Phaco Fundamentals Part 4: Poiseuille's equation for fluidics in cataract surgery

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The basic equation that governs all fluid flow during phacoemulsification surgery is Poiseuille’s Equation. You already understand this equation if you've ever used a drinking straw to enjoy a milkshake. And the same principles even apply to setting up an irrigation system in your garden. The larger the bore of the tubing, the less resistance to flow.

We are concerned with the relative relationship and not the exact values, therefore, for simplicity we can simplify this formula. The viscosity of the fluid is relatively constant, as is the length of the tubing. And the values of pi and 8 are constant. This leaves us with a simpler equation.

Flow is proportional to the change in pressure times the radius of the tubing to the fourth power. Because the value for tubing size is exponential, a small change to the radius results in a large change in the relative flow. This is clearly illustrated in a common-sense situation of drinking with straws: With a small bore straw, very high vacuum is required to achieve relatively little flow. However, with a large bore stray, low vacuum is needed to achieve good fluid flow.

The source of fluid inflow is the bottle of balanced salt solution that is hanging on the phaco machine. The two factors that determine the rate of inflow are: the change in pressure and the radius of the inflow tubing. The change in pressure, can be modulated by raising or lowering the height of the bottle relative to the patient’s eye: the higher the bottle, the higher the infusion pressure. The inflow tubing has a large radius in order to maximize the flow and make sure that we keep our inflow greater than the outflow. Similarly, the size of the infusion channel within the phaco probe (or other infusion instrument) is kept as large as possible so as to not cause a bottleneck effect.

For fluid outflow, there are two sources of fluid leaving the eye: (1) the fluid that is removed via the phaco probe as a result of the vacuum level generated by the fluid pump, and (2) fluid leakage from the incisions. The rate of the fluid outflow via the phaco needle is determined by the radius of the needle and tubing, as well as the change in pressure generated by the phaco machine’s fluid pump. The rate of the fluid outflow loss via the incisions depends on their size and the relative fit of the instruments within these incisions.

Some degree of fluid leakage from the incisions is helpful to allow cooling of the phaco needle and to prevent thermal injury during surgery, particularly in early in the learning stages of phacoemulsification. With the use of advanced phaco power modulations, more experienced phaco surgeons tend to move towards tighter incisions which can give more stable fluidics.

The composition, nature, and size of the inflow and outflow tubing are different, and this is important for safe and efficient phaco surgery. Surge is the situation when the outflow of fluid from the eye exceeds the inflow, even for just a fraction of a second. When this occurs, the chamber tends to collapse and the posterior capsule can be sucked into the phaco probe in an instant, resulting in a ruptured posterior capsule and vitreous loss.

In order to maintain this flow balance, where the inflow is always greater than the outflow, we can use different sized tubing. If we look at the inflow tubing we notice that it is significantly different than the outflow tubing.