FUNDAMENTALS
Introduction
This block establishes the foundation for all subsequent topics: How does inert gas enter the body, how is it released, and why do we use mathematical models (e.g., Bühlmann) to plan ascent profiles? It’s not about formulas, but about connections and practical relevance. We work with the core ideas of the Bühlmann models (compartments, half-times, M-values) and their modification through Gradient Factors. You will understand how to apply them—and also where the limits and uncertainties lie.
Before we get started, a quick note on the prerequisites: You should have the physical fundamentals from your OWD course fresh in your mind, especially the gas laws. That’s why we’ll start with a short quiz. If you find you’d like to read up on something, check your manuals—or our Science of Diving course.
Saturation and desaturation
As soon as you descend, the ambient pressure increases, and with it, the partial pressure of the inert gases in the breathing gas. In the lungs, inert gas diffuses into the blood and is transported from there throughout the entire body. If the inert gas pressure in the blood is higher than in the surrounding tissues, the gas diffuses into the tissues—if the inert gas pressure in the blood is lower, it leaves the tissues again and can exit the body through the lungs.
Saturation: What happens under pressure?
The fundamental principle of saturation and desaturation is Henry’s Law. When gas borders a liquid, or different tissues border each other, the gas pressure on both sides will equalize over time. During descent, ambient pressure increases, which also increases the nitrogen partial pressure in the breathing gas. This leads to increased inert gas absorption in the body. During ascent, the pressure drops again—the gas must leave the body. You can take a closer look at this process in the animation.
Tissue Compartments and Half-times
In reality, different tissues have very different saturation and desaturation rates. This cannot be calculated individually for every single organ. That’s why models work with artificial “compartments”: They assign half-times that together cover the entire spectrum of possible human tissues.
The half-time describes how long a compartment needs to adapt halfway to a new pressure situation. Example: 5-minute half-time → after 5 min 50%, after 10 min 75%, after 15 min 87.5%.
The model commonly used today, the Bühlmann ZHL-16C algorithm, calculates with 16 different model tissues with half-times between 5 and 635 minutes. You can see how saturation progresses in these tissues over a certain period in the next tool.
Saturation of a model tissue
We now have the individual building blocks: tissues saturate, they do so at different speeds, and when the pressure decreases, they desaturate again.
This plot helps to describe the desaturation process and discuss the limits of supersaturation. Here, saturation and especially the desaturation of a model tissue are visualized.
With this fundamental image, you are well-prepared to look at the limits of supersaturation in the next section.
Video: The Saturation Plot
What do the fields in the plot mean that we use to explain the saturation and desaturation of a model tissue? A short video provides an easy-to-understand explanation.
Video: Saturation During a Dive
Short video in which we explain how a model tissue saturates and desaturates during a dive and how this can be shown in our plot
Limits of Supersaturation: M-values and Gradient Factors
Since we cannot look directly into the body, decompression models exist. These are intended to map the processes as accurately as possible and allow for a plausible assessment of risk. The most common model is the Bühlmann ZHL-16C algorithm, which we focus on here to understand the concepts.
We have just seen that the core question of all decompression theory is: How supersaturated can a tissue be before the risk of DCS becomes too high? This is exactly what M-values and their modification by Gradient Factors are about.
M values
Each model tissue has a limit of tolerable gas supersaturation. This is what lies behind the M-value. The M-value is the inert gas pressure that a tissue “can just barely tolerate” at a certain ambient pressure. If it is exceeded, the risk of DCS symptoms increases.
The M-values are different for each model tissue. The model assumes that fast tissues can tolerate higher supersaturation than slow tissues.
And M-values are depth-dependent. The M-value is always composed of the current pressure plus the tolerated supersaturation. At a higher ambient pressure, the Bühlmann model also provides for a higher tolerable supersaturation. The model assumes that a higher overpressure is tolerated at depth than on land.
Term: M-value
Maximum allowable inert gas pressure in a tissue before the model assumes a significantly increased risk of DCS. It is tissue-specific and depends on the ambient pressure.
What do M-values, the no-decompression limit, and decompression look like in practice for a model tissue? Let’s take another look at our desaturation plot.
As we saw earlier, the risk of getting DCS increases the further a tissue penetrates into the supersaturation range. It is never possible to predict exactly when symptoms will occur in a specific person. One can only determine a general statistical risk and set a limit based on that. This is exactly what M-values do: they define a limit of acceptable risk. Even though an M-value is an exact number, precise to several decimal places, there is no exact boundary behind it. It is more of a boundary drawn sharply within the fuzzy area of increasing risk.
These M-values result in an M-line for each model tissue, which limits the ascent. If the tissue is only saturated to the point where the M-line is not exceeded during ascent, it is called a no-decompression dive. As soon as this limit would be exceeded during a direct ascent, deco stops become necessary to desaturate the tissue slightly during the ascent and thus keep it below the line. Upon reaching the surface, this limit should then no longer be exceeded.
False Precision
M-values and the No-Decompression Limit
“No-decompression limit” (NDL) means that no M-value is exceeded during a direct ascent. This doesn’t eliminate risk, but keeps it within a framework defined as acceptable.
At different depths, different tissues are the first to reach their maximum saturation and thus end the no-stop time. In this tool, you can see for each depth which tissue limits the time.
If you look at which tissue reaches a critical inert gas pressure first at different depths, you will notice the following:
On deep dives, 40m, the no-decompression limit is reached very quickly—because the fastest tissue would reach its M-value if you ascended directly. At more moderate depths, the “leading tissue”—the tissue that comes closest to its M-value during ascent—shifts. The fastest tissues tolerate such high supersaturation that they can be fully saturated at 20m without it becoming critical. Which model tissue is the leading tissue therefore shifts to the higher numbers.
The animation stops when the original Bühlmann M-values are reached. Of course, you can also exceed this limit—then you have to plan stops during the ascent to give the overly supersaturated tissues time to desaturate a little. And of course, you can modify the M-values and thus shift the no-decompression limits or extend the decompression.
Gradient Factors—or “What is this GF on my computer?”
Gradient Factors are a way to modify M-values and build in an additional safety margin.
To understand how they work, let’s look at our basic plot for the desaturation of a model tissue once more.
Additional lines are now drawn below the original M-line: the modified M-lines. If you consider the original M-values too risky—which is the consensus today—you can simply reduce the supersaturation you are willing to accept. This is done using a percentage of the supersaturation—you draw a new line at 80, 60, or even fewer percent of the supersaturation.
If you stick with this simple shifted line, you have simply built in some extra safety. Usually, however, two Gradient Factors are used: GF Low and GF High. This is represented, for example, as GF 40/80—the first number denotes the GF Low, the second the GF High.
Why is this done? This practice goes back to the idea that deeper stops during ascent are useful for controlling bubble growth. We discuss how useful this is in the block on current research.
If you choose a lower GF Low, you move slowly from the lower to the higher GF during the ascent. The GF Low determines the depth at which the first stop occurs; the GF High determines the supersaturation with which you reach the surface.
Choosing Gradient Factors
So what should you choose? Stick with a computer’s default setting, or personalize the GFs after all? We discuss this in detail in this blog post.
GF: Percentage of Supersaturation
Keeping an eye on all tissues: Dive planning
So far, we’ve primarily looked at what happens in a single model tissue and defined the limits of supersaturation based on that.
However, the model calculates with 16 tissues with very different properties. So during ascent, we need to keep all these tissues in view.
The no-stop finder has already shown that different tissues are critical at different depths. What applies to determining no-stop time is also relevant in deco. Which tissue comes closest to the M-value changes during ascent. We need a way to keep all model tissues in view simultaneously.
Heatmaps provide such a visualization. To make getting started as easy as possible, here’s a very simple deco planner that displays the profile and a heatmap.
You can enter one or more depths and times, choose your breathing gas and your GF. When you click calculate, you’ll get the dive profile, the heatmap, and a runtime.
The heatmap shows the saturation of individual tissues in shades of blue. The darker it is, the closer the inert gas in the tissue comes to the state of saturation. During ascent, the tissues reach the range of supersaturation, which is shown here in traffic light colors. Green means the gradient is still very low; at red, 100% of the M-value is reached.
While you should use a real, validated planner for dive planning, here you can see exactly what changes when you adjust the gradient factors. The complete dive planning is covered later in the course—focus here on the different dive profiles and what the heatmaps look like for them.
What you can try with the planner
If you’d like to compare dive profiles and gradient factors in a somewhat structured way, here are a few suggestions:
- Look at a normal dive at OWD level: 20 m for 20 minutes, then 10 m for 25 minutes. A typical guided reef-right, reef-left dive. Regardless of how you’ve set the GFs, what does the supersaturation look like at the end?
- Take a dive for 20 minutes at 30 m—a no-stop dive according to standard tables. Set the GFs to 100/100 and see what the supersaturation looks like with an almost direct ascent.
- Add a segment at 20 m for 10 minutes and at 10 m for 15 minutes to get a relatively typical multilevel profile. What happens to the supersaturation compared to the direct ascent?
- Plan a dive to 40 m for 8 minutes with a direct ascent. Note which tissues reach the highest supersaturation. Now add significantly shallower levels—how does the supersaturation shift? Which tissues are now most affected?
- Change the gas to nitrox on a planned dive and see what difference it makes to the supersaturation at the end.
- Change the gradient factors and observe at what point “no-stop dives” become deco dives.
Once you’ve seen enough profiles and heatmaps, continue with a quiz. The graphics here are similar and come from the planning program Subsurface.
