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.

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	Medium
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	Slow
10	146	0.9222	0.3798	0.3798	0.3500	Slow
11	187	0.9319	0.3497	0.3497	0.3295	Slow
12	239	0.9403	0.3223	0.3223	0.3065	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:

// 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:

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

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

Used by Model-02-Haldane-Equation and Model-03-Schreiner-Equation 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):

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

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, 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

// 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:

// 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/charts/MValueChart.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 for how $a$ and $b$ are actually used to compute the M-value line.