Hydrostatics in the shunt system

So, what do people, bottles and beakers have in common? At first glance, it might seem easier to describe how they are different. However, we will see that both of the latter can be used as substitutes for people, as (albeit very grossly) simplified examples, if they are looked at in a certain way. Bottles and beakers can be used to create simple models that can help us to understand basic hydrostatic effects within the human body.

However, we should begin by defining what exactly we mean when we talk about beakers, bottles and people in terms of fluid mechanics.

Here, beakers represent open containers for water or other liquids where there IS direct contact between the fluid and the surrounding air. The pressure on the "exposed surface" of the liquid in the beaker is known, corresponding to the prevailing atmospheric pressure.

In this context a bottle is a rigid container for liquids that is closed on all sides, meaning there IS NOT any contact between the liquid and the surrounding air. The liquid pressure on the "open surface" of the liquid in the container is "frozen" and is no longer evident from outside.

People constitute a type of container, in both a philosophical and physical sense: containing thoughts, organs and all types of fluids. Air circulates in our lungs, blood circulates through our brains and CSF circulates through our cerebral cavity system.


The term "fluid" refers to a substance, which, unlike a solid, does not offer any resistance against external forces, but rather allows itself to be continuously morphed by external forces.

If, when it is forced to change shape in this way, there is no change in volume (meaning the fluid cannot be compressed), then we can generally refer to it as a liquid, as is the case with water and even Liquor cerebrospinalis.

We will see, that in this context, a person is more similar to a closed bottle than a beaker that is open to the surrounding environment. However, more about that later. We will begin by focusing on the water in our cerebral cavity system - cerebrospinal fluid:

Cerebrospinal fluid (or CSF for short) is a clear liquid, similar to water, which is mainly composed of blood plasma, with only a small proportion of cellular components. These mainly consist of lymphocytes, but also include protein and albumin. This is produced through arterial circulation in the inner parts of the brain, mainly in the choroid plexus. According to current knowledge, it is resorbed again in the arachnoid granulations, as well as other places.

A person has between approximately 100-200 ml of CSF in their cerebral cavity system and spinal cavity at all times. A healthy person produces around 500 ml of this fluid daily, meaning that the CSF is completely replaced several times over the course of one day - the ventricles and spinal cavity are thoroughly rinsed out.

CSF has a wide range of functions, some of which are still currently being researched. One of its functions is to protect the human body's central nervous system from external shocks and pressure. Its cellular components allow it to carry out immunological functions, it helps detoxify the brain by absorbing and removing metabolic end products and it absorbs part of the brain's weight due to the effect of neutral buoyancy.


The term "buoyancy" refers to a fundamental phenomenon in fluid mechanics. According to this phenomenon, a body in a fluid is subjected to a force that acts against the force of gravity being exerted from outside. A ship floating in water or the human brain suspended in CSF are both examples of this. According to Archimedes' principle, the buoyant force produced by the weight is equal to the weight of the liquid displaced by the body. The weight of the water displaced by a ship in the sea "pushes" the ship "upwards".

The causes of buoyancy stem from the nature of liquids at rest in the gravitational field of the earth. To be more specific: the pressures the liquid is subject to. The scientific subfield dealing with the phenomena that arise from this is known as "hydrostatics".

In physical terms, pressure is defined, very generally, as "the weight exerted on a specific surface area". Pressure p is generated when a physical force F is exerted on the surface of a solid or fluid: in fluids the pressure is exerted evenly p = F/A as long as gravity is not taken into account. A good example of this is a balloon, in which the force F of the gas or water presses against the tension generated by the balloon's skin. In this case, there will be overpressure in the balloon relative to the surrounding atmosphere.

Overpressure (hydrocephalus) can also arise inside the skull, including as a result of the "masses" mentioned above, e.g. excess buildup of CSF, bleeds or a growing tumour. The necessary force is generated by their expansion or growth.

If we then take gravity into account, another special form of pressure will arise due to the weight of the fluid itself. This is known as "hydrostatic pressure". This phenomenon is known as the "basic hydrostatic law" and in physics, is referred to as the "basic hydrostatic equation". This law is essential for understanding why differences in pressure are generated in shunts regardless of the position the body is in. It is also important for understanding why, in the worst case scenario, ventricles can literally be sucked dry, as well how to prevent this from occurring.

To describe this in the simplest possible terms: Every liquid has a mass, and this is subject to a weight within the Earth's gravitational field. Therefore, the load on an imaginary body within the liquid, stemming from the "open surface" (i.e. the boundary between the liquid and the surrounding atmosphere, which is subject to a known amount of (air) pressure) increases in proportion to the depth of the liquid. However, the amount of liquid pressure this generates depends solely on the height of the column of liquid above. This is not affected by the shape of the vessel or the mass of the liquid that is above the area subject to observation.

A good example is a beaker (of any shape) filled with water: unlike in a balloon, the water does not have to be pushed down into the glass by a special force, it only has to be filled up. Naturally, the water's surface is always subject to the ambient pressure, i.e. the atmospheric pressure (which will be approximately 1 bar, depending on the weather). The bottom of the beaker is still subject to the same ambient pressure, but is also subject to the load consisting of the entire weight of the column of water (not the weight of the water in its entirety) above the bottom of the glass. The latter generates additional pressure. This is the hydrostatic pressure mentioned that was mentioned the start. It begins at "zero" on the water's surface, and gets closer to the maximum the deeper the point is under the water (relative to the surface). This is due to the fact that an increasing weight of water is exerting a load on the area in which pressure is being observed.


For experts and those who want to learn more: Hydrostatic pressure can worked out very easily. To do this, all you need are a few simple physical formulae:

(1)Pressure = force/area;
p = F/A (general definition)

(2)Hydrostatic pressure = weight/area;
pHP = G/A (special definition)

(3)Weight = mass * constant; W = G * const.
(in which M is the mass of the body in g or kg, const./natural constant)

(4)Density = mass/volume; d = M/V
(Density of water: d = approx. 1 g/cm3/material constant)

Equation (4) can be used to calculate the mass of the water:
M = d * V (5).

The volume of the "water cylinder" in cases where there is a glass of water is calculated using the following image of V = h * A (6) in which A is the area of the base of the glass and h is the height of the water level in the glass: see the diagram on the right

When (6) is inserted into (5) it results in:
M = d * V = d* h* A (7)

Placing the hydrostatic pressure from (2) into (3) and (7) produces the following equation:
pHP= G/A = M*const./A = d*h*A const./A (8).

By simplifying this we finally come to the basic hydrostatic equation:
pHP = D * const.*h (9).

It is therefore clear that hydrostatic pressure is solely and exclusively dependent on the height of the column of liquid (h) (except for the density of the liquid (d)).


The hydrostatic paradox

At first glance, this situation seems counterintuitive. Because of this, we also refer to the so-called hydrostatic paradox in this context.


Our everyday experience teaches us all that whether we dive down 10 metres into a swimming pool or 10 metres into the ocean, makes no difference to the pressure we feel in our ears.

Therefore, depth is the only thing that matters in terms of hydrostatic pressure.

Hydrostatic pressure in cmH2O

To use technical jargon, pressure in the CFS is measured using the non-SI unit "cmH2O" ("SI" stands for Système international d'unités or the "International System of Units"). This unit is otherwise known as the "centimetre of water". This is a type of so-called "differential pressure", which is used to describe the difference in pressure between the cranial cavity and the external air pressure.

cmH2O is defined as the hydrostatic pressure exerted by a one-centimeter-high column of water, in which the density of the water is precisely one gram per cubic centimetre. It is expressed differently to the unit "Pa", which is normally used to measure pressure. Unlike a "Pascal", which is defined as the force of one Newton applied to an area of one cubic metre, the cmH2O is a unit that does not have to refer to an effective surface area. It only refers to a one-dimensional measure of length, namely the height of the column of water exerting force on the relevant pressure point. This goes against our intuitive understanding of pressure, however, in doing so, it makes the effect of hydrostatic pressure (i.e. the pressure in a medium, such as a liquid, that is generated by the weight of the medium itself) clearer. In other words: the pressure is generated because the medium is pressing against itself with its own weight.

One cmH2O corresponds roughly to one millibar, or, in SI units: 1,000 Pascal.

Hydrostatic pressure can be calculated using the following formula:
HSP = rho * g * h
In this formula h (the height of the column of water), rho and g are physical constants.

In the past, mercury, which is much heavier than water, was also commonly used in columns of liquid. 1 mm of mercury (1 mmHg, also known as torr) generates roughly the same pressure as 1.36 cm of water. The old unit "torr" is still frequently used today, especially in medicine.

The pressure distribution in the CSF contained in the cerebral cavity system and spinal cavity of the human body is no different to that of a beaker filled with water. However, there is one crucial difference between the two: there no "open surface" with a known level of atmospheric pressure in the human body.

Because of this, upon closer observation, the column of CSF in the spinal cavity in fact resembles an upright bottle in the Earth's gravitational field, in which the absolute pressure ratios cannot be determined from the outside. However, we can draw conclusions about the pressure gradient in CSF by making analogies with simple hydrostatic systems: the pressure steadily increases from the top to the bottom in proportion to the height of the column of CSF. Even this model is not entirely accurate, after all, the human body is not rigid. However, to begin with, this is a high enough level of detail for the purpose of examining the hydrostatic phenomena set out here.

The following example will demonstrate how pressure ratios in real hydrostatic systems (similar to those the human body or in a shunt, for example) can quickly become complex and confusing, despite the simplicity of the basic law (the basic hydrostatic equation):

In the diagram below there are eight pipes labelled A-H, which are very similar at first glance. However, despite their similarity, they are subject to fundamentally different hydrostatic, and in some cases, hydrodynamic forces (where the water is moving):

A A liquid with px of overpressure was squeezed into the rigid pipe "A". The system was then tightly sealed immediately afterwards. In the rigid pipes, the overpressure is being maintained. If the pipes had been flexible, they would blow up like a balloon due to the px of overpressure. When it is placed in an upright position, the bottom of the pipe is subject to overpressure of px plus the hydrostatic pressure (HP)+ 10 cm.

B Pipe B has an opening, through which it is exposed to the outside air. As a result, there is no longer an overpressure of px. Therefore, by definition, it is 0 at the top and at +10 cmH2O at the base below.

Pipe C is open at the bottom and sealed at the top. By definition, the bottom is subject to 0 cmH2O. The water cannot flow away, as this would create a vacuum above, as has previously been mentioned. However, it will attempt to flow away: the hanging column of water pulls the cap at the top down, generating a negative hydrostatic pressure of -10 cmH2O, which is also known as suction force.

D Pipe D is identical to C, but in this case the cap is slightly flexible, therefore clearly demonstrating the real existence and effect of the suction. This is important, as "nothing", in the fullest sense of the word, can be seen. There is "no flow" to be seen either, meaning that the existence of suction is a mere assertion.

Pipe E is open at the top and bottom and therefore just empties out. The driving force behind this process is simply the water, which is able to "fall" down unimpeded.

In pipe F the hole out to the external air, at which point there is a differential pressure of 0 cmH2O, is right in the middle. Nothing can flow away, but the hydrostatic pressure at the bottom is now only +5 cmH2O and the suction at the top is only -5 cmH2O, due to the lower hydrostatic level.

In pipe G there is also a flexible cap, to show the real existence and effect of the suction. If the lower cap was also flexible it would bulge outwards due to the positive overpressure.

In pipe H there is no upper cap, meaning that the liquid flows away, leaving it half-full. Only a positive hydrostatic pressure of + 5 cmH2O remains at the base.

This section will very specifically look at pipes (C) and (D), which illustrate how the so-called "siphon effect" occurs. This is very important in relation to shunt therapy. As long as the patient is standing up, the catheter full of liquid, which runs from the ventricles (the closed end) to the abdomen (the peritoneum, at the open end), actually constitutes the same type of system. The high level of suction that this produces in the ventricles is physically unavoidable and special implants are required to counteract it.

In essence, this effect is also responsible for the fact that cerebral pressure of a healthy person who is standing up is slightly negative. When in this position, the CSF therefore sinks out of the ventricles down into the dural sac (in the vertebrae). Although the dural sac is not open at the bottom like in pipes C and D, it is quite flexible and is capable of taking in some extra CSF. Luckily, there are also a few other physiological mechanisms to ensure that "physiological" (healthy) cerebral pressure does not drop to -100 cmH2O when a person stands up, instead only dropping to around -5 to -15 cmH2O.

If one of the pipes were to fall over (or if a person lies down) the height of the column of water would suddenly increase. The difference in pressure between two different places (such as the neck and base of the bottle) will become level within the Earth's gravitational field as soon as they are at the same hydrostatic level.

To summarise: When using a very rough model, we can treat a person as an upright bottle in the Earth's gravitational field, filled with CSF. When this bottle is in an upright position, the liquid pressure of the CSF in the head will be lower than that in the spinal cavity. When the bottle has been closed we cannot determine what the pressure is simply by looking at it.

It is therefore possible to infer what is happening to the pressure of the CSF in the human body when it is leaning over, bending or lying down on the basis of these simple physical thought experiments based on beakers and bottles. The hydrostatic pressure of the CSF in different parts of the human body is not constant, instead "adapting" to the position it is in and the activity it is doing.