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HAL Id: tel-02171417

https://tel.archives-ouvertes.fr/tel-02171417

Submitted on 2 Jul 2019

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Development of a 3D time reversal cavity for pulsed

cavitational ultrasound : application to non-invasive

cardiac therapy.

Justine Robin

To cite this version:

Justine Robin. Development of a 3D time reversal cavity for pulsed cavitational ultrasound : appli-cation to non-invasive cardiac therapy.. Acoustics [physics.class-ph]. Université Sorbonne Paris Cité, 2017. English. �NNT : 2017USPCC273�. �tel-02171417�

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31 %

25 % 75

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𝐻(𝜔) 𝐸(𝜔) 𝐹(𝜔) 𝐹(𝜔) = 𝐻(𝜔). 𝐸(𝜔) ⇔ 𝐸(𝜔) = 𝐻(𝜔)−1_{. 𝐹(𝜔)} 𝐹 𝐸 𝐹 𝐻−1(𝜔) 𝐻(𝜔) 𝐹

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916 𝑘𝐻𝑧

64 𝑚𝑚

8 µ𝑠 100 𝐻𝑧

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𝑛 = 5

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𝑛 = 7 0.5 𝑚𝐿/𝑘𝑔 15 𝑚𝐿/𝑘𝑔

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≥

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4 𝐿/𝑚𝑖𝑛 21.1 ± 3.9 𝑚𝑚𝐻𝑔 39 ± 6.9 𝑚𝑚𝐻𝑔 9.6 ± 1.7 𝑚𝑚𝐻𝑔 55 ± 10 % 19.6 ± 3.5 𝑚𝑚𝐻𝑔 51 ± 9 % 3𝐿/𝑚𝑖𝑛 5𝐿/𝑚𝑖𝑛 9.0 ± 4.3 4.9 ± 2.9 𝑚𝑚𝐻𝑔/𝐿/𝑚𝑖𝑛

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37.8 ± 4.6 𝑘𝑔

60 ± 13

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Before Therapy After Therapy Variation* (%) p

Shear Wave Imaging

Elastography (kPa) 76.1 ± 23.7 35.6 ± 7.2 - 52 ± 7 <0.001

Echocardiography

Doppler Mitral Valve (figure 5A)

- Maximal Velocity (m/s) 2.41 ± 0.50 1.73 ± 0.21 - 28 ± 6 0.007

- Maximal Pressure Gradient

(mmHg) 24.0 ± 4.4 12.1 ± 1.4 - 49 ± 11 0.003

- Mean Velocity (m/s) 1.95 ± 0.36 1.38 ± 0.24 - 29 ± 6 0.001

- Mean Pressure Gradient (mmHg) 16.2 ± 3.2 8.2 ± 1.3 - 48 ± 7 <0.001

Mitral Valve Area (cm2₎

- By pressure half time (PHT, fig 5B) 1.09 ± 0.09 1.57 ± 0.08 + 143 ± 18 <0.001

- By continuity equation 1.10 ± 0.15 1.58 ± 0.15 + 142 ± 15 <0.001

- By planimetry (fig 5C) 1.13 ± 0.13 1.54 ± 0.14 + 137 ± 14 <0.001

Pulmonary artery pressure (mmHg)

- Maximal (Tricuspid Valve) 64.7 ± 12.8 34.1 ± 10.2 - 47 ± 12 <0.001

Cardiac Output#_(L/min) _{2.98 ± 0.1} _{2.96 ± 0.14} _{- 1 ± 0.2} _0.83

Pressure Sensors (Millar) (mmHg)

Mean Diastolic Left Atrium pressure (LAP) 36.8 ± 6.2 20.2 ± 5.1 - 44 ± 11 0.004

Mean Diastolic Left Ventricle pressure (LVP) 17.4 ± 2.7 11.4 ± 1.9 - 35 ± 10 0.014

Mean Diastolic Gradient LVP-LAP 17.4 ± 2.4 8.8 ± 1.2 - 50 ± 13 0.002

Cardiac Flow Captor (L/min)

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105 ± 9 𝑘𝑃𝑎

46 ± 4 𝑘𝑃𝑎 55 ± 8 %

82 ± 10𝑘𝑃𝑎

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–

– –

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  

–

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– λ λ – – – λ λ λ –

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𝑓/𝐷 = 1

𝑓(𝑡) = 𝑓0+ (𝑓1−𝑓0).

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3 µ𝑠 0.85 𝑀𝐻𝑧 – 3 𝑑𝐵

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– 𝑛 = 3 – (3 𝜆 𝑥 3 𝜆) – – –

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– – – – – – –

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–

𝟏 √𝑺⁄

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–

– –

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–

– >

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–

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– – 𝐺 𝐺 =∫ |𝑠(𝑡)|.𝑑𝑡 𝑇 0 𝑀 ’ ’ ’

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’ –

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– –

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“ ”

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“

“ ”

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“ ”

Diffusion through the MSM medium

≫ 𝑙𝑒 𝑙∗ < 𝑐𝑜𝑠 > 𝐴𝑐𝑜ℎ= 𝐴 ∙ 𝑒−𝛼∙𝑐∙𝑡∙ 𝑒 −𝐿 𝑙𝑒 𝑡~0,1 ∙2∙ 𝐿2 𝑙∗_∙𝑐 𝜏 = 𝐿2 2∙𝑙∗_∙𝑐

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𝛼 = 1.5 𝑚−1

𝑇 ∝𝑙∗

𝐿

Reverberation of the empty cavity

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– 0.1 rod/𝑚𝑚2 2 to 20. 10−2/𝑚𝑚3 𝒍𝒆 𝒍∗ < 𝒄𝒐𝒔 >

Description of the 2D – TRC

– λ λ

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General Setup description

f D = μ 600 µ𝑠 [20 − 50] 𝑚𝑚 𝐿 > 3 ∙ 𝑙∗₌ 30 𝑚𝑚

Description of the 2D and 3D-TRC

– 20 𝜆 𝑥 0.5 𝜆

λ λ

λ –

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Simulation process and gain evaluation

3 µ𝑠 – – 𝐺 𝐺 =∫ |𝑠(𝑡)|.𝑑𝑡 𝑇 0 𝑀

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λ λ λ

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–

𝐿 ≥ 3 ∙ 𝑙∗ 3 ∙ 𝑙∗= 30 𝑚𝑚

– –

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2D – TRC optimisation.

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𝑛 = 10−2 𝑡𝑜 3. 10−1 𝑚𝑚−2

–

3D – TRC optimisation

–

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𝜏𝑐𝑎𝑣~10 µ𝑠 ≪ 𝜏𝑀𝑆𝑀 ~ 50 𝑡𝑜 200 µ𝑠

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3. 𝑙∗

–

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“

”

𝜏𝑐𝑎𝑣~10 µ𝑠 ≪ 𝜏𝑀𝑆𝑀 ~ 50 𝑡𝑜 200 µ𝑠 𝜏𝑐𝑎𝑣~100 µ𝑠 “ ” – “ ” “ ” “ ” 𝑓/𝐷 = 1 3 µ𝑠 = 0.85 𝑀𝐻𝑧 60% – 3 𝑑𝐵 𝑠(𝑡) – 𝑠𝑖𝑔𝑛(𝑠(𝑇 − 𝑡)) 𝐿 ∈ [0 5𝑐𝑚] 1 𝑃𝑎

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“ ” λ λ “ ” 1 𝑐𝑚 “ ” –

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“ ” –

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–

200 𝑐𝑚3

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 λ   𝑓 − 𝑛𝑢𝑚𝑏𝑒𝑟 < 1  

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60 𝑊

5. 𝜆 𝑥 5. 𝜆

𝑓 − 𝑛𝑢𝑚𝑏𝑒𝑟 < 1

 

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

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𝑁 ∗ 𝑁

𝐾(𝜔) 𝜔

𝐾(𝜔) 𝐾(𝜔) =

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𝐻 𝐻(𝜔) 𝐸(𝜔) 𝐹(𝜔), 𝐹(𝜔) = 𝐻(𝜔). 𝐸(𝜔) ⇔ 𝐸(𝜔) = 𝐻(𝜔)−1_{. 𝐹(𝜔)} 𝐹 𝐸 𝐹 𝐻−1(𝜔) 𝐻(𝜔) 𝐹 𝐸 𝐻 𝐸 𝐻

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𝐹

𝐸

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𝜔 𝐻(𝜔)𝐻∗(𝜔) 𝐻 𝐻 = 𝑈𝛬𝑉† _𝑉 𝜔 𝑀(𝜔) 𝑀𝑐𝑡𝑟𝑙_𝑝𝑜𝑖𝑛𝑡𝑠(𝜔) = 𝐻(𝜔)𝑀(𝜔) 𝑀𝑐𝑡𝑟𝑙_𝑝𝑜𝑖𝑛𝑡𝑠(𝜔) = 𝑈1(𝜔)𝛬1(𝜔) 𝑉1†(𝜔) 𝑉1 𝑉𝑡𝑟𝑎𝑛𝑠(𝜔) = 𝐻∗(𝜔)𝑉1(𝜔)

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𝐸(𝜔) 𝐸(𝜔) 𝐸𝑝𝑟𝑜𝑗(𝜔) = 𝐸 − ∑ ( 𝑉𝑡𝑟𝑎𝑛𝑠,𝑖 † _{(𝜔)𝐸(𝜔)) 𝑉} 𝑡𝑟𝑎𝑛𝑠,𝑖(𝜔) 𝑝 𝑖=1 𝐸𝑝𝑟𝑜𝑗

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𝐹(𝜔)

± ± 0.7 ± 0.4

± 0.16 ± 0.7 ± 0.04

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± ± 0.7 ± 0.4

± 0.14 ± 0.8 ± 0.3

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2700 𝑚. 𝑠−1 𝑐 ≈ 3000 𝑚. 𝑠−1

𝑐 ≈ 3000 𝑚. 𝑠−1 _{𝜌 ≈ 1000 kg. 𝑚}−3

𝛼 ≈ 1.67 𝑐𝑚−1

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𝜆

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𝑑𝑥 = 𝑑𝑧 = 𝜆

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𝜌 = 1000 𝑘𝑔 ∙ 𝑚−3 𝑐 = 1500 𝑚 ∙ 𝑠−1 𝐻 = 1000 ∙ µ𝑥−µ𝑤𝑎𝑡𝑒𝑟 µ_{𝑏𝑜𝑛𝑒}−µ_{𝑤𝑎𝑡𝑒𝑟} 𝜑 = 1 − 𝐻 1000

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𝑠𝑖(𝑡) 𝑖

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𝑠𝑖ℎ(𝑡) 𝜏𝑖 𝑎𝑖 = 𝑚𝑎𝑥_𝑡{|𝑠𝑖(𝑡)|} 𝑚𝑎𝑥𝑡{|𝑠𝑖ℎ(𝑡)|} 1 𝑎𝑖 𝑎𝑖 𝑎𝑖

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5.5 ± 2.5 𝑚𝑖𝑛

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70 ± 12 𝑚𝑖𝑛

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λ λ)

λ λ

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