Abstract

Problem

When a ventilator's exhalation valve is replaced with one from a different manufacturer, the machine's tidal volume display can become silently and systematically wrong — with no alarm, no warning, and no visible sign on the screen. This report describes how that error was discovered, quantified, and corrected at the bedside of one patient, and provides a mathematical framework for identifying the same problem in other setups.

This is a case report. Error magnitudes are model-derived from manufacturer-published valve flow data and require independent bench validation to confirm. Single-limb ventilators estimate tidal volume by subtracting an assumed intentional leak flow based on the manufacturer's own exhalation valve calibration. When a valve from a different manufacturer is substituted, the assumed leak curve may not match the actual valve's flow characteristics — producing a systematic tidal volume measurement error that generates no alarm and is invisible on the ventilator display.

Methods

Flow characteristics of the native ResMed 24991 Leak Valve and the substituted Philips Whisper Swivel II were derived from manufacturer source data using power-law curve fitting (37-point ResMed curve digitized from manufacturer instruction sheet; 9-point Philips published table). The crossover pressure was solved analytically and verified numerically. Tidal volume error was computed across the patient's operating IPAP range (22–30 cm-H₂O) and integrated over the full range.

Results

The two valve flow curves intersect at 18.38 cm-H₂O. Above this crossover, the Philips valve leaks more than the ResMed algorithm assumes. Across the patient's IPAP range (RR 18, EPAP fixed at 5 cm-H₂O), tidal volume was overestimated by 40–129 mL per breath in this setup, with an integrated average of 84.3 mL/breath — equivalent to approximately 91 litres of phantom ventilation per hour (volume the machine believed it had delivered but which never reached the patient's lungs). An empirical correction of \(\sim\)100 mL to the iVAPS target tidal volume resolved the clinical problem and was subsequently confirmed by the mathematical analysis. No independent flow measurement was performed; all quantitative findings represent model-derived predictions, not measured values. The direction of the error is robust to parameter uncertainty; the magnitude is sensitive to the fitted Philips exponent \(n\) (see Appendix B.4).

Implications

The empirical bedside correction confirmed the direction of the error; the mathematical model quantifies the magnitude. The two together constitute the finding: valve mismatch produces a systematic, alarm-free \(V_T\) overestimation whose direction is robust and whose magnitude is model-derived and awaits bench validation. Exhalation valves are calibration-critical components, not interchangeable accessories. The magnitude of error depends on the specific valve pair, pressure settings, and respiratory rate, and will differ across setups. Clinicians and caregivers should verify that the exhalation valve in use matches the ventilator manufacturer's specification, particularly when closed-loop ventilation modes are active — and especially in home settings where inline spirometry or independent flow measurement is unavailable. All quantitative findings are model-derived; no objective clinical outcome data (ABGs, nocturnal oximetry, transcutaneous CO₂) are presented, and bench validation remains the essential next step.

Background

This report is a single-patient, model-based engineering case study describing the identification, quantification, and correction of a systematic tidal volume measurement error caused by exhalation valve mismatch in a single-limb ventilator circuit. It is not a clinical outcomes study and should be interpreted accordingly.

Amyotrophic Lateral Sclerosis (ALS) is a progressive neurodegenerative disease that causes loss of voluntary motor function, including the muscles of respiration. As the disease advances, patients require mechanical ventilatory support — initially non-invasive, and in many cases progressing to invasive tracheostomy ventilation. Long-term home ventilation in ALS typically uses single-limb circuits, in which expired gas is vented through a dedicated intentional leak valve rather than a separate expiratory limb. These valves are calibration-critical components: the ventilator's algorithm estimates tidal volume by subtracting an assumed leak flow — derived from the manufacturer's own valve — from the total measured flow. When a non-native valve is substituted, this calibration assumption is violated, and the tidal volume estimate may become systematically incorrect. The flow characterisation methodology builds on established bench work on intentional leak valve behaviour in NIV circuits [1], extending that framework to a specific mixed-manufacturer valve mismatch in an invasive tracheostomy setting.

Prior bench studies have characterised tidal volume measurement errors in single-limb NIV circuits, but from different mechanisms. Luján et al. (2013) documented \(V_T\) underestimation of 21.7–83.5 mL (3.6–14.7%) across five commercial home ventilators, attributable to leak magnitude, breathing pattern variation, and algorithm differences between ventilator brands [2]. Pasquina et al. (2012) and Janssens et al. (2022) identified gaps in home ventilation monitoring [3, 4]. The present case differs from these prior reports in both mechanism and direction: the error here arises specifically from valve substitution rather than leak magnitude or breathing pattern, and produces overestimation rather than underestimation — a direction that is more dangerous because it generates false reassurance rather than clinical concern. To our knowledge, this is the first case to characterise valve mismatch error mathematically using power-law flow curve analysis, and the first to document the resulting silent failure mode in a closed-loop ventilation algorithm.

Part I: Our Father

Our father, Surendra Kumar Narula, was not given to complaint. A state government employee in Rajasthan, he worked through the early weakness in his hands without a word of self-pity, completing his service and retiring honourably in April 2017 — eight months after being diagnosed with Amyotrophic Lateral Sclerosis (ALS) at Fortis Hospital, Jaipur, in August 2016. He was 59 years old. The doctors gave him two years to live.

He is still here, in his ninth year.

What followed his diagnosis was a progression that stripped away his speech, his swallowing, his movement, and finally his ability to breathe unassisted:

• September 2018 — PEG feeding tube inserted
• October/November 2018 — BiPAP for non-invasive ventilatory support during sleep
• December 2018 — wheelchair-dependent
• May 11th, 2019 — emergency tracheostomy after a mucus plug caused respiratory collapse
• End of May 2019 — home from the ICU on invasive tracheostomy ventilation; the mode he remains on today
• December 2020 — last hospital admission

He has not been back to a hospital since December 2020.

He has survived GI sepsis, which carries a 72% mortality rate, as well as metabolic acidosis, paralytic ileus, and complete loss of voluntary movement. He has survived because my sister Reena and I refused to let the protocols slip — and because, when something was wrong, we kept asking why until we found the answer.

"Life is struggle and struggle is life." — Papa's lifelong catchphrase. Still true.

Our Caregiving Roles

I am Dr. Harsh Kumar Narula. I left my research career to become our father's primary caregiver in Jaipur. My sister, Dr. Reena Narula, PT, is a physiotherapist at Fortis Hospital Jaipur. Despite her own professional and personal responsibilities, she has continued to return regularly for hands-on caregiving support ever since. Together, we manage a home ICU: ventilator monitoring, tracheostomy care, PEG tube management, catheter changes, physiotherapy, medication protocols, nutrition charts, and emergency response — all at home, every day.

This article comes from that world. I am writing it for ALS families, for respiratory therapists, for clinicians who manage invasive and non-invasive ventilation, and for anyone who cares for a ventilator-dependent patient at home. We have been sharing Papa's journey and our experience of ALS caregiving at www.livewithals.com [5] since 2022.

Part II: The Problem Nobody Could Explain

Papa is ventilated on a ResMed Stellar 150 — a life-support grade invasive ventilator designed for tracheostomy-dependent patients with high ventilatory demand. It runs in iVAPS mode (intelligent Volume-Assured Pressure Support), a closed-loop algorithm that continuously adjusts inspiratory pressure to maintain a target alveolar ventilation. The circuit is single-limb, and intentional leak is managed through an exhalation valve attached at the patient connection. The valve the Stellar 150's algorithm is calibrated against is the ResMed 24991 Leak Valve.

We had not always been on ResMed. Papa was previously ventilated on Philips Respironics machines, and the Philips Whisper Swivel II was part of our standard circuit setup — the correct, native accessory for those devices.

When Philips initiated a global recall of their ventilators due to degradation of polyester-based polyurethane (PE-PUR) foam used for sound dampening — a quality issue with serious inhalation risk — we were forced to migrate to the ResMed Stellar 150. We made that transition, but the Philips accessories — including several Whisper Swivel II valves — remained in our supplies.

In 2022, our authorised ResMed dealer advised us that the Whisper Swivel II could be used with the Stellar 150 interchangeably — without any issues. It was a reasonable thing to try: the valve was already in hand, it was physically compatible, and we had an expert's assurance. This appears to be an assumption that is not widely questioned, even among equipment specialists — valve interchangeability is taken for granted, and the flow calibration implications are rarely discussed. Within a few hours, however, it was clear something was wrong: Papa was uncomfortable, his breathing unsettled. We restored the ResMed 24991 Leak Valve immediately and did not revisit the question.

For three years, the Whisper Swivel II sat unused.

The reason we wanted it was practical and legitimate. The Whisper Swivel II is designed to rotate freely along its own axis, which means the entire ventilator circuit can be pivoted around it during position changes — supine to left lateral to right lateral — without disconnecting or stressing the tracheostomy connection.

So recently, I decided to revisit it — this time not just practically, but theoretically. I was not willing to accept "it doesn't work" without understanding why. Over 10–15 days, I worked on both fronts: empirically adjusting ventilator settings while Papa used the valve, observing his response breath by breath and position by position — and in parallel, pulling the published flow data for both valves and working through the mathematics from first principles.

The empirical fix came first. The theory followed. And when the theory arrived, it explained the fix with a precision I had not expected. That sequence — bedside hunch to mathematical proof — is the approach this article documents. The dual method — hands-on adjustments by day, equations by night — uncovered a flaw that had been hiding in plain sight inside the ventilator's own assumptions.

Papa's survival has never been about luck. It has been about spotting what the machines could not tell us — and understanding why.

Part III: The Physics of Exhalation Valves in Ventilator Circuits

The investigation that follows begins with the physics of how ventilators measure what they deliver.

What is an Exhalation Valve?

Single-limb ventilator circuits — whether used for non-invasive or invasive (tracheostomy) ventilation — do not have a separate exhalation limb. Instead, expired gas (including CO₂) is flushed from the circuit through a dedicated exhalation valve that leaks continuously. The ventilator must know, at every moment, how much gas is escaping through this valve.

It uses this estimate to calculate displayed tidal volume (\(V_T\)):

\[ V_{T,\text{displayed}} = \text{Total Delivered Flow} - \text{Estimated Leak Flow} \]

This estimated leak is calculated using a flow model embedded in the ventilator's algorithm — built around the pressure–flow behaviour of the manufacturer's own valve. Attach a different valve, and the flow model no longer reflects what is physically in the circuit. Every breath, the subtracted leak is wrong by a pressure-dependent amount.

In plain terms: an exhalation valve behaves like a pressure-driven resistive element. As circuit pressure rises, gas escapes through the valve faster. For an ideal orifice, this relationship follows the square root of pressure — double the pressure, and flow increases by a factor of roughly 1.4, not 2. Each manufacturer's valve has a slightly different internal geometry, which means a slightly different relationship between pressure and leak flow.

\[\begin{align} \text{Patient Flow} &= \text{Total Measured Flow} - \text{Assumed Leak}\\ &\text{If Assumed Leak} \neq \text{Actual Leak}\\ &\text{Then Calculated Patient Flow} \neq \text{True Patient Flow}\\ &\quad\to \text{Tidal Volume Error} \end{align}\]

Curve Fitting: Deriving the Flow Equations

I independently derived flow characteristic equations for both valves from their source data. The general form is the power law \(Q = k \cdot P^{n}\), where:

• \(Q\) = intentional leak flow rate, in litres per minute (L/min)
• \(P\) = circuit pressure, in centimetres of water (cm-H₂O)
• \(k,\, n\) = valve-specific constants fitted from manufacturer data

The full source data and digitization methodology are documented in Appendices A and B.

ResMed 24991 Leak Valve — Native Valve

I digitized the vent flow rate curve published in the ResMed 24991 Leak Valve instruction sheet [6] using pixel-level image analysis. Axis calibration was performed by detecting gridline positions within the image. The curve was sampled at every integer pressure from \(P = 4\) to \(P = 40\) cm-H₂O (37 points) using centroid-based pixel extraction.

Fitting the orifice model \(Q = k\sqrt{P}\) (i.e. \(n = 0.500\) fixed, per Torricelli's law for ideal orifice flow) via Q-space least-squares regression:

\[ Q_{\text{ResMed}} = 8.7168 \cdot \sqrt{P} \qquad R^2 = 99.72\%,\quad \text{RMSE} = 0.558\;\text{L/min} \]

Philips Whisper Swivel II — Substituted Valve

Flow data were taken from the Philips Respironics official published table [7] (9 data points, 2.5–40 cm-H₂O). Fitting a free power law:

\[ Q_{\text{Philips}} = 6.5803 \cdot P^{0.5966} \qquad R^2 = 99.96\%,\quad \text{RMSE} = 0.313\;\text{L/min} \]

Simultaneous Solution: The Crossover Point

Because the two exponents differ, the flow curves intersect at exactly one pressure. Solving simultaneously:

\[\begin{align} 8.7168 \cdot P^{0.500} &= 6.5803 \cdot P^{0.5966}\\ P^{(0.5966 - 0.500)} &= \frac{8.7168}{6.5803}\\ P^{0.0966} &= 1.3247\\ P &= 1.3247^{1/0.0966} \end{align}\]

Verified by Brent's numerical method to six decimal places with zero residual at the crossover point. Bootstrap uncertainty analysis (Appendix B.4) places the 95% confidence interval on this crossover at 16.98–19.75 cm-H₂O; even at the upper bound, the crossover lies 2.25 cm-H₂O below Papa's IPAP floor of 22 cm-H₂O, and the clinical conclusion is preserved.

Part IV: Our Father's Pressure Profile

Papa is ventilated in iVAPS mode with the following prescription:

• IPAP range: 22–30 cm-H₂O
• EPAP: 5 cm-H₂O
• Respiratory rate: 18 breaths/min
• I:E ratio 1:2 \(\;\Rightarrow\;\) \(T_i = 1.11\) s, \(T_e = 2.22\) s

His entire IPAP operating range — from 22 to 30 cm-H₂O — lies above the crossover point of 18.38 cm-H₂O. Every inspiratory phase, the Philips valve leaks more gas than the ResMed algorithm assumes. EPAP = 5 cm-H₂O lies well below the crossover; the Philips valve leaks less than expected during expiration, but this difference is not clinically significant, as demonstrated in Part VIII.

Part V: The Measurement Error — Why the Machine Lies

Mechanism

The ventilator computes tidal volume by subtracting its expected leak from total measured flow. That expected value is derived from the native valve's flow curve. With the Philips valve in circuit at IPAP \(> 18.38\) cm-H₂O, the actual escaping gas exceeds the expected amount. The residual flow left after subtraction — which the machine calls patient flow — is inflated. \(V_T\) displayed is falsely elevated.

The Error Equation

\[ V_{T,\text{error}}\;(\text{mL/breath}) = \frac{Q_{\text{Philips}} - Q_{\text{ResMed}}}{\text{RR}} \times 1000 \]

where \(Q\) values are in L/min and RR is the respiratory rate in breaths per minute. At any pressure above crossover, \(Q_{\text{Philips}} > Q_{\text{ResMed}}\), making the error positive — the display reads high.

Quantified Error: IPAP 22–30 cm-H₂O

Average Error — Integration over Full IPAP Range

Rather than relying on point estimates at individual pressures, the true average unaccounted leak across Papa's full IPAP operating range was computed by integration. Formally, integrating \(\Delta Q(P)\) from 22 to 30 cm-H₂O:

\[\begin{align} \Delta Q(P) &= 6.5803 \cdot P^{0.5966} - 8.7168 \cdot P^{0.500}\\[4pt] \overline{\Delta Q} &= \frac{1}{8}\int_{22}^{30} \Delta Q(P)\,dP \end{align}\]

Antiderivatives evaluated analytically:

\[\begin{align} \int 6.5803 \cdot P^{0.5966}\,dP &= 4.1213 \cdot P^{1.5966} + C\\ \int 8.7168 \cdot P^{0.5000}\,dP &= 5.8112 \cdot P^{1.5000} + C\\[6pt] \Bigl[4.1213 \cdot P^{1.5966}\Bigr]_{22}^{30} &= 940.64 - 573.27 = 367.36\\ \Bigl[5.8112 \cdot P^{1.5000}\Bigr]_{22}^{30} &= 954.88 - 599.65 = 355.22\\[6pt] \int_{22}^{30} \Delta Q(P)\,dP &= 367.36 - 355.22 = 12.14\;\text{L·cm-H}_2\text{O/min}\\[4pt] \overline{\Delta Q} &= 12.14/8 = 1.517\;\text{L/min}\\ &\;\Rightarrow\;\mathbf{Average}\; V_T\;\mathbf{error} = \mathbf{84.3\;\text{mL/breath}} \end{align}\]

Verified numerically (scipy.quad): residual \(3 \times 10^{-14}\) — analytically exact.

On average, across every breath Papa takes in his full IPAP operating range, the machine overestimates tidal volume by 84.3 mL. The hourly accumulation follows directly: phantom ventilation per hour \(= 84.3\;\text{mL} \times 18 \times 60 \div 1000\). At RR = 18, this represents approximately 91 litres of phantom ventilation per hour — volume the machine believes it has delivered, but which never reached Papa's lungs.

These four numbers — 40–129 mL, 84.3 mL, 73 mL, and \(\sim\)100 mL — appear at different points in this article and are fully consistent with one another: the 40–129 mL range is the per-breath error across the full IPAP operating range (22–30 cm-H₂O, from Table 3); the 84.3 mL integrated average is the mean of that range weighted equally across all operating pressures; the 73 mL at IPAP = 25 is the point estimate at his typical operating pressure; and the \(\sim\)100 mL empirical correction is the bedside adjustment that resolved the clinical problem.

Part VI: The Symmetric Error — Both Directions Are Dangerous

The analysis so far has focused on one specific configuration: a Philips valve used with a ResMed ventilator. But the physics is symmetric, and the implications extend in both directions. Understanding the full error matrix is important for any clinician or caregiver working with mixed-manufacturer circuits.

The crossover point — 18.38 cm-H₂O in this valve pair — is the pressure at which the two curves intersect. Below it, the Philips valve leaks less than the ResMed algorithm assumes. Above it, it leaks more. The direction of the tidal volume error depends entirely on which valve is in the circuit and which algorithm is running. Reverse the combination, and the error reverses — with the same mechanism producing either hypoventilation or hyperventilation depending on which side of the crossover the patient's operating pressure falls.

The clinical consequences of the two directions are different in character. Hypoventilation — the case in our investigation — tends to manifest as discomfort, unsettled breathing, and eventually CO₂ retention. It is dangerous, but the patient often signals it. Hyperventilation is in some ways more insidious: CO₂ is washed out below normal, respiratory alkalosis develops silently, and if IPAP is being driven progressively higher by iVAPS, the risks include barotrauma, air trapping, and haemodynamic compromise. The machine appears to be working correctly — even working hard. Neither direction triggers an alarm.

The complete error matrix — four configurations, two pressure regions:

All four cases produce silent, alarm-free mismatch. The direction of the error depends on which valve is installed and whether operating pressure is above or below the crossover point of 18.38 cm-H₂O.

The direction of the error depends on which valve is in the circuit. Hypoventilation and hyperventilation are both possible — silently, in the same class of mismatch, with no alarm in either case.

One important qualification: the Philips-in-ResMed configuration (hypoventilation) is the case directly observed and empirically corrected in this investigation. The reverse configuration — ResMed valve in a Philips ventilator — is an inference from the same manufacturer flow curves and the symmetric physics of the mismatch. It has not been observed at the bedside in this case, and its quantitative magnitude in practice may differ from the model-based estimate due to differences in algorithm implementation between manufacturers. The direction of the error is analytically certain; its precise clinical magnitude in the reverse case requires independent validation.

Part VII: Why iVAPS Makes This Worse

In S/T mode, IPAP is fixed and the error, while significant, is at least constant — the machine is wrong by a predictable amount at a fixed pressure. iVAPS is fundamentally different. It is a closed-loop control mode: it continuously monitors displayed \(V_T\) and autonomously adjusts IPAP breath-by-breath to achieve a target alveolar ventilation [8]. When the Philips valve is attached and displayed \(V_T\) is falsely elevated, the entire feedback loop is corrupted — and it is corrupted in a direction the algorithm cannot detect.

To understand why, it helps to follow what iVAPS does on each breath. At the start of every inspiratory phase, the ventilator delivers a pressure-supported breath, measures the resulting flow, subtracts its assumed leak, and computes displayed \(V_T\). It then compares this to the target. If displayed \(V_T\) appears to meet the target, IPAP stays at or decreases. If it falls short, IPAP is stepped up on the next breath. The algorithm is continuously tuning itself, breath by breath, toward what it believes is adequate alveolar ventilation.

Now introduce the Philips valve at IPAP above 18.38 cm-H₂O. The valve leaks more than the algorithm assumes. The subtracted leak is too small. Displayed \(V_T\) is falsely high — appearing to meet or exceed the target. The algorithm therefore has no signal to escalate. It sees a satisfied target and holds or reduces IPAP. Meanwhile, the actual volume reaching the patient's lungs is consistently less than intended — by 40 to 129 mL per breath across the operating range. The patient is under-ventilated. The machine is content.

There is a further compounding effect. If the patient's condition deteriorates — increased secretions, positional atelectasis, respiratory muscle fatigue — iVAPS would ordinarily respond by escalating IPAP. But with the Philips valve in circuit, any increase in IPAP moves the operating point further above the crossover, where the mismatch is largest. Higher IPAP means greater overestimation. The algorithm's corrective response makes the measurement error worse, not better. It is self-defeating: the harder it tries to compensate, the more it is misled.

• The machine sees its \(V_T\) target apparently being met.
• It has no reason to increase IPAP.
• Papa continues to receive less volume than intended.
• If he deteriorates and iVAPS pushes IPAP higher, the error grows larger — because the mismatch increases with pressure.

The feedback chain that iVAPS relies on:

Part VIII: CO₂ Washout — Is It a Problem?

At EPAP = 5 cm-H₂O — well below the crossover of 18.38 cm-H₂O — the Philips valve leaks less than the ResMed. The calculated expiratory washout volumes for both valves are shown below.

The dead space range of 250–350 mL reflects published estimates for invasive tracheostomy circuits: anatomical dead space in an adult is approximately 150–180 mL, with the tracheostomy tube, ventilator elbow, and proximal circuit adding a further 80–150 mL depending on circuit configuration.

Dead-space washout alone does not guarantee adequate CO₂ removal. If tidal volume is chronically under-delivered due to valve mismatch, alveolar ventilation falls accordingly, allowing CO₂ to accumulate despite adequate circuit flushing. In our setup, the under-delivery ranged from 40 to 129 mL per breath across Papa's IPAP range — but the magnitude will vary with pressure settings, respiratory rate, and the specific valve pair in use. No expiratory valve can compensate for chronically under-delivered tidal volume.

This washout analysis assumes no significant unintentional circuit leak — that is, all gas exits through the intentional leak valve and there are no mask, elbow, or tubing leaks adding to the total expiratory flow. It is worth noting the nature of the compounding: the valve mismatch described in this article produces a systematic error — predictable, pressure-dependent, and present on every breath — while unintentional leaks introduce a variable error on top of it, one that fluctuates with circuit condition, patient position, and secretion load.

Part IX: My Workaround — Intuition Before the Math

Long before I understood the mathematics, I had an observation: Papa was uncomfortable when the Philips valve was in use. I asked doctors, biomedical engineers, and equipment providers. No one had an answer. Over time, after trying other approaches that failed, I arrived at a practical solution: increase the iVAPS target tidal volume by approximately 100 mL above the set target.

When I subsequently performed the curve fitting and calculated the mismatch error, I found that at IPAP = 25 cm-H₂O — his typical operating pressure — the \(V_T\) overestimation is 73 mL/breath. My empirical correction was approximately 100 mL. The closeness reflects the kind of calibrated observation that develops when you pay close enough attention to a patient over years.

In control-systems terms, what I did has a specific name. The iVAPS controller was compensating for a measurement bias it could not see. My instinct was to bypass the corrupted sensor — the displayed \(V_T\) — and anchor the system instead on the physical variable that actually determines ventilation: pressure. By observing that Papa was comfortable when his IPAP settled in the 23–30 cm-H₂O band, and adjusting the target until that behaviour was restored, I was effectively recalibrating the controller around the actuator output rather than the false measurement.

There is a deeper physiological reason why this works — and why it is valid specifically for fully passive patients. For a patient with no residual respiratory muscle effort, as in advanced ALS, tidal volume is not self-generated. It is entirely pressure-driven. The relationship is:

\[ V_T \approx C \times (\text{IPAP} - \text{EPAP}) \]

With EPAP fixed at 5 cm-H₂O, tidal volume is determined almost entirely by IPAP. When iVAPS suppressed IPAP in response to the false \(V_T\) reading, it directly reduced the actual volume delivered to Papa's lungs. Restoring IPAP — which is precisely what the \(\sim\)100 mL target correction achieved — restored actual \(V_T\).

A Reproducible Heuristic: Pressure-Anchored \(V_T\) Correction

PAVC has five properties that distinguish it from a simple numerical adjustment:

• Requires no additional measurement equipment.
• Requires no bench measurement or digitization of valve flow curves.
• Requires only clinical knowledge of the patient's validated IPAP operating band.
• Works regardless of which specific valve pair is causing the mismatch.
• Is physically grounded: when IPAP returns to the validated range, actual \(V_T\) is restored by the compliance relationship \(V_T \approx C \times (\text{IPAP} - \text{EPAP})\), not by assumption.

Why the Workaround is Safe in Papa's Case

The correction is bounded on both sides. From below: the target increase was calibrated empirically until Papa achieved comfortable, consistent ventilation across all three sleeping positions — supine, left lateral, and right lateral — with IPAP settling in the 23–30 cm-H₂O range independently validated over years of care. From above: his IPAP ceiling of 30 cm-H₂O provides adequate headroom; at no point during the adjustment was he driven to the pressure limit. CO₂ clearance was not compromised: as shown in Part VIII, the Philips valve at EPAP = 5 still flushes circuit dead space by nearly twice per breath. The empirical correction (\(\sim\)100 mL) is consistent with the calculated mismatch error (\(\sim\)73 mL at IPAP = 25), providing mathematical corroboration for a bedside adjustment that had already proven clinically effective.

Important distinction: The valve mismatch error described in this article affects all patients on single-limb ventilators with a non-native exhalation valve — including those with residual spontaneous respiratory effort. PAVC, however, is valid only for fully passive patients. In patients with any residual inspiratory muscle effort, actual tidal volume is determined by both ventilator pressure and patient effort, so the relationship \(V_T \approx C \times (\text{IPAP} - \text{EPAP})\) no longer holds and IPAP alone cannot be used to infer or restore actual \(V_T\).

Recognising over-correction: In a fully passive patient, over-correction of the \(V_T\) target drives IPAP above the validated operating band. The clinical signals are the mirror image of under-ventilation: the patient may appear over-distended breath by breath (visible chest excursion larger than baseline), IPAP may be sitting persistently at or near the pressure ceiling, and — if capnography is available — end-tidal CO₂ will fall below the patient's established normal range.

Part X: Summary of Errors

The valve mismatch does not produce a single isolated error. It initiates a cascade: the wrong leak assumption corrupts the \(V_T\) display, which corrupts the iVAPS feedback loop, which suppresses the pressure support the patient needs. Each stage is invisible to the machine's alarms.

Part XI: What I Am Asking of You

For Clinicians and Respiratory Therapists

• Exhalation valves are calibration-critical components, not generic accessories. Using a valve from a different manufacturer introduces a systematic error into the machine's \(V_T\) calculation — in both invasive (tracheostomy) and non-invasive ventilation. This appears to be poorly documented in routine clinical guidance.
• If a patient on iVAPS or any closed-loop mode is not responding as expected despite apparently normal \(V_T\) readings, ask which exhalation valve is attached.
• Know the crossover pressure for the valve combination in use. If the patient's IPAP lies above it, the machine is overestimating \(V_T\).
• Validate displayed \(V_T\) against capnography or independent measurement when mixed-manufacturer equipment is in use.

Practical Checklist — If You Suspect Valve Mismatch

• Step 0 — Confirm you have the right valve: Before anything else, physically inspect the exhalation valve in the circuit. Check the part number on the valve itself against the ventilator manufacturer's specification. If you cannot confirm the valve identity, treat it as non-native until verified.
• Step 1 — Compare leak curves: If the valve is non-native, look up the published flow characteristics for both valves. Calculate or estimate the crossover pressure. If your patient's IPAP lies above it, the ventilator is overestimating tidal volume.
• Step 2 — Assess the patient: Do not rely solely on displayed \(V_T\). Observe comfort, work of breathing, and positional consistency. In iVAPS, check whether IPAP is tracking as expected or sitting statically despite patient effort.
• Step 3 — Quantify the error if possible: Using the valve flow equations and the patient's RR and IPAP, calculate the expected \(V_T\) overestimation using: \[ V_{T,\text{error}}\;(\text{mL/breath}) = \frac{\Delta Q\;(\text{L/min})}{\text{RR}\;(\text{breaths/min})} \times 1000 \] Worked example at IPAP = 25 cm-H₂O: \(Q_{\text{Philips}} = 44.90\) L/min, \(Q_{\text{ResMed}} = 43.58\) L/min, \(\Delta Q = 1.317\) L/min. At RR = 18: \(V_{T,\text{error}} = 1.317 / 18 \times 1000 = 73.2\) mL/breath.
• Step 4 — Adjust under supervision: Any compensatory change to \(V_T\) targets must be made under clinical supervision. Monitor EtCO₂ where available. Document the change and the rationale clearly.

This observation applies to our specific setup and has not been validated in controlled trials. Anyone considering a similar adjustment should do so only under clinical supervision and with a clear understanding of their own valve mismatch profile.

For ALS Families and Home Caregivers

• If your patient is uncomfortable on the ventilator and the machine's numbers look normal, the machine may be wrong. Trust your observation. This applies equally to tracheostomy ventilation and to non-invasive masks.
• Ask your equipment provider which exhalation valve is attached and whether it matches the ventilator brand.
• Document everything: discomfort, pressure readings, positional differences. Your notes are clinical data.
• You do not need a medical degree to understand your patient's ventilator. You need time, patience, and the willingness to ask questions nobody else has thought to ask.

For Equipment Providers and Manufacturers

• It would be helpful if exhalation valve compatibility and its effect on \(V_T\) measurement were disclosed more explicitly in device documentation — for both invasive and non-invasive circuit configurations.
• Ventilators in closed-loop modes like iVAPS could benefit from allowing the user to select the attached exhalation valve model, enabling the algorithm to apply the correct leak estimate for that valve's flow curve.

Have you encountered a similar issue with your ventilator and exhalation valve? Share your experience at livewithals.com — every data point helps build a clearer picture of how widespread valve mismatch truly is, and which combinations are most affected.

Implications for Further Research

• Bench validation: Independent measurement of tidal volume error using a test lung and pneumotachograph or inline spirometer with mixed-manufacturer valve combinations would convert this model-based analysis into experimentally validated data. The recommended protocol: ResMed Stellar 150 with Philips Whisper Swivel II vs. native ResMed 24991, test lung at representative compliance, IPAP range 22–30 cm-H₂O, respiratory rates 12–24 breaths/min, minimum 10 steady-state breaths per condition, mean ± SD reported. This is the single most impactful next step for journal publication.
• Multi-patient case series: Systematic documentation of valve mismatch cases across ALS and other neuromuscular disease populations would establish prevalence and identify which ventilator–valve combinations carry the highest clinical risk.
• Algorithm-selectable leak curves: Ventilator firmware that allows the clinician to select the attached exhalation valve model — so the algorithm applies the correct pressure–flow curve — would eliminate this class of error entirely.
• Valve ageing and tolerance effects: Studies characterising how valve flow curves drift with use would inform how frequently valve-specific calibration checks are needed.
• Cross-manufacturer compatibility registry: A publicly maintained database of valve crossover pressures and error magnitudes for common ventilator–valve combinations.

Conclusion

This investigation demonstrates that exhalation valve mismatch can introduce systematic tidal volume measurement error in single-limb ventilators — an error that grows with inspiratory pressure, accumulates silently across every breath, and generates no alarm. In closed-loop ventilation modes such as iVAPS, this error alters ventilator behaviour at a fundamental level: the algorithm responds to a false signal, failing to escalate pressure support when the patient needs it. Clinicians and caregivers should ensure that the exhalation valve in use matches the ventilator manufacturer's specification whenever the ventilator algorithm relies on leak modelling to estimate tidal volume.

The quantitative predictions of this analysis — crossover at 18.38 cm-H₂O, \(V_T\) overestimation of 40–129 mL/breath — are grounded in manufacturer data and first principles, but require confirmation by bench testing with a pneumotachograph or inline spirometer before the error magnitude can be stated with clinical certainty. This paper presents the hypothesis and the framework; experimental validation is the essential next step. Notably, the direction of the error — Philips valve leaks more than the ResMed algorithm assumes above the crossover — is robust to parameter uncertainty; the magnitude (40–129 mL/breath) is more sensitive, particularly to the fitted Philips exponent \(n\), as the sensitivity analysis in Appendix B.4 shows.

The patient safety implications are direct:

• Misleading clinicians: Displayed \(V_T\) appears adequate even when delivered ventilation is substantially below target — the screen shows normal numbers while the patient is under-ventilated.
• Suppressing adaptive modes: In iVAPS, the false signal prevents appropriate IPAP escalation, locking the machine in a false equilibrium it cannot self-correct.
• Hidden hypoventilation risk: The patient is systematically under-ventilated without any alarm, flag, or visible indication on the display.

The central finding of this investigation rests on two pillars that reinforce each other: the empirical bedside correction confirmed the direction of the error, and the mathematical model quantifies its magnitude. Neither alone would be sufficient — the direction without quantification is anecdote; the quantification without empirical confirmation is modelling. Together they constitute a coherent, testable hypothesis whose next step is bench validation.

Limitations

• Steady-pressure assumption: The mathematical analysis treats inspiratory pressure as constant during each breath. In practice, iVAPS delivers pressure-supported breaths with a rising and plateau profile. Because the instantaneous pressure during the rising phase is lower than the set IPAP, the actual leak during that phase is also lower than the model assumes — meaning the true error is slightly smaller than the steady-pressure estimates reported here. The bias is conservative: the model slightly overestimates the magnitude of the error.
• Internal algorithm implementation: This analysis assumes the ventilator subtracts leak flow using a single continuous power-law curve derived from the native valve's published data. Real firmware may implement leak compensation via lookup tables, smoothed interpolations, or additional empirical corrections. The direction of the mismatch error is determined by the physical valve characteristics and is robust to this uncertainty; the precise magnitude depends on the exact algorithm implementation, which is not publicly documented by the manufacturer.
• Single valve pair: The quantitative results — crossover pressure, error range, integrated average — are specific to the ResMed 24991 Leak Valve and Philips Whisper Swivel II combination. Other valve pairings will have different crossover pressures and different error magnitudes.
• Single patient profile: The IPAP range (22–30 cm-H₂O) and respiratory rate (18 breaths/min) are specific to this patient.
• No independent flow measurement: The mismatch was quantified from manufacturer-published flow data, not from direct bench measurement of the specific valves in use. The quantitative predictions — crossover pressure, \(V_T\) error range, integrated average — are model-derived and have not been verified by bench testing. They should be treated as testable hypotheses, not confirmed measurements.
• Empirical workaround not formally validated: The \(\sim\)100 mL target adjustment resolved the clinical presentation in this patient. It has not been validated in a controlled study. No objective clinical outcome data — ABGs, nocturnal oximetry, transcutaneous CO₂, or ventilator download records — from before and after the correction are presented.
• Confounding factors not excluded: This is a retrospective, single-patient analysis. Disease progression, changes in circuit maintenance, and positional or secretion-related factors were not formally excluded as contributing causes.

These limitations do not invalidate the core finding. The mechanism — that a non-native exhalation valve produces a systematic, pressure-dependent, alarm-free tidal volume measurement error in single-limb ventilators — follows directly from first principles and published manufacturer data.

Glossary

ALS

Amyotrophic Lateral Sclerosis — a progressive neurodegenerative disease causing loss of voluntary motor function including respiration.

BiPAP

Bilevel Positive Airway Pressure — non-invasive ventilation delivering separate inspiratory (IPAP) and expiratory (EPAP) pressures.

EPAP

Expiratory Positive Airway Pressure — the lower pressure level during expiration; set to 5 cm-H₂O in this patient.

IPAP

Inspiratory Positive Airway Pressure — the higher pressure level during inspiration; operating range 22–30 cm-H₂O in this patient.

iVAPS

intelligent Volume-Assured Pressure Support — a closed-loop ventilation mode (ResMed) that automatically adjusts IPAP breath-by-breath to maintain a target alveolar ventilation.

NIV

Non-Invasive Ventilation — ventilatory support delivered via mask rather than tracheostomy.

PAVC

Pressure-Anchored \(V_T\) Correction — the heuristic described in Part IX for correcting the iVAPS \(V_T\) target in fully passive patients when valve mismatch is suspected.

PE-PUR

Polyester-based polyurethane — the foam material used for sound dampening in Philips Respironics ventilators, subject to the global recall announced in 2021.

PEG

Percutaneous Endoscopic Gastrostomy — a feeding tube inserted through the abdominal wall into the stomach.

RR

Respiratory Rate — number of breaths per minute; set to 18 breaths/min in this patient.

\(V_T\)

Tidal Volume — the volume of gas delivered to the patient per breath; the quantity affected by the valve mismatch error described in this paper.

References

Acknowledgements: To my wife Neha Tandon and to Reena's husband, for holding everything else together so that we could hold Papa. To Satvinder Kaur and the ALS Care and Support Group India (linktr.ee/alscasindia), for being the community that showed us we were not alone. To every caregiver reading this — your dedication is seen.

Ethics and Consent Statement

Informed consent for publication was provided by the authors — Dr. Harsh Kumar Narula and Dr. Reena Narula, PT — in their capacity as the patient's children and primary caregivers. The patient, Surendra Kumar Narula, is unable to communicate due to advanced Amyotrophic Lateral Sclerosis and cannot provide consent directly. As his family and sole caregivers, the authors act as his representatives in all medical decisions.

The personal narrative and clinical details pertaining to the patient are shared with the full knowledge and endorsement of the authors in their representative capacity. The patient is identified by his given name with family consent, in keeping with the authors' long-standing commitment to open, attributed advocacy for ALS caregivers at www.livewithals.com.

No ethics board review was sought, as this is a single-patient caregiver case report documenting an adjustment made in the course of ordinary home caregiving, not a research intervention on a third party.

Epilogue: For the Family Reading This at 2 AM

Somewhere tonight, there is a family managing a ventilator at home. The machine is beeping, or not beeping when it should. The numbers look fine but something feels wrong. They have called the doctor, the equipment provider, the helpline. Nobody has a clear answer.

I wrote this for you.

Our father was given two years to live in August 2016. He is in his ninth year. He has survived things that would have ended the care of most patients — not because of anything extraordinary about his biology, but because Reena and I paid attention. Because we asked questions nobody else thought to ask. Because we trusted what we saw over what the screen displayed.

Papa always said: "Life is struggle and struggle is life." He taught me to be honest and hardworking. I am trying, every day, to be worthy of that lesson — and to share what I learn so that another family does not have to start from scratch.

The mathematical analysis and physical assumptions in this article are consistent with the published flow characteristics of both valves. But the origin of all of it was something much simpler: I noticed that our father was uncomfortable, and I refused to stop asking why.

There is a broader lesson here that extends beyond this specific valve pair. Ventilators do not measure tidal volume directly. They infer it — using an internal model of the breathing circuit, including an assumed leak curve for the exhalation valve. When that assumed model matches the physical reality of the circuit, the displayed numbers are trustworthy. When it does not, the numbers may be confidently reported, precisely displayed, and completely wrong — with no alarm, no flag, and no indication that anything is amiss.

The machine does not know what it does not know.

If this article helps even one family, one respiratory therapist, or one clinician catch a valve mismatch before it becomes a crisis — then the nine years of learning it took to write this were worth it.

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Appendix A: ResMed 24991 Leak Valve — Digitized Flow Data

Source: ResMed 24991 Leak Valve instruction sheet, accessed at msa.sm.ee/ctrl/en/Fail/laadi_alla/88502.

A.1 Digitization Methodology

The ResMed 24991 Leak Valve flow characteristic is published as a graphical curve (vent flow rate vs circuit pressure) rather than a numerical table. Digitization was performed using custom Python/OpenCV pixel analysis — a reproducible procedure equivalent in methodology to WebPlotDigitizer. Axis calibration was performed by detecting gridline positions within the image. Gridline regression confirmed: 35.40 px per cm-H₂O on the x-axis, 17.67 px per L/min on the y-axis. The curve was sampled at every integer pressure \(P\) from 4 to 40 cm-H₂O (37 points) using centroid-based pixel extraction. Dark pixels (gray value < 80) in each column were identified, excluding rows coinciding with known horizontal gridlines (±4 pixel tolerance).

A.2 Original Manufacturer Curve

A.3 Extracted Data Points

A.4 Fit Result

\[ Q = 8.7168 \cdot \sqrt{P} \] \[ R^2 = 99.72\% \qquad \text{RMSE} = 0.558\;\text{L/min} \qquad n = 37\;\text{points} \]

Note: The orifice model (\(n = 0.500\) fixed) was selected because the ResMed 24991 Leak Valve is designed as a fixed orifice and the fit is excellent across the full pressure range. A free power law fit gave \(n = 0.489\) — statistically indistinguishable from 0.500 — confirming the orifice model is appropriate. The coefficient \(k\) was estimated by Q-space ordinary least squares (OLS); see Appendix B.3 for a full explanation of this fitting method and why it was chosen over log-space OLS for both valves.

Appendix B: Philips Whisper Swivel II — Published Flow Data

Source: Philips Respironics. Intentional Leak Rates for Masks and Exhalation Ports. Document ID: MCI 4104973, June 2012.

B.1 Original Published Table

B.2 Fit Results

Power law: \(Q = 6.5803 \cdot P^{0.5966}\)

\[ R^2 = 99.96\% \qquad \text{RMSE} = 0.313\;\text{L/min} \qquad n = 9\;\text{points} \]

Orifice: \(Q = 8.9957 \cdot \sqrt{P}\)

\[ R^2 = 98.34\% \qquad \text{RMSE} = 2.046\;\text{L/min} \qquad n = 9\;\text{points} \]

The power law model is clearly superior. The orifice model systematically overestimates flow at low pressures (error +29% at \(P = 2.5\) cm-H₂O) and underestimates at high pressures. The non-ideal exponent of 0.5966 reflects the additional turbulent resistance introduced by the Whisper Swivel II's rotary geometry and internal diffuser.

B.3 Fitting Method: Q-Space Ordinary Least Squares

What it is

All curve fits in this article — for both the ResMed 24991 and the Philips Whisper Swivel II — were performed using Q-space ordinary least squares (OLS). This means the fitting algorithm minimises the sum of squared errors in the raw flow values:

\[ \text{minimise} \sum_{i=1}^{n} \bigl[Q_i - \hat{Q}(P_i)\bigr]^2 \]

where \(Q_i\) is the published or digitized flow value at pressure \(P_i\), and \(\hat{Q}(P_i) = k \cdot P_i^{n}\) is the model prediction.

The alternative: log-space OLS

A natural alternative for power-law models is to linearise by taking logarithms:

\[ \log Q = \log k + n \log P \]

and then apply OLS to the transformed data. This minimises squared errors in \(\log Q\) rather than in \(Q\) itself — which is equivalent to minimising squared relative (percentage) errors in \(Q\):

\[ \text{minimise} \sum_{i=1}^{n} \left[\frac{Q_i - \hat{Q}(P_i)}{Q_i}\right]^2 \approx \sum_{i=1}^{n} \bigl[\log Q_i - \log \hat{Q}(P_i)\bigr]^2 \]

Why Q-space OLS was chosen

For the specific application in this article — computing the absolute flow difference \(\Delta Q(P) = Q_{\text{Philips}}(P) - Q_{\text{ResMed}}(P)\) and converting it directly to a tidal volume error in mL/breath — the relevant error metric is an absolute one in L/min, not a relative one. The quantity that harms the patient is the raw unaccounted leak in litres per minute; a 1 L/min discrepancy at high IPAP matters just as much as a 1 L/min discrepancy at low IPAP.

Numerical comparison for the Philips Whisper Swivel II

The crossover pressure shifts by 0.29 cm-H₂O between methods, and the \(V_T\) error at IPAP = 25 cm-H₂O shifts from 73 mL (Q-space) to 77 mL (log-space). Both crossovers sit well below Papa's IPAP floor of 22 cm-H₂O, and both \(V_T\) error estimates are within the empirical correction of \(\sim\)100 mL. The clinical conclusions of this article are unchanged by the choice of fitting method.

B.4 Uncertainty Quantification

Bootstrap confidence intervals

To quantify uncertainty in the crossover pressure and \(V_T\) error estimates arising from curve-fitting and data noise, a bootstrap analysis (\(N = 10{,}000\) resamples) was performed. The Philips data were resampled with uniform noise \(\pm\)0.5 SLPM (reflecting the integer rounding of the published table); the ResMed digitized data were resampled with Gaussian noise at the fit RMSE of 0.558 L/min.

Manufacturing tolerance sensitivity

To assess sensitivity, ±5% variation was applied independently to each valve's \(k\) constant (a conservative estimate of unit-to-unit variability for moulded polymer valves):

Sensitivity to the fitted exponent \(n\)

The exponent \(n\) in the power law \(Q = k \cdot P^{n}\) controls the shape of the flow curve — how rapidly leak flow increases with pressure. Because the crossover arises precisely from the difference in exponents between the two valves (0.5966 vs 0.500), uncertainty in \(n\) has a larger effect on the crossover location than uncertainty in \(k\).

The exponent sensitivity reveals a more important finding than the \(k\) sensitivity: a −2% shift in \(n\) (within plausible fitting uncertainty for 9 data points) moves the crossover to 27.68 cm-H₂O — above Papa's IPAP floor — and reduces the integrated average error to near zero, with the sign already reversing at IPAP = 22. This underscores why bench measurement with the specific valves in use is essential: the quantitative predictions are sensitive to exponent values that cannot be determined precisely from the available data.