Educational Use Only — Interactive walk-through of the Schreiner equation for linear-rate ambient pressure changes.

Schreiner Equation

Linear-rate companion to the Haldane page — watch the equation evolve as ambient pressure slides.

Pt(t) = Palv,0 + R · (t − 1/k) − (Palv,0 − Pt,0 − R/k) · e−kt
3.1217 bar = 3.1217 + −0.7902 · (0.00 − 1/0.0257) − (3.1217 − 3.1217 − −0.7902/0.0257) · 1.0000
Palv,0 | alveolar N2 at start depth
= (Pamb,start − 0.0627) · FN₂
= (4.0133 − 0.0627) · 0.7902
3.1217 bar
Starting alveolar pressure. Slope-zero point of the moving alveolar source.
Pt,0 | tissue pressure at t=0
= (Pamb,start − 0.0627) · FN₂
= (4.0133 − 0.0627) · 0.7902
3.1217 bar
Tissue assumed equilibrated at start depth → equals Palv,0.
R | alveolar pressure rate
= FN₂ · depth_rate · 0.1
= 0.7902 · (−10) · 0.1
−0.7902 bar/min
Positive = descent (alveolar climbing), negative = ascent. R = 0 → equation collapses to Haldane.
k | rate constant
= ln(2) / T½
= 0.6931 / 27.0
0.0257 min⁻¹
Faster compartments → bigger k → catch up sooner.
e−kt | exponential decay factor
= e−k · t
= e−0.0257 · 0.00
1.0000
1.0 at t=0, decays toward 0. Multiplied by the initial-disequilibrium term.
Three-term decomposition · the formula's structural pieces
Moving alveolar source
= Palv,0 + R · t
= 3.1217 + (−0.7902) · 0.00
3.1217 bar
Where the alveolar source is right now (linear in t).
Phase lag (R/k)
= R / k
= −0.7902 / 0.0257
−30.74 bar
How far below (ascent) or above (descent) the source a perfectly-tracking tissue would settle. Equivalent to 1/k minutes of slope.
Decaying initial gap
= (Palv,0 − Pt,0 − R/k) · e−kt
= 30.74 · 1.0000
30.74 bar
The initial offset between actual Pt and the tracking line — settles exponentially toward zero.
Pt(t) = [moving] − [phase lag] − [decaying gap]
M-value check
M
Palv
Pamb
Pt
Pt = 0.7510 bar | M = 2.50 bar within
M = a + Pamb / b