Heart rate persistence index (HRPI): a threshold-free wearable metric for sustained HR elevation

This paper introduces the Heart Rate Persistence Index (HRPI), a novel, threshold-free metric that condenses sustained heart rate elevation into a single interpretable value by capturing both magnitude and duration, demonstrating robust stability and physiological relevance across diverse wearable datasets.

The Gist

Imagine your heart is like a car engine. For years, doctors and fitness trackers have mostly told you two things about your engine:

1. The Average Speed: How fast the engine was running overall today (Mean Heart Rate).
2. The Top Speed: How fast it revved at its absolute highest point for a split second (Maximum Heart Rate).

But there's a missing piece of the puzzle. What if your engine ran at a "highway speed" for two hours straight, versus just spiking to that speed for 10 seconds? The average might look the same, but the stress on the engine is completely different.

This paper introduces a new way to measure that stress called the Heart Rate Persistence Index (HRPI).

The "Persistence" Analogy: The Marathon vs. The Sprint

Think of your heart rate throughout the day as a runner.

• Mean Heart Rate is like the runner's average speed over the whole day.
• Maximum Heart Rate is just the one time they sprinted as fast as they could.
• HRPI asks a different question: "How long could this runner keep running at a specific speed without stopping?"

The HRPI is a clever, self-adjusting number. It finds the "sweet spot" where the speed and the time match up perfectly.

Here is how it works in plain English:
Imagine you look at your heart rate data for the whole day.

• Did you spend at least 100 minutes with your heart beating 100 times per minute? If yes, your score is at least 100.
• Did you spend at least 120 minutes with your heart beating 120 times per minute? If yes, your score is at least 120.
• The HRPI is simply the highest number where this rule holds true.

If your HRPI is 105, it means: "For at least 105 minutes today, my heart was beating at 105 beats per minute or faster."

Why is this better than the old ways?

The author, Ren Zhang, argues that old methods are like trying to describe a movie by only giving the average brightness or the loudest sound. You miss the plot!

1. No Arbitrary Lines: Old methods often say, "Count how many minutes your heart was over 100." But why 100? Why not 95 or 105? That's an arbitrary line in the sand. HRPI has no lines. It adapts to your specific day.
2. It Catches the "Sustained" Stuff: If you have a stressful day where your heart is elevated for hours, HRPI goes up. If you have a day with the same average heart rate but it's just a few random spikes, HRPI stays lower. It tells the difference between a marathon (sustained stress) and a sprint (brief spike).
3. It's Stable: The paper tested this over many days. They found that while some metrics (like "how much your heart rate varies") jump around wildly from day to day, HRPI is as reliable as your average heart rate. It's a steady, trustworthy number.

The "Age" Connection

The researchers also tested this on a huge group of healthy people, from babies to adults. They found something very logical: As people get older, their HRPI goes down.

Think of it like a rubber band. Young hearts are bouncy and can sustain higher rates for longer periods (maybe during play or stress). As we age, our hearts naturally become less "persistent" at those higher speeds. This proves that HRPI isn't just a random math trick; it actually measures real, biological changes in how our bodies work.

The Bottom Line

This paper gives us a new, simple tool to look at our heart health. Instead of just saying, "Your average heart rate was 75," we can now say, "Your heart was working hard for a sustained period today."

It's like upgrading from a speedometer that only shows your average speed to one that tells you how long you've been driving in the fast lane. It's easy to understand, doesn't require complex settings, and gives a clearer picture of what your heart is actually doing.

Technical Summary

1. Problem Statement

Wearable devices generate dense, longitudinal heart rate (HR) data, yet summarizing sustained HR elevation into a single, interpretable daily metric remains a challenge. Existing metrics have significant limitations:

• Mean HR: Reflects overall levels but fails to distinguish between transient spikes and sustained elevation.
• Maximum HR: Dominated by brief, isolated peaks rather than sustained states.
• Threshold-based metrics (e.g., minutes >100 bpm): Intuitive but rely on arbitrary, fixed cutoffs that may not apply universally.
• Percentile-based metrics: Characterize the upper tail of the distribution but do not directly unify magnitude and duration into a single interpretable quantity.

There is a critical need for a threshold-free, parameter-free metric that captures the persistence of elevated HR by jointly integrating magnitude and duration.

2. Methodology

Definition of HRPI

The authors propose the Heart Rate Persistence Index (HRPI), defined as the largest integer $k$ such that at least $k$ minutes in a day have an HR $\ge k$ bpm.

• Geometric Interpretation: If minute-level HR values are sorted in descending order and plotted against cumulative time, HRPI is the intersection point of this ranked curve with the identity line ($y = x$).
• Example: An HRPI of 105 means the subject had an HR $\ge 105$ bpm for at least 105 minutes that day.

Data Sources

Two distinct datasets were utilized:

1. Wearable Dataset (PhysioNet "BIG IDEAs"): Multi-day recordings from 16 participants using Empatica E4 devices. Data was aggregated to minute-level resolution to assess day-to-day stability and correlation with conventional metrics.
2. Healthy Reference Cohort (PhysioNet "RR interval time series"): 24-hour RR interval recordings from 138 healthy individuals spanning infancy to adulthood. RR intervals were converted to instantaneous HR ($60000 / RR$) to evaluate physiological relevance across age groups.

Statistical Analysis

• Correlation: Pearson correlation was used to assess relationships between HRPI and conventional metrics (Mean HR, SD, CV, percentiles, and threshold-based minutes).
• Residual Analysis: Linear regression was performed with HRPI as the dependent variable and Mean HR as the predictor to isolate the "residual HRPI" (the component independent of mean HR).
• Stability: Within-subject Coefficient of Variation (CV) across days was calculated to measure reproducibility.
• Age Association: Linear regression of subject-level HRPI against age (log-transformed for visualization) to test for physiological trends.

3. Key Contributions

• Novel Metric: Introduction of HRPI, a rank-based, non-parametric metric that unifies magnitude and duration without arbitrary thresholds.
• Interpretability: The metric is self-explanatory (e.g., HRPI = $X$ implies $X$ minutes above $X$ bpm), making it accessible to both specialists and non-specialists.
• Decoupling from Mean HR: Demonstration that HRPI captures structural information about HR distribution (specifically variability and persistence) that is distinct from simple average HR.
• Robustness: Validation of HRPI's stability across different data modalities (wearable optical HR vs. Holter-derived RR intervals).

4. Key Results

Relationship with Conventional Metrics

• HRPI is strongly positively correlated with Mean HR ($r = 0.83$) and Coefficient of Variation (CV HR) ($r = 0.48$).
• Distinct Information: Days with identical Mean HR (e.g., 71 bpm) exhibited different HRPI values (89 vs. 101), indicating HRPI captures sustained elevation patterns missed by the mean.
• Residual Analysis: After regressing out Mean HR, the Residual HRPI remained strongly associated with CV HR ($r = 0.92, p < 0.001$), confirming that HRPI reflects a variability-related component independent of the overall HR level.

Day-to-Day Stability

HRPI demonstrated high reproducibility within individuals, outperforming variability-based and threshold-based metrics:

• Mean HR: Median within-subject CV = 4.67% (Most stable).
• HRPI: Median within-subject CV = 5.49% (Nearly as stable as Mean HR).
• Percentiles (p90/p95): CV $\approx$ 6.4%.
• Variability Metrics (CV HR/SD HR): CV $\approx$ 13–15% (Less stable).
• Threshold-based (>100 bpm): CV = 33.33% (Least stable).

Age Dependence

In the healthy reference cohort, HRPI showed a strong inverse association with age:

• Correlation: $r = -0.715$ ($p = 7.27 \times 10^{-23}$).
• Regression: Slope of -1.657 HRPI units per year ($R^2 = 0.511$).
• This confirms that HRPI declines progressively with age, consistent with known physiological changes in heart rate dynamics.

5. Significance and Conclusion

The Heart Rate Persistence Index (HRPI) offers a compact, robust, and interpretable solution for summarizing sustained heart rate elevation in longitudinal wearable studies.

• Clinical/Research Utility: It provides a single number that reflects the "burden" of sustained tachycardia without relying on arbitrary cutoffs (like 100 bpm) or being skewed by brief peaks.
• Physiological Relevance: Its strong correlation with age and its ability to capture variability beyond the mean suggest it is a biologically meaningful marker of autonomic state and cardiovascular health.
• Future Directions: The authors suggest future studies should validate HRPI in larger, diverse cohorts and investigate its utility in predicting clinical outcomes, exercise recovery, and autonomic phenotyping.

In conclusion, HRPI bridges the gap between complex continuous HR data and actionable daily summaries, offering a superior alternative to mean HR or fixed-threshold metrics for monitoring sustained physiological stress.