A Bezier Profiled Horn for Reducing Penetration Force with Applications in Surgery Dung-An WANG and Hai-Dang Tam NGUYEN Graduate Institute of Precision Engineering, National Chung Hsing University Taiwan, ROC

2 Motivation n Reduced strain for patients pain relief n Increased precision of cutting tissue n Reduce necrosis of patients tissue Liao et al., 2012.

3 Market for hard tissue removal Millennium Research Group, 2010

4 Industrial and medical interests n Decrease cutting force (penetration force) n Decrease thermal effects: temperature may depend on Ultrasonic frequency Penetration force Cutting speed Geometry of cutting blade

5 Aims n Design of an ultrasonic horn with a new profile To increase in tool-tip vibration amplitude, allowing a significant amount of material to be removed To decrease the penetration force, reducing tissue necrosis

6 Design n Working frequency, 28.0 kHz

7 Bézier profile n Parametric curve based geometry is flexible enough to give a much better control over the profile of horns for design purpose. n The profile of the horn is based on a cubic Bézier curve. n Four-point Bézier polygon Q 0 Q 1 Q 2 Q 3

8 Parametric cubic Bézier curve

9 Design n The profile of the horn is optimized by allowing points Q 1 and Q 2 to move in the design space Specify W 1 20mm, W 2 =1.5mm, L=94mm. Thickness 1.2 mm f = 28.0 kHz

10 Design n Finite element analysis to obtain f 0 and M of the horn n Material: SS41

11 Optimized Bézier horn

12 Comparison n Catenoidal horn: same back and front end widths and length as those of the proposed horn. n Stepped and linear horn: same back and front end widths of the proposed horn. The length of the stepped/linear horn is calculated to have the same working frequency of 28.0 kHz as the proposed horn.

13 Comparison n Normalized displacements along the normalized length of the horns based on finite element computations

14 Comparison n The stepped horn: highest displacement amplification, but high stress concentration at the step discontinuity

15 Experiments n A Bézier horn and a catenoidal horn are fabricated by a laser cutting process from a stainless steel SS41

16 Experiments n Investigate the effects of ultrasound and horn types on the penetration force of ultrasonic cutting

17 Specimens n A tissue stimulant, raw potato, as representative for soft material n A polymethylmethacrylate (PMMA) material as representative for hard material n Specimen: 70 mm x 35 mm x 5 mm

18 Results n Penetration speed 0.25 mm/s n Five repeated trials n Penetration force by the Bézier horn is 75% of that of the catenoidal horn

19 Results n Penetration force as a function of penetration speed n Use Bezier horn n Penetration depths: the tissue stimulant 2 mm, PMMA material 3 mm Tissue stimulantPMMA material

20 Mechanics n Reduced penetration force is an effective measure for increasing the critical cutting depth in ultrasonic cutting, and below the critical cutting depth, material can be removed plastically (Zhou et al., 2002). n When the plastic deformation is the predominant mode of deformation, a very smooth and fine surface can be obtained.

21 Conclusions n A planar Bézier horn with high displacement amplification and low stress concentration is developed. n The displacement amplification of the Bézier horn is 30% higher than that of the traditional catenoidal horn with the same length and end surface widths n The penetration force by the Bézier horn is 75% of that by the catenoidal horn with a penetration speed of 0.25 mm/s during cutting of the tissue stimulant.