⚠️ Educational Use Only — This tool is NOT intended for real dive planning. Never use this for actual dives. Always use certified dive computers, tables, and proper training.

📈 M-Values & Surfacing Limits

Understanding the limits of supersaturation

🔄 What We Know So Far

The Pressure Relationships

From the previous sections, we learned about three key pressures and how they relate:

Tissue Inert Gas Pressure

The nitrogen (or helium) dissolved in body tissues

vs
Alveolar Pressure

The ppN₂ in our lungs (≈0.79 × ambient for air)

vs
Ambient Pressure

Total pressure at current depth

💡 The Key Insight

Tissue > Alveolar ✅ Off-gassing — nitrogen flows from tissue to lungs. This is good!
Tissue > Ambient ⚠️ Supersaturation — dissolved gas exceeds what pressure can hold. Bubble risk!

The challenge: during ascent, we want tissue pressure to exceed alveolar (to off-gas), but we need to limit how much it exceeds ambient pressure (to avoid bubbles).

🫧 The Supersaturation Problem

Critical Supersaturation

When tissue pressure exceeds ambient pressure, we're in a state called supersaturation. Think of it like a carbonated drink—the CO₂ is dissolved under pressure. Open the bottle (reduce pressure) and bubbles form.

The same happens in our tissues if we ascend too fast. But here's the fascinating discovery: the body can tolerate some supersaturation without forming dangerous bubbles. The question is: how much?

Early finding 2:1 Divers could ascend from 10m to surface safely (2 bar → 1 bar ambient)
→
Refined to 1.58:1 More accurate critical ratio (accounting for tissue specifics)
📚 The History: How We Discovered Safe Limits

John Scott Haldane (1908)

The Scottish physiologist observed that workers in compressed-air tunnels and caissons could safely decompress from 2 atmospheres to 1 (a 2:1 ratio). This became the foundation of staged decompression—if the body can tolerate 2:1, we can plan safe depth-ratio ascents.

Robert Workman (1960s)

U.S. Navy researcher who discovered the 2:1 ratio wasn't quite accurate and varied by tissue type. He coined the term "M-value" (Maximum value) for the maximum tolerable tissue pressure at any given depth. His refined ratio of approximately 1.58:1 accounted for the fact that different tissues have different tolerances.

Workman's key insight: faster tissues (brain, blood) tolerate higher supersaturation than slower tissues (fat, bones).

🧮 Bühlmann's Solution

Tissue-Specific Limits

Swiss physician Prof. Albert A. Bühlmann took this further in his ZH-L16 algorithm. Instead of a single ratio for all tissues, he defined specific tolerance limits for each of the 16 tissue compartments.

The Core Concept

Each tissue compartment has its own M-value line that defines the maximum tolerable tissue pressure for any given ambient pressure. This is the limit—cross it, and bubble formation becomes likely.

  • Faster tissues (short half-times like 5 min) → tolerate MORE supersaturation
  • Slower tissues (long half-times like 635 min) → tolerate LESS supersaturation
📐 The Formula Behind M-Values

Bühlmann's M-value formula for each compartment:

M = a + \frac{P_{amb}}{b}

Where:

  • M = Maximum tolerable tissue inert gas pressure (bar)
  • Pamb = Ambient pressure at current depth (bar)
  • a = Intercept coefficient (bar) — tissue-specific
  • b = Slope coefficient (dimensionless) — tissue-specific

The "a" coefficient represents the base tolerance at very low ambient pressure. Faster tissues have higher "a" values, meaning they can handle more supersaturation.

📊 The Pressure-Pressure Diagram

Visualizing the Limits

The chart below plots Ambient Pressure (X-axis) against Tissue N₂ Pressure (Y-axis). Watch how your tissue compartments move through the different zones during a dive:

Below blue line (y = x) Tissue pressure < ambient (not supersaturated)
Between blue & M-value lines Supersaturated but safe ✓
Above tissue's M-value line ⚠️ Critical supersaturation!
🎯 How to Read the Movement
  • Descent: Move right (↑ ambient) and up (↑ tissue loading)
  • At depth: Stay at same X position, slowly move up toward equilibrium
  • Ascent: Move left (↓ ambient) — this is where you enter supersaturation

⚠️ The danger: ascending too fast moves you left faster than you off-gas down — risking crossing above the M-value line!

✅ Example 1: Safe Dive (30m/28min with Safety Stop)

This dive includes a 10-minute safety stop at 3m. Notice how the tissue pressure stays well below the M-value line throughout the ascent.

📊 Dive Profile

📈 Pressure-Pressure Diagram

🔬 Open in Sandbox →

⚠️ Example 2: Ceiling Violation (DANGEROUS!)

Same dive, but with a direct ascent to surface. Watch how the tissue pressure crosses above the M-value line — this is a decompression sickness risk!

📊 Dive Profile

📈 Pressure-Pressure Diagram

🔬 Open in Sandbox →
📖 Chart Legend

Blue solid (Ambient Line): y = x. Above this = tissue is supersaturated.

Gray dashed (Surface): x = 1 bar. Must be below M-value when reaching this.

Colored dashed (M-Value): Critical limit for each tissue. Each tissue compartment has its own color.

Trail: The path traced by the tissue point throughout the dive.

🎚️ Gradient Factors (Advanced)

Adding Conservatism

Gradient Factors (GF) are a way to add conservatism to the Bühlmann algorithm. Instead of allowing tissues to reach the raw M-value limit, we use only a fraction of the allowed supersaturation.

GF Low / GF High

GF Low Applied at the first (deepest) deco stop. Controls how deep stops start.
GF High Applied at the surface. Controls final supersaturation when you surface.
Between GF is linearly interpolated between GF Low and GF High.

Common Settings

GF 100/100 Raw Bühlmann — theoretical limits, not recommended
GF 70/85 Moderate conservatism — popular starting point
GF 50/80 More conservative — common for technical diving

⚠️ Research suggests very low GF Low values (like 30%) may not reduce DCS risk.

📐 The GF Formula
M_{adjusted} = P_{amb} + GF \times (M_{raw} - P_{amb})
  • GF = 100% — Full Bühlmann M-value (no conservatism)
  • GF = 70% — Use only 70% of allowed supersaturation
  • GF = 0% — No supersaturation allowed

📋 ZH-L16A M-Value Coefficients

View coefficient table
TC# Half-Time (min) a (bar) b M₀ (bar)*

* M₀ = a + 1/b = Maximum tolerable tissue pressure at surface (1 bar ambient)