Flow-Encoding Axes

Flow sensitivity occurs in the orientation of the applied bipolar gradient. For example, if the bipolar gradient pulses are applied in the z-axis, the resulting motion-induced phase shifts are induced along that axis, and the velocity of blood moving from the head to the feet is encoded. Bipolar gradients can be applied in all three dimensions, allowing flow encoding in any direction. However, increasing the number of flow-encoding axes also increases scan time.

Flow quantification is performed by prescribing an imaging plane orthogonal to the direction of flow within a vessel. During postprocessing, the borders of the vessel are delineated with a flexible region of interest for each segment of the cardiac cycle. This creates a cross-sectional area for each time point and defines the pixels that contain velocities representing intravascular flow. The spatial mean velocity is then calculated from these pixels and multiplied by the cross-sectional area for each time point in the cardiac cycle (Fig. 17-2). The result is blood flow calculated in milliliters per heartbeat.¹

FIGURE 17-2 A, Two-dimensional velocity-encoded cine phase contrast scan planes in the proximal (plane 1) and distal (plane 2) descending thoracic aorta. B, Typical aortic blood flow with two-dimensional velocity-encoded cine phase contrast MR imaging.

Pressure gradients can be estimated with the modified Bernoulli equation, ΔP = 4ν², where ΔP is the peak pressure gradient in millimeters of mercury and ν is the peak blood flow velocity in meters per second. Unlike flow quantification, phase contrast imaging planes may be prescribed in a parallel or perpendicular orientation with respect to the direction of blood flow to capture the point of peak velocity of flow downstream from a stenosis (Fig. 17-3). It is important to select a relatively high velocity encoding (Venc) value because peak velocities associated with stenotic valves can exceed 5 m/sec.²

FIGURE 17-3 A and B, Two-dimensional velocity-encoded cine phase contrast scan planes in the proximal (plane 1) and distal (plane 2) descending thoracic aorta for quantification of collateral blood flow in coarctation of the aorta. Plane 3 is prescribed in the direction of flow to measure peak velocity, which is used to derive the pressure gradient across the stenosis used in the modified Bernoulli equation.¹¹ C, Typical aortic blood flow with two-dimensional velocity-encoded phase contrast MR imaging. Note that the distal blood flow (plane 2) is higher than the proximal flow (plane 1). The area between the curves represents collateral flow.

Velocity Encoding

Phase contrast MRI can be optimized for different velocities of blood flow. The encoding velocity of a given sequence, or Venc, is selected on the basis of the maximum anticipated velocity of the blood flow of interest. The scanner will use this value to adjust the amplitude and duration of the phase contrast bipolar gradients so that a proton moving at the selected Venc value will give rise to a phase shift of 180 degrees. For example, for a Venc value of 100 cm/sec, the range of phase shifts will be adjusted to encode velocities from −100 cm/sec to +100 cm/sec (Fig. 17-4). The lower the Venc value selected, the greater the sensitivity to slower flow but also the stronger the required gradients and the longer the repetition time (TR) of the sequence. An ideal Venc value is slightly greater than the maximum expected velocity.

FIGURE 17-4 Diagram of phase shifts and velocity for a given velocity encoding value (Venc).

(Modified from Lee VS. Cardiovascular MR Imaging: Physical Principles to Practical Protocols. Philadelphia, Lippincott Williams & Wilkins, 2005.)

Imaging Limitations and Pitfalls

There are some pitfalls to be aware of in employing phase contrast MRI for blood flow quantification. Signal aliasing will occur if the peak velocity of blood flow surpasses the Venc value at any point in the cardiac cycle. This phenomenon takes place because positive velocities that surpass the Venc value will give rise to phase shifts that are interpreted as negative velocities (e.g., a phase shift of 185 degrees will be interpreted as −175 degrees). On phase images, areas of aliasing are easily identifiable: the sudden loss of signal in regions of maximum signal brightness (Figs. 17-5 and 17-6).

FIGURE 17-5 Diagram of aliasing with low but not with high velocity encoding value (Venc).

(Modified from Westbrook C, Roth CK, Talbot J. MRI in Practice, 3rd ed. Oxford, Wiley-Blackwell, 2005.)

FIGURE 17-6 Signal aliasing in the descending thoracic aorta. Axial magnitude data in A demonstrate the ascending aorta (AAo) and descending aorta (DAo) in cross section and the bifurcation of the main pulmonary artery (MPA) into the right and left pulmonary arteries. Corresponding phase images demonstrate flow toward the head in the ascending aorta (white area) and toward the feet in the descending aorta (black area) during systole depicted in B, with aliasing of signal in the descending aorta at a slightly later systolic time point in C. The abrupt loss of signal within the fast flow channel in the descending aorta (arrow) is characteristic for aliasing.

Underestimation of velocity and flow can occur if a vessel is not evaluated in a plane orthogonal to the direction of flow or if partial volume averaging occurs. In addition, peak flow velocity downstream of a stenosis, and thus the associated pressure gradient, can be underestimated for two reasons: (1) as the accuracy of peak velocity measurement is dependent on temporal resolution, the value may be underestimated by MRI compared with echocardiography, which has a higher temporal resolution; and (2) the precise, three-dimensional location of the peak velocity downstream from a stenosis may not be included in the two-dimensional phase contrast evaluation.^3,4

Valvular Disease

Although echocardiography is the initial imaging modality of choice for assessment of cardiac valves because it is significantly cheaper and faster than MRI, cardiac MRI does play an important role in evaluation of valvular heart disease. MRI can augment the echocardiographic assessment with (1) reproducible and accurate calculation of ventricular size, function, and mass with steady-state free precession sequences and (2) quantitative evaluation of the severity of valvular stenosis and regurgitation with phase contrast sequences.

Precise quantification of aortic, pulmonary, and mitral regurgitation has been demonstrated with phase contrast MRI.^5–7 Aortic and pulmonary regurgitant volume can be quantified directly, resulting in more accurate and reproducible data than with echocardiography, by which blood flow is estimated on the basis of the apparent size of flow jets, which can be significantly affected by imaging parameters and orientation. The imaging plane is prescribed perpendicular to the direction of blood flow at approximately 1 to 2 cm above the level of the semilunar valve in question (Fig. 17-7). Valvular regurgitant fraction is the ratio of retrograde to antegrade flow across a valve.

FIGURE 17-7 Quantification of aortic regurgitation. Axial magnitude data in A demonstrate the aorta (Ao) and main pulmonary artery (MPA). Corresponding phase images demonstrate flow toward the head in the aorta (white) during systole in B but flow toward the feet (black) in diastole in C, consistent with aortic regurgitation. The degree of aortic regurgitation is demonstrated graphically over the cardiac cycle in D.

Mitral regurgitation can also be assessed directly, but through-plane movement of the valve during systole may introduce significant error.⁸ Another approach for estimation of mitral regurgitation is subtraction of the flow in the aorta during systole (left ventricular outflow) from flow across the mitral valve during diastole (left ventricular inflow); the base of the heart is less prone to movement during diastole, so by prescribing a two-dimensional plane across the mitral valve during end-diastole, diastolic flow can be reliably calculated. Assuming normal aortic valve function, any difference between the outflow and inflow measurements can be attributed to mitral regurgitation.⁵ Tricuspid regurgitation can be estimated in a similar fashion from measurements of pulmonic outflow and right ventricular inflow.

The degree of valvular stenosis is estimated by use of the modified Bernoulli equation, ΔP = 4ν² (discussed earlier in the section on flow-encoding axes), which is also used routinely for Doppler echocardiography. The technique has demonstrated good accuracy compared with Doppler echocardiography for both mitral and aortic stenosis.^9,10

Aortic Coarctation

Aortic coarctation is narrowing of the aortic arch that restricts forward flow at or near the junction with the descending aorta. MRI can lend to the evaluation and management of coarctation by providing both anatomic and functional data on the location and degree of stenosis. Specifically, phase contrast MRI allows quantification of the functional significance of coarctation in two ways: (1) estimation of the pressure gradient across the lesion by using the maximum associated flow velocity in conjunction with the modified Bernoulli equation as discussed elsewhere¹¹ and (2) quantification of collateral flow.

Collateral flow arises in coarctation as blood must find an alternate path to the descending thoracic aorta and below. It indicates a hemodynamically significant lesion that may require intervention. Evaluation of collateral flow is achieved by prescribing imaging planes orthogonal to aortic blood flow just distal to the coarctation and at the level of the diaphragm (Figs. 17-3 and 17-8). In healthy individuals, blood flow will decrease by approximately 7% over this interval spanning the descending aorta.¹² In hemodynamically significant coarctation, however, blood flow will increase rather than decrease over this interval as blood bypassing the coarctation will be delivered to the distal descending aorta through collaterals; the percentage increase in blood flow gives a quantitative measure of the degree of collateralization.^12–14 Study of surgically created coarctation in a porcine model confirms that phase contrast MRI is an accurate method of measuring collateral flow and that these collaterals develop within weeks.¹⁵

FIGURE 17-8 Quantification of collateral flow for aortic coarctation. A is an oblique sagittal T1 spin-echo image demonstrating a moderate juxtaductal coarctation. Two planes are depicted for quantification of collateral flow. Magnitude and phase images from the more superior plane just downstream of the coarctation in the proximal descending aorta are shown in B and C, respectively, and from the more inferior plane in the distal descending aorta at the level of the diaphragm in D and E, respectively. Relative flow at these planes is graphically demonstrated in F and reveals collateral flow of 35%, consistent with a hemodynamically significant aortic coarctation.

For an accurate assessment of collateral flow, phase images must be reviewed carefully for aliasing. If aliasing is present in the imaging plane just downstream of the coarctation, blood flow in the proximal descending aorta will be underestimated, and consequently, there may be an apparent but erroneous increase in flow in the distal descending aorta. Correction of this artifact can be achieved by increasing the Venc value in subsequent acquisitions.

Shunts

Quantification of shunt severity is performed clinically to determine if a patient may need surgery or to assess postsurgical outcomes. Intracardiac shunt quantification is achieved with phase contrast MRI by determining the ratio of flow in the pulmonary artery to that in the aorta, referred to as the Qp:Qs ratio, where Qp is the net flow in the main pulmonary artery and Qs is the net flow in the ascending aorta. This type of analysis can be used for both left-to-right and right-to-left shunts; the shunted volume is the difference between the pulmonary and aortic blood flow in either case. Phase contrast MRI has been deemed a first-line clinical study for quantification of shunt volume.¹⁶

Measurement of the Qp:Qs ratio is performed with two separate phase contrast acquisitions orthogonal to the direction of blood flow in the main pulmonary artery and ascending aorta, both at approximately 1 cm above the respective semilunar valves (Fig. 17-9). As the placement of this plane will be distal to the coronary ostia in the aorta, aortic flow will be approximately 3% to 5% less than pulmonic flow because of coronary runoff. A normal Qp:Qs ratio, therefore, should be slightly greater than 1. MRI-based measurement of Qp : Qs ratio in this fashion has been extensively validated.^17–20

FIGURE 17-9 Quantification of left-to-right shunt with atrial septal defect. A is a bright blood gradient echo image in a four-chamber orientation demonstrating an atrial septal defect (arrowhead). To quantify the degree of shunting across the atrial septum, relative flow in the aorta and main pulmonary artery is measured. Magnitude and phase images from the aorta are shown in B and C, respectively, and from the main pulmonary artery in D and E, respectively. Relative flow is graphically demonstrated in F, revealing a ratio of pulmonary to aortic blood flow (Qp:Qs) of 2 to 1, consistent with a significant left-to-right shunt.

Pulmonary Flow Evaluation

Phase contrast MRI can be used to assess differential flow in the right and left pulmonary arteries and relative flow within the pulmonary veins. Branch pulmonary artery stenosis, which can be seen after arterial switch repair performed for transposition of the great vessels, may go undetected with other imaging modalities.²¹ Direct quantification of blood flow to both lungs is crucial for determination of the hemodynamic significance of such a stenosis. Measurement of differential pulmonary flow is achieved with two phase contrast acquisitions orthogonal to the direction of blood flow in the proximal right and left pulmonary arteries (Fig. 17-10). The normal blood flow distribution is 55% to the right lung and 45% to the left lung.

FIGURE 17-10 Quantification of differential flow in the right and left pulmonary arteries. A is an axial T1 spin-echo image at the bifurcation of the main pulmonary artery with two planes depicted for quantification of flow into the right and left pulmonary arteries. Magnitude and phase images from the right pulmonary artery are shown in B and C, respectively, and from the left pulmonary artery in D and E, respectively. Relative flow at these planes is graphically demonstrated in F and reveals that 55% of pulmonary flow is directed toward the right lung and 45% to the left, which is a normal distribution.

MR blood flow evaluation has also been used clinically to assess pulmonary venous obstruction²² and to characterize the complex postsurgical pulmonary inflow in patients after total cavopulmonary connection, with quantification of the relative contributions of the superior and inferior caval veins to the right and left lungs.²³ In addition, some investigators have proposed use of the time-resolved velocity data that underlie MR flow evaluations to noninvasively estimate the degree of pulmonary artery hypertension.²⁴

Time-Resolved, Three-Dimensional Phase Contrast MRI

Acquisition of three-dimensional phase contrast data in a time-resolved fashion over the cardiac cycle for an imaging volume that contains the heart and great vessels is an attractive approach to cardiac MRI flow evaluation, but one that has been limited in its clinical application by long scan time. Work in the early 1990s with two-dimensional planes stacked to achieve three-dimensional data sets showed the utility of this type of imaging for uncovering of complex, secondary aortic blood flow characteristics such as helices and vortices, which are not easily appreciated by two-dimensional imaging.²⁵ More recently, true three-dimensional phase contrast acquisitions have been validated, and time-saving measures such as parallel imaging and other approaches to k-space subsampling have been implemented to make this type of comprehensive MR flow evaluation a more viable clinical tool.^26–28 The technique has been termed flow-sensitive four-dimensional MRI or simply four-dimensional flow, where the fourth dimension refers to time, and seven-dimensional flow, referring to the seven data components that are encoded for each voxel that composes a data set.

Advantages of this technique include complete temporal and spatial coverage of the vascular area of interest, continuous breathing, no requirement for prospective placement of two-dimensional planes for phase contrast acquisition, and a variety of unique visualization and quantification options for velocity data that are not available by conventional two-dimensional phase contrast imaging. Rich and extensive data analysis is possible in the postprocessing stage with appropriate software. Interactive navigation throughout these volumetric data sets allows evaluation of blood velocity and flow in user-defined regions of interest at any phase of the cardiac cycle (Fig. 17-11). Three-dimensional visualization tools such as streamlines and particle traces allow four-dimensional visual presentation of secondary blood flow features that may not otherwise be evident (Figs. 17-12 and 17-13).

FIGURE 17-11 Visualization of three-dimensional phase contrast data from a healthy subject in oblique sagittal orientation from the right (A) and left (B) sides of the aortic arch with streamlines during mid-systole. Streamlines are imaginary lines aligned with local vector fields and represent the flow field at a given moment in the cardiac cycle. They are color coded for velocity. Note the smooth trajectory of streamlines and absence of significant secondary flow features throughout the thoracic aorta. Flow quantification was performed for the three planes depicted in B: orthogonal to aortic blood flow in the proximal ascending aorta (plane 1), in the proximal descending aorta (plane 2), and at the level of the diaphragm (plane 3). C is a graph of blood flow over the cardiac cycle at these three planes.

(Hope MD, Meadows AK, Hope TA, et al: Clinical evaluation of aortic coarctation with 4D flow MR imaging. J Magn Reson Imaging 31:711-8, 2010.)

FIGURE 17-12 Abnormal helical flow in a patient with aortic coarctation. A, Three-dimensional contrast-enhanced MR angiography demonstrates a focal juxtaductal coarctation (arrow). B and C, Views of the right and left aspect of the aortic arch, respectively, with streamlines to visualize three-dimensional phase contrast data in mid-systole. Marked flow disturbance is seen at and distal to the coarctation, with abnormal right-handed helical flow in the descending thoracic aorta. D, Oblique sagittal T1 spin-echo image in the same orientation as C demonstrating the coarctation (arrow).

FIGURE 17-13 Abnormal circular-type flow in a patient after repair of aortic coarctation. A and B demonstrate minimal residual narrowing (arrow) of the mid-aortic arch with three-dimensional contrast-enhanced MR angiography and oblique sagittal T1 spin-echo imaging, respectively. C and D represent streamline evaluation of the aortic arch at mid and late systole, respectively. Disturbed flow is revealed, with acceleration and signal dropout secondary to aliasing as well as circular-type flow (arrow) downstream of the focal region of mild aortic narrowing.

(Hope MD, Meadows AK, Hope TA, et al: Clinical evaluation of aortic coarctation with 4D flow MR imaging. J Magn Reson Imaging 31:711-8, 2010.)

Secondary Parameters

The three-dimensional velocity vector fields that are generated by this technique can be used for applications beyond the mapping and quantification of blood velocity and flow. These data are starting to be used clinically to estimate important secondary vascular parameters including vascular wall shear stress, relative blood pressure, and pulse wave velocity.

Wall shear stress refers to the force per unit area exerted on the vascular wall by fluid in motion in a tangential plane. Abnormal shear values have been strongly implicated in atherogenesis.²⁹ Recently, this parameter has been estimated by use of near wall velocity gradients generated by three-dimensional phase contrast MRI and reported for the carotid arteries as well as for thoracic and intracranial aneurysms.^30–33 Confirmation of these reported shear stress values with an accepted standard such as computational fluid dynamics is forthcoming.

Relative pressure mapping has been demonstrated and validated in vivo by use of multidirectional velocity data and the Navier-Stokes equations.^34,35 Pulse wave velocity, which reflects the degree of vascular stiffness, is another secondary parameter that can be estimated with time-resolved velocity data, although a much higher temporal resolution than that typically provided by the three-dimensional phase contrast sequence is required for accurate calculation.³⁶

KEY POINTS

Velocity-encoded cine phase contrast MRI can be used to evaluate velocity, flow, and pressure gradients.

Phase contrast MRI can be applied for quantitative assessment of regurgitant volume and fraction in valvular regurgitation; pressure gradient in valvular stenosis; collateral flow and pressure gradient in coarctation of the aorta; differential pulmonary blood flow in the presence of pulmonary artery stenosis; and pulmonary-to-systemic flow ratio in the setting of a cardiac shunt.