Aberration and harmonic imaging

Transcription

1 Aberration and harmonic imaging IEEE Ultrasonics Symposium 25 Trond Varslot, Svein-Erik Måsøy and Bjørn Angelsen Norwegian University of Science and Technology

2 2/12 Motivation Good understanding of wavefront aberration and linear wave propagation. time-delays and amplitude filter / generalised screen time-reversal / DORT

3 2/12 Motivation Good understanding of wavefront aberration and linear wave propagation. time-delays and amplitude filter / generalised screen time-reversal / DORT "... but harmonic imaging works so well... why bother... "

4 2/12 Motivation Good understanding of wavefront aberration and linear wave propagation. time-delays and amplitude filter / generalised screen time-reversal / DORT "... but harmonic imaging works so well... why bother... " "... harmonic imaging has solved the problem of aberration... "

5 3/12 Theory Westervelt equation 2 p 1 2 p c 2 t = 1 2 Lp 2 p 2 ɛ 2 c 2 t 2 n t 2

6 3/12 Theory Westervelt equation 2 p 1 2 p c 2 t = 1 2 Lp 2 p 2 ɛ 2 c 2 t 2 n t 2 Define linear and nonlinear parts p = p l + p nl 2 p l 1 c 2 2 p l t 2 2 p nl 1 c 2 2 p nl t 2 = 1 c 2 2 Lp l t 2 = 1 c 2 2 Lp nl t 2 ɛ n 2 p 2 t 2.

7 3/12 Theory Westervelt equation 2 p 1 2 p c 2 t = 1 2 Lp 2 p 2 ɛ 2 c 2 t 2 n t 2 Define linear and nonlinear parts in frequency domain p = p l + p nl 2ˆp l + ω2 c 2 ˆp l = ω2 c 2 Lˆp l 2ˆp nl + ω2 c 2 ˆp nl = ω2 c 2 Lˆp nl + ɛ n ω 2ˆp ω ˆp.

8 3/12 Theory Westervelt equation 2 p 1 2 p c 2 t = 1 2 Lp 2 p 2 ɛ 2 c 2 t 2 n t 2 Define linear and nonlinear parts in frequency domain for p nl << p l p = p l + p nl 2ˆp l + ω2 c 2 ˆp l = ω2 c 2 Lˆp l 2ˆp nl + ω2 c 2 ˆp nl = ω2 c 2 Lˆp nl + ɛ n ω 2ˆp l ω ˆp l.

9 4/12 Observations Aberration of linear part is well understood Nonlinear part is governed by the same equation with additional source term Source for the nonlinear part is an aberrated linear part Expect the nonlinear part to be as aberrated as the linear part.

10 5/12 Simulations xd d F TX frequency Focal depth XD Wall model Tissue Simulation : 2.5 MHz : 6. cm : cm : abdominal 2. cm : muscle : 3D

11 6/12 Energy distr. fundamental

12 6/12 Energy distr. fundamental

13 7/12 Energy distr. harmonic

14 7/12 Energy distr. harmonic

15 8/12 Energy distr

16 9/12 Peak pressure 15 [db]

17 1/12 Energy [db] E(z) = p(r, t) 2 dtdr. T z

18 1/12 Energy [db] [db]

19 11/12 Beam profiles 5 [db]

20 11/12 Beam profiles 5 [db]

21 11/12 Beam profiles x y y 5 15

22 12/12 Summary Second harmonic is governed by the same equation as fundamental, with additional source term

23 12/12 Summary Second harmonic is governed by the same equation as fundamental, with additional source term Source for the second harmonic is aberrated fundamental

24 12/12 Summary Second harmonic is governed by the same equation as fundamental, with additional source term Source for the second harmonic is aberrated fundamental Aberration of second harmonic is similar to that of fundamental

25 12/12 Summary Second harmonic is governed by the same equation as fundamental, with additional source term Source for the second harmonic is aberrated fundamental Aberration of second harmonic is similar to that of fundamental Reduced aberration for fundamental at lower frequency

26 12/12 Summary Second harmonic is governed by the same equation as fundamental, with additional source term Source for the second harmonic is aberrated fundamental Aberration of second harmonic is similar to that of fundamental Reduced aberration for fundamental at lower frequency Other sources for improved image quality in harmonic imaging