Model 01 Compartments

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	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:

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