Rethinking the Resonance Frequency (RF) - Part 1: Understanding Resonance

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Heart


Randomized controlled trials have demonstrated the efficacy of HRV biofeedback for diverse clinical disorders like depression, diabetes, and preeclampsia (Lehrer et al., 2020, Meehan & Shaffer, in press).


The resonance frequency (RF) training protocol has strongly influenced heart rate variability (HRV) assessment and training. Steffen and colleagues (2017) ingeniously showed that RF training produced better mood and lower systolic blood pressure than RF+1 (breathing 1-bpm faster than the RF) or control conditions.


This series of posts seeks to demystify resonance frequency assessment for clinicians and performance trainers who use heart rate variability biofeedback in their practice. This first post explains resonance, the resonance frequency, two closed loops that regulate blood pressure and heart rate, and strategies to stimulate them to increase vagal tone and HRV.



What is the Resonance Frequency?


Resonance is an amplification process that relies on simple physics (Lehrer, 2020). An external force causes a closed-loop (negative feedback) system with a fixed delay to oscillate with greater amplitude at its inherent resonance frequency (RF). Here are four examples. First, striking one tuning fork causes the second to vibrate in unison, causing the ball to swing. Graphic © Designua/Shutterstock.com.

Resonance

Second, a bell struck by a Buddhist monk for prayer time resonates after the initial strike. Graphic © Amith Nag/Shutterstock.com.


Prayer bell


Third, visualize pushing a child on a swing. There is a single frequency that moves the child the highest. The best pushing rate is analogous to its RF (Khazan, 2020). Graphic © Billion Photos/Shutterstock.com.


Child on a swing

Finally, overloading a wine glass with sound at its RF can cause it to shatter because it cannot withstand the vibrational energy. Graphic courtesy of MARTY33 of YouTube.


Vibrating Glass


Dr. Paul Lehrer provides valuable insights about resonance in this video segment © Association for Applied Psychophysiology and Biofeedback (AAPB).





Vaschillo's Two Closed-Loop Model

Vaschillo’s two closed-loop model explains how HRV biofeedback procedures like slow-paced breathing (SPB) and slow-paced contraction (SPC) can increase HRV. Vaschillo et al. (2002) described the heart rate (HR) and vascular tone (VT) baroreflexes as closed loops and proposed that stimulating one closed loop activates its counterpart. Graphic adapted from Vaschillo et al. (2002).


Each baroreflex is a potential target for HRV biofeedback training. SPB and SPC at ~ 6 bpm/cpm can stimulate the HR baroreflex, separately or synergistically. SPC at ~ 1 cpm can activate the VT baroreflex.


Note. Bottom left: the lung and muscle icons indicate that SPB and SPC, alone or together, can stimulate the HR baroreflex at ~ 6 bpm/cpm. Bottom right: the muscle icon signals that SPC can activate the VT baroreflex at ~ 2 cpm.



Heart Rate Baroreceptor Reflex


Although HRV promotes health and performance, BP variability can endanger each. The HR baroreflex regulates acute BP changes to ensure stability. The HR baroreflex exhibits resonance since it is a feedback system with a fixed delay. Inertia due to blood volume in the vascular tree accounts for most of this delay. Graphic © Design_Cells/Shutterstock.com.


Vascular Tree


The HR baroreflex has a ~ 5-second delay with a resonance frequency of ~ 0.1 Hz. Graphic © Alila Sai Mai/Shutterstock.com.

Baroreceptor reflex


Vascular Tone Baroreceptor Reflex


The vascular tone (VT) baroreflex regulates resistance blood vessel diameter. It has a 15-second delay and 0.03 Hz resonance frequency. Vaschillo and colleagues (2002) proposed that the VT and HR baroreflexes work together to regulate BP and HR. Graphic © SciePro/Shutterstock.com.


Resistance Blood Vessels



Respiratory Sinus Arrhythmia

Respiratory sinus arrhythmia (RSA), HR speeding and slowing across each breathing cycle, is the primary and entirely parasympathetic source of HRV (Gevirtz, 2020). In the graphic adapted from Elite Academy below, the blue waveform represents the breathing cycle, and the red signals are heartbeats. Note that the heartbeats are spaced more closely (HR speeds) during inhalation and farther apart (HR slows) during exhalation.


Respiratory Sinus Arrhythmia

Inhalation partially disengages the vagal brake, speeding HR. This is purely parasympathetic. The red tracing is instantaneous HR; the blue is the breathing waveform measured by a respirometer. Graphics inspired by Dr. Richard Gevirtz.


Inhalation

Exhalation reapplies the vagal brake, slowing HR.

Exhalation

Inhalation speeds the heart, and about 5 seconds later, BP falls. During exhalation, the heart slows, and about 5 seconds later, BP increases. Graphic adapted from Evgeny Vaschillo.


Respiratory Sinus Arrhythmia

Note. The bottom line represents respiration. A rising black bar is inhalation, and a falling black bar means exhalation. The following lines represent HR and BP. This diagram allows us to see the changes in HR and BP produced by breathing.


Slow-Paced Breathing and Slow-Paced Muscle Contraction Stimulate Vaschillo's Two Closed Loops

Respiratory sinus arrhythmia, the HR baroreflex, and the vascular tone baroreflex are the most important sources of short-term (~ 5-minute) HRV. These processes are exclusively parasympathetic (Hayano & Yuda, 2019; Vaschillo et al., 2002).

Three Parasympathetic Sources of HRV


We can stimulate the HR and VT baroreflexes using slow-paced breathing and slow-paced contraction protocols.


Targeting the Heart Rate Baroreflex


Slow-paced breathing (~ 6 bpm) and slow-paced contraction (~ 6 cpm) can increase HR oscillations and HRV, separately or synergistically.


Slow-Paced Breathing


Let's start with slow-paced breathing. Respiration can produce blood pressure oscillations via changes in thoracic pressure (Pinsky, 2018) that can stimulate the closed loops.


Before HRVB, respiration and the HR baroreflex are usually out of phase, resulting in weak resonance effects (i.e., HR changes).

Weak resonance effects

HRV biofeedback training slows breathing to the HR baroreflex’s rhythm, which aligns these processes and significantly increases resonance effects.


Strong resonance effects


Slowing breathing to rates between 4.5-6.5 bpm for adults and 6.5-9.5 bpm for children increases RSA (Lehrer & Gevirtz, 2014). Increased RSA immediately “exercises” the HR baroreflex without changing vagal tone or tightening BP regulation. Those changes require weeks to months of practice. HRV biofeedback can immediately increase RSA 4-10 times compared to a resting baseline (Lehrer et al., 2020b; Vaschillo et al., 2002). Graphic adapted from Gevirtz et al. (2016).


RSA

Note. The red waveform shows HR oscillations while resting without breathing instructions or feedback. The blue waveform shows HR oscillations with HRV biofeedback and breathing from 4.5-6.5 bpm.


Slow-Paced Contraction


Slow-paced contraction (wrists-core-ankles with legs crossed) at ~ 6 and 2 cpm may stimulate blood pressure, HR, and VT control systems without slowing respiration (Vaschillo et al., 2011). This video does not include an audio track.



Like slow-paced breathing, slow-paced contraction amplifies heart rate oscillations. Slow-paced contraction stimulates the HR baroreflex at ~ 6 cpm and the VT baroreflex at ~ 2 cpm to immediately increase HRV. Weeks to months of practice are required to increase vagal tone.

SPC

Maximum-Minimum HR for each breath indexes RSA. The peak frequency is the HRV frequency with the greatest power. In the screen captures below, slow-paced contraction stimulated the HR baroreflex at the intended frequency (0.2 Hz for 12 cpm and 0.1 Hz for 6 cpm).


Below is a BioGraph Infiniti display of 12-cpm slow-paced contraction. At the top right, note that the Maximum - Minimum heart rate for each breath is 5 bpm. At the left, the peak frequency is 0.2 Hz. The red waveform is instantaneous HR; the purple is respirometer expansion/contraction. Graphic © BioSource Software LLC.


12-CPM

Next, is a 6-cpm slow-paced contraction display. The Maximum - Minimum heart rate for each breath is 13 bpm. At the left, the peak frequency is 0.1 Hz. The red waveform is instantaneous HR; the purple is respirometer expansion/contraction. Graphic © BioSource Software LLC.

6 CPM


Targeting the Vascular Tone Baroreflex


Shaffer, Moss, and Meehan (2022) reported that slow-paced contraction at 1 and 6 cpm increased five time-domain metrics (HR Max – HR Min, RMSSD, SDNN, TI, and TINN), one frequency-domain metric (LF power), and three non-linear metrics (D2, SD1, SD2) to a greater degree than slow-paced contraction at 12 cpm. There were no differences between the 1 and 6 cpm conditions.


Meehan and Shaffer (in press) compared 6-cpm wrist-ankle slow-paced contraction with 6-cpm wrist-core-ankle slow-paced contraction. Both conditions produced greater HR, HR Max-HR Min, and LF power than the control condition. The wrist-core-ankle method yielded greater HR and HR Max-HR Min than wrist-ankle slow-paced contraction.


HR Max-HR Min

Note. Descriptive statistics represent the results of untransformed, raw data. Error bars represent the 95% confidence interval around the mean.


LF Power

Note. Descriptive statistics represent the results of untransformed, raw data. Error bars represent the 95% confidence interval around the mean.



Summary


Every closed-loop regulatory system with a fixed delay possesses a resonance frequency. Stimulating these systems at their intrinsic frequencies amplifies the oscillations of the physiological variables they control. Slow-paced breathing and slow-paced contraction target the resonance frequencies of the HR and VT baroreflexes to immediately increase the amplitude of HR fluctuations, HRV, and, over weeks to months, vagal tone. Wrist-core-ankle (legs crossed) SPC produced greater RSA than wrist-ankle (legs uncrossed) SPC.



Glossary


baroreflex: baroreceptor reflex that provides negative feedback control of BP. Elevated BP activates the baroreflex to lower BP, and low BP suppresses the baroreflex to raise BP. D2: correlation dimension estimates the minimum number of variables required to construct a system dynamics model.


heart rate (HR) baroreflex: the closed-loop encompassing the cardiovascular control center, heart rate control system, and blood pressure control system. high-frequency (HF) band: an HRV frequency range from 0.15-0.40 Hz representing the vagus nerve's inhibition and activation by breathing (respiratory sinus arrhythmia).


HR Max – HR Min: an HRV index that calculates the average difference between the highest and lowest HRs during each respiratory cycle.


HRV frequency-domain measurements: metrics that quantify absolute or relative power distribution into four frequency bands, revealing the sources of HRV.


HRV nonlinear measurements: metrics that quantify the unpredictability of a time series, resulting from the complexity of the mechanisms that regulate the measured variable.


HRV time-domain measurements: metrics that quantify the total amount of HRV.


low-frequency (LF) band: an HRV frequency range of 0.04-0.15 Hz that may represent the influence of PNS and baroreflex activity when breathing or contracting muscles between 4.5-6.5 times a minute.


peak frequency: the HRV frequency with the greatest power.


resonance: an amplification process in which an external force causes a closed-loop (negative feedback) system to oscillate with greater amplitude at its inherent resonance frequency (RF).


resonance frequency: the frequency at which a negative-feedback system with a fixed delay, like the cardiovascular system, can be activated or stimulated.


respiratory sinus arrhythmia (RSA): the respiration-driven heart rhythm that contributes to the high frequency (HF) component of heart rate variability. Inhalation inhibits vagal nerve slowing of the heart (increasing HR), while exhalation restores vagal slowing (decreasing HR).


RMSSD: the square root of the mean squared difference of adjacent NN intervals in milliseconds.


SD1: the standard deviation of the distance of each point from the y = x-axis that measures short-term HRV.


SD2: the standard deviation of each point from the y = x + average RR interval that measures short- and long-term HRV.


SDNN: the standard deviation of the normal (NN) sinus-initiated IBI measured in milliseconds.


slow-paced breathing (SPB): low-and-slow breathing at ~ 6 bpm for adults with longer exhalation than inhalation.


slow-paced contraction (SPC): wrist-core-ankle contraction with legs supported and crossed at rates of ~1 or ~ 6 cpm.


time-domain measurements: quantify the total amount of heart rate variability.