兽研Abstract
Heart rate variability (HRV) analysis is widely used to evaluate autonomic nervous system activity. Although a fixed 16th-order autoregressive (AR) model is commonly used for human short-term frequency-domain HRV analysis, its applicability to dogs has not been validated. This study evaluated the suitability of the fixed 16th-order AR model for canine HRV analysis by comparing HRV indices obtained using AR(16) with those derived from Akaike’s Information Criterion (AIC)- and Bayesian Information Criterion (BIC)-selected AR models and the conventional fast Fourier transform (FFT) method. Twenty-three clinically healthy dogs underwent continuous heart rate monitoring for approximately 3 days using a wearable device. One stationary 5-min R-R interval segment was selected from each recording, and frequency-domain HRV indices were calculated using AR(16), AIC-selected AR models, BIC-selected AR models, and FFT. Agreement among methods was evaluated using intraclass correlation coefficients and Bland–Altman analysis. HRV indices obtained using AR(16) showed excellent agreement with AIC-selected model orders and good agreement with FFT, whereas agreement with BIC-selected model orders was lower, particularly for low-frequency-related indices. These findings support the applicability of the conventional fixed 16th-order AR model for canine frequency-domain HRV analysis and provide methodological validation for its use in future veterinary HRV research.
Keywords: autoregressive model, dog, heart rate variability, model order, spectral analysis
INTRODUCTION
Heart rate variability (HRV) reflects the dynamic interplay between sympathetic and parasympathetic nervous system activity, and its quantitative assessment provides valuable information on autonomic regulation and cardiovascular function [10, 19]. HRV analysis is widely used as a non-invasive tool to evaluate physiological and pathological conditions, including cardiovascular diseases [10], stress responses [12], and behavioral states [1], in both human and veterinary medicine. As HRV-derived indices are increasingly applied in both clinical practice and physiological research, reliable spectral analysis methods are essential to ensure accurate assessment of autonomic function and meaningful interpretation of HRV measurements.
In frequency-domain HRV analysis of HRV, fluctuations in R-R intervals (RRIs) are decomposed into spectral components that reflect different physiological mechanisms. While low-frequency (LF) components are generally considered to reflect both sympathetic and parasympathetic influences, high-frequency (HF) components primarily reflect parasympathetic activity and respiratory sinus arrhythmia (RSA) [3, 10]. Spectral estimation of HRV signals is commonly performed using either the fast Fourier transform (FFT) or autoregressive (AR) modeling, both of which are well-established and widely accepted analytical approaches for HRV analysis [4, 10]. FFT-based spectral analysis remains the standard approach because of its simplicity, computational efficiency, and widespread implementation in commercially available HRV software. Since FFT requires evenly sampled data, unevenly spaced RRIs must first be converted into uniformly sampled tachograms by interpolation [10]. Although this preprocessing step is generally appropriate, interpolation may influence spectral estimation when beat-to-beat variability is particularly large. AR spectral analysis, in contrast, estimates the power spectrum directly from the RRI series without resampling and has been widely adopted in human HRV research as an alternative analytical approach.
In human HRV analysis, a fixed AR model order of 16 has been widely adopted as a conventional analytical setting for short-term HRV analysis [13,14,15]. However, the suitability of this conventional model order for canine HRV analysis has not been established. Dogs exhibit substantially greater respiratory sinus arrhythmia (RSA) and larger beat-to-beat fluctuations in RRI than humans, resulting in HRV characteristics that differ markedly from those of humans [2, 6]. Consequently, validation of the conventional fixed 16th-order AR model is an essential prerequisite for its appropriate application to canine HRV analysis.
Therefore, the present study aimed to validate the applicability of the conventional fixed 16th-order AR model for canine HRV analysis under stationary conditions by comparing HRV indices obtained using AR(16) with those derived from Akaike’s Information Criterion (AIC)- and Bayesian Information Criterion (BIC)-selected AR models and the conventional FFT method.
MATERIALS AND METHODS
Study design
This was a prospective, observational study. Dogs that underwent health checkups at the Kakogawa Animal Hospital in Japan were recruited from April 2017 to March 2019. All procedures were approved by the Institutional Review Board for Clinical Research at the Osaka Prefecture University Veterinary Clinical Center (Approval No. H27-002). Written consent to participate in this study was obtained from all dog owners.
Animals
During the study period, 118 privately owned dogs presented to Kakogawa Animal Hospital for routine health examinations were enrolled in the study after owner consent had been obtained and underwent continuous RRI recording for approximately 3 days. For the present validation study, 23 dogs fulfilled the predefined clinical inclusion criteria and had complete datasets that satisfied the predefined analytical criteria, and were therefore included. All included dogs underwent routine health screening, including physical examination, complete blood count, serum biochemical analysis, and thoracic auscultation. Dogs with no clinically evident cardiovascular or systemic disease based on these routine screening examinations were included. Because echocardiography and electrocardiography were not performed as part of the screening protocol, subclinical cardiovascular disease could not be completely excluded. The study population comprised privately owned dogs of various breeds, ages, sexes, and body weights. A summary of the study population is presented in Table 1, and detailed information for each dog is provided in Supplementary Table 1.
Table 1.. Characteristics of the study population
| Number of dogs | 23 |
| Age (months), median (range) | 32 (7–129) |
| Body weight (kg), median (range) | 4.5 (2.4–11.0) |
| Sex | Male: 15 (9 neutered, 6 intact) |
| Female: 8 (6 spayed, 2 intact) | |
| Breeds | Toy Poodle (8), Chihuahua (5), Miniature Dachshund (4), Welsh Corgi (2), Maltese (1), Papillon (1), Yorkshire Terrier (1), Pug (1) |
| Mean RRI of analyzed segments (msec) | 953.2 ± 355.2 |
RRI recording
RRI data were recorded continuously using a custom-built wearable electrocardiographic sensor, which has previously been used for HRV research in dogs [15]. The sensor was attached at the animal hospital, and owners were instructed to return with their dogs approximately 3 days later for device retrieval. Therefore, the actual recording duration varied slightly depending on the timing of device retrieval and owner availability. The device consisted of a harness-type wearable unit equipped with surface electrodes positioned bilaterally in the axillary regions. Four harness sizes were available, and the length of the electrode belts was individually adjusted according to each dog’s body size to ensure stable contact between the electrodes and the skin throughout the recording period. Electrical activity detected through the surface electrodes was processed within the device to identify R waves, and consecutive R-R intervals (RRIs) were recorded directly without storing the raw ECG waveform. No clipping of the hair or skin preparation was performed before sensor attachment. Dogs remained in their normal home environment during data collection, and no restrictions were imposed on their routine daily activities.
Selection of RRI segments
From each RRI recording for approximately 3 days, one 5-min RRI segment was selected for HRV analysis. Segment selection was performed to identify RRI data suitable for stationary frequency-domain HRV analysis rather than to characterize physiological or clinical conditions during the recording period.
Candidate segments were selected according to the following criteria:1. Minimal body movement confirmed using the simultaneously recorded accelerometer data;2. Absence of abrupt fluctuations in the rri time series on visual inspection;3. A stable respiratory rhythm identified from the hrv spectrum; and4. An estimated respiratory rate ≥10 breaths/min.
Respiratory rhythm was evaluated from the frequency spectrum generated from consecutive 1-min RRI data. The dominant peak within the high-frequency band was regarded as representing respiratory activity when its spectral power was at least twice that of the second-highest peak within the same frequency band. The corresponding peak frequency was used to estimate respiratory rate. This procedure was applied to confirm the presence of a stable respiratory rhythm rather than to determine the exact respiratory rate.
Because multiple segments satisfying these criteria were generally available for each dog, one representative segment was selected for subsequent analysis. The recording time and estimated respiratory rate of each selected segment are summarized in Supplementary Table 1.
RRI extraction and artifact correction
Artifact correction was performed using the Kubios HRV software (version 4.3.0; University of Eastern Finland, Kuopio, Finland) with a custom threshold set at 0.9, where an RRI deviating by more than 90% from adjacent intervals waw identified and corrected. Only RRI segments with an artifact correction rate of <5% of the total beats were included in subsequent HRV analyzes.
Stationarity assessment
The selected RRI segments were subsequently subjected to stationarity assessment before HRV analysis. Because frequency-domain HRV analysis assumes stationarity of the analyzed RRI series, three complementary statistical tests were applied: the Augmented Dickey–Fuller (ADF) test, the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test, and a trend analysis. The ADF test evaluates the null hypothesis that the time series contains a unit root (i.e., is non-stationary), whereas the KPSS test evaluates the null hypothesis that the time series is stationary. Because these tests have complementary null hypotheses, their combined use has been recommended to improve the robustness of stationarity assessment in time-series analysis [9, 10, 16]. Trend analysis was additionally performed to identify systematic linear trends that could influence spectral estimation. Only RRI segments satisfying the predefined stationarity criteria were included in the subsequent HRV analysis.
Frequency-domain HRV analysis
Frequency-domain HRV analysis was performed using both FFT and AR spectral analysis. HRV indices were calculated from the selected stationary 5-min RRI segments using Kubios HRV Premium software. For AR analysis, a fixed model order of 16 was used because this model order has been conventionally adopted in many human short-term HRV studies. To evaluate its applicability to dogs, HRV indices obtained using AR(16) were compared with those obtained using objectively optimized model orders selected according to the AIC and the BIC. The following frequency-domain HRV indices were calculated for each analytical method: low-frequency (LF) power, high-frequency (HF) power, and the LF/HF ratio.
Statistical analysis
Statistical analyzes were performed using R (version 11.0.0; R Foundation for Statistical Computing, Vienna, Austria) and GraphPad Prism (version 11; GraphPad Software, San Diego, CA, USA). Agreement between HRV indices obtained using the fixed AR(16) model and those obtained using the AIC-selected, BIC-selected, and FFT methods was evaluated using intraclass correlation coefficients (ICC) and Bland–Altman analysis. ICC was calculated using a two-way random-effects model for absolute agreement (ICC[2, 1]) and was used to quantify the degree of agreement between analytical methods. ICC values were interpreted as follows: <0.5, poor; 0.5–0.75, moderate; 0.75–0.9, good; and >0.9, excellent agreement. Bland–Altman analysis was performed to evaluate systematic bias and the 95% limits of agreement (LoA) between analytical methods. Bias was calculated as the mean difference, and the LoA were defined as the mean difference ± 1.96 standard deviations.
To investigate whether respiratory sinus arrhythmia (RSA) amplitude influenced the differences between analytical methods, linear regression analysis was performed using RMSSD as an index of RSA amplitude, and the significance of the regression slope was evaluated. A P value <0.05 was considered statistically significant.
RESULTS
Study population
Twenty-three clinically healthy dogs were included in the final analysis from a total of 118 dogs that underwent continuous RRI recording during the study period. The study population comprised Toy Poodles (n=8), Chihuahuas (n=5), Miniature Dachshunds (n=4), Welsh Corgis (n=2), Maltese (n=1), Papillon (n=1), Yorkshire Terrier (n=1), and Pug (n=1). Fifteen dogs were male (9 neutered and 6 intact) and eight were female (6 spayed and 2 intact). The dogs ranged in age from 7 to 129 months (median, 32 months) and weighed between 2.4 and 11.0 kg (median, 4.5 kg). A summary of the study population is presented in Table 1, with individual animal information provided in Supplementary Table 1. For each dog, one stationary 5-min RRI segment satisfying the predefined selection criteria was identified from the approximately 3-day recording and used for HRV analysis. The mean RRI of the analyzed segments was 953.2 ± 355.2 msec.
Distribution of AR model orders
The autoregressive model order determined using AIC ranged from 4 to 24 whereas that determined using BIC ranged from 3 to 9 (Fig. 1). Although both criteria showed inter-individual variability, the BIC consistently selected lower model orders than the AIC. Most AIC-selected model orders were distributed between 8 and 12, whereas BIC most frequently selected model orders between 4 and 6.
[图：Distribution of autoregressive model orders selected by AIC and BIC. Each pair of points represents an individual dog, w]
Agreement between AR(16) and model orders determined by AIC and BIC
HRV indices obtained using AR(16) showed high agreement with those obtained using AIC-selected model orders (Table 2). HF demonstrated the highest agreement (ICC=0.99), whereas agreement for LF/HF was lower when compared with BIC-selected model orders (ICC=0.61). Overall, ICC values obtained using AIC-selected model orders were consistently higher than those obtained using BIC-selected model orders. Bland–Altman analysis demonstrated small mean biases for all HRV indices (Fig. 2). The limits of agreement were generally narrower for comparisons between AR(16) and AIC-selected model orders than for those between AR(16) and BIC-selected model orders, particularly for LF and LF/HF.
Table 2.. Agreement between HRV indices derived from AR(16) and those obtained using model orders determined by information criteria (AIC and BIC)
| Variable | Comparison | ICC (95% IC) | Bland–Altman | |
|---|---|---|---|---|
| Bias | 95% LoA | |||
| HF power | AR(16) vs. AR (AIC) | 1.00 (0.99–1.00) | 0.012 | −0.067–0.092 |
| HF power | AR(16) vs. AR (BIC) | 0.99 (0.97–1.00) | 0.037 | −0.073–0.147 |
| LF power | AR(16) vs. AR (AIC) | 0.90 (0.75–0.96) | −0.19 | −0.973–0.594 |
| LF power | AR(16) vs. AR (BIC) | 0.74 (0.20–0.90) | −0.503 | −1.616–0.610 |
| LF/HF | AR(16) vs. AR (AIC) | 0.80 (0.55–0.91) | −0.019 | −0.098–0.060 |
| LF/HF | AR(16) vs. AR (BIC) | 0.61 (0.04–0.85) | −0.05 | −0.151–0.515 |
[图：Bland–Altman analysis comparing HRV indices derived from AR(16) with those derived from AIC- and BIC-based model orders.]
Agreement between AR(16) and FFT-based spectral analysis
The HRV indices derived from AR(16) showed good overall agreement with those obtained using the FFT-based spectral analysis (Table 3). Agreement was highest for HF (ICC=0.99), whereas relatively lower agreement was observed for LF/HF (ICC=0.90). Bland–Altman analysis demonstrated small mean biases for all HRV indices and relatively narrow limits of agreement, indicating generally consistent measurements between the AR(16) and FFT methods (Fig. 3).
Table 3.. Agreement between HRV indices derived from AR(16) and FFT-based spectral analysis
| Variable | Comparison | ICC (95% IC) | Bland–Altman | |
|---|---|---|---|---|
| Bias | 95% LoA | |||
| HF power | AR(16) vs. FFT | 0.99 (0.98–1.00) | −0.009 | −0.132–0.116 |
| LF power | AR(16) vs. FFT | 0.94 (0.85–0.97) | −0.111 | −0.728–0.507 |
| LF/HF | AR(16) vs. FFT | 0.90 (0.78–0.96) | −0.005 | −0.056–0.047 |
[图：Bland–Altman analysis comparing HRV indices derived from AR(16) and FFT-based spectral analysis. Panels show comparisons]
Relationship between RSA amplitude and method differences
Linear regression analysis revealed no significant association between the RMSSD and differences between the AR(16)- and FFT-derived HRV indices for LF, HF, and LF/HF (Fig. 4). Regression slopes were not significantly different from zero for any parameter, indicating that the magnitude of RSA was not associated with differences between the two analytical methods.
[图：Relationship between RMSSD and differences between AR(16)- and FFT-derived HRV indices. Scatter plots show the relations]
DISCUSSION
The principal finding of the present study was that the conventional fixed 16th-order autoregressive (AR) model, which has been widely adopted for short-term HRV analysis in humans, also provided reliable frequency-domain HRV estimates in dogs under stationary conditions. HRV indices obtained using AR(16) showed close agreement with those derived from AIC-selected model orders and good overall agreement with those obtained using the conventional FFT method. Furthermore, the differences between AR- and FFT-derived HRV indices were not associated with RMSSD, suggesting that the larger respiratory sinus arrhythmia typically observed in dogs did not substantially influence the agreement between the two analytical approaches under the conditions examined. Collectively, these findings support the applicability of the conventional fixed 16th-order AR model for canine HRV analysis and provide a methodological basis for its use in future veterinary HRV studies.
The close agreement between AR(16) and the AIC-selected model orders suggests that the conventional fixed 16th-order model provides a level of model complexity that is appropriate for canine short-term HRV analysis. Because the AIC determines model order according to the characteristics of the analyzed data, the observed agreement indicates that a fixed model order of 16 yielded HRV estimates comparable to those obtained using data-driven optimization. This finding is consistent with previous human studies, in which AR(16) has been shown to provide stable spectral estimates comparable to those obtained using optimized model orders [8, 17]. Collectively, the present results support the applicability of the conventional fixed 16th-order AR model to canine HRV analysis while demonstrating consistency with observations previously reported in human HRV studies. In contrast, agreement between AR(16) and BIC-selected model orders was lower, particularly for LF-related indices. LF power reflects relatively slow oscillatory components of autonomic regulation [10], which require sufficient model complexity for stable spectral estimation. Consequently, the lower model orders selected by the BIC may not adequately capture these slower fluctuations, resulting in reduced agreement with AR(16). Because the BIC applies a stronger penalty for model complexity than the AIC, these findings most likely reflect the different model-selection strategies represented by the two information criteria rather than indicating that either approach is inherently superior.
The present study also demonstrated good agreement between HRV indices obtained using AR(16) and those derived from the conventional FFT-based spectral analysis. FFT remains the most widely used method for frequency-domain HRV analysis in both human and veterinary research and continues to serve as a well-established reference method [10]. Although FFT requires interpolation of unevenly spaced RRI data, whereas AR analysis can be applied directly to RRI series, these methodological differences did not result in substantial discrepancies in HRV indices when stationary 5-min segments were analyzed. These findings are consistent with previous human studies reporting comparable HRV estimates obtained using AR and FFT under stationary conditions [7]. Therefore, rather than suggesting that AR should replace FFT, the present results indicate that the conventional fixed 16th-order AR model provides HRV estimates that are consistent with those obtained using the current standard analytical approach. This supports the use of AR(16) as an additional analytical option for canine HRV analysis under stationary conditions.
The agreement between HRV indices obtained using AR(16) and FFT was not influenced by the magnitude of respiratory sinus arrhythmia (RSA), as no significant association was observed between the inter-method differences and RMSSD. RMSSD is widely accepted as a surrogate index of vagally mediated beat-to-beat variability associated with respiration and has been extensively used as an indirect measure of RSA in HRV studies [3, 10, 18]. Dogs generally exhibit greater RSA and larger beat-to-beat heart rate variability than humans [11], raising the possibility that methodological differences between AR and FFT might become more pronounced in this species. However, such an effect was not observed in the present study. A likely explanation is that HRV analysis was restricted to carefully selected stationary 5-min RRI segments. Because both AR- and FFT-based spectral analyzes assume stationarity of the analyzed signal, minimizing non-stationary fluctuations associated with changes in posture, activity, or respiration probably contributed to the close agreement observed between the two analytical approaches. Therefore, the present findings should be interpreted within the context of stationary short-term recordings and should not be extrapolated directly to non-stationary conditions. Nevertheless, the results suggest that the methodological framework widely adopted for human short-term HRV analysis is also applicable to dogs when stationary conditions are ensured.
From a clinical perspective, the present findings provide methodological support for the use of the conventional fixed 16th-order AR model in canine HRV analysis under stationary conditions. Frequency-domain HRV analysis is increasingly being incorporated into veterinary research to evaluate autonomic nervous system activity in a variety of physiological and clinical settings [2, 11, 12, 15]. In this context, demonstrating that the conventionally adopted AR(16) model provides HRV estimates consistent with both data-driven model selection and the widely used FFT method provides confidence that this analytical approach can be applied appropriately in dogs. Rather than establishing a replacement for FFT, the present study expands the methodological options available for canine HRV analysis and provides a validated analytical framework for future veterinary HRV research.
Several limitations of this study should be acknowledged. First, although the sample size (n=23) was determined based on an established approximation method for ICC precision [5], it remains relatively small for precise estimation of moderate agreement levels. This limitation should be interpreted in the context of the primary objective of the present study, which was to validate the applicability of the conventional fixed 16th-order AR model. For the principal comparisons between AR(16), AIC-selected model orders, and FFT, agreement was consistently high, supporting the main conclusions of the present study, although wider confidence intervals observed in some comparisons indicate that further validation in a larger population would be valuable. Second, the dogs were considered clinically healthy based on routine clinical screening, including physical examination, complete blood count, serum biochemical analysis, and thoracic auscultation. Because echocardiography and electrocardiography were not performed, subclinical cardiovascular abnormalities could not be completely excluded. Although inclusion of multiple breeds improves the generalizability of the present methodological validation, the limited number of dogs within each breed prevented breed-specific analyzes. Future studies including larger breed-specific populations will be required to determine whether breed influences HRV characteristics and the applicability of AR-based HRV analysis. Third, the present validation was performed using carefully selected stationary 5-min RRI segments. Consequently, the applicability of the conventional fixed 16th-order AR model to non-stationary recordings, such as those obtained during changes in posture, activity, or emotional state, remains to be determined. Finally, respiratory stability was evaluated from the dominant high-frequency spectral peak identified in the RRI-derived power spectrum rather than by direct measurement of respiratory movements. Although this approach was adopted to identify segments with stable respiratory rhythm rather than to estimate respiratory rate precisely, further validation of this procedure would strengthen its applicability in future studies.
In conclusion, the present study demonstrated that the conventional fixed 16th-order autoregressive model provides reliable frequency-domain HRV estimates in dogs under stationary conditions. The close agreement with AIC-selected model orders and the good overall agreement with the conventional FFT method support the applicability of AR(16) for canine HRV analysis. These findings provide methodological validation for the use of the conventional fixed 16th-order AR model in future veterinary HRV research.
Conflicts of Interest
None of the authors have any financial or personal relationships that would inappropriately influence or bias the content of the study.
Supplementary Material
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Acknowledgments
This work was supported by JSPS KAKENHI Grant Numbers JP25K16011 and JP22K12943.
REFERENCES
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