahara et al., 1994). Standard time‐averaged HRV measures often fail to capture ongoing physiological dynamics because the averaging process, typically spanning a few minutes, masks fluctuations that occur at the level of seconds. For example, invasive recordings on the left cervical vagus nerve in rats have revealed that tonic vagal activity does not correlate with commonly used HRV metrics (Marmerstein et al., 2021). This indicates the need for further development of methods to understand the modulation of sympathetic and parasympathetic activity on cardiac dynamics.

We developed and validated a method using a rat heart dataset, where pharmacological autonomic elicitation was induced with dobutamine. This drug, a positive inotropic agent, is known to mimic sympathetic activation and parasympathetic deactivation, as observed in conditions like physical exercise (Mahoney et al., 2016). In our proposed method, previously validated in humans (Candia‐Rivera & Chavez, 2024b, 2024a; Candia‐Rivera et al., 2025), we accurately show the time‐dependent effects of autonomic elicitation induced by dobutamine in rats, unravelling some of the key components of cardiac regulation by both sympathetic and parasympathetic systems. As expected, our results show that dobutamine triggers an increase in sympathetic activity, shown as a sudden increase in slow fluctuations in HRV, followed by a transient increase in the baseline heart rate. In parallel, a transient decrease in parasympathetic activity occurs. We did not observe notable differences on the effects in the WKY with respect to the SHR strain, although sympathetic hyperreactivity is expected in the SHR strain, as compared to WKY (Luft et al., 1986). However, the sympathetic reactivity has been reported only in changes in the baseline heart rate, and not necessarily in the slow fluctuations in HRV (Ricksten et al., 1984). Importantly, our approach surpasses the spectral counterparts, LF and HF, in the description of sympathetic and parasympathetic activities, respectively.

Our method offers various advantages, as compared to state‐of‐the‐art methods. First, it is based on the Poincaré plot, which is a computationally efficient tool to depict the beat‐to‐beat alterations in IBIs (Brennan et al., 2001; Woo et al., 1992). Second, it considers parallel autonomic modulations in both baseline heart rate and HRV. It is important to study baseline heart rate in conjunction with HRV to fully comprehend sympathetic dynamics (Sacha et al., 2013) because sympathetic modulations of heartbeat dynamics may be reflected solely in changes in the baseline heart rate, rather than changes in HRV (e.g. LF or LF/HF ratio), and vice versa (Gonçalves et al., 2010). Third, our proposal focuses on developing a time‐resolved estimation method, which could reduce the need for several minutes of averaging to assess a single experimental condition, but also enabling a comprehensive exploration of the dynamic shifts in autonomic regulations occurring in parallel with other organs, such as the brain (Bashan et al., 2012; Samuels, 2007; Silvani et al., 2016), This underscores the importance of modelling brain–heart interactions to better understand multisystem dysfunctions (Chen et al., 2021).

Further exploration is needed to elucidate the dynamics of rat cardiac activity that extend beyond baseline heart rate or variations in HRV. Specially in the context of diesel exhaust exposure, which can potentially trigger cardiac arrythmias that can be capture as non‐linear patterns of activity (Hazari et al., 2017; Rossi et al., 2021). Linear mixed models suggest that cardiac sympathetic activity is influenced by the interaction between diesel exhaust exposure and the SHR rat type. Although the available data may be limited, we cannot exclude the possibility that diesel exhaust exposure induces short‐term changes in cardiac sympathetic or parasympathetic indices, potentially driven by cardiac conduction instability and inflammatory processes (Hazari et al., 2017; Rossi et al., 2021). Non‐linear methods have been suggested as an alternative for investigating autonomic dynamics. However, these methods have produced conflicting results, suggesting that increased sympathetic modulation may contribute to non‐linear dynamics (Silva et al., 2017), at the same time as indicating that increased sympathetic modulation is probably the main cause of lower entropy (Silva et al., 2016).

Although our study has some limitations, such as a small sample size or the inclusion of all‐male strains, the results demonstrate the effectiveness of our estimation of autonomic system parameters. Another limitation of this study is the inability to determine whether specific dobutamine doses or their cumulative effects after repeated administrations influence CSI or CPI values. Linear mixed models revealed that CSI was best explained by the interaction between exposure and rat type, whereas CPI was best explained by the interaction among all three factors studied. These findings suggest that a dose effect, although minimal, cannot be ruled out. Such an effect would probably manifest as rapid sympathetic and parasympathetic modulation of the heart, occurring immediately after a perturbing element, within a complex interplay of regulatory loops spanning multiple timescales (Pathak et al., 2006).

Our proposal has not been tested under other standard conditions of autonomic elicitation, such as monitoring heart rate during cold exposure (Kuwahara et al., 2009), which constitutes the main limitation of our study. However, our proposal constitutes a first attempt for a developing field of research on time‐resolved brain–heart analysis, applied to animal models. It is worth mentioning that studies under pharmacological interventions to modulate autonomic nervous system activity remain a standard approach (Aubert et al., 1999; Beckers et al., 2006; Bernat et al., 2023; Coleman, 1980; Kuwahara et al., 1994; Mangin et al., 1998; Ohnuki et al., 2001; Ramaekers, Beckers, Demeulemeester & Aubert, 2002).

For accurate time‐resolved estimation, it is crucial to set a sliding time window that captures cardiac rhythm oscillations. We established a 3 s window to balance high time resolution with the ability to capture slow fluctuations in HRV, a key marker of sympathetic activity. In future studies, determining this window size should rely on the known physiological priors, considering expected response latency and the involved frequencies.

Our method opens new research opportunities for clinical and translational studies to explore the potential of using heartbeat dynamics as biomarkers for assessing conditions characterized by disrupted autonomic dynamics. In severe conditions such as cardiogenic shock or heart failure, a significant alteration in arterial tension can critically compromise hemodynamics, potentially leading to organ failure. To optimize organ perfusion, sympathomimetic agents such as dobutamine, a β1‐adrenergic agonist, have been developed to enhance heart contractility and output (Dubin et al., 2017). However, a comprehensive understanding of this intricacy requires further rigorous investigations in well‐controlled in vivo settings.

Future research may include the description of our developed markers under different stressors (Inagaki et al., 2004; Park et al., 2017; Raffai et al., 2006; Ramaekers, Beckers, Demeulemeester, Bert et al., 2002) and cardiovascular conditions (Han et al., 2014; Henze et al., 2008; Scridon et al., 2012). Further research could deepen our understanding of the fluctuations of cardiac rhythmicity in the context of circadian rhythms, which are typically limited to describing long‐term changes in the baseline heart rate alone (Van Den Buuse, 1994).

Our development may also enable the investigation of disruptions that may impact the connection between the brain and heart, and their subsequent effects on neural functions; for example, in the study of severe brain damage resulting from cardiovascular conditions such as stroke (Kodama et al., 2018) or anoxia (Gonçalves et al., 2008), as well as in cases of damage to the spinal cord (Inskip et al., 2012). These conditions present compelling areas of interest for further exploration in which the time‐resolved estimation of autonomic dynamics can be a hallmark in the comprehension of nervous system‐wise complex dynamics.

Conclusions

Our study presents a robust approach for time‐resolved estimation of sympathetic and parasympathetic modulations in rat cardiac dynamics, demonstrating its efficacy in capturing autonomic responses triggered by pharmacological interventions. The application of our method in animal models paves the way for future research aimed at unravelling the complex interplay between cardiac and brain activity in various pathological conditions.

Competing interests

The authors declare that they have no competing interests.

Author contributions

D.C.R. was responsible for conceptualization, figures, data analysis and writing the draft manuscript. D.C.R., S.C.F., F.D.V.F. and M.C. were responsible for reviewing and editing. Final approval of the version to be published; Agreement to be accountable for all aspects of the work

Funding

This research was supported by the European Commission, Horizon MSCA Program (grant n° 101151118).

Supporting information

Peer Review History

Biography

Diego Candia‐Rivera is a researcher at the Paris Brain Institute, Sorbonne Université, Paris. He received his PhD degree in information engineering from the University of Pisa, Italy, in 2022. His research interests include the development of methods for studying brain–heart interactions and the understanding of the role of these interactions in consciousness. One of his significant research findings reveals that brain–heart interactions reflect the presence and levels of consciousness in severely brain‐damaged patients. Furthermore, these interactions serve as the catalyst for affective processing, shaping emotional arousal. Diego Candia‐Rivera has performed research under the financial support from the European Commission's Marie Skłodowska–Curie Actions program and the French National Agency for Research.

Data availability statement

The data were gathered from the United States Environmental Protection Agency website (https://doi.org/10.23719/1503098). For further detail on the dataset, please refer to the original studies (Hazari et al., 2017, 2012).

Relevant code for this research are stored in a GitHub repository: https://github.com/diegocandiar/robust_hrv.