Hertz Contact Based Scaling of Puncture Forces for Large Scale Needle Prototypes Using a Gelatinous Tissue Phantom

In order to test small scale medical devices, it is often necessary to prototype them on a larger scale such that proof-of-concept tests can be made more affordably and design details can be tested more easily. This article discusses a method of scaling large needle prototypes for testing in a gelatin phantom such that puncture forces match those expected for the actual-size needle when puncturing tissue. Using Hertz contact force equations to account for the differences in prototype materials and size, as well as for the tissue phantom properties, 10× scale prototype needles were inserted into a gelatin phantom and puncture forces were compared with those of a real scale prototype in bovine liver tissue. Results showed that for a 19 gauge (1.06 mm) stainless steel needle tip, where a maximum doctor-applied load of 5 N was desired to pierce liver tissue, loads of 0.44 N using Hertz point contact, and 0.31 N using Hertz line contact methods were predicted to puncture liver tissue, and an average load of 0.31 N was observed in force-displacement measurements. With a 10× scale stereolithographed needle prototype, Hertz point contact predicted a load of 0.31 N to puncture a gelatin phantom, Hertz line contact theory predicted 0.37 N, and an average load of 0.73 N observed in force displacement measurements. Similar contact mechanics based scaling methods might be applied to cutting devices.