# Calculate pressure gradient between 2 compartments so that 4 ml of fluid would flow through a 0.413 mm hole in 72 hours

Introduction.

This question refers to the medical field. Human spinal cord is surrounded by 3 layers: the PIA MATER is in direct contact with the spinal cord itself; the next one is the ARACHNOID MATER and between this one and the PIA MATER there is a space filled with liquid (this liquid is termed CEREBROSPINAL FLUID, CSF); the 3'rd one is called DURA MATER and this one is in close contact with the arachnoid (the 2'nd layer) but above these two there can exist a space called the EPIDURAL SPACE; normally this space is considered virtual because it is filled with fat but sometimes fluid is inserted there on purpose (usually this is done by the Anesthetist and is called EPIDURAL ANESTHESIA).

For the purpose of this question another anesthetic technique is of importance. This is called SPINAL ANESTHESIA. This is done by inserting a fine needle through the DURA MATER and the ARACHNOID (the 2'nd and 3'rd layers) until the tip of the needle enters the CSF in the space between the PIA MATER and the ARACHNOID also called SUBARACHOID SPACE. There the anesthetist deposits a solution of local anesthetic (usually 4 ml) that results in numbing the lower part of the body. The needle used would be a 27 Gauge for the purpose of this question. If we measure the CSF pressure (using a probe inserted in the subarachnoid space) this would be 20–30 cmH2O (16–24 mmHg or 2.1–3.2 kPa). The density of CSF is 1.00059 g/ml. After the 27 G (=0.413 mm outer diameter) needle is inserted and 4 ml of liquid is administered in a total of 125 ml of CSF (probably increasing the CSF pressure a little from the baseline of 16-24 mmHg), the needle is retracted but the hole left by the needle through the arachnoid and the dura mater allows CSF leakage into the epidural space. It is hypothesized that this leakage causes a drop in CSF pressure and this in turn causes a HEADACHE termed PDPH (postdural puncture headache) that usually is evident after 72 hours. But I find this hard to believe because it would mean that through the 0.413 mm hole in the dura mater would leak more than 4 ml in less than 72 hours.

Question. I would like to know what would be the necessary pressure gradient between the CSF space (the subarachnoid space) and the epidural space in order to cause such leakage (more than 4 ml in less than 72 hours).

Thank you!

Resources.

https://en.wikipedia.org/wiki/Cerebrospinal_fluid

Image of meninges (pia, arachnoid and dura)

Another image of meninges

Spinal anesthesia

• How much more than 4ml? Commented Sep 9, 2023 at 8:17
• this space doesn't solve problems for you. It helps you in your problem solving. What have you tried so far? Commented Sep 9, 2023 at 15:53
• @ Solar Mike - for the purpose of this question let's assume an exact 4 ml leaked volume Commented Sep 10, 2023 at 15:51
• @ Tiger Guy - ups! than I must admit that I'm in error. Big misunderstanding om my side. Thanks for clearing this! I'll post back after I refresh my Fluid Dynamics :)) Commented Sep 10, 2023 at 15:54