Ultra-High-Dimensional Flow Imaging (N-D Flow)
Joseph Y. Cheng1, Tao Zhang1, Marcus T. Alley1, Michael Lustig2, John M. Pauly3, and Shreyas S. Vasanawala1

1Radiology, Stanford University, Stanford, CA, United States, 2Electrical Engineering & Computer Sciences, University of California, Berkeley, CA, United States, 3Electrical Engineering, Stanford University, Stanford, CA, United States


Volumetric cardiac-resolved flow imaging (4D flow) can enable the assessment of flow, function, and anatomy from a single sequence. Here, 4D flow is extended to higher dimensional space as N-D flow. By resolving different dynamics such as respiration or contrast enhancement, more diagnostic information can be extracted for a single-sequence protocol. Furthermore, this potentially improves image quality and quantification accuracy. N-D flow is enabled by a compressed-sensing and parallel imaging based acquisition and reconstruction. The feasibility of this approach is demonstrated for pediatric imaging.


Cardiac-resolved volumetric flow imaging[1,2] (4D flow) can be extended to higher-dimensional space to yield more diagnostic information. Additionally, the ability to resolve different dynamics, such as respiration or contrast enhancement, potentially increases reconstruction accuracy compared to conventional approaches that either ignore or attempt to correct for their effects. The purpose of this work is to demonstrate the feasibility of an ultra-high-dimensional flow imaging sequence (N-D flow) for improved image accuracy and for comprehensive single-sequence exams.


Data Acquisition: A standard Cartesian 4D flow sequence (RF-spoiled GRE with velocity encoding) is modified to use VDRad[3] to produce unique pseudo-random sampling patterns for each cardiac phase and for each velocity-encoding echo. The velocity-encoding gradients are modified to monitor motion using Butterfly navigators[4]. The sequence is prescribed to run for 5–10 min. Contrast is intravenously administered either before the sequence or 1–2 min after the sequence is started (Figure 1).

Image Reconstruction: From one data acquisition, different compressed-sensing-based parallel-imaging reconstructions[5,6] are performed with the following optimization problem:

$$\textbf{m}=\arg\min_\textbf{m} \frac{1}{2}\left\|W(A\textbf{m}-\textbf{y})\right\|_2^2+\lambda_x|R_x(\textbf{m})|_1+\lambda_t|R_t(\textbf{m})|_1+\lambda_{cph}|R_{cph}(\textbf{m})|_1+\lambda_{rph}|R_{rph}(\textbf{m})|_1.$$

Matrix $$$A$$$ models the acquisition process with ESPIRiT sensitivity maps[7], Fourier transform, and subsampling. Matrix $$$A$$$ transforms the image set $$$\textbf{m}$$$ to the acquired k-space data $$$\textbf{y}$$$. For compressed sensing, regularization functions $$$R_*$$$ and regularization parameters $$$\lambda_*$$$ penalize non-sparse solutions in the spatial ($$$x$$$), temporal ($$$t$$$), cardiac-phase ($$$cph$$$), and respiratory-phase dimensions ($$$rph$$$). Here, temporal dimension refers to time over the scan (relative to contrast injection bolus). In this work, wavelet transform is used for $$$R_x$$$, and finite difference operator is used for all other dimensions. The Butterfly signal is used to determine the respiratory phase of each data point and time of contrast injection. Data are binned according to time of acquisition, respiratory phase, and cardiac phase. Diagonal matrix $$$W$$$ weighs the data according to how far the data is from the center of each bin. For non-respiratory-resolved imaging, $$$W$$$ soft-gates the data to suppress image artifacts from respiratory motion[4].

Three different reconstructions are performed:

Recon 1: Respiratory-resolved 4D flow: Cardiac-resolved volumetric flow datasets are reconstructed for each respiratory state.

Recon 2: High-resolution 4D flow: The acquisition is binned into large temporal windows in $$$t$$$, and high-resolution cardiac-resolved volumetric flow data are reconstructed.

Recon 3: Dynamic-contrast-enhancement/perfusion: For a 1­–2 min window during the contrast injection, data are binned into 2-sec temporal windows with fewer cardiac phases (≤5). All other data are binned into either the first or last temporal bin. Velocity-encoding echoes are “view-shared” as one echo.

Experimental Setup: With IRB approval and informed consent/assent, pediatric patients referred for contrast-enhanced 3T MRI were recruited and scanned in a GE MR750 scanner using a 32-channel cardiac coil array. Specific scan parameters are described in Table 1. Reconstruction was implemented using BART[8].


With the respiratory-resolved 4D flow (Recon 1), respiratory-dependent blood flow can be measured[9,10]. A decrease in net flow in the inferior vena cava and an increase in net flow in the superior vena cava can be seen when comparing expiration versus inspiration (Figure 2).

Figure 3 demonstrates the impact of contrast dynamics on flow imaging (Recon 2). When ignoring the effects of the changing contrast signal for gadolinium-based agents, more noise can be observed in the velocity data (Figure 3a). By dividing the acquisition into three temporal windows, the 4D flow dataset for each temporal window has more consistent contrast dynamics. Additionally, the optimal contrast phase can be chosen for flow analysis (Figure 3d).

In Recon 3, the contrast dynamics can be assessed as shown in Figure 4. The dataset can be analyzed to depict the contrast dynamics in important structures including left/right lung for pulmonary perfusion and myocardium for cardiac perfusion.


Ideally, the different datasets can be generated through one large reconstruction that properly shares the redundant information. However, for clinical feasibility, we perform three separate reconstructions that are relatively faster and more manageable to perform.

Better resolution of dynamics can be achieved at the cost of increasing residual aliasing artifacts due to the increase in total acceleration. For certain applications such as contrast-dynamic/perfusion analysis, this increased aliasing is tolerable.

A single sequence that can be used for flow quantification, cardiac/respiratory function analysis, anatomical assessment, and contrast-enhancement/perfusion evaluation is developed. This comprehensive sequence simplifies the MR protocol. Furthermore, by generating different reconstructions from the same data acquisition, the post-processing analysis for each feature are automatically registered to each other. Thus, there is potential to improve post-processing analysis.


A single comprehensive sequence with N-D flow imaging has been developed to improve image quality and to provide additional information (respiratory, contrast dynamics) for assessment.


NIH R01-EB009690, NIH R01-EB019241, NIH P41-EB015891, AHA 12BGIA9660006, Tashia and John Morgridge Faculty Scholars Fund, Sloan Research Fellowship, and GE Healthcare.


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FIG 1: Method overview. The data acquisition consists of a RF-spoiled GRE sequence with velocity encoding. Since the velocity-encoding gradients are repeated throughout the scan, these gradients provide the setup for intrinsic navigation using Butterfly navigators. The sampling scheme, VDRad, is synchronized with the cardiac cycle. Other dynamics during the acquisition include respiration and contrast injection.

FIG 2: Respiratory-resolved 4D flow (6 resp, 20 cardiac phases) of a 3-yr-old female with right aortic arch. a: Net flow measured for superior vena cava (SVC), inferior vena cava (IVC), and main pulmonary artery (PA). b: Flow for each respiratory phase. c: Short-axis reformats of diastole and systole for expiration and inspiration. d: Coronal surface renderings with velocity vectors. From expiration to inspiration, increase flow in IVC and decrease in SVC agrees with previous literature[9].

FIG 3: High-resolution 4D flow of a 3-year-old female with the administration of gadofosveset. In a, the 4D flow (20 cardiac phases) was reconstructed as one temporal window. In bc, the 6-min dataset was binned into three temporal bins (~2 min each), and 4D flow dataset was reconstructed for each bin. All reconstructions are displayed as surface renderings with velocity overlay. Decrease in noise in the velocity can be appreciated in c.

FIG 4: Dynamic-contrast-enhancement/perfusion reconstruction with 4D flow of a 2-year-old male with the administration of gadobutrol. Contrast dynamics (2-sec temporal resolution) of specific tissues are depicted in a with the corresponding ROI drawn in b. The same dataset can also be reconstructed to depict flow information as rendered and visualized in c.

TABLE 1: Scan parameters.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)