Gradient Factors… a simplified primer

This short article is based on a series of presentations made in various locations during the late winter and spring of 2015, and is a shortened version of a more detailed treatment to be included in an upcoming book.

Let’s start off with a disclaimer and an outline of some assumptions made while working on this blog post.

First off, I did not start out intending to write a definitive piece on decompression theory or on the stellar work of Professor Albert Bühlmann. Also, this contains no detailed explanation of the internal workings of the maths behind a decompression algorithm and the challenges it meets while trying to model human physiology. Simply put, this was written to help the average punter better understand what gradient factors describe; and the potential impact of playing around with the GF settings on your personal dive computer (for example, a Shearwater Petrel).

Secondly, I’ve made several assumptions… not the least of which is that readers have a basic understanding what happens to an individual after spending more than a couple of minutes sub-surface breathing compressed gas. (That’s just another way of saying that I’m writing for certified and reasonably experienced divers who understand that diving can result in decompression stress of one flavor or another.)

OK, that settled, here we go.

All dives are decompression dives, ergo all divers are decompression divers. Our acknowledgement of this and the depth of that acknowledgement can greatly influence our behavior when we dive: most specifically, our ascent behavior. How deep we dive, what gases we breathe, and how long we spend at depth vary considerably from dive to dive; but all dives share one common threat for individual divers: the risk of getting bent.

Smart divers consider many factors when planning dives, many of which help to alleviate that risk. One is choosing to dive a “conservative profile.” I guess there are many interpretations of what that means… but for our purposes here, it means choosing a decompression algorithm that’s proven, and choosing a setting for that algorithm that will generate stress-tolerant dive tables.

Many PDC (personal dive computers) use a Bühlmann ZHL-8 or ZHL-16 algorithm to model decompression stress in divers and their decompression obligation on ascent. In a way this is odd because both deco models are not only dated (Herr Doktor Professor Bühlmann died of heart failure in early 1994), but are based on the faulty premise that we can prevent bubbles from forming in our bodies during our ascent if we follow the schedules the algorithm kicks out.

The data set on all recreational diving, but in particular staged decompression diving, has grown considerably since the Professor’s unfortunate and untimely death, and we now have considerable evidence that in fact bubbles do form even after the most benign sport dives conducted well inside the boundaries suggested by Bühlmann’s tables. Some newer decompression models make the assumption that bubbles do form in a diver’s body during ascent and make adjustments to the maths which are intended to control their growth and propagation. Many divers believe bubble models better predict what goes on in a diver’s body and are therefore, safer. VPM and RGBM are examples of “bubble models.” Versions of both are available for use in PDCs.

Yet Bühlmann tables remain popular. They are in fact perfectly functional, and are helping to keep tens of thousands of divers safe from the bends every week. The secret is that with very simple tweaking, a Bühlmann schedule can be made to follow a time-and-place curve very similar to those produced by bubble models slowing ascent and beginning staged stops deeper in the water column.

OK, a little very simple nuts and bolts discussion.

Traditional decompression algorithms – Bühlmann’s included – attempt to model what happens in a diver’s body using a number of different calculations each representing a different “theoretical tissue group:” and each filling up with and emptying inert-gas at different speeds. Important to note that these tissue groups are mathematical constructs and are not directly related to any actual body tissue such as blood, bone, muscle or brain. Those tissues – in fact all the tissues in a human body – are far too complex in their architecture, component makeup and construction to fit into any of the algorithm’s simplified tissue categories. The human body is a mass of variables that defy the constraints of pure maths. So, individual “tissue groups” don’t relate to a specific body part, but are a series of mathematical calculations which as a whole attempt to track inert gas uptake and elimination in vivo.

In Bühlmann’s ZHL-16 algorithm the fastest group has a four-minute halftime, the slowest (the 16^th in this particular series) has a 635-minute halftime. Since we can regard a tissue group as saturated after six halftimes (standard science stuff), the fastest group will be “full” in 24 minutes, while the slowest takes 63 hours and 30 minutes to reach the same state! For the record, the halftimes or the 14 other groups in the ZHL-16 algorithm are: 8, 12.5, 18.5, 27, 38.3, 54.3, 77, 109, 146, 187, 239, 305, 390, and 498 minutes.)

Clearly, Now that we have some concept of the relationship between variable times and various group saturations, let’s look at M-values.

In the Bühlmann algorithm, each theoretical tissue group has a maximum internal pressure it can withstand. This pressure is exerted by dissolved inert gas and as long as the maximum is not exceeded, the gas stays in solution, and no bubbles form… well, in theory.

Like Robert Workman before him, Bühlmann termed this maximum internal pressure, its M-Value. Workman had coined the phrase while researching decompression for the U.S. Navy in the 1960s. His M-Value calculations were based on dives done at sea-level… perfectly predictable for Navy work. Bühlmann’s modifications took into account attitude and are slightly more conservative. Like a tissue group, an M-Value is mathematics and not physiology, and it is used to track how close a particular tissue group has become to super-saturation (critical bubbling). When a tissue group reaches 100 percent of its M-Value, the likelihood of decompression stress is statistically high.

And finally, gradient factors.

One can think of gradient factors (GF) as a way of adjusting the decompression algorithm to suit our needs, and GF can range between 0 and 100 percent. One hundred percent is the point where M-Value is on the verge of critical bubbling (1), and zero percent is the same as ambient pressure (M-Value of 0 where there is no force driving gas out of solution at all). Therefore, effective decompression can be found somewhere between those two points.

When one uses GFs to set the “conservatism” for one’s decompression, one uses two numbers: these represent the Low Gradient Factor and the High Gradient Factor.

In simply terms, the Low Gradient Factor (LGF) defines how deeply in the water column one takes one’s first decompression stop. The High Gradient Factor (HGF) defines how close to the 100 percent M-Value one surfaces with at the end of the dive.

Obviously we need to set up some gradient to begin the process of off-gassing (decompression). The slope of that gradient – how much pressure we allow – is a matter of personal faith, comfort and willingness to act as a guinea pig. This is the LGF and one option that seems to have been adopted by many divers – and incidentally recommended by Dr. Neal Pollock from DAN – is 30%.

This setting promotes off-gassing but stops one’s ascent deep in the water column but above the gas transition point (the theoretical spot on the water column at which more gas is eliminated than is taken up according to the algorithm).

Setting the HGF is a question of how close to the 100 percent M-Value limit we are willing to venture. Many divers recommend and use 80 percent. Again, Dr. Pollock’s suggestion is lower: 70 percent.

Therefore a 30/70 setting is considered by some, including me, to be an acceptable default GF setting.

However, before forming a rigid interpretation of GFs: just as different speed limits are applied to different road conditions, different GFs may be more appropriate for different dives. A 30/70 may work for trimix dives to 60 metres but may be unnecessary conservative for a short warm-water dive to 18-metres… and not sufficiently conservative for deeper dives.

The message then is to experiment with Variable Gradient Factors when planning your dives. Run what-if scenarios… Take notes… Alternatively, read what people are doing and what organizations such as DAN suggest

Most of all, be aware, nobody and no organization can predict precisely the outcome of any dive!