---
title: 'Heart Rate Efficiency: Metrics and Trade-offs'
url: https://www.emergentmind.com/topics/heart-rate-efficiency-hre
type: topic
---

# Heart Rate Efficiency: Metrics and Trade-offs

Heart Rate Efficiency (HRE) is used in multiple, only partially overlapping senses across the literature. The available work suggests that the term is not a single standardized construct, but rather a family of efficiency notions linking heart rate to mechanical work, locomotor economy, or computational cost. In cardiovascular modeling, HRE is closely aligned with left ventricular efficiency, quantified as the ratio of stroke work to pressure-volume area, $\mathrm{SW}/\mathrm{PVA}$, during atrial fibrillation simulations [1503.04591]. In endurance running, HRE is explicitly defined as $\text{HR} \times \text{Pace}$ and interpreted as the number of heartbeats required to cover one kilometer [2509.05961]. In wearable and ubiquitous sensing, the same broad efficiency idea is operationalized as an accuracy–resource trade-off involving sampling frequency, model size, inference time, latency, memory use, and energy expenditure in heart-rate estimation systems [2303.13636], [1807.04667], [2306.06129], [2410.19279].

## 1. Terminological scope and conceptual variants

Three technical usages dominate the available literature. The first is **cardiac mechanical efficiency**, where the relevant quantity is the fraction of ventricular mechanical energy converted into useful external work. In the atrial-fibrillation model of Scarsoglio, Guala, and Ridolfi, this is represented by $\mathrm{SW}/\mathrm{PVA}$, with stroke work given by the area enclosed by the left ventricular pressure-volume loop and pressure-volume area treated as a surrogate for myocardial oxygen consumption [1503.04591].

The second is **exercise-efficiency as a longitudinal training metric**. In the amateur-running study introducing Fitplotter, HRE is defined directly as
$$
\text{HRE} = \text{HR} \times \text{Pace},
$$
with HR in beats per minute and pace in minutes per kilometer, yielding units of beats per kilometer. The interpretation given is “the number of heartbeats required to cover one kilometer,” and lower values are taken to indicate improved cardiovascular economy [2509.05961].

The third is **systems efficiency in heart-rate sensing**. Here HRE is not a single scalar physiological variable, but an engineering objective. The wearable and ubiquitous-computing papers frame efficiency as obtaining usable HR estimates while minimizing costly sensing, computation, memory, latency, or communication. Concrete levers include reducing PPG sampling from 125 Hz to 25 Hz, querying PPG only on uncertain samples, dynamically offloading inference from a smartwatch to a phone, or duty-cycling a camera for rPPG sensing [2303.13636], [1807.04667], [2306.06129], [2410.19279].

This multiplicity matters because numerical values are not comparable across domains. A lower HRE in running means fewer heartbeats per kilometer, whereas a lower $\mathrm{SW}/\mathrm{PVA}$ in atrial fibrillation indicates worse ventricular efficiency. The same acronym therefore denotes distinct objects with different units, scales, and inferential roles.

## 2. Mechanical and energetic efficiency in atrial fibrillation

In permanent atrial fibrillation, heart-rate efficiency has been studied through a lumped-parameter cardiovascular model comprising the pumping heart together with the systemic and pulmonary circuits. The state variables are pressure $P$, volume $V$, and flow rate $Q$, and the governing equations are based on mass conservation, equations of motion, and linear state relations. The differential system is solved numerically in MATLAB with `ode15s`. Atrial fibrillation is simulated by making the atria passive and by generating beat-to-beat RR intervals from an exponentially modified Gaussian distribution with coefficient of variation fixed at 0.24. Each heart-rate condition is averaged over 5000 cardiac cycles at 50, 70, 90, 110, and 130 bpm [1503.04591].

The key efficiency-related quantities are defined as follows. Stroke volume is
$$
SV = V_{lv,ed} - V_{lv,es}.
$$
Stroke work is the area enclosed by the left ventricular pressure-volume loop. Pressure-volume area is
$$
PVA = PE + SW,
$$
with elastic potential energy
$$
PE = \frac{P_{lv,es}(V_{lv,es} - V_{lv,un})}{2} - \frac{P_{lv,ed}(V_{lv,ed} - V_{lv,un})}{4},
$$
and $V_{lv,un} = 5$ mL. Left ventricular efficiency is then
$$
\mathrm{SW}/\mathrm{PVA}.
$$
Additional oxygen-demand surrogates are rate pressure product,
$$
RPP = P_{sas,syst} \times HR,
$$
tension time index per minute,
$$
TTI/min = P_{lv,mean} \times RR \times HR,
$$
and pressure-volume area per minute,
$$
PVA/min = (PE + SW) \times HR.
$$

Across the simulated range from 50 to 130 bpm, faster ventricular rates increased pressure load and oxygen-demand surrogates while degrading beat-level mechanical performance [1503.04591].

| Metric | 50 bpm | 130 bpm |
|---|---:|---:|
| Mean LV pressure | 33.92 ± 37.56 mmHg | 53.15 ± 47.56 mmHg |
| Mean systemic arterial pressure | 82.66 ± 14.04 mmHg | 105.29 ± 7.63 mmHg |
| Stroke volume | 77.45 ± 8.5 mL | 39.09 ± 8.08 mL |
| Ejection fraction | 61.1 ± 4.4% | 39.32 ± 5.42% |
| Stroke work | 0.88 ± 0.04 J | 0.58 ± 0.09 J |
| RPP | 5598 ± 1939 mmHg/min | 15995 ± 3219 mmHg/min |
| TTI/min | 2094 ± 265 mmHg s/min | 3257 ± 301 mmHg s/min |
| PVA/min | 57.99 ± 17.9 J/min | 117.37 ± 25.96 J/min |
| LV efficiency $(SW/PVA)$ | 80.91 ± 2.91% | 66.43 ± 3.72% |

These results support a specific physiological meaning of HRE: lower ventricular rates in permanent AF allow the fibrillating heart to convert a larger fraction of generated mechanical energy into external work while simultaneously lowering indirect indices of myocardial oxygen consumption. The model reports a 49.5% decrease in stroke volume, a 35.6% decrease in ejection fraction, and a 34.2% decrease in stroke work between 50 and 130 bpm, while RPP increases by 185.7%, TTI/min by 55.5%, and PVA/min by 102.4% over the same range [1503.04591].

The study is explicit that this conclusion is model-based rather than definitive clinical evidence. Its significance lies in formalizing the intuition that rate control in AF affects not only rhythm or pressure but also the energetic conversion efficiency of the ventricle.

## 3. HRE as a longitudinal aerobic-fitness metric in running

A distinct formulation appears in the study of amateur runners, where HRE is formalized as
$$
\text{HRE} = \text{HR} \times \text{Pace},
$$
with units of beats per kilometer. Pace is expressed in decimal minutes per kilometer for computation; for example, 5:25 becomes 5.42 min/km, and $140 \times 5.42 \approx 758.8$, reported as 758 bpkm [2509.05961]. The authors interpret this quantity as the number of heartbeats required to cover one kilometer and state that lower HRE reflects fewer heartbeats per kilometer, which is an indicator of improved cardiovascular economy.

The motivation is methodological as much as physiological. Heart rate alone is sensitive to caffeine, stress, poor sensor contact, and heat, while pace alone varies with terrain, wind, fatigue, route, and intentional pacing. HRE is proposed as a synthesized measure that combines cardiovascular effort and locomotor output into a single longitudinal indicator that is less influenced by the athlete’s instantaneous effort compared to pace or HR. This suggests a practical role for HRE as an explainable proxy for aerobic fitness rather than a laboratory substitute for VO\(_2\) max or lactate-threshold testing [2509.05961].

The empirical basis consists of three data sources. The principal longitudinal dataset, “Athlete A,” spans 2011–2024, contains over 4,000 sessions, and includes GPS, elevation, timestamps, average heart rate, pace, distance, and event type. This is supplemented by publicly available logs from twelve endurance runners, labeled B–M, each with several hundred sessions from RunningAHEAD or Strava, and by 16 marathon activity records used for case-specific race analyses [2509.05961].

The reported longitudinal patterns are consistent with the proposed interpretation. For Athlete A, HRE improved steadily during the initial structured-training years from 2011 to 2013, tracked seasonal and annual structure, and aligned with increases in training volume. The athlete’s minimum HRE improved from 740 bpkm in 2011 to 685 bpkm in 2016, identified as a personal best; later years from 2020 to 2024 show gradual regression that is attributed to aging, reduced monthly mileage, and less frequent race participation [2509.05961].

Cross-runner comparisons reinforce the same reading. Highly experienced runners with high training volume, especially F and G, exhibited low and stable HRE around roughly 600–650 bpkm. Less mature or lower-volume runners showed higher and more variable HRE, and runner K is described as showing high HRE associated with low running volume. In a post-injury August 2018 example, HRE improved by about 10–15% over the month under similar conditions, which the authors interpret as sensitivity to short-term recovery and aerobic rebuilding [2509.05961].

Long-run behavior further clarifies the metric’s intended use. For runs longer than 90 minutes, well-trained runners often maintain stable HRE on flat routes, whereas less-trained runners often show HRE deterioration after 30–40 minutes, interpreted as fatigue. In marathon analyses, HRE is often stable for the first 30–35 km and then deteriorates in the final kilometers, consistent with “hitting the wall”; marathons with stable and lower HRE curves tend to be associated with faster finishing times [2509.05961].

## 4. Embedded wearable HRE: sampling, sensing, and inference efficiency

In wearable computing, HRE is treated as a design problem: estimate heart rate with acceptable error while minimizing the expensive components of the pipeline. Three recurring bottlenecks are sensor sampling frequency, model or feature size, and inference-time or communication cost [2303.13636], [1807.04667], [2306.06129].

For contact-based PPG sensing, one study uses a two-stage pipeline in which signal processing first converts PPG signals into rough HR estimates and a lightweight ML model then refines these estimates from short HR histories rather than raw high-rate waveforms. The system uses peak detection, a Z-score outlier filter with threshold 3, averaging of four HR readings per second into one HR/sec, and a 5% temporal boundary rule. Its main result is that PPG sampling can be reduced from 125 Hz to 25 Hz while maintaining strong accuracy: the combined signal-processing and ML approach yields about 5% MAPE overall, 3.33% MAPE on the ISPC dataset, and outperforms the signal-processing-only baseline by 5.17%. The comparative analysis further reports that Decision Tree models with 10–20 input features usually have good accuracy while being around 10 KB and below 3 microseconds in inference time [2303.13636].

A second efficiency strategy minimizes PPG usage itself by predicting HR from a cheaper sensor. In the online method PPAW, heart rate is inferred from acceleration gathered by a wrist-worn wearable, and true PPG HR is requested only when prediction uncertainty is high or the model has become stale. The work is motivated by the claim that PPG can use “up to 5000 times” more power than the accelerometer. The ensemble-based online learner stores a recent history of size $N$, uses a time-to-live parameter $TTL$, and in the reported experiments fixes $N=5$ and $TTL=10$ while varying the uncertainty threshold parameter $O$. In free-living monitoring of three patients, the method achieves an example result of MAE = 2.89 and MSE = 21.07 while querying true heart rate only 20.25% of the time [1807.04667].

A third formulation treats HRE as collaborative systems optimization across devices. The CHRIS runtime on a smartwatch selects, for each incoming PPG window, which HR model to use and whether it should execute locally or on a connected phone. Difficulty is estimated from accelerometer activity classification using a Random Forest over mean, energy, standard deviation, and number of peaks, and difficult windows can be offloaded when the configuration allows it. On a custom HWatch prototype with an STM32WB55 MCU, BLE 5.0, MAX30101 PPG sensor, and LSM6DSM IMU, CHRIS yields Pareto-optimal trade-offs in MAE-versus-energy space. One reported configuration achieves approximately the same MAE as TimePPG-Small, 5.54 BPM versus 5.60 BPM, while reducing smartwatch energy by 2.03x through offloading about 80% of predictions. A more aggressive operating point accepts 7.16 BPM MAE and achieves 179 $\mu$J per prediction, 3.03x less than running TimePPG-Small on the smartwatch and 1.82x less than streaming all input data to the phone [2306.06129].

Taken together, these studies make the systems meaning of HRE precise. Efficiency may arise from sampling more slowly, sensing less often, learning on compressed features, or moving inference to the most energy-favorable device. The common objective is not maximizing a single physiological quantity, but optimizing the accuracy–resource frontier of heart-rate monitoring.

## 5. Ubiquitous non-contact HRE and long-range rPPG sensing

Non-contact heart-rate sensing extends the engineering notion of HRE to open, uncontrolled environments. UbiHR is designed for commodity mobile devices and emphasizes end-to-end resource efficiency in long-range remote photoplethysmography. The motivating user study reports that among 80 participants, 60% were unwilling to stream raw videos to the cloud, 70% preferred local interaction for privacy and network independence, 70% wanted results within 30 ms, and over 85% worried about battery drain. This pushes the system toward low-latency, low-energy, local sensing [2410.19279].

The system integrates three mechanisms. The first is adaptive duty-cycling facial video sampling with sleeping, short-term listening, and long-term listening states. Short-term sampling checks whether a complete face is present and whether a heart-rate-related event may be occurring; if not, the system sleeps for 1 s. The event logic uses the pNN50 heart-rate-variability index: if pNN50 exceeds 20%, sampling continues until it falls below 20% or the user leaves the view; if average heart rate changes more than 5×, the system re-enters long-term sampling. The second mechanism is a dynamic noise-aware preprocessing pipeline using ASM facial keypoint detection on the forehead and cheek regions together with a temporal difference layer:
$$
C_k(t) = (I(t)\cdot (v_s(t)+v_d(t)) + U_n(t)) - (I(t-1)\cdot (v_s(t-1)+v_d(t-1)) + U_n(t-1)).
$$
After differencing, a learnable batch-normalization layer with learnable scale and shift parameters $\beta$ and $\gamma$ stabilizes the frame-difference magnitudes. The third mechanism is a lightweight long-range spatio-temporal network that uses a zero-parameter temporal shift strategy inside 2D convolution, parallel short-range and long-range branches, residual shift, and soft-attention masks computed using $1\times1$ convolutions followed by sigmoid activation [2410.19279].

The purpose of the long-range design is to preserve periodicity cues over noisy video streams without transformer-scale overhead. This is significant because short-range baselines are reported to degrade sharply under motion and speech. PhysNet’s MAE rises from 1.86 under slight head motion to 8.20 when the user is speaking, and DeepPhys rises from 2.11 to 12.82. By contrast, UbiHR is designed to exploit the observation that heart-rate peaks retain similar abrupt transition patterns over time even when amplitude varies [2410.19279].

The efficiency metrics are broad and explicitly linked to system design. On Raspberry Pi 4B, Jetson Orin, and Jetson AGX, UbiHR achieves 30.1 FPS, 98.3 FPS, and 201.8 FPS, respectively. It reports near real-time latency in the range of 5.01–30.9 ms depending on device and task, and claims up to a 51.2% latency reduction. In the Raspberry Pi memory study, end-to-end memory use averages 2.32 GB. In a smartphone deployment case, total system memory averages 660.5 MB, with the system itself accounting for about 230 MB, and average power consumption is 2.77 W, of which UbiHR inference contributes about 1.1 W. Adaptive duty cycling reduces memory usage and power consumption by 13.3% and 19% compared with continuous inference [2410.19279].

Accuracy is reported jointly with efficiency. On Raspberry Pi, UbiHR reduces MAE by 22.6% versus POS and by 32% versus TS-CAN, while MAPE drops by 0.73% versus TS-CAN. Across baselines, it reports recognizing-error reductions of up to 74.2%. On the iQOO9 smartphone, it achieves 12.4 ms per frame and MAE values of 4.13, 5.07, and 5.28 on UBFC-Phys, SCAMPS, and UCLA-rPPG, respectively. Under diverse lighting, its MAE fluctuation is 0.64 across natural, red, green, and green-blue lighting, whereas DeepPhys shows a 4.25 fluctuation, and its SNR under natural light is better than TS-CAN by 67.6% [2410.19279].

Within the engineering literature, UbiHR therefore represents a full-stack version of HRE: sparse sampling, cheap preprocessing, and long-range recognition are jointly optimized so that accuracy gains do not come at the cost of prohibitive resource use.

## 6. Limitations, interpretive cautions, and misattributions

The main limitation across the literature is that HRE is domain-specific. In atrial fibrillation, the conclusion that lower heart rates improve efficiency is derived from a mathematical model, not from compulsory direct clinical evidences. The AF results therefore support a mechanistic hypothesis about rate control rather than a settled treatment target [1503.04591].

In running, the evidence base is explicitly exploratory. The study relies on one long-term self-tracking case, twelve additional runners from public logs, and case-specific marathon records. The authors note that terrain, weather, fatigue, and sensor quality can make HRE difficult to interpret, that marathon plots can contain spikes due to poor heart-rate sensor contact, and that generalizability to older adults, people with health conditions, or sports beyond running has not been evaluated. They also state that HRE is most meaningful in sustainable aerobic conditions and less meaningful in highly irregular or stop-start activity [2509.05961].

In wearable and ubiquitous sensing, efficiency metrics are heterogeneous by design. Some papers optimize MAPE under reduced sampling frequency, others minimize PPG query rate, others minimize energy per prediction under offload constraints, and others balance latency, power, memory, and robustness in camera-based rPPG. This suggests that “HRE” in the systems literature is best understood as a family of task-specific trade-offs rather than a canonical metric shared across modalities [2303.13636], [1807.04667], [2306.06129], [2410.19279].

A separate interpretive caution concerns bibliographic misattribution. The record associated with arXiv:2208.07981 does not contain content on Heart Rate Efficiency, Tiny-HR, heart-rate estimation, edge deployment, ESP32, signal quality classification, CNNs, peak detection, or related benchmarks. It is described instead as an IEEEtran LaTeX template and formatting tutorial covering document class options, title and author formatting, abstracts, figures, tables, lists, equations, bibliography, biographies, and math typography examples. No HRE-like metric is defined there, and the equations present are generic typesetting examples rather than system metrics [2208.07981].

Taken together, these caveats indicate that HRE is best treated as a contextual construct. Its meaning depends on whether the problem is ventricular energetics, longitudinal running economy, or efficient heart-rate sensing under resource constraints. The common thread is efficiency, but the object being optimized differs substantially across these literatures.

Source: https://www.emergentmind.com/topics/heart-rate-efficiency-hre