Qp/Qs ratio
Earlier studies used the more clinically oriented Qp/Qs ratio, because this value is expected to be around 1.05 in patients not suspected of shunts [
3,
6,
19]. While Qp/Qs was not the initial setup of this study, we further assessed its value in an subset. We did not detect a significant change in Qp/Qs with correction, probably due to low numbers, but the variance over the subjects was significantly decreased after interpolation-based correction (
p = 0.01). Rigsby et al. also found inconclusive results for change in the Qp/Qs ratio in a single-center study with a similar interpolation-based offset correction [
19], but found improvement by correction in comparing the main pulmonary artery flow with the combined flow in the left and right pulmonary arteries [
19]. This might be explained by the system and protocol dependence of velocity offset errors, in that using a specific protocol on a specific system offsets are sometimes small, as can be seen in our results for system 4. Also Meierhofen et al. used the Qp/Qs ratio in 24 subjects in a single center study and concluded that, according to a normal ratio range of 0.9–1.2 that more patients without shunts incorrectly showed a calculated shunt after phantom-based correction [
12]. Applying that same normal range in our study, we saw that interpolation-based correction removed incorrect shunts in 6 cases, and created in 2 cases a shunt (which we have not checked), and therefore improved the overall results.
Spatial order of interpolation
In this study we examined the order of spatial interpolation of the offset fit to the mask pixels to the rest of the image including pertinently the location of the vessel of interest. The initial implementation of Walker et al. [
8] applied a linear interpolation. Others have claimed later that higher spatial orders of interpolation should be applied [
9,
15,
16]. Lankhaar et al. tested higher interpolation order for the pulmonary artery in a single center study, and found that errors increased for higher order fits [
14]. In this study we also found that for 5 out of 6 CMR systems the RMS velocity error across all scans increased for 2nd order fitting compared to linear fitting. It is not that the velocity offset field per se is completely linear for systems 1–5, for in several patient studies these systems also showed offset fields with components of 2nd and 3rd order spatial variations. However, by making the interpolation-based correction operate at higher order instead of linear, the interpolation method became more sensitive to any other variation of the velocity error across the image FOV, resulting in greater variability over the group of studies as a whole. Among other factors, for higher-order fitting the error sensitivity increases to noise in the image, errors in the stationary mask, and small amounts of missed spatial wrap around. Giese et al. observed in phantom measurements that the largest component was linear and that 2nd order correction contributed much less [
9]. Only for system 6 in our results (GE), linear interpolation increased the error and the clearly more effective 2nd order interpolation was applied in the final cardiac output results. A similar GE system 5 in our results showed also a slightly smaller RMS error by 3rd order interpolation, but we did not apply this to the cardiac output assessment because 3rd order interpolation makes the technique too sensitive to other errors in this setting. An earlier study on a GE system also included higher order terms in its correction algorithm [
16]. A possible explanation may be imperfections in the Maxwell term correction, as those show primarily 2nd order spatial variations. Thus the interpolation-based offset correction method would require finally some tuning depending on the CMR system it is applied to, but this is probably a system/software specific property that can be more generally assessed.
Finally, these conclusions are for the aorta and main pulmonary artery, which usually are situated reasonably near the center of the FOV, and for every measurement the patient table was adjusted to place the FOV center in the z = 0 plane. To reduce offsets it would be better to put the vessel of interest at the z = 0 plane. However, this would require user input and manufacturers did not implement this. Placing the vessel of interest at the FOV center is not desirable, as this will induce spatial wraparound or requires a large FOV. Placing the FOV center in the z = 0 plane can be easily implemented in the regular workflow. For vessels further away from the center higher order corrections might be required. This is also the situation for velocity quantification in 4D Flow [
20]; velocity quantification in this application includes vessels further away from the isocenter. The 3D slab of images includes more stationary tissue and spatial information so this application may benefit from higher order spatial interpolation depending on the specific system [
5,
20,
21], but is outside the scope of the present study. Busch et al. published a recent study on this [
17].
Limitations
A limitation of the interpolation-based offset correction is that it is sensitive to phase-encode FOV wraparound (spatial aliasing). Ideally this should be prevented in scanning, but this is quite a stringent limitation and tends to increase breath-hold time, unless other sequence parameters are adjusted, with all their consequences. If phase-encode wraparound does not reach as far as overlapping the direct image, or overlaps only small regions, it can be excluded manually before correction. However, any such dependence on intervention can be an obstacle to reliable clinical use. For some protocols it can be helpful to increase the phase-encoding FOV using parallel imaging [
22], because it can be difficult to sufficiently control phase-encode aliasing, especially for the typical oblique angulation of the cross-section of the pulmonary artery.
A second protocol optimization specific for this interpolation-based correction is to ensure that the posterior RF receiver coils are switched on, even in cases where the vessel of interest, such as the main pulmonary artery is in the anterior part of the thorax. The posterior coils are not of interest for the SNR at the level of the vessel, but they are essential to provide sufficient SNR for the CMR signal of the stationary tissue on the posterior side of the thorax.
In this study we considered only 1.5 T whole body superconducting CMR systems. Most CMR studies are still performed at this type of CMR system. However, there is an increased application of 3 T for CMR. The origin of the velocity offset is within the gradient system and its associated errors, and the overall specification of these does not change at 3 T (because it is already close to the limit of nerve stimulation), except that Maxwell terms are smaller, so any imperfections in their software correction might be expected to reduce as well. Therefore, we expect that these results should also be valid at 3 T CMR systems. However, another aspect in which these systems might deviate physically from 1.5 T is mechanical vibration, as the mechanical force for the same gradient performance scales with main field strength. A recent small single-center study at 3 T found similar results as this study considering Qp/Qs ratios [
23].
Care should be taken not to interpret the specific offsets found in this study as definitely linked to particular vendor models of CMR systems. In this study we used on purpose as much as possible each site’s customary CMR protocols, thus specific settings such as breath-holding, typical slice orientation and measurement location at the vessel of interest would be likely to give a strong bias on the velocity offset observed using the different CMR systems [
11]. The absence of any rigorous set of scanning parameters means that this study cannot be applied to compare velocity offsets between CMR systems and such comparison was not part of the study design.
Notwithstanding the above, we noticed incidentally that the two Philips CMR systems (1,2) in this study showed a relatively high uncorrected velocity offset. Besides the issue of the protocol differences between sites as mentioned before, one should realize that some systems may apply in their default protocols a background phase-offset correction filter. On Philips machines this is known as the ‘LPC filter’, developed to reduce the phase offset in CMR contrast angiography, where it is expected to reduce the velocity offset [
24]. On the other hand, there is no published validation study for the application of this filter for vessels around the heart. The applied filter kernel is expected to be influenced to some unknown extent by the presence of sufficient non-stationary tissues around the vessel of interest. Due to the principles of the interpolation-based offset correction and the ‘LPC filter’, a combination of applying the LPC filter before the interpolation-based correction is not useful to test. Therefore, we switched the ‘LPC filter’ off on Philips systems.
Retrospective ECG gating was used in this study. In case of unstable heart rhythms, prospective ECG gating shows clinically more reliable measurements. In the case of prospective ECG gating it has been shown that the amount of velocity offset varies with the timing after the sequence starts running in each cardiac cycle, and tends to be larger directly after the ECG trigger [
9]. The interpolation-based offset correction should then be implemented per cardiac phase, instead of the time-averaged offset value as in this study. Giese et al., implemented this using linear correction, but did not report good results [
9]. This might need additional validation as the variation per phase after sequence start is highly complex dependent on incomplete sequence spoiling [
25]. However, this is solved on newer systems as prospective ECG gating keeps on running the sequence continuously while watching the ECG. At some centres it was not possible to set a simulated ECG to the patient heart-rate and sometimes 60 bpm was used. Because of the use of retrospective cine gating, we do not expect the difference in heart rate to cause any change in the velocity offset, between the in-vivo measurement and the phantom measurement.
In this study, the velocity offset was assessed at the vessel position in the first cardiac phase. In reality the vessel position varies somewhat over the cardiac phases. This effect was neglected, but the phantom data show that the spatial variation of the offset in this motion range is limited.
The ‘phantom measurement accuracy check’ was performed with a relatively small ROI. Ideally, we would perform this check on the total mask of stationary tissue. However, this would require a stationary phantom of the size of a large adult thorax at all centers. Because of practical reasons, we were compelled to use a smaller phantom allowing only the vessel and a part of the anterior thorax wall to be covered by the phantom. Instead of the phantom, the possibility of some form of “internal validation”, for example using LV stroke volume from cine stack, or by Qp/Qs, was limited by requiring definitely normal subjects, by other well-known sources of inaccuracy and also by having no permission to make any extra patient acquisitions for this unfunded work.
The study protocol was open on the use of breath-hold or non-breath-hold techniques, as well as the precise acquisition parameters and method of positioning the measurement plane in the two vessels. Every site applied the technique in their own regular manner (this was necessary for recruitment at all without funding). Therefore, this study shows a realistic variability of protocol settings, but of course this might have introduced also variations between the different sites and systems. We emphasise that the acquisition parameters were checked as identical for each in-vivo scan and its phantom scan, so controllable differences there were not a source.
Even in nominally breath-hold scans, phase-encode ghosting artefacts of the bright superficial tissues (especially fat) are often problematic, and furthermore might sometimes be relatively constant over the cardiac cycle (depending on a few factors not to go into here), and so the impact of artefacts on chest wall phase might get past the temporal variance test of the interpolation-based correction method (which aims to exclude flow ghosting as described in Methods). It is uncertain whether this corrupting effect is usually small (because the subtracted reference and velocity-encoded scans are normally almost simultaneous in terms of the respiratory motion) compared to the true pixel brightness at the wall, and is of some possible concern (as are other variations [
25]) because the background offset we seek to correct is also often small.
Finally, the subset of Qp/Qs studies was acquired at many different centres where the placement of the aortic plane might have varied relative to the coronary ostia, that can require a few % correction in the ‘normal’ Qp/Qs value.