Blood Velocity Measurement by RF Phase Gradient Differences between Receiver Coils: Initial Work towards Stenotic Jet Velocity
Jonathan Wagner1, Peter David Gatehouse2, and David Nigel Firmin2

1Imperial College, London, United Kingdom, 2Cardiac MRI, Royal Brompton Hospital, London, United Kingdom


Fluid velocity was measured in vitro using the difference between spatial phase responses of array coils in 1993 by Famili, Wright and Porter. Aiming at application to cardiovascular stenotic jets, this abstract re-investigates their method with newer coil arrays and adds a multi-echo approach enabling aortic velocity measurement in normal subjects, with moderate results.


Cardiovascular stenoses are sometimes assessed by "jet" velocity indicative of clinically relevant systolic pressure overload1-3. Doppler ultrasound is useful clinically but acoustic access is sometimes limited, when phase-contrast MRI4 may assist, under well-described limitations in jets5-9. Another MRI velocity measurement method was demonstrated in vitro10 using phase differences between multiple RF coils. The method needs only fully velocity-rephased imaging and is fundamentally increasingly responsive to faster velocities. This abstract re-investigates the 1993 work10 using modern arrays hypothesised to improve performance, adding a multi-echo approach enabling application to aortic valves and first in vivo demonstration.


The phase detected by a receiver coil channel contains three terms: φu = spatially-uniform phase shift from electronics and processing of that channel. φIoc = spatially-dependent phase sensitivity of its coil11,12. φc = the precession phase at a given location, including errors like Maxwell terms, imperfect eddy-current correction, transmit B1 phase, gradient motion sensitivity. The precession phase is the same for all channels so it is eliminated by phase-image subtraction between channels. The phase difference between two channels contains two terms: uniform delta φu and spatially-dependent delta φIoc by which this method localizes the received signal. First, delta φu requires elimination by "flow off" reference or multi-echo approach. Velocity measurement requires accurate knowledge of delta φIoc (i.e. the spatially-dependent phase difference) profile along the flow (PAF) using in-plane imaging under strong magnitude responses for the coils (Figure 1). The velocity measurement itself is imaged transverse to the flow to minimise partial-volume and obtain spatial phase difference (SPD) images (between flow on/off or multiecho) (Figure 2) giving (via the PAF) the time-of-flight (TOF) displacement and (via TE or delta TE) the velocity10.


Phantom tests in a straight 15mm OD tube compared steady velocities up to 4.27m/s against phase-contrast. Spoiled gradient-echo (SGE) imaging obtained the PAF along the tube (TE 5.23ms, TR 100ms, FA 20deg, 4 averages). Flow on/off SGE single-echo SPD imaging (10) was obtained, but (see below) was flawed in vivo; only multiecho (ME) imaging is presented. ME SPD scans acquired each velocity at TE=[3.15,7.07,10.99ms] and phase images gave velocity using PAF and TOF for 3 echo pairs, i.e. 3 measurements per scan. Mean tube velocity was taken over the central 70% by diameter.

Four normal subjects were scanned supine with anterior mid-sagittal linear array, adjusting using separate coil images to ensure a pair of coils gave strong magnitude in the left-ventricular outflow tract (LVOT). Phase-contrast cines were the comparison standard.

The PAF was acquired through the valve (Figure 3) using turbo-SGE (16 cycle breathhold TE=3.2ms TR=88.2ms, FA 20deg. 1 average, 8 rawdata lines per cycle). Single-echo SPD was not evaluated in-vivo because it requires diastolic repetition assuming zero flow, further confounded by inplane LVOT movement from systole. Cross-sectional SPD valve slices were acquired using the following three ME sequences. Breathholds (BH) were 16 cycles and free-breathing (FB) scans approximately 2 minutes. To estimate intra-session reproducibility, each method was repeated as shown below, with phase-contrast BH cines for comparison.

1. Multi-echo BH single peak systolic image (timed from PC velocity cine) x 4. TE=[2.81,6.49,10.17ms], TR=47ms, FA 20deg, NEX 1, FOV 300x225mm(FExPE)

2. Multi-echo BH cine x 4. TE=[3.01,6.69,10.37ms], TR=54ms, FA 20deg, NEX 1, FOV 360x214mm(FExPE)

3. Multi-echo FB cine x 2. TE=[3.01,6.69,10.37ms], TR=54ms, FA 20deg, NEX 4, FOV 360x214mm(FExPE)


Phantom results are plotted in Figure 4. For volunteers 1-4, the 3 methods above gave peak velocities (1.04, 1.42, 0.97, 1.14), (1.37, 1.41, 1.13, 1.03), (1.20, 1.55, 0.99, 0.93) m/s (first echo pair) against phase-contrast (1.21, 1.12, 1.17, 1.03)m/s. Figure 5 shows cine temporal waveforms.


The phantom gave close agreement over the tested velocity range. The normal subject aortic results showed scatter by limited TOF leverage on the PAF, which might improve for higher jet velocities, because only fully velocity compensated imaging is needed unlike phase-contrast; to some unknown extent, this may overcome the obvious dilemma between TE and TOF on PAF leverage. A smaller delta-TE may be sufficient for fast jet velocities. The major limitation was coil positioning for a coil pair to sense the jet; here a linear array was tested because of unsolved difficulties with 2D cardiac arrays. Attention to locating SPD data along the PAF profile was essential but operator-independent after correct programming. Unidentified phase shifts at desirable shorter echo times obstructed ME, perhaps transient after coil-decoupling.


In vivo results by multi-echo SPD at normal aortic velocities were moderate but might even improve in aortic stenoses. Coil responses complicate array placement on a patient and might rule out routine SPD.


We acknowledge the support of the Royal Brompton Hospital


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Theory: Illustration of the spatially-dependent intercoil phase difference profile along the flow (PAF). Tube horizontally across each image. A, B = separate magnitude images of coils 1 and 2 sensing the tube. C, D = phase images from coils 1 and 2 respectively. E = the phase difference between coils 1 and 2. F = Profile along the flow (PAF).

Theory: Illustration of how the inter-coil difference in spatial phase profile along the flow (PAF) is used in combination with time-of-flight effects on the coils' received phases in order to derive the velocity.

Aortic velocity measurement: From image A, the PAF is acquired along the yellow rectangle along the LVOT crossing the orange dotted line which represents the location of the cross-sectional velocity measurement SPD scan (example SPD magnitude image in B with blue ROI on aorta). The PAF is plotted in C.

Multi-echo SPD sequence flow phantom comparison against phase-contrast. The plots in A,B,C compare pairs of echoes ( E1 3.15ms, E2 7.07ms, E3 10.99ms) against the phase-contrast velocity. Plot D compares all three ME pairs against the (black line) single-echo flow on:off method of reference 10. The dotted blue is the line of identity.

Multi-echo sequence aortic valve cardiac cycle velocity waveforms. The four graphs in each column are the four volunteers. Left column: breath hold cine which was measured 4 times plotted as 4 cycles across each volunteer's plot. Right column: free breathing cine which was measured twice for each volunteer. Further, every plot shows three curves of the different echo time pairs: blue for (TE1,TE2); red for (TE1,TE3); and yellow (TE2,TE3). Systematic error occurred between the 3 pairs in most scans and a significant baseline error affects low velocities.

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)