Attenuation Coefficient Estimation Farah Deeba, Ricky Hu, Jefferson - PowerPoint PPT Presentation

A Spatially Weighted Regularization Method for Attenuation Coefficient Estimation Farah Deeba, Ricky Hu, Jefferson Terry, Denise Pugash, Jennifer A. Hutcheon, Chantal Mayer, Septimiu Salcudean, Robert Rohling The University of British Columbia, Vancouver, British Columbia, Canada

Attenuation Coefficient Estimate (ACE) • C:\k-WAVE\k-Wave\miccai\IUS\IUS • A promising clinical tool to detect and monitor fatty liver Oral ACE Fat Fraction (%) 2

Attenuation Coefficient Estimate (ACE) • A promising clinical tool to detect and • C:\k-WAVE\k- monitor fatty liver Wave\miccai\IUS\IUS Oral Fetal Maternal • Potential for placental tissue characterization; ACE 3

Trade-off: Resolution and Measurement Quality • C:\k-WAVE\k- Reference Phantom Method (RPM) Window Size = 2 mm Window Size = 3 mm Window Size = 5 mm Window Size = 6 mm Window Size = 7 mm Window Size = 8 mm Window Size = 4 mm Wave\miccai\IUS\IUS Accuracy & Oral Precision ACE Error Resolution Window Size (mm) 4

TV Regularization: A Solution to Extend the Trade-off • C:\k-WAVE\k- 𝜇 =0.125 Wave\miccai\IUS\IUS Oral 2 +𝜇. 𝑈𝑊 𝛽 + 𝜇. 𝑈𝑊 𝛾 } Regularization 𝑦 = arg min ො 𝑦 {||𝑧 − 𝐵𝑦|| 2 𝑈𝑊(𝑦) 𝑦 = [𝛽 𝛾] 𝜇 =8.0 𝛽 = Attenuation Coefficient Estimate (ACE) 𝜇 =1.0 𝛾 = Backscatter Coefficient (BSC) 2 ) Data Misfit ( ||𝑧 − 𝐵𝑦|| 2 5

TV Regularization: A Solution to Extend the Trade-off • C:\k-WAVE\k- RPM TV Window Size = 7 mm Window Size = 2 mm Window Size = 3 mm Window Size = 4 mm Window Size = 5 mm Window Size = 6 mm Window Size = 7 mm Window Size = 8 mm Wave\miccai\IUS\IUS Oral ACE Error Window Size (mm) 6

Inhomogeneity • C:\k-WAVE\k-Wave\miccai\IUS\IUS Oral ACE Error Map CIRS 040 Phantom (ACE = 0.7 dB/cm/MHz) TV regularization • introduces large ACE error; • fails to capture BSC BSC Map variation at the target locations. Scatterers with different size Scatterers with different density 7

In Search for an Inhomogeneity Indicator Imaginary 𝑄𝐸𝐺 (𝐵) Real 𝐵 Homogeneous Received US Signal Amplitude 𝜌 = 𝜏 2 [2 − 𝜌 | ҧ Envelope SNR, 𝑇𝑂𝑆 opt 𝐵| = 𝜏 2 ; var A 2 ] Medium (from a large number of uniformly distributed scatteres) | ҧ 𝐵| = 𝜌(4 − 𝜌) =1.9 = var A 8

In Search for an Inhomogeneity Indicator • C:\k-WAVE\k- CIRS 040 Phantom Wave\miccai\IUS\IUS (ACE = 0.7 dB/cm/MHz) Δ𝑇𝑂𝑆 𝑓 Map 𝑄𝐸𝐺 (𝐵) Oral Envelope SNR, 𝑇𝑂𝑆 opt = 1.9 Scatterers with different size 𝑇𝑂𝑆 e − 𝑇𝑂𝑆 opt Δ𝑇𝑂𝑆 e = × 100% Scatterers with different density 𝑇𝑂𝑆 opt 9

SWTV-ACE 2 +𝜇 1 𝑈𝑊 𝛽 + 𝜇 2 𝑇𝑋𝑈𝑊 𝛾 𝑦 = arg min ො 𝑦 {||𝑧 − 𝐵𝑦|| 2 𝑗,𝑘 |𝛾 𝑗+1,𝑘 − 𝛾 𝑗,𝑘 +|𝛾 𝑗,𝑘+1 − 𝛾 𝑗,𝑘 𝑇𝑋𝑈𝑊 𝛾 = ෍ 𝑋 𝛾 𝑗,𝑘 𝑏 𝑋 𝛾 (Δ𝑇𝑂𝑆 𝑓 ) = 𝑛𝑗𝑜 ) 1 + exp(𝑐(Δ𝑇𝑂𝑆 𝑓 − Δ𝑇𝑂𝑆 𝑓 10

SWTV-ACE • C:\k-WAVE\k-Wave\miccai\IUS\IUS Oral ACE Error Map 2 +𝜇 1 𝑈𝑊 𝛽 + 𝜇 2 𝑇𝑋𝑈𝑊 𝛾 𝑦 = arg min ො 𝑦 {||𝑧 − 𝐵𝑦|| 2 TV Regularization CIRS 040 Phantom SWTV-ACE ACE Error Map (ACE = 0.7 dB/cm/MHz) 𝑗,𝑘 |𝛾 𝑗+1,𝑘 − 𝛾 𝑗,𝑘 +|𝛾 𝑗,𝑘+1 − 𝛾 𝑗,𝑘 𝑇𝑋𝑈𝑊 𝛾 = ෍ 𝑋 𝛾 𝑗,𝑘 𝑏 BSC Map 𝑋 𝛾 (Δ𝑇𝑂𝑆 𝑓 ) = 𝑛𝑗𝑜 ) 1 + exp(𝑐(Δ𝑇𝑂𝑆 𝑓 − Δ𝑇𝑂𝑆 𝑓 BSC Map Scatterers with different size Scatterers with different density 11

Phantom 1: Uniform ACE and Uniform BSC Ground Truth Mean Absolute Error (%) Standard Deviation (%) Phantom 1 (dB/cm/MHz) RPM TV SWTV RPM TV SWTV 1.3 47.6 2.6 5.9 58.7 1.6 1.2 12

Phantom 2: Variable ACE and Uniform BSC Ground Truth Mean Absolute Error (%) Standard Deviation (%) Phantom 2 (dB/cm/MHz) RPM TV SWTV RPM TV SWTV Background 0.84 106.4 10.5 7.2 134.9 16.1 10.5 Inclusion 1.18 55.1 8.7 8.9 75.1 9.5 4.0 13 13

Phantom 3: Similar ACE and Variable BSC Ground Truth Mean Absolute Error (%) Standard Deviation (%) Phantom 3 (dB/cm/MHz) RPM TV SWTV RPM TV SWTV Background 0.72 103.5 19.2 15.6 132.0 26.1 12.1 Inclusion 0.65 74.9 21.0 10.2 88.0 28.3 5.0 14

Results: Placenta ex-vivo Δ𝑇𝑂𝑆 e RPM TV SWTV-ACE 15

Conclusion SWTV TV Reference Phantom • SWTV-ACE improves the quality of ACE computation by reducing the estimation Homogeneous variance irrespective of window size and window size ROI inhomogeneity inhomogeneity. • Improved resolution will provide local variation information within the liver. Improved precision would be required to qualify as a reliable diagnostic tool. • The precise ACE estimation of thin and heterogeneous tissues shows promise Inhomogeneous for placental tissue characterization. ROI 16

Appendix: Inhomogeneity Simplified System Equation: 𝑇 = Power Spectrum term; • C:\k-WAVE\k- CIRS 040 Phantom 𝑻 = 𝑩𝑫𝑭 + 𝑪𝑻𝑫 𝐵𝐷𝐹 = ACE term; (ACE = 0.7 dB/cm/MHz) Wave\miccai\IUS\IUS 𝐶𝑇𝐷 = BSC term; Oral Total Attenuation, ACE Scattering Absorption Scatterers with different size Both RPM and TV regularization introduce Scatterers with different density large ACE error and fail to account for BSC variation at the target locations. 17