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Observation-time dependence of apparent compliance is the change in an inferred volume-per-pressure response when the measurement is made at different stages of filling or relaxation. For an original single passive compartment exposed to a pressure step,The equilibrium compliance is $C$, but a finite-time observation is smaller whenever $T$ and $\tau$ are positive and finite. A short observation can therefore confound stiffness with slow filling.

Two observation times identify the parameters only within the assumed model. Taking measurements at $T$ and $2T$ and defining $r=A(2T)/A(T)$ givesFor stipulated $A(1\mathrm{s})=0.10$ and $A(2\mathrm{s})=0.15\mathrm{L}(\mathrm{cm}{\mathrm{H}}_2\mathrm{O}{)}^{-1}$, this model gives $C=0.20$ and $\tau =1/\log 2\approx 1.44$ s. The parameter values follow from the model as well as the data.

A second original example exposes finite-time ambiguity between stiffness and slow filling. Suppose the real response is the sum of two compartments, each with compliance 0.10, but time constants 0.2 and 2 s. Then $A(0.5\mathrm{s})\approx 0.11391$ and $A(1\mathrm{s})\approx 0.13867$. Fitting the single-compartment formulas to just those two values gives $\tau \approx 0.328$ s and equilibrium compliance about 0.146, although the actual equilibrium sum is 0.20. Two exact measurements can fit the wrong model exactly.

Even one perfect finite-time value supplies no finite upper bound on equilibrium compliance without further restrictions. For an observed $A>0$ at time $T$, every choice $C>A$ can reproduce it withIncreasing compliance while increasing the filling time can preserve the measured response. Additional times, an independently bounded time scale or a validated compartment model add information.

The primary pilot study's discussion of non-uniexponential deflation and multiple time constants illustrates the experimental importance of this distinction.^[ref] The constructed calculations here are pressure-step examples, not patient measurements or a replacement for the study's actual compliance definitions.