Optimal Metric of Surgical Freedom: Volume of Surgical Freedom Compared with Other Metrics of Instrument Maneuverability

Objective: Surgical freedom is the most important metric to gauge a surgeon's maneuverability. Heron's formula is the mathematical method used to calculate surgical freedom. Multiple inaccuracies and limitations hinder the utility and applicability of this design. The volume of surgical freedom (VSF) is a methodology that may produce the optimal qualitative and quantitative representation of an access corridor and provide the surgeon with an anatomical, spatially accurate, and clinically applicable metric.

Methods: A total of 297 dataset measurements assessing surgical freedom were completed for cadaveric brain neurosurgical approach dissections. Heron's formula and the VSF were calculated specific to different surgical target anatomical structures and compared for accuracy and human error.

Results: All exemplary models of Heron's formula for irregularly shaped surgical corridors resulted in an overestimation of the respective areas of the datasets. The minimum overestimation was 31.3%.

Conclusion: VSF is an innovative concept which can develop a model of a surgical corridor that yields better assessment and prediction of the ability to maneuver and manipulate surgical instruments. VSF corrects for deficits in Heron's method by producing the correct area for an irregular shape using the shoelace formula, adjusting the data points to account for offset, and attempting to correct for human error. VSF accounts for inaccuracies in the practical and mathematical method and provides the ability to produce three-dimensional models and therefore is a preferable and applicable standard for assessing surgical freedom ([Figs. 1]–[3]).

Fig. 1 Distribution of the overestimations of area produced by an incorrectly applied Heron's formula. Graphs detail the distribution of overestimations when the 4 triangle division choices are applied to a total of 297 datasets. (A) Division choice 1, applied to 93 datasets, resulted in an overestimation of 8.93% (12.18%). (B) Division choice 2, applied to 143 datasets, resulted in an overestimation of 14.10% (20.39%). (C) Division choice 3, applied to 129 datasets, resulted in an overestimation of 15.14% (20.16%). (D) Division choice 4, applied to 107 datasets, resulted in an overestimation of 13.76% (19.10%).

Fig. 2 In 92% (188 of 204) of datasets reviewed for the influence of offset, the area calculated on the basis of the measured data points was larger than the area calculated on the basis of the translated best-fit plane points, with a mean overestimation of 2.14%.

Fig. 3 Distribution of 2232 probe length measurements calculated from the measurement datasets when using a 190-mm probe showing the influence of human error in the data collection process, giving a mean calculated probe length of 190.26 mm (5.57 mm). For a 190-mm probe, this standard deviation results in a 6% error in the measured volume, which is corrected by the normalized volume of the volume of surgical freedom.

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Artikel online veröffentlicht:
15. Februar 2022