A sine wave is not a breath

The lung simulator's spontaneous breathing issue

Introduction

For decades, lung simulators have modeled spontaneous breathing with sinusoidal or half-sinusoidal muscle-pressure curves. Real respiratory muscle tone does not have that shape. This post walks through what the gap means for clinical training, asynchrony research, and ventilator development — and what a more realistic model would have to provide.

Where the sine wave came from

Modern programmable lung simulators are used to qualify ventilators against IEC and ISO standards. Those benches need a reproducible inspiratory effort. A half-sine or sine was the natural choice: smooth, fully described by an amplitude, a period, and timing fractions.

When simulators moved into training centers and ventilation-research labs, the sine came with them. Operators learned to dial in in- or expiratory Rise, Hold, and Release as percentages of a breath cycle, and to set inspiratory muscular pressure (P_Mus) as the peak amplitude. The shape worked for the original problem: testing whether a ventilator triggers, whether it delivers a target tidal volume, and whether it handles a defined load. It has stayed in place ever since.

The issues start when the simulator must do something that the test bench or simulators were never designed for: training a clinician on patient-ventilator interaction, developing an algorithm that must detect spontaneous effort in real time, or reproducing a specific asynchrony phenotype seen in a real ICU patient. At that point, the simplifications that made the half-sine or sine convenient start to bite.

Figure 1 — Schematic: conventional sinusoidal P_Mus (top) vs asymmetric exponential P_Mus with breath-to-breath variability (bottom).

The difference between a real spontaneous breath and a sine wave

Four documented properties of real inspiratory muscle activation are visible in the literature. A sinusoidal P_Mus generator cannot reproduce them generically.

1. A breath's curvature is not sinusoidal

This one is worth being precise about, because a sine wave is often described as "symmetric" — and that is not quite what is wrong with it.

A sine-based generator with separate Rise, Hold, and Release durations is not necessarily symmetric. Rise and Release can be set to different fractions of the breath cycle, and the overall waveform can be timed asymmetrically. What the sine cannot be is curvature asymmetric. Whatever fraction of the cycle the rise occupies, the shape inside that fraction follows the sine curve: slow start, fast middle, slow approach to peak. The same is true on the way down.

Real respiratory muscle activity does not behave that way. Active contraction of the diaphragm follows roughly first-order RC-circuit kinetics — a fast onset that decelerates as it approaches peak. Relaxation is also exponential, slower, with a relaxation time constant about twice the contraction time constant in healthy muscle (Easton et al., 1999). The Fresnel, Muir, and Letellier model, published in 2014, was introduced specifically to capture this behavior. A sine can vary its rise and fall durations, but not its underlying curvature.

Overlay a real patient's Pes recording with a sine curvature of the same period and amplitude, and the peaks will always align. The shapes between them do not.

2. There is a brief post-inspiratory hold

Between the rise and the fall, real inspiratory effort has a brief plateau — post-inspiratory inspiratory activity (PIIA). The diaphragm continues to contract for a short period after the peak, slowing the initial phase of lung deflation. Clinicians sometimes call this "expiratory braking", and it is part of how the body defends end-expiratory lung volume (Easton et al., 1999).

Existing simulators do offer an inspiratory hold percentage in addition to the inspiratory waveform. In real patients, it is not an arbitrary number. It ranges from essentially none in severe distress, short in adult quiet breathing, long in sleep, and deep sedation. Mapping that range to named clinical scenarios — rather than to an unlabeled slider — allows an instructor to choose a breathing pattern by patient profile.

3. Expiration is often active

In COPD with expiratory flow limitation, in severe asthma, during exercise, and in respiratory distress, the abdominal and accessory expiratory muscles are recruited (Vaporidi et al., 2020). So, there is a real, measurable P_Mus on the expiratory side in such cases.

This is well-known. Many lung simulators have offered an expiratory P_Mus parameter for years. The deeper question is the model paradigm. If the spontaneous-breathing engine treats expiration as a possible add-on to an inspiratory waveform — same shape, just negative — the model is structurally inspiration-centric. If it treats inspiratory and expiratory effort as paired components, each with its own curvature and timing, the model reflects how real respiratory muscle activity works.

Figure 2 — Schematic: inspiratory P_Mus only (top) vs inspiratory + active expiratory P_Mus (bottom).

4. Real breathing is variable

Patients do not breathe at a fixed rate, with a fixed effort, breath after breath. Variability spans respiratory rate, tidal volume, and drive amplitude, and is evident in every public spontaneous-breathing dataset examined. Many waveform databases or PEEP study cohorts — all show wide distributions of variability metrics across subjects, never a single point at zero.

A sinusoidal generator at a fixed rate has, by construction, a coefficient of variation of zero. The conventional fix is to add variation parameters that inject breath-to-breath noise on top of the stationary sine. The underlying engine is still a stationary generator with noise added — not a model whose primitive is variability. That distinction matters when the scenario goal is to reproduce the irregular drive seen in distressed or unstable patients, where the irregularity is part of the clinical picture rather than a cosmetic addition.

Figure 3 — Schematic: eight breaths of stationary sine (top, CV = 0) vs eight breaths of asymmetric P_Mus with realistic variability (bottom).

5. The fifth gap: Language

This issue often lives in the language the operator uses, not in the model's mathematics.

The patient's neural inspiratory time — the duration during which the brainstem is sending active drive to the inspiratory muscles — is not the number that the ventilator displays as inspiratory time. The ventilator detects the onset of inspiration via a flow or pressure trigger and terminates inspiration when a timer expires, or inspiratory flow falls below a threshold. The patient is driving with neural activity that the ventilator usually cannot detect (Parthasarathy et al., 2000).

The mismatch between Ti_Neural and the ventilator's T_insp is the documented root cause of cycling asynchrony. A simulator that does not expose neural Ti as a named, separately configurable parameter makes the gap harder to teach.

Why this matters clinically

Patient-ventilator asynchrony, defined as an Asynchrony Index (AI) above 10%, was reported in 24% of mechanically ventilated patients in the original prevalence study by Thille et al. 2006. The same body of work links high asynchrony burden to longer ICU stays and worse outcomes (Blanch et al., 2015). The phenotypes that drive these — reverse-triggered breaths (Akoumianaki et al., 2013), double-triggering, ineffective triggering, occult pendelluft, and spontaneous-effort-driven patient-self-inflicted lung injury (Yoshida et al., 2013) — all depend on the shape and timing of the inspiratory effort.

Simulators that train clinicians to recognize these phenomena, and the bench setups behind the algorithms designed to detect them, must accurately reproduce them. A sine-curvature, inspiration-centric, fixed-rate generator with optional variability and an optional expiratory afterthought can be made to look right after enough operator effort. That is still different from being right.

What a more honest model would require

All the requirements are visible in the publications:

1. Exponential, not sinusoidal, curvature. Distinct contraction and relaxation kinetics derived from physiology rather than from operator-set fractions. The Fresnel 2014 RC formulation is one published option.
2. A formal phase structure. Contraction, hold, relaxation, pause — for inspiration and expiration alike.
3. Clinically anchored presets. Hold durations, effort amplitudes, and rate ranges are mapped to specific patient profiles, so that an instructor picks a scenario by name rather than by slider.
4. Variability as a primitive. Breath-to-breath variation is built into the model rather than injected on top of a stationary signal.
5. Neural inspiratory time exposed. Ti_Neural is a named, configurable quantity, making clear it is not the ventilator's T_insp.

The sine wave does not disappear from this list. There are use cases where a stationary, sinusoidal input is exactly what the bench requires. The point is that it becomes one option among several, rather than the default carried forward by inertia.

Christian Remus
Director Product Management
IMT Analytics AG

References

• Fresnel E, Muir J-F, Letellier C (2014). Realistic human muscle pressure for driving a mechanical lung. EPJ Nonlinear Biomedical Physics 2:7. doi:10.1140/epjnbp/s40366-014-0007-8
• Easton PA, Katagiri M, Kieser TM, Platt RS (1999). Postinspiratory activity of the costal and crural diaphragm. Journal of Applied Physiology 87(2):582–589. doi:10.1152/jappl.1999.87.2.582
• Vaporidi K, Akoumianaki E, Telias I, Goligher EC, Brochard L, Georgopoulos D (2020). Respiratory drive in critically ill patients: pathophysiology and clinical implications. AJRCCM 201(1):20–32. doi:10.1164/rccm.201903-0596SO
• Parthasarathy S, Jubran A, Tobin MJ (2000). Assessment of neural inspiratory time in ventilator-supported patients. AJRCCM 162(2 Pt 1):546–552. doi:10.1164/ajrccm.162.2.9901024
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