# Model-01 — Compartments

Bühlmann ZH-L16 is a parallel-compartment model: 16 theoretical tissue groups, each with a half-time $T_{1/2}$ (how fast it on-/off-gasses) and two Bühlmann coefficients $a$ (bar) and $b$ (dimensionless) defining its M-value line. The letter suffix (A/B/C) picks one of three coefficient tables — same half-times, different `a` values (plus one $b$ quirk at TC1). See [References](References.md#6-zh-l16-constant-tables).

## All 16 compartments — full A/B/C table

Drawn directly from `js/tissueCompartments.js`. **Bold** values differ from variant A.

| ID | $T_{1/2}$ (min)¹ | $b$ ² | $a$ (16A) | $a$ (16B) | $a$ (16C) | Category |
|----|------------------|--------|-----------|-----------|-----------|----------|
| 1  | 4 / 5            | 0.5050 / 0.5578 | 1.2599 | **1.1696** | **1.1696** | Fast |
| 2  | 8                | 0.6514 | 1.0000 | 1.0000 | 1.0000 | Fast |
| 3  | 12.5             | 0.7222 | 0.8618 | 0.8618 | 0.8618 | Fast |
| 4  | 18.5             | 0.7825 | 0.7562 | 0.7562 | 0.7562 | Fast |
| 5  | 27               | 0.8126 | 0.6667 | 0.6667 | **0.6200** | Medium |
| 6  | 38.3             | 0.8434 | 0.5933 | **0.5600** | **0.5043** | Medium |
| 7  | 54.3             | 0.8693 | 0.5282 | **0.4947** | **0.4410** | Medium |
| 8  | 77               | 0.8910 | 0.4710 | **0.4500** | **0.4000** | Medium |
| 9  | 109              | 0.9092 | 0.4187 | 0.4187 | **0.3750** | Medium-Slow |
| 10 | 146              | 0.9222 | 0.3798 | 0.3798 | **0.3500** | Medium-Slow |
| 11 | 187              | 0.9319 | 0.3497 | 0.3497 | **0.3295** | Medium-Slow |
| 12 | 239              | 0.9403 | 0.3223 | 0.3223 | **0.3065** | Medium-Slow |
| 13 | 305              | 0.9477 | 0.2971 | **0.2850** | **0.2835** | Slow |
| 14 | 390              | 0.9544 | 0.2737 | 0.2737 | **0.2610** | Slow |
| 15 | 498              | 0.9602 | 0.2523 | 0.2523 | **0.2480** | Slow |
| 16 | 635              | 0.9653 | 0.2327 | 0.2327 | 0.2327 | Slow |

¹ TC1 is the only half-time that varies across variants: 4 min in A, 5 min in B/C.
² TC1 is the only $b$ that varies across variants: 0.5050 in A, 0.5578 in B/C. The half-time and $b$ swap together as a pair.

Pattern at a glance: **B** changes TC1 + TC6-8 + TC13 (4 compartments). **C** changes TC1 + TC5-15 (12 compartments). TC2-4 and TC16 are identical across all three variants. Smaller $a$ = more conservative (lower M-value at any depth).

The TC1 pairing is immutable — half-time and $b$ swap together when the variant changes. See `js/tissueCompartments.js:46-61`:

```javascript
// js/tissueCompartments.js:46-61
const COMPARTMENT_1_HALFTIME = {
    [ZHL16_VARIANTS.A]: 4.0,   // Original Bühlmann specification
    [ZHL16_VARIANTS.B]: 5.0,   // Modified for printed tables
    [ZHL16_VARIANTS.C]: 5.0    // Modified for dive computers
};

const COMPARTMENT_1_B_N2 = {
    [ZHL16_VARIANTS.A]: 0.5050, // Paired with 4 min half-time
    [ZHL16_VARIANTS.B]: 0.5578, // Paired with 5 min half-time
    [ZHL16_VARIANTS.C]: 0.5578
};
```

## Rate constant

The exponential loading/unloading rate follows directly from the half-time:

$$k = \frac{\ln 2}{T_{1/2}}$$

```javascript
// js/tissueCompartments.js:216
export function getRateConstant(halfTime) {
    return Math.LN2 / halfTime;
}
```

Used by [Model-02-Haldane-Equation](Haldane.md) and [Model-03-Schreiner-Equation](Schreiner.md) equations.

## Bühlmann a/b — where they come from

Tabulated in `js/tissueCompartments.js` rather than computed at runtime, but they follow Baker's half-time formulas (see [References](References.md#24-erik-baker--gradient-factors-articles)):

$$a = 2 \cdot T_{1/2}^{-1/3} \quad (\text{bar}) \qquad b = 1.005 - T_{1/2}^{-1/2}$$

These give the **ZH-L16A** (experimental) values exactly. The **B** and **C** variants share A's $b$ values for TC2–TC16 (TC1 has its own pairing) and selectively lower the $a$ coefficient on a subset of compartments to produce tables / computer firmware that proved more conservative in practice. See the table above for which compartments differ in B vs. C.

See also: [Sandbox: M-Values](https://decotheory.eu/sandbox/m-values.html), whose bottom playground visualizes these formulas alongside the 16 stored compartment values — toggling between A and C lifts the adjusted dots off the analytical curves.

## Variant semantics

| Variant | Purpose | Conservatism |
|---------|---------|--------------|
| ZH-L16A | Experimental (derived from formulas) | Least — found too permissive in middle compartments in use |
| ZH-L16B | Printed dive tables | More conservative $a$ for TC6–8 and TC13 |
| ZH-L16C | Dive computers (**DecoJS default**) | Most conservative — lowered $a$ for TC5 through TC15 |

```javascript
// js/tissueCompartments.js:40
let currentVariant = ZHL16_VARIANTS.C;
```

## Runtime switching

`setZHL16Variant()` mutates the exported `COMPARTMENTS` array in place (no reassignment) so downstream modules holding a reference pick up the change:

```javascript
// js/tissueCompartments.js:182-192
export function setZHL16Variant(variant) {
    if (!Object.values(ZHL16_VARIANTS).includes(variant)) {
        console.warn(`Unknown ZH-L16 variant: ${variant}, defaulting to ZH-L16C`);
        variant = ZHL16_VARIANTS.C;
    }
    currentVariant = variant;
    const newCompartments = buildCompartments(variant);
    COMPARTMENTS.length = 0;
    COMPARTMENTS.push(...newCompartments);
}
```

Callers must recalculate any cached tissue loading after switching (the charts in `js/mvalues.js` do this on the variant-select handler).

## Color coding

Used by the M-value and profile charts for quick visual grouping:

- **Reds / oranges** (TC1–4): fast compartments
- **Greens** (TC5–8): medium-fast
- **Blues** (TC9–12): medium-slow
- **Purples / magentas** (TC13–16): slow

See [Model-04-M-Values](Model-04-M-Values.md) for how $a$ and $b$ are actually used to compute the M-value line.