From 2D to 4D Flow Image Acquisition

Flow imaging with MRI is based on the phase contrast (PC) technique, which enables the acquisition of spatially registered information on blood flow velocities simultaneously with morphological data within a single MRI measurement. In current clinical routine, PC-MRI is typically accomplished using methods that resolve two spatial dimensions (2D) in individual slices and encode a single time-resolved component of velocity directed perpendicularly to the 2D slice (through-plane velocity encoding). This approach allows measurements of forward, regurgitant, and shunt flows in congenital and acquired heart disease. In MRI, magnetic field gradient coils can create linearly varying magnetic fields along all three spatial dimensions on top of the main (static) magnetic field B₀. These magnetic field gradients cause spatially varying phase shifts of the source of the MRI signal (¹H proton spins in the human body) depending on the location of the source along the gradient. Spins that move along the direction of the gradient, e.g., flowing blood, acquire a different phase shift than the spins in adjacent static tissue [14].

The phase shift of the static media can be nulled by applying a magnetic field gradient with opposite polarity, whereas a phase shift for the moving spins will accumulate. The combination of both gradients is called a bipolar gradient [4] (see Fig. 16.1).

Using appropriate bipolar velocity encoding gradients, flow-dependent phase changes can be measured by playing out two acquisitions with different velocity dependent signal phase but otherwise identical sequence parameters. Subtraction of the two resulting phase images (i.e., calculation of phase difference images) allows for the removal of the unknown background phase and calculation of velocity images [9].

With a bipolar gradient applied to the main direction of the blood flow, single-direction (e.g., through-plane) blood flow velocity is measured. Bipolar gradients can also be subsequently applied to two or three orthogonal axes to resolved blood flow velocities in two or three dimensions [15, 16].

To measure temporally resolved pulsatile blood flow velocities, a time-resolved (CINE) measurement can be performed [17, 18]. As illustrated in Fig. 16.2, PC-MRI data acquisition is split over multiple heartbeats, and data acquisition is gated to the cardiac cycle using the ECG signal (e.g., the R-wave) or a pulse oximeter reading. A series of time-resolved (CINE) images is collected representing the dynamics of the pulsatile blood flow during the cardiac cycle. Usually, one-directional (“through-plane”) velocity encoding along the predominant blood flow direction is used to quantify blood flow in the heart, through cardiac valves, and in arteries and veins throughout the body. Typical 2D CINE PC-MRI images are illustrated in Fig. 16.2.

For over three decades, 2D CINE PC-MRI has been widely used for flow quantification in the aorta [19], the carotid arteries [20] and the intracranial vessels [21]. For routinely used 2D CINE PC-MRI, a slice for a 2D measurement is manually positioned perpendicular to a vessel, and blood flow velocity is encoded in one direction through the 2D slice. However, placement of the acquisition plane remains challenging and can lead to the underestimation of peak velocities if misplaced or not orthogonal to the flow of interest. This is a common occurrence in cases involving complex flow and where changes in flow direction occur throughout the cardiac cycle, such as with valvular stenosis, valvular regurgitation, complex congenital heart disease, or aneurysms. These challenges can be addressed by three-dimensional (3D) PC-MRI with three-directional velocity encoding which can provide comprehensive information on the in vivo 3D blood flow dynamics with full volumetric coverage of the vascular region of interest. Wigström et al. were the first to implement a high spatial resolution and electrocardiogram (ECG)-gated 3D cine phase contrast pulse sequence, currently known as 4D flow MRI (4D = 3D+ time over the cardiac cycle, flow = three-directional velocity encoding) [22].

Data Acquisition

In 4D flow MRI, velocity is encoded along all three spatial dimensions throughout the cardiac cycle, thus providing a time-resolved 3D velocity field [8, 23, 24]. As shown in Fig. 16.3a, three-directional velocity measurements can be achieved by interleaved four-point velocity encoding which acquires one reference image and three velocity-encoded images along three orthogonal (x, y, z) directions [25–27]. As for 2D CINE PC-MRI, data acquisition is synchronized with the cardiac cycle, and data collection is distributed over multiple cardiac cycles using “k-space segmentation” techniques (only a fraction of the entire 4D flow data is measured during each cardiac cycle; the data is successively collected over multiple RR intervals). For prospective ECG gating, where the acquisition starts after receiving the R signal of the QRS complex, some dead time toward the next R-wave should be reserved to account for heartbeat variations. The late portion of diastole is therefore not measured [17]. With retrospective gating, continuous acquisition is not synchronized to the heartbeat. Each k-space line is time-stamped and retrospectively interpolated to fixed time frames in the cardiac cycle, thereby enabling acquisition of the diastolic phases. After completion of the 4D flow acquisition, four time-resolved (CINE) 3D data sets are generated (“magnitude” data depicting anatomy and three flow data sets representing velocities “V_x, V_y, and V_z”) as illustrated in Fig. 16.3b.

It should be noted that increasing 4D flow spatial resolution by reducing voxel size is possible but is accompanied by a decrease in signal-to-noise ratio (SNR) and thus image quality. Moreover, for volumetric acquisitions such as 4D flow MRI, scan times increase cubically with isotropic voxel size reduction.

An important (user-defined) 4D flow MRI parameter is the velocity encoding sensitivity (VENC), which represents the maximum flow velocity that can be acquired without velocity aliasing. When a velocity in a voxel exceeds VENC, velocity aliasing can occur which is typically visible as a sudden change from high to low velocity within a region of flow (see Fig. 16.4). If aliasing artifacts are present, accurate flow visualization and quantification may be compromised unless antialiasing correction can be successfully performed [28]. It is important to note, however, that velocity noise is directly related to the VENC [8]. Therefore, selecting a high VENC may alleviate the issue of velocity aliasing but will also increase the level of velocity noise in flow velocity images. VENC should thus be chosen as close to the peak velocity as possible. This is often accomplished by performing a fast low-resolution 2D PC-MRI “VENC scout” scan prior to 4D flow MRI to estimate the highest velocity in the vessel of interest and adjust VENC accordingly.

In Fig. 16.4, the principle of VENC is shown for through-plane 2D phase difference images of the aorta with severe velocity aliasing when the VENC is selected too low (high bipolar gradient). Unaliased flow velocities are achieved when the VENC is tailored to the expected maximum velocity (lower bipolar gradient).

Data Acquisitions: Imaging Acceleration Techniques

Long scan times on the order of 10–20 minutes have previously relegated 4D flower MRI to the realm of research. However, current implementations are quickly approaching clinically feasible scan times, on the order of 2–8 minutes. Methodological improvements include echo planar imaging (EPI), where multiple Cartesian readouts are acquired after one excitation to obtain high spatial resolution [29]. Additional imaging acceptation is based on parole imaging such as sensitivity encoding (SENSE) [30, 31], generalized autocalibrating partially parallel acquisitions (GRAPPA) [32], k-t acquisition speed-up techniques (k-t BLAST) [33, 34], k-t GRAPPA [35], k-t principal component analysis (k-t PCA) [36, 37], and CIRCUS [38]. Another promising technique to accelerate 4D flow MRI is compressed sensing where data is acquired in a sparse and random manner followed by nonlinear recovery of data [39, 40]. For example, aortic 4D flow MRI is now possible with a scan time of less than 2 minutes without substantial degradation of image quality [41].

Data Acquisitions: Non-Cartesian Sampling

An alternative technique that is increasingly used to accelerate 4D flow MRI is radial data sampling combined with undersampling (e.g., PC-VIPR – vastly undersampled isotropic projection reconstruction [42]). Radial sampling has two important advantages over Cartesian readouts: (1) sparse sampling results in streak image instead of fold-over artifacts which allows for higher undersampling factors [42] and (2) the center of k-space is continuously sampled and results in insensitivity to subject motion [43]. As an alternative, spiral k-space sampling can cover the entire k-space uniformly and rapidly [44], allowing for rapid 4D flow MRI velocity measurements [45–47]. However, both radial and spiral sampling are sensitive to eddy current effects which require efficient correction strategies, and image reconstruction is more computationally demanding. Alternatively, radial- and spiral -like trajectories can be implemented on a Cartesian grid, called pseudo-radial and pseudo-spiral trajectories [48, 49]. For example, a recently reported combination of pseudo-Cartesian acquisition schemes coupled with compressed sensing for imaging acceleration has shown great potential for fast and robust pediatric 4D flow MRI [50].

Data Acquisitions: Respiratory Control (Gating, Self-Gating)

For cardiothoracic and abdominal applications, methods for respiration control are needed to prevent image deterioration due to respiratory motion. Early efforts in MRI have focused on gating of the respiratory signal using bellows [51] or navigator echoes in a longitudinal beam placed on the diaphragm [52]. Most methods are based on accepting data in the expiration phase when chest motion is minimal and rejecting data acquired in the inspiration phase when the chest is moving. Other strategies minimize respiration-related image degradation by respiratory ordered phase encoding (ROPE): measurements at inspiration are attributed to the center of k-space, whereas the measurements at expiration are attributed to the edges of k-space [53]. Such strategies have been successfully implemented for 4D flow MRI [54] in combination with navigator gating [55]. Other promising approaches employ self-gating techniques, e.g., cross-correlation with reference breathing motion to identify different respiratory phases [56] or extracting respiratory and cardiac motion signals from additional and repeatedly sampled central k-space data [57].

Preprocessing and Phase Offset Error Corrections

4D flow MRI data are affected by systematic velocity encoding errors caused by magnetic field inhomogeneity, concomitant magnetic fields (Maxwell terms) [58], and eddy currents [59, 60]. Correction of these errors typically includes the identification of image regions that contain static tissue in order to estimate the spatial distribution of background phase offsets (using a first- or second-order fit to the static tissue phase difference data) [61]. Background phase errors can subsequently be removed by subtraction of the estimated offset from the entire velocity data [62].

It is common in 4D flow MRI that the VENC setting is lower than the maximum velocity in the measurement and that velocity aliasing occurs. With the assumption that adjacent pixel velocities in the temporal or slice direction should not differ more than VENC [28], aliased velocities can be automatically detected and corrected [63].

Visualization and Quantification of 4D Flow MRI Hemodynamics

For effective visualization of the information encoded in the large 4D flow MRI data sets (see Fig. 16.3b), many methods have been developed and include velocity vector display in three-dimensional space [64, 65] streamlines [66, 67], and path lines/particle traces [67].

Figure 16.3c illustrates 4D flow MRI-based evaluation of fundamental (flow, peak velocity) and advanced hemodynamic metrics (wall shear stress, WSS) based on a single acquisition. Visualization of the vascular geometry can be achieved from a 4D flow acquisition by generating a non-contrast 3D PC-MR angiogram (MRA). A surface rendering of the vascular structure of interest (see Fig. 16.3c, left) allows for regional orientation, analysis, and flow visualization. For qualitative visualization of 4D flow MRI data, 3D streamlines or time-resolved 3D path lines can be used for flow pattern visualization. Streamlines represent the instantaneous blood flow vector field for a single cardiac time-frame. For example, Fig. 16.3c illustrates the use of systolic 3D streamlines to visualize the spatial distribution and orientation of blood flow velocities. Color-coding by velocity magnitude facilitates the visual identification of regions with high systolic flow velocities. For visualization of the temporal evolution of 3D blood flow, time-resolved path lines are the method of choice. Time-resolved path lines are best viewed and displayed dynamically (movie mode) to fully appreciate the dynamic information and changes in blood flow over the cardiac cycle. It is important to differentiate between streamlines and path lines since the former represents the instantaneous tangent to the velocity vector at a given time in the cardiac cycle (e.g., peak systole), while the latter resemble traces of the dynamically time-varying blood flow over the cardiac cycle. 4D flow MRI can also be used to derive volumetric and maximum intensity projections (MIPs) of peak velocity for easy volumetric identification of peak flow velocities (see Fig. 16.3c).

For quantification of flow in a vessel, 2D analysis planes can be placed at any location along the vessel of interest (Fig. 16.3c) to calculate peak and mean velocities, total flow, net flow, or retrograde flow. Figure 16.5a illustrates aortic 4D flow MRI with subsequent 3D flow visualization (path lines) and flow quantification in six 2D analysis planes distributed along the thoracic aorta. Figure 16.5b depicts an example of comprehensive cerebrovascular 4D flow with 3D blood flow visualization in the large intracranial arteries and quantification of flow-time curves at all major circle of Willis arteries.

Advanced Hemodynamic Vessel Wall Metrics

In addition to 3D blood flow visualization and planar flow quantification, 4D flow MRI offers the opportunity to derive advanced hemodynamic measures such as vorticity [69, 70] and helicity [71, 72], wall shear stress (WSS) [73, 74], pressure gradients [75, 76], viscous energy loss [77, 78], turbulent kinetic energy [79, 80], or pulse wave velocity (PWV) [81, 82]. This article will focus on the two parameters most relevant for vascular wall characterization: PWV and WSS.

Pulse Wave Velocity

It is well understood that arterial vascular stiffening (i.e., reduction of vessel wall elasticity) can lead to atherosclerosis and the development of vessel wall abnormalities and atherosclerotic plaques. Pulse wave velocity (PWV), the best known surrogate measure for arterial stiffness, is the speed of the pulsatile pressure wave that propagates along arteries in a heartbeat [83–85]. PWV is determined by the elastic modulus of the vessel, the vessel wall thickness, the vessel radius, and the density of blood (Moens-Korteweg equation) [85]. Thus, increased PWV is directly associated increased elastic modulus (i.e., stiffening) and vessel wall thickness. Both processes occur in early atherosclerosis, and PWV is thus considered an important indicator for the onset of this disease. A meta-analysis revealed that increased PWV and thus reduced aortic compliance is a strong predictor of future cardiovascular events and all-cause mortality. Moreover, an increase in aortic PWV by 1 m/s corresponded to an age-, sex-, and risk factor-adjusted risk increase of ca. 15% in total cardiovascular events [86]. Reliable measurement of PWV is thus of high interest, e.g., for monitoring vessel compliance during therapy [87, 88].

Carotid-femoral PWV using tonometry is the current reference standard to measure aortic compliance [89]. This method, however, is prone to errors and does not focus on regional compliance. Time-resolved 2D CINE PC -MRI provides a noninvasive estimate of PWV based on flow waveform measurements in analysis planes and allows focusing on the region of interest in patients, e.g., the thoracic aorta or carotid arteries [90–92]. Transit-time (TT) methods are typically employed to calculate temporal differences of specific flow waveforms features, e.g., timing differences of the foot of the waveform between two locations with known distance, as first described in 1989 for the aortic arch [93]. The accuracy of PWV quantification can be improved by adding velocity encoding directions [81] or using multiple measurement locations [94, 95].

PWV can be retrospectively quantified from 4D flow MRI data based on multiple pulsatile flow waveforms distributed homogenously along the entire course of the vessel. As shown in Fig. 16.6 for 4D flow-based PWV estimation in the thoracic aorta, flow-time curves are automatically extracted for each analysis plane, and a measure of blood travel time (e.g., time-to-foot) is derived. Aortic PWV (in m/s) is determined by a linear fit from data of the entire aorta [82, 96]. However, reliable PWV assessment requires measure of the rapid changes of which can only be achieved with sufficient temporal resolution.

Wall Shear Stress

The three-directional velocity fields can be used to calculate WSS (i.e., the blood shear rate on the endothelial cells that line the vessel wall multiplied by blood viscosity), a known pathophysiological stimulus cited to alter gene expression and endothelial cell function [97]. Altered shear forces at the intimal surface can promote endothelial changes and create areas at risk for vascular remodeling, i.e., when high WSS is sensitized, growth factors and other molecules such as nitric oxide (NO) and matrix metalloproteinases (MMPs) are released to dilate the vessel to restore the normal WSS value [98]. Altered WSS has been associated with the development of vulnerable plaques in the carotid arteries [99], progressive aortic dilation [100, 101], or development of cerebrovascular aneurysms [102–104]. WSS can be estimated from 4D flow MRI data by multiplying the deformation tensor that contains the velocity gradients in all directions at the wall, with the viscosity of blood. As schematically illustrated in Fig. 16.7 (top), initial studies have employed 4D flow MRI to quantify regional time-resolved WSS based on 2D analysis planes [105]. The variation of WSS direction over the cardiac cycle can be used to calculate the oscillatory shear index (OSI) [106]. More recently, methods have been developed to compute volumetric 3D WSS along the 3D surface of the entire aorta, carotid or intracranial vasculature, or aneurysms (Fig. 16.7, bottom) [74, 107–109]. For the aorta, a method for the quantification of turbulent WSS variation was recently developed [110].

Although 3D WSS mapping allows for compact visualization of hemodynamic parameters (see Fig. 16.7, (2)), it does not detect where “abnormal” values are present. In addition, aortic WSS undergoes significant changes during healthy aging which underlines the importance of age-matched control cohorts in clinical studies to identify patients with altered WSS [111]. To address this limitation, a “WSS heatmap concept” was recently developed which offers the opportunity to quantify the extent of altered WSS [112]. The method is based on aortic 4D flow MRI data of a healthy control population to create an aortic “WSS atlas.” As shown in Fig. 16.8, the aortic atlas establishes regional confidence intervals for normal physiologic WSS throughout the aorta. Patient-specific WSS is then co-registered to the healthy control atlas to calculate heatmaps which represent regions of abnormally low or high WSS (i.e., outside of the 95% confidence interval provided by the control WSS atlas).

It should be noted that the discrete nature of the 4D flow MRI measured velocity field will result in a systematic underestimation of WSS. This is a common limitation of the technique. While absolute accuracy when assessing WSS in vivo is challenging, the relative pattern of expression (and magnitude) can reliably be inferred, especially if scan parameters and the procedure for WSS estimation are consistent between study populations [113, 114].

Head

In clinical practice, transcranial Doppler ultrasound is routinely used for cerebrovascular flow measurements. However, the technique is operator-dependent and limited by the acoustic windows of the head. 2D PC-MRI can provide reliable flow measurements in large intracranial arteries and veins, not limited by location. However, challenges for using 2D PC-MRI for flow measurement include small and tortuous vessels [115], complex vascular anatomy, and need for the manual placement of 2D imaging planes in multiple vessel segments. As an alternative, 4D flow MRI is increasingly used to assess cerebrovascular 3D blood flow [116, 117]. Emerging applications include the hemodynamic evaluation of intracranial aneurysms, arteriovenous malformations (AVM), and intracranial atherosclerotic disease (ICAD). Several groups have reported the successful measurement and evaluation of flow and WSS in intracranial aneurysms in patient feasibility studies [107, 118–121], indicating the potential of flow MRI to assist in the classification of individual aneurysms pre-intervention.

Arteriovenous Malformations (AVMs)

In patients with cerebral AVMs, flow information is potentially valuable for a better understanding of the impact of a focal AVM on the flow redistribution in the brain and/or in treatment planning by attempting to identify the feeding arteries with highest flow (see Fig. 16.9), enabling efficient and targeted embolization treatment. Recent reports include the quantification of flow and WSS in patients using a highly optimized radial 4D flow technique [108, 122]. Additional studies demonstrated the potential of 4D flow MRI for the evaluation of global and regional AVM flow characteristics [123, 124]. The findings showed that 4D flow MRI can assess treatment-induced changes in cerebrovascular flow distribution and was able to demonstrate significant associations between 4D flow metrics, cerebral perfusion indices, and AVM risk factors such as the Spetzler-Martin grade [124].

Neck

Carotid artery stenosis is a leading cause of ischemic stroke, and detailed insights into the causes for the development of atherosclerosis at this site are of interest. Among other risk factors, it is assumed that the development of atherosclerosis in the naturally bulbic ICA is related to local hemodynamic conditions such as flow deceleration or recirculation associated with reduced and oscillating WSS [138]. Particularly, low absolute WSS and high OSI are hypothesized to determine the composition of atherosclerotic lesions and the development of high-risk plaques [99, 102]. Since blood flow through the carotid bifurcation is complex with nonsymmetric flow profiles, the full three-directional velocity information by 4D flow MRI can be useful for a complete in vivo assessment of the segmental distribution of WSS.

4D flow studies analyzing WSS in the normal carotid bifurcation confirmed that potentially atherogenic wall (e.g., low WSS) parameters were predominantly concentrated at the posterior wall of the proximal ICA [139, 140]. Cibis et al. found lower WSS in regions of higher wall thickness in the carotid bifurcation [141, 142]. An example of a cohort-averaged map showing low WSS at locations of high wall thickness is displayed in Fig. 16.10. The wall thickness map is in concordance with the tendency of carotid atherosclerosis to affect the outer walls of arterial bifurcations and to mostly develop in the proximal part of the ICA bulb [143, 144]. Moreover, a significant relationship between the size of regions exposed to altered wall parameters and the individual bifurcation geometry was demonstrated, similar to carotid bifurcation study using CFD [138]. In patients with ICA stenosis, markedly altered filling and helix formation in the ICA bulb were observed, while revascularization partly restored normal filling and helix formation [145]. Furthermore, a direct comparison of mean and absolute flow velocities in the common carotid artery (CCA) between 4D flow MRI and Doppler ultrasound showed good agreement despite general underestimation of peak velocities by MRI [146].

4D flow MRI-derived WSS quantification could thus be a valuable technique to assess the individual risk of flow-mediated atherosclerosis and carotid plaque progression.

The assessment of PWV in the carotid arteries as a measure of vessel stiffness (and thus atherosclerotic burden) is challenging due its small size that necessitates high spatial and temporal resolution [147]. It is thus challenging to derive PWV using 4D flow MRI in the carotid arteries. For the determination of local PWV in the carotid arteries, the temporal resolution of through-plane 2D CINE PC-MRI was recently drastically improved by compressed sensing acceleration [148]. These novel acquisition strategies hold promise for future applications of either 2D or 4D flow MRI-derived PWV.

Thorax

Cardiothoracic 4D flow imaging is typically performed as part of a standard-of-care aortic/pulmonary imaging protocol, which includes additional MRI techniques for the assessment of cardiac function and wall motion (CINE imaging), aortic and pulmonary dimensions and geometry (MR angiography), as well as aortic and pulmonary valve morphology and dynamics (CINE imaging). The combination with 4D flow MRI provides a comprehensive assessment of aortic/pulmonary structure and function. These data have contributed to the understanding of the development of vessel wall abnormalities (atherosclerosis, aortic dilation, aneurysm) as a consequence of thoracic vascular diseases such as aortic valve diseases (stenosis, insufficiency, congenital bicuspid aortic valve (BAV)), aortic coarctation, or Marfan syndrome.

Aortic Valve Disease and Aortopathy

The presence of aortic valve disease significantly alters the hemodynamic environment in the thoracic aorta. Several studies have shown promise of 4D flow MRI-based blood flow visualization for the investigation of valve-related abnormal flow patterns (e.g., aberrant vortex or helix flow) as shown in Fig. 16.11. However, the visual evaluation of changes in aortic flow patterns (e.g., grading of vortex of helix flow) can be limited by lack of standardization, observer bias, and thus reproducibility. A more effective and representative assessment is provided by the calculation of 4D flow-derived measures that quantify the impact of altered flow characteristics on the vessel wall, such as flow displacement and WSS.

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