User manual update: Heat map

[Rick Walsh]

Hi Willem,

On 24 October 2016 at 16:42, Willem Ferguson <
willemferguson at zoology.up.ac.za> wrote:

> Sent from my phone. Thank you very much for your feedback. Two questions.
> 1) if the demarcation is moved to the equilibrium gas pressure, then the
> zero point on the offgassing scale is *above* the start of the range. If
> the unit for the offgassing scale is "percentage distance from ambient
> pressure to M-value", then the tissue pressures between equil pressure and
> ambient pressure would have negative values since they are *below* the zero
> value. Am I missing something?
>
You are correct.  The percentages on the scale from bright green to red are
the "percentage distance from ambient pressure to M-value", where the
M-value is the Buhlmann M-value.  The paper by Eric Baker
http://www.ddplan.com/reference/mvalues.pdf refers to the percentage as the
"M-value gradient", to mean the same thing, but uses fewer words, which is
a good thing in a diagram with limited space.

Referring to the values as the percentage of M-value (as I did) is not
correct as the M-value according to
http://www.ddplan.com/reference/mvalues.pdf was dubbed by Workmann to be
the maximum tolerable inert gas pressure in the hypothetical tissue.  What
the percentages really represent are the maximum tolerable "gradient", i.e.
the difference between the ambient pressure and the M-value.

I said previously, and incorrectly, that "M-value" implies "Buhlmann
M-value".  As I think you pointed out, the term was actually used by
Workman, and he used a different linear equation to estimate it.  A simple
M-value linear equation can be calculated for Haldane's values too.

The section between the equilibrium pressure and the ambient pressure is
offgassing because the tissue inert gas pressure is greater than the
equilibrium pressure.  And yes, if it were to be assigned value on the
M-value gradient scale, that value would be negative.  But a negative value
doesn't have any real significance, and is likely to be confusing.  I think
it is better just to show that the colour range in this section is below
the ambient pressure but above the equilibrium pressure.

> 2) in the correspondence somewhere Robert mentioned that the VPM-B
> calculations include a term that amounts to the M-value. Maybe I
> misinterpreted him. What I am trying to understand is the relevance of the
> heat map when using the bubble approach. What I get from the discussion is
> that even if one uses the VPM-B, the heat map is based on Buehlmann
> calculations. How should one then interpret the heat map when using VPM-B?
>
Yes, an M-value can be calculated for the VPM-B model, but it is much more
complicated than the linear function of ambient pressure used in the
Buhlmann (and Workman and Haldane) model.  As the VPM-B model attempts to
track bubble formation, the equivalent M-value for each tissue is a
function of the ambient pressure, as well as everything that has already
occurred on the dive, and even the ascent phase that is yet to happen on
the dive.

The heat map needs to be interpreted exactly the same way when using VPM-B
as when using the Buhlmann model.  The colours are the same regardless of
what model is chosen at the time, and what gradient factors or conservatism
level is selected.  This is deliberate so that different dives and plans
can be compared on a consistent scale.  If our user wants to do a
decompression dive with 30 min at 50 metres, she can use the planner to
compare where the "hot spots" are on the heat map if she uses for example
VPM-B +3 with where the hot spots are if she uses Buhlmann with GF 60/70.
If the scale changed according to the model (or conservatism), then a
direct comparison would not be possible.

Does this help?  Sorry for the confusion before regarding my incorrect use
of the term M-value - I really meant Buhlmann M-value gradient.

Cheers,

Rick
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