TY - JOUR

T1 - Improved acceleration of phase-contrast flow imaging with magnitude difference regularization

AU - Shin, Taehoon

AU - Shin, Wanyong

N1 - Funding Information:
This work has been supported by NRF - 2019R1F1A1058872 and NIH R01 HL135500 . Appendix A Let R MD denotes the regularization of the magnitude difference among the images obtained using j th bipolar gradient. (A1) R MD = ∑ j = 1 N v m j − m j + 1 2 2 The k th pixel of m ( j ) can be written as (A2) m k j = m k j e j ϕ k j where ϕ k ( j ) is the phase of m k ( j ) . Then the partial derivative of R MD with respective to m k ( j ) is written as (A3) ∂ R MD ∂ m k j = 2 m j − m j + 1 e j ϕ k j When m denotes a column vector where all m ( j ) are concatenated, i.e. (A4) m = m 1 m 2 ⋮ m N v The gradient of R MD with respect to m can be written as (A5) ∇ m R MD = 2 Φ H Τ H ΤΦ m Φ is a block diagonal matrix defined as (A6) Φ = Φ 1 Φ 2 ⋱ Φ N v where Φ j = e j ϕ 1 j 0 ⋯ 0 0 e j ϕ 2 j 0 ⋮ ⋱ 0 0 e j ϕ N j Τ is a block two-band matrix defined as (A7) Τ = Τ − 1 Τ 1 Τ − 1 Τ 1 ⋱ Ο where Τ − 1 = − 1 0 ⋯ 0 0 − 1 0 ⋮ ⋱ 0 0 − 1 and Τ 1 = 1 0 ⋯ 0 0 1 0 ⋮ ⋱ 0 0 1
Funding Information:
This work has been supported by NRF-2019R1F1A1058872 and NIH R01 HL135500.
Publisher Copyright:
© 2019 Elsevier Inc.

PY - 2020/4

Y1 - 2020/4

N2 - Purpose: To develop a regularized image reconstruction algorithm for improved scan acceleration of phase-contrast (PC) flow MRI. Methods: Based on the magnitude similarity between bipolar-encoded k-space data, magnitude-difference regularization was incorporated into the conventional compressed sensing (CS) reconstruction. The gradient of the magnitude regularization was derived so the reconstruction problem can be solved using non-linear conjugate gradient with backtracking line search. Phase contrast flow data obtained in the peripheral arteries of healthy and patient subjects were retrospectively undersampled for testing the proposed reconstruction method. Three-dimensional velocity-encoded PC flow MRI was performed with prospective 4-fold undersampling for measuring arotic flow velocity in a healthy volunteer. Results: In the femoral arteries of healthy volunteers, the root-mean-square (RMS) errors of mean velocities were 0.56 ± 0.09 cm/s with CS-only reconstruction and 0.46 ± 0.08 cm/s with addition of magnitude regularization for three-fold acceleration; 1.34 ± 0.17 cm/s (CS only) and 1.08 ± 0.15 cm/s (magnitude regularized) for four-fold acceleration. In the iliac arteries of the patient, the RMS errors of mean velocities were 0.72 ± 0.12 cm/s and 0.56 ± 0.10 for three-fold acceleration, and 1.75 ± 0.21 and 1.24 ± 0.19 cm/s for four-fold acceleration (in the order of CS-only and magnitude regularized reconstructions). In the popliteal arteries, the RMS errors were 0.61 ± 0.10 cm/s and 0.42 ± 0.11 for three-fold acceleration, and 1.41 ± 0.19 and 1.12 ± 0.17 cm/s for four-fold acceleration. The maximum through-plane mean flow velocities were measured as 63.2 cm/s and 84.5 cm/s in ascending and descending aortas, respectively. Conclusion: The addition of magnitude-difference regularization into conventional CS reconstruction improves the accuracy of image reconstruction using highly undersampled phase-contrast flow MR data.

AB - Purpose: To develop a regularized image reconstruction algorithm for improved scan acceleration of phase-contrast (PC) flow MRI. Methods: Based on the magnitude similarity between bipolar-encoded k-space data, magnitude-difference regularization was incorporated into the conventional compressed sensing (CS) reconstruction. The gradient of the magnitude regularization was derived so the reconstruction problem can be solved using non-linear conjugate gradient with backtracking line search. Phase contrast flow data obtained in the peripheral arteries of healthy and patient subjects were retrospectively undersampled for testing the proposed reconstruction method. Three-dimensional velocity-encoded PC flow MRI was performed with prospective 4-fold undersampling for measuring arotic flow velocity in a healthy volunteer. Results: In the femoral arteries of healthy volunteers, the root-mean-square (RMS) errors of mean velocities were 0.56 ± 0.09 cm/s with CS-only reconstruction and 0.46 ± 0.08 cm/s with addition of magnitude regularization for three-fold acceleration; 1.34 ± 0.17 cm/s (CS only) and 1.08 ± 0.15 cm/s (magnitude regularized) for four-fold acceleration. In the iliac arteries of the patient, the RMS errors of mean velocities were 0.72 ± 0.12 cm/s and 0.56 ± 0.10 for three-fold acceleration, and 1.75 ± 0.21 and 1.24 ± 0.19 cm/s for four-fold acceleration (in the order of CS-only and magnitude regularized reconstructions). In the popliteal arteries, the RMS errors were 0.61 ± 0.10 cm/s and 0.42 ± 0.11 for three-fold acceleration, and 1.41 ± 0.19 and 1.12 ± 0.17 cm/s for four-fold acceleration. The maximum through-plane mean flow velocities were measured as 63.2 cm/s and 84.5 cm/s in ascending and descending aortas, respectively. Conclusion: The addition of magnitude-difference regularization into conventional CS reconstruction improves the accuracy of image reconstruction using highly undersampled phase-contrast flow MR data.

KW - Iterative image reconstruction

KW - Phase-contrast flow imaging

KW - Regularization

KW - Scan acceleration

UR - http://www.scopus.com/inward/record.url?scp=85075997976&partnerID=8YFLogxK

U2 - 10.1016/j.mri.2019.12.001

DO - 10.1016/j.mri.2019.12.001

M3 - Article

C2 - 31805336

AN - SCOPUS:85075997976

SN - 0730-725X

VL - 67

SP - 1

EP - 6

JO - Magnetic Resonance Imaging

JF - Magnetic Resonance Imaging

ER -