Table 3.

The failure rate, axis error, angle error and tip error results obtained by the previous method introduced in [21] for 18G needles inserted in three types of animal tissues as a function of the needle insertion angle.

Range of Needle Insertion Angles	Tissue Type	Failure Rate	Angel Error (${}^{\circ }$)	Axis Error (mm)	Tip Error (mm)
Shallow angles ($0^{\circ }$–${20}^{\circ }$)	Bovine muscle	$0.0\%$	1.7 ± 0.9	1.2 ± 0.6	1.2 ± 0.7
	Bovine liver	$0.0\%$	1.8 ± 0.8	1.0 ± 0.4	1.1 ± 0.4
	Porcine muscle	$0.0\%$	1.8 ± 0.3	1.1 ± 0.5	1.1 ± 0.5
Moderate angles (${20}^{\circ }$–${40}^{\circ }$)	Bovine muscle	$0.0\%$	2.0 ± 1.0	1.6 ± 0.7	1.6 ± 0.8
	Bovine liver	$0.0\%$	2.2 ± 1.1	1.5 ± 0.7	1.6 ± 0.9
	Porcine muscle	$0.0\%$	2.3 ± 0.7	1.7 ± 0.6	1.8 ± 0.8
Steep angles (${40}^{\circ }$–${65}^{\circ }$)	Bovine muscle	$46.7\%$	2.6 ± 1.2	1.9 ± 0.5	2.1 ± 0.3
	Bovine liver	$40.0\%$	2.7 ± 1.0	1.9 ± 0.7	2.0 ± 0.5
	Porcine muscle	$40.0\%$	2.9 ± 1.5	2.0 ± 0.4	2.0 ± 0.5
All angles ($0^{\circ }$–${65}^{\circ }$)	Bovine muscle	$17.9\%$	2.0 ± 1.1	1.5 ± 0.7	1.6 ± 0.7
	Bovine liver	$15.4\%$	2.2 ± 1.0	1.4 ± 0.7	1.5 ± 0.7
	Porcine muscle	$15.4\%$	2.3 ± 1.0	1.6 ± 0.6	1.6 ± 0.7