= Balloon inflation hydraulic time constant
The balloon inflation hydraulic time constant is the response scale produced by combining an inflation path's <hydraulic resistance> with a balloon's <balloon volumetric compliance>. It characterizes a stated fluid-mechanical model; it is not a universal inflation duration for a <balloon catheter>.
Let $p_s$ be a maintained source pressure, $p_b$ balloon pressure relative to a fixed exterior, $R_h>0$ a linear path resistance and $C_b=dV/dp_b>0$ constant compliance. Conservation of injected volume gives
$$
C_b\frac{dp_b}{dt}=\frac{p_s-p_b}{R_h},\qquad
\tau=R_hC_b.
$$
Thus $p_b(t)=p_s+(p_b(0)-p_s)e^{-t/\tau}$. The product has units $(\mathrm{Pa\,s\,m^{-3}})(\mathrm{m^3\,Pa^{-1}})=\mathrm s$. Reaching a fraction $f$ of the pressure change takes $t_f=-\tau\log(1-f)$, so $t_{90}\approx2.303\tau$ and $t_{99}\approx4.605\tau$.
For chosen values $R_h=2\,\mathrm{kPa\,s\,\mu L^{-1}}$ and $C_b=0.50\,\mathrm{\mu L\,kPa^{-1}}$, $\tau=1\,\mathrm s$ and the modeled $90\%$ time is $2.303\,\mathrm s$. Under the <Hagen-Poiseuille equation> for a rigid circular lumen, $R_h=8\mu L/(\pi r^4)$. Reducing radius to $0.8r$ raises resistance, and hence this time constant, by $1/0.8^4\approx2.44$ if the other assumptions remain valid.
The motivating apparatus is the separate <catheter balloon inflation lumen> joining the inflation port to the balloon. The EAUN two-channel description distinguishes it from the drainage lumen.<Indwelling catheterisation in adults by EAUN (2024)>[Section 5.1.1 and Figure 5, separate balloon and drainage channels]{ref} A bench test that records source pressure, local balloon pressure and injected volume can distinguish a channel pressure drop from stored volume response. This is an experimental model outline, not a clinical operating protocol.
Pressure-dependent compliance gives $R_hC_b(p_b)\,dp_b/dt=p_s-p_b$, generally with no single exponential. Apparatus storage, trapped gas, moving external pressure or a deformable lumen can also alter the response. A <balloon compliance fixture correction> measured only after equilibration need not describe distributed transient storage.
Back to article page
