Trigonometry in daily ultrasound practice
We have read with interest the editorial by Piton et al.  regarding application of Pythagoras’ theorem in central venous cannulation. Geometry is at the base of our daily life and we should apply his theorems and axioms to obtain the best result in our daily practice.
As already stated by Piton , in our ultrasound daily practice, we constantly build right-angled triangles: the hypotenuse is the needle route, side A is the distance measured on the skin between needle insertion point and target projection on the skin, and side B is the depth of the target.
Side B is determined by the patient’s anatomy and the operator cannot modify it. As reported by Schulman et al. , needle/skin angulation between 30° and 45° is considered to be ideal while performing ultrasound procedure.
Trigonometry is helpful in determining which targets can be reached with such needle angulation. At 45° angulation tan(α) is equal to 1, meaning that side A and side B have to be equal. For example, if our target jugular internal vein is 2 cm deep, the needle has to be inserted 2 cm from the target. Generalizing, we have a good needle visualization whenever Tan(α) ≤ 1 with side B equal to or shorter than side A.
In conclusion, physicians have to take into account target depth while choosing the ultrasound linear probe of appropriate size to be able to visualize all needle routes and the needle skin entrance site.
Availability of data and materials
ADC, LS, and MC wrote the manuscript and created the figure. The authors read and approved the final version of the manuscript.
Ethics approval and consent to participate
Consent for publication
The authors declare that they have no competing interests.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.