Dissolved Gas Models and Haldanian Theory

Hello! Welcome to your first lesson in the "Decompression Theory and Models" module.

Introduction

In this lesson, we will explore the fundamental principles behind how dive computers and decompression tables work. The goal is to understand the theoretical basis of dissolved gas models, with a special focus on the pioneering work of John Scott Haldane.

Essentially, every time you dive, your body absorbs inert gases (like nitrogen) from the air you breathe. The deeper you go and the longer you stay, the more gas dissolves into your tissues. Decompression models are the scientific "recipes" that allow us to manage this gas loading and return to the surface safely, avoiding Decompression Sickness (DCS). Understanding this theory is the first step toward planning more advanced dives and truly comprehending what your dive computer is telling you.

Let's begin by looking at the core problem these models were designed to solve.

The Problem: Gas, Pressure, and Your Body

As you descend, the surrounding water pressure increases. This increased pressure allows more inert gas from your breathing mix to dissolve into your blood and tissues. This process is known as on-gassing.

The challenge arises during ascent. As you come up, the ambient pressure decreases, and the dissolved gas must come back out of solution—a process called off-gassing. If the pressure is reduced too quickly, the gas can form bubbles directly within your tissues or bloodstream, which can lead to Decompression Sickness.

The central task of a decompression model is to predict the gas loading in your body and define a safe rate of ascent to ensure the gas comes out of solution in a controlled manner, primarily through your lungs.

![resource_id=74152]
This image illustrates the two possible outcomes of off-gassing. On the left, a safe ascent allows inert gas to be transported by the blood and eliminated through the lungs. On the right, a rapid ascent causes the gas pressure in the tissues (PT) to exceed a critical limit relative to the ambient pressure (PA), leading to bubble formation and DCS.

Haldane's Model: Tissues as "Compartments"

In the early 20th century, Scottish physiologist John Scott Haldane was tasked with solving this problem for caisson workers and divers. His solution was both elegant and revolutionary. He realized that modeling the entire human body, with its myriad tissues, was impossibly complex. Instead, he proposed a simplified model.

Haldane's key ideas were:

1. The body can be modeled as a group of parallel "compartments." These are not literal anatomical parts (like your liver or bones) but theoretical tissues that all absorb and release gas at different rates.
2. Each compartment has a specific "half-time." This determines how quickly it on-gasses and off-gasses.

To get a clear introduction to these concepts, please watch the first few minutes of the following video.

Understanding Half-Times

As the video explained, a half-time is the time required for a theoretical compartment to go halfway from its initial inert gas pressure to being fully saturated at a new, constant ambient pressure.

This process is exponential:

• After 1 half-time, the compartment is 50% saturated.
• After 2 half-times, it's 75% saturated (half of the remaining 50%).
• After 3 half-times, it's 87.5% saturated.
• ...and so on. After about 6 half-times, a compartment is considered effectively saturated (or desaturated).

Compartments with short half-times are called "fast" tissues. They saturate and desaturate quickly (e.g., blood, lungs). Compartments with long half-times are "slow" tissues (e.g., dense tissues like bone and cartilage).

To see this process in action, the next video provides a great visual demonstration of how different compartments load with nitrogen during a dive.

The Mathematical Foundation

Now that we have the concepts, let's look at the "recipe" itself. Haldane's model is mathematical at its core. It uses an equation to calculate the inert gas pressure in any compartment at any time.

For a deeper dive into the theory and its mathematical formulation, the following reading is very useful.

As you read, you saw this equation, which is the heart of the model:

P_comp = P_begin + [ P_gas - P_begin ] x [ 1 - 2 ^ ( -t_e / t_ht ) ]

Let's break it down:

• P_comp: The final inert gas pressure in the compartment. This is what we want to calculate.
• P_begin: The initial inert gas pressure in the compartment.
• P_gas: The inert gas pressure in the breathing gas at the current depth. This is the "driving" pressure.
• t_e: The exposure time (e.g., bottom time at a certain depth).
• t_ht: The half-time of the specific compartment.

This equation, often called the Haldane equation (or Schreiner equation in a more general form), allows a dive computer to track the theoretical gas loading in all its modeled compartments throughout a dive.

![resource_id=fc0ad]
This graph shows the calculated nitrogen pressure (on-gassing) in several different tissue compartments during a short, shallow dive. Each colored line represents a compartment with a different half-time, clearly showing the 'fast' tissues loading gas more quickly than the 'slow' ones.

From Gas Loading to a Dive Plan

So, how does knowing the gas pressure in a set of theoretical compartments help us dive safely?

This is Haldane's second crucial insight: each compartment can tolerate a certain amount of supersaturation—that is, an internal gas pressure that is higher than the surrounding ambient pressure—without forming bubbles.

The model calculates the gas load for all compartments continuously. When you want to ascend, it calculates the maximum pressure drop each compartment can handle. The shallowest depth you can ascend to is determined by the most restrictive compartment, also known as the controlling compartment. This depth is your decompression ceiling.

By performing a decompression stop at or below this ceiling, you give your controlling compartments (and others) time to off-gas, which in turn makes the ceiling shallower, allowing you to ascend further.

Conclusion

In this lesson, we've unpacked the theoretical core of modern decompression models. You are now equipped with the foundational knowledge to understand how your dive computer makes its calculations.

Key Takeaways:

• Decompression models are mathematical tools used to manage inert gas uptake and elimination to prevent DCS.
• The Haldanian model simplifies the body into a series of theoretical compartments, each absorbing and releasing gas at a different rate.
• This rate is defined by a compartment's half-time. Fast compartments have short half-times; slow compartments have long ones.
• A mathematical formula allows us to calculate the inert gas pressure in each compartment at any point during a dive profile.
• The concept of a tolerable pressure limit for each compartment is what determines no-decompression limits and required decompression stops.

Preview of the Next Lesson:

We've mentioned the idea of "tolerable supersaturation." In our next lesson, we will explore this critical concept in detail, explaining how it relates to decompression stress and introducing M-values and gradient factors—the specific parameters that control risk and conservatism in your dive computer's algorithm.