Time-Varying Glottal Pressure and Flow

Having explored the mechanisms of self-sustained oscillation, we now examine the temporal patterns of airflow and pressure that emerge during sustained phonation. These waveforms reveal how energy transfer occurs throughout the vibratory cycle and connect theoretical mechanisms to observable phenomena.

Recap of Self-Sustained Oscillation

Two mechanisms enable continuous energy transfer from the airstream to vocal fold tissue:

Vocal Tract Inertance: Delayed response of the air column creates pressure that is positive during opening and negative during closing, synchronized with tissue velocity.

Nonuniform Tissue Movement: Convergent glottal shape during opening produces higher mean intraglottal pressure than divergent shape during closing, again synchronized with velocity.

Both mechanisms share a common requirement: asymmetry in driving pressure between opening and closing phases. This asymmetry ensures that net energy flows into the tissue over a complete cycle, overcoming damping losses.

Temporal Events During Oscillation

The relationship between tissue displacement, velocity, airflow, and pressure reveals the detailed physics of energy transfer.

Waveforms during sustained oscillation Figure 4.11: (a) Vocal fold displacement and velocity at glottal center, (b) glottal airflow, (c) air particle velocity, and (d) mean intraglottal pressure. Note the phase relationships among these quantities.

Tissue Displacement and Velocity

Displacement Waveform (x):

Shows lateral position of vocal fold edge over time
Maximum during peak opening
Minimum during closure (often zero with collision)
Roughly sinusoidal but with asymmetries

Velocity Waveform (ẋ):

Rate of change of displacement
Positive during outward (opening) movement
Negative during inward (closing) movement
Maximum magnitude occurs near equilibrium position
Zero at peak displacement and at closure

The velocity waveform is critical because energy transfer depends on the product of force and velocity. When driving pressure and velocity have the same sign (both positive or both negative), energy flows into the tissue.

Glottal Airflow

The glottal airflow U represents volume velocity—the volume of air per second passing through the glottis. Its temporal characteristics are distinctive:

Slow Rise: Flow increases gradually during opening as glottal area increases. The rate of rise is limited by:

Inertia of the air column (takes time to accelerate)
Gradual increase in glottal conductance
Buildup of pressure gradient

Abrupt Fall: Flow decreases suddenly during closure as glottal area rapidly decreases to zero. The abrupt termination occurs because:

Collision creates immediate area reduction
Air column momentum cannot maintain flow through closed glottis
Sudden impedance change

Skewing: The combination of slow rise and abrupt fall creates rightward skewing of the flow waveform—the peak occurs later in time than the midpoint between onset and offset. This asymmetry is a crucial feature affecting voice quality and acoustic output.

Peak Delay: The peak in airflow occurs after the peak in vocal fold displacement. This delay reflects the inertia of the air column—flow continues to increase even as the glottis begins to narrow.

Air Particle Velocity

While glottal airflow U measures volume per second, air particle velocity v measures how fast individual air molecules move through the glottis. These quantities relate through the continuity equation:

U = a × v

where:

U = volume velocity (flow)
a = glottal cross-sectional area
v = air particle velocity

Since glottal area a is proportional to vocal fold displacement x (for both folds moving symmetrically), we can write:

v = U / x

This division operation creates the air particle velocity waveform shown in Figure 4.11c.

Asymmetric Shape: Dividing the flow waveform by the displacement waveform amplifies the asymmetry:

During the rising portion of flow, displacement is increasing, so v increases less than U
During the falling portion of flow, displacement is decreasing, so v decreases more rapidly than U
Result: Air particle velocity is higher during closing than during opening for the same flow value

Increasing Trend: The average air particle velocity shows an upward trend from left to right—velocity is systematically higher in the latter half of the open phase than in the first half. This increasing trend is the key to understanding pressure asymmetry.

Intraglottal Pressure Dynamics

The mean intraglottal pressure P drives the vocal folds laterally. Its temporal variation creates the asymmetry needed for energy transfer.

Bernoulli Relationship

Bernoulli’s energy conservation law states that in a duct at constant flow:

P + ½ρv² ≈ constant

where:

P = static pressure against walls
ρ = air density
v = air particle velocity

This relationship means that when air particle velocity increases, pressure decreases, and vice versa. The constant represents total pressure (static + dynamic).

Pressure Asymmetry

Comparing two points with identical airflow U (marked by dots in Figure 4.11b):

Point 1 (Early in Cycle):

Lower air particle velocity v
Higher static pressure P
Convergent glottal shape (if nonuniform movement present)

Point 2 (Later in Cycle):

Higher air particle velocity v
Lower static pressure P
Divergent glottal shape (if nonuniform movement present)

Even though the flow is identical at these two points, the pressure is lower at Point 2 than at Point 1. This is shown in Figure 4.11d, where the pressure waveform decreases from left to right despite the flow waveform being symmetric about its peak.

Synchronization with Velocity

The critical feature is how intraglottal pressure P correlates with tissue velocity ẋ (dotted line in Figure 4.11a):

During Opening (ẋ > 0):

Tissue moving outward
Early in cycle
Lower air particle velocity
Higher intraglottal pressure
Pressure helps push folds apart
Energy added to tissue

During Closing (ẋ < 0):

Tissue moving inward
Late in cycle
Higher air particle velocity
Lower intraglottal pressure (even negative/suction)
Pressure offers less resistance or actively assists
Less energy extracted from tissue

The downward trend in pressure matches the downward trend in tissue velocity. This positive correlation between driving force and velocity over the cycle enables net energy transfer.

Small Negative Dip

A small dip below zero pressure often occurs just before closure (visible in Figure 4.11d). This represents:

Very high air particle velocity as glottis narrows
Strong Bernoulli suction effect
Assists final closure
Brief but not necessary for overall mechanism

Importantly, sustained oscillation does not require pressure to become negative. What matters is that pressure is higher during opening than during closing.

The Role of Asymmetry

The essential feature enabling self-sustained oscillation is asymmetry—the fact that conditions during opening differ from conditions during closing:

Airflow Asymmetry:

Slow rise vs. abrupt fall
Created by vocal tract inertance
Results in flow waveform skewing

Velocity Asymmetry:

Lower during early opening
Higher during late closing
Created by dividing flow by changing area

Pressure Asymmetry:

Higher during opening
Lower during closing
Created by velocity asymmetry via Bernoulli effect
Enhanced by convergent-divergent shape changes

Energy Transfer:

Positive pressure during positive velocity → energy in
Negative pressure during negative velocity → energy in
Lower pressure magnitude during negative velocity than during positive → net energy in

Without these asymmetries, oscillation would damp out. The Bernoulli effect alone cannot create asymmetry—it requires either vocal tract inertance, nonuniform tissue movement, or both.

Comparison with Classical View

The classical myoelastic-aerodynamic theory emphasized negative Bernoulli pressure “sucking” the vocal folds together. This description captures part of the phenomenon but misses the crucial point:

Classical Emphasis: Negative pressure closes the glottis Complete Mechanism: Pressure is more positive during opening than during closing, regardless of whether it becomes negative

The complete picture recognizes that:

Pressure need not be negative to assist closing
What matters is the difference between opening and closing phases
Multiple mechanisms (vocal tract inertance, tissue wave) create this difference
Bernoulli effect contributes but does not alone determine oscillation

Clinical Relevance

Understanding these waveforms has practical implications:

Flow Waveform Shape: The degree of skewing (abruptness of closure) affects:

Spectral content of the voice source
Voice quality (brightness, breathiness)
Efficiency of acoustic energy production

Collision Timing: The abrupt flow termination indicates:

Whether vocal folds contact
Timing and force of impact
Potential for impact stress

Pressure Requirements: The mean and peak intraglottal pressure relate to:

Phonation threshold pressure
Efficiency of oscillation
Vocal effort required

These temporal patterns can be estimated from audio recordings (through inverse filtering) or measured directly with specialized instrumentation, providing diagnostic information about vocal fold function.

Summary

During sustained vocal fold oscillation, temporal patterns of displacement, velocity, airflow, and pressure reveal the mechanism of energy transfer. Glottal airflow exhibits characteristic skewing with slow rise and abrupt fall due to vocal tract inertance and collision. Air particle velocity increases throughout the open phase as glottal area decreases while flow remains relatively high.

Mean intraglottal pressure decreases from opening to closing due to increasing air particle velocity (via Bernoulli’s law) and changing glottal shape (from convergent to divergent). This pressure asymmetry synchronizes with tissue velocity—higher pressure during outward movement, lower during inward movement—enabling net energy transfer from the steady airstream to oscillating tissue.

The critical feature is not whether pressure becomes negative, but rather that pressure differs between opening and closing phases in a way that correlates positively with tissue velocity. Multiple mechanisms (vocal tract inertance and nonuniform tissue movement) create this essential asymmetry.

Key Takeaways

✅ Glottal airflow exhibits rightward skewing with slow rise and abrupt fall characteristic of vocal source
✅ Air particle velocity increases throughout open phase as area decreases while flow remains high
✅ Mean intraglottal pressure decreases from opening to closing due to velocity increase via Bernoulli effect
✅ Pressure asymmetry synchronized with tissue velocity enables energy transfer regardless of absolute pressure sign
✅ Multiple mechanisms create essential asymmetry between opening and closing phases

Time-Varying Glottal Pressure and Flow

Time-Varying Glottal Pressure and Flow

Recap of Self-Sustained Oscillation

Temporal Events During Oscillation

Tissue Displacement and Velocity

Glottal Airflow

Air Particle Velocity

Intraglottal Pressure Dynamics

Bernoulli Relationship

Pressure Asymmetry

Synchronization with Velocity

Small Negative Dip

The Role of Asymmetry

Comparison with Classical View

Clinical Relevance

Summary

Key Takeaways

Related Topics

Further Reading