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Needles used in surgery come in various sizes, shapes and properties. In laparoscopic surgery, the trocars create the communication ports to the environment and these ports are used for instrument introduction to the surgical field. Needles need also to be passed through these cannulas, a fact that creates a barrier regarding the size of a certain needle.
The user has the ability to select six different trocar sizes (3, 5, 10, 11, 12 and 15mm) and four different types of curved needles. The final result is the maximum length of a curved needle that can fit into a specific trocar during laparoscopic surgery.
The mathematical problem is to define the maximum height of this part of a circle that can fit inside a larger circle (cylinder) which is the lumen of the cannula. Using basic mathematics and trigonometric functions we calculated the theoretical maximum length of a needle that can fit inside a lumen with a given diameter. In these calculations, percentile approximation was used.