Simultaneous Acquisition of Water, Fat, and Velocity Images Using a Phase‐Contrast T2*‐IDEAL Method

ABSTRACT

Water‐fat separation MRI techniques use frequency differences between water and fat encoded in the phase of the MR signal. Similarly, phase‐contrast MRI (2D PC‐MRI) uses phase differences to estimate blood flow velocity. This study proposes to enhance efficiency by acquiring both images in a single scan, resulting in co‐registered images of water‐fat species and velocity. This work introduces a method that combines phase‐contrast with T2*‐IDEAL to acquire water‐fat components and velocity images in a single MR acquisition. We developed a phase‐contrast multi‐echo (PCME‐MRI) acquisition to obtain IDEAL MR images with velocity encoding. Our T2*‐IDEAL method estimates velocity and separates water‐fat components by considering three chemical species: fat concentration and two water components with velocity information. The proposed PC T2*‐IDEAL method was validated with a numerical phantom and 2D MR axial images of the neck in 14 healthy volunteers, measuring blood flow in the carotid arteries and water‐fat components around the region of interest. In volunteers, the median and range MAE when comparing PC T2*‐IDEAL and standard T2*‐IDEAL fat fraction was 0.06 $\pm$ 0.02. The median and range of velocity for PC T2*‐IDEAL were 8.44 and [6.23, 10.6] mL, compared to 7.16 and [4.79, 8.78] mL obtained by 2D PC‐MRI. Numerical phantom simulations demonstrated similar results in water‐fat components and velocity information compared to standard T2*‐IDEAL and 2D PC‐MRI methods. Volunteer images showed accurate estimations of water‐fat components and differences in velocity information using PC T2*‐IDEAL in comparison with standard 2D PC‐MRI.

We present a novel MRI method that simultaneously acquires water‐fat and velocity images using a phase‐contrast T2*‐IDEAL technique. This single‐scan approach improves efficiency by combining fat quantification and flow imaging. Validated with numerical phantoms and in vivo scans of carotid arteries, the method demonstrates accuracy comparable to standard techniques, with improved robustness in the presence of fat.

Abbreviations

2D PC‐MRI

2D phase‐contrast MRI

MAE

Mean absolute error

MASLD

Metabolic dysfunction associated steatotic liver disease

PCME‐MRI

Phase‐contrast multi‐echo

ROI

Region‐of‐interest

SSIM

Structural similarity index

SNR

Signal‐to‐noise ratio

TE

Echo time

VNR

Velocity‐to‐noise ratio

1. Introduction

Water‐fat separation MRI techniques that use iterative least‐squares estimation methods offer flexibility, compared to traditional Dixon methods [1, 2, 3], allowing the use of variable echo time (TE) increments to optimize signal‐to‐noise ratio (SNR) or improve speed [4, 5, 6]. Along with measuring water‐fat components, it would be beneficial to simultaneously measure velocity information in the same acquisition [7, 8].

Phase‐contrast MRI (2D PC‐MRI) is a non‐invasive technique that can provide quantitative flow and anatomic information [9, 10], detect abnormal flow dynamics [10, 11], and compute relevant hemodynamic parameters [12, 13, 14, 15]. To do so, 2D PC‐MRI requires acquisitions with bipolar gradients. These gradients induce a velocity‐dependent MR phase on the tissue magnetization [9].

Capturing both water‐fat components and velocity images concurrently implies a significant technical challenge. Johnson et al. [16] proposed a chemical shift and radial dual‐echo sequence to simultaneously obtain water‐fat and velocity imaging. This technique recovered velocity images of blood corrected by the influence of fat. The results are promising; however, they require a non‐linear reconstruction algorithm. To our knowledge, no other publications have attempted to simultaneously assess water‐fat and flow velocity. We recently presented a work where Dixon and 2D PC‐MRI were combined to obtain water‐fat and flow velocity [17, 18]. Combining Dixon and 2D PC‐MRI has several limitations, including the difficulties in incorporating a multipeak model of the fat and T2* decay, as well as the inflexibility in choosing the echo times.

In this work, we introduced a method that combines 2D PC‐MRI and a T2*‐IDEAL technique to obtain water‐fat components and velocity images in a single MR acquisition. Some preliminary results of this work were also presented recently [19]. We used a phase‐contrast multi‐echo pulse sequence (PCME‐MRI) that combines two different IDEAL acquisitions with bipolar gradients of opposed polarity before the readouts to encode blood flow velocity. Our PC T2*‐IDEAL method computes the fat concentration and two water components to compute the 2D PC‐MRI.

The proposed method uses a single acquisition for water‐fat separation and velocity estimation. Our study focused on voxels containing both moving water and static fat. This approach enhances the efficiency of obtaining both types of images simultaneously. Moreover, it reduces echo spacing between acquired TEs, allowing more flexibility in the determination of echo times. This method could have potential applications in cardiovascular [20, 21] and fatty liver diseases [22, 23] such as metabolic dysfunction associated steatotic liver disease (MASLD) [22, 23], diabetes [24], and cardiac steatosis [20, 21]. However, those applications are out of the scope of this manuscript, here we present a proof‐of‐concept study applied to the carotid artery of healthy volunteers.

2. Theory and Methods

2.1. Signal Model

The measured signal $S_n$, at the echo time (TE) $t_n$, is the sum of water and fat components, represented by ${\mathrm{\rho }}_W$ and ${\mathrm{\rho }}_F$ respectively in Equation 1. To model the combined effect of velocity and water‐fat encoding, we assumed that only water components had velocity and were encoded in the signal phase and characterized by ${\mathrm{\varphi }}_V$ in Equation 1. Fat components were assumed static. The fat concentration is multiplied by a chemical shift factor $C_{\mathit{sh}}$ (Equation 1b), which is expressed as a weighted sum of exponentials. This factor accounts for a multi‐peak fat model, incorporating six spectral peaks with corresponding weighting coefficients ${\mathrm{\alpha }}_k$ [25, 26, 27]. The MR signal is affected by inhomogeneities of the main field $B_0$ and T2* decay. In Equation 1, the inhomogeneities are represented by $\mathrm{\Delta }B$.

$$S_n=\left({\mathrm{\rho }}_W{e}^{i{\mathrm{\varphi }}_V}+{\mathrm{\rho }}_F{C}_{\mathit{sh}}\left(t_n\right)\right)e^{-i\mathrm{\gamma \Delta }B{t}_n}{e}^{-t_n/T_2^{*}}$$ (1a)

$$\begin{array}{c}{C}_{\mathit{sh}}\left(t_n\right)={\sum }_k{\mathrm{\alpha }}_k{e}^{i2\mathrm{\pi \Delta }{f}_k{t}_n}\text{where}{\sum }_k{\mathrm{\alpha }}_k=1\hfill \end{array}$$ (1b)

We considered water and fat components as complex values composed of magnitude ($M_W$ and $M_F$) and phase (${\mathrm{\varphi }}_W$ and ${\mathrm{\varphi }}_F$). Therefore, we can represent ${\mathrm{\rho }}_W=M_W{e}^{i{\mathrm{\varphi }}_W}$ and ${\mathrm{\rho }}_F=M_F{e}^{i{\mathrm{\varphi }}_F}$, then, the MRI signal in each voxel can be described as shown in Equation 2.

$$S_n=\left(M_W{e}^{i\left[{\mathrm{\varphi }}_W+{\mathrm{\varphi }}_V\right]}+M_F{e}^{i{\mathrm{\varphi }}_F}{C}_{\mathit{sh}}\left(t_n\right)\right)e^{-i\mathrm{\gamma \Delta }B{t}_n}{e}^{-t_n/T_2^{*}}$$ (2)

2.2. Phase‐Contrast T2*‐IDEAL Method

This method requires acquiring a gradient echo multi‐echo sequence of two echo trains preceded by two bipolar gradients of opposite polarity. Then, we assemble all the echoes and apply the T2*‐IDEAL algorithm for three chemical species: two different water species with positive and negative polarity for velocity encoding and static fat species. The model assumes a unique $\mathrm{\Delta }B$ and T2*. Figure 1 summarizes the PC T2*‐IDEAL method and Figure 2 shows a diagram of the pulse sequence implementation.

FIGURE 1.

Diagram of PC T2*‐IDEAL method. We performed two IDEAL acquisitions with bipolar gradients of opposite polarities. We separated the water and fat components of each acquisition. We estimated the fat component as the magnitude of the fat complex image and the water component as the average magnitudes of both water complex images obtained. We performed 2D PC‐MRI using the two water components to estimate the velocity images.

FIGURE 2.

Pulse sequence diagram of the PC T2*‐IDEAL sequence. (A) Velocity encoding gradients are applied immediately after RF excitation, followed by three readout gradients. (B) The velocity encoding gradients are applied with opposite polarity, and the TEs are displaced by a temporal shift to obtain six different TEs for water‐fat separation.

Iterative least‐squares estimation methods for water‐fat separation [4, 5] solve a least‐squares optimization problem, shown in Equation 3, to fit the acquired data S , into a linear model for the chemical species, represented by $A·\mathrm{\rho }$, and a non‐linear part that considers the $\mathrm{\Delta }B$ and T2* effects, represented by matrix P .

$$S=P\left(\mathrm{\psi }\right)·A·\mathrm{\rho }\text{where}\mathrm{\psi }=\frac{\mathrm{\gamma \Delta }\mathrm{B}}{2\mathrm{\pi }}+\mathrm{i}\frac{1}{2\mathrm{\pi }{\mathrm{T}}_2^{*}}$$ (3)

We modeled the least‐squares optimization problem with two water components. The first three echoes preceding by a bipolar gradient of negative polarity contribute to the first water component ${\rho }_{W-}$ and the fat component ${\rho }_F$, as shown in Equation 4. The second three‐echo train contributes to the second water component ${\rho }_{W+}$ and to ${\rho }_F$. Equation 4 shows the least‐squares problem that solves PC T2*‐IDEAL.

$$\left[\begin{array}{c}{S}_{-}\left(t_1\right)\\ S_{-}\left(t_2\right)\\ S_{-}\left(t_3\right)\\ S_{+}\left(t_4\right)\\ S_{+}\left(t_5\right)\\ S_{+}\left(t_6\right)\end{array}\right]=\mathit{P}\left(\psi \right)·\left[\begin{array}{ccc}1& 0& C_{\mathit{sh}}\left(t_1\right)\\ 1& 0& C_{\mathit{sh}}\left(t_2\right)\\ 1& 0& C_{\mathit{sh}}\left(t_3\right)\\ 0& 1& C_{\mathit{sh}}\left(t_4\right)\\ 0& 1& C_{\mathit{sh}}\left(t_5\right)\\ 0& 1& C_{\mathit{sh}}\left(t_6\right)\end{array}\right]·\left[\begin{array}{c}{\rho }_{W-}\\ {\rho }_{W+}\\ {\rho }_F\end{array}\right]$$ (4)

To increase the SNR of the water component and compute the final fat fraction, we averaged the magnitudes of both water complex images obtained. Finally, we performed 2D PC‐MRI using both water components as in standard phase contrast MRI.

2.3. Experiments

2.3.1. Numerical Phantom Experiments

2.3.1.1. Impact of fat on Velocity Measurement

To determine velocity bias in the presence of fat, relative to the ground truth, we used Monte Carlo simulations in PC T2*‐IDEAL, following the approach of Johnson et al. [16]. Our simulations involved 16 single pixels using 16 different fat fraction values evenly spaced between 0 and 0.5. In each simulation, we performed 10,000 realizations for each of the 16 distinct velocity values evenly spaced between 0 and 100 cm/s (160,000 realizations in total), and the velocity encoding (VENC) was set at 100 cm/s. For each realization, we assigned random values of $\mathrm{\Delta }B$ using a uniform distribution, ranging from −1.65 to 1.65 ppm. For each realization, we simulated multiple echo signals. These simulations were based on a multi‐peak model that considered T2* decay, with values spanning from 10 to 200 ms and Gaussian noise. We compared simulations using SNRs of 100 and 20. We computed the SNR as the magnitude of the signal divided by the standard deviation of Gaussian noise.

Subsequently, using the same parameters of previous Monte Carlo simulations, we performed 16 single‐pixel simulations using 16 different velocity values evenly spaced between 0 and 100 cm/s, the VENC was set at 100 cm/s. In each simulation, we performed 10,000 realizations for each of the 16 distinct fat fractions values evenly spaced from 0 to 1. To evaluate the simulation results, we calculated the velocity‐to‐noise ratio (VNR). The VNR was computed using the formula shown in Equation 5 [28].

$$\mathrm{VNR}=\frac{\mathrm{\pi }}{\sqrt{2}}·\frac{V}{\text{VENC}}·\mathrm{SNR}$$ (5)

2.3.1.2. Numerical In Silico Phantom

We evaluated the PC T2*‐IDEAL in a numerical phantom of 13 vials with water‐fat compositions from 0 to 1 fat fraction. We incorporated three vials containing 100% water and uniform velocities (two at 80 cm/s, while the third one at 40 m/s). To further enhance the realism of our phantom, we introduced T2* decay from 10 ms in fat fraction 1 to 200 ms in fat fraction 0, we interpolated linearly the T2* for different fat fraction values. We also introduced a gradient field of inhomogeneities from −70 to 70 Hz across the entire phantom, from the left upper corner to the right bottom corner.

The signal model used to construct this numerical phantom correspond to the Equation 2 and incorporating additive Gaussian noise [25, 26, 27].

This numerical phantom considers a multi‐peak model for fat and customizable additive complex Gaussian noise, all of which contribute to a more realistic simulation environment.

Random Gaussian noise values with zero mean and SD were added to the phantom. We tested the sensitivity to noise by performing 20 different phantom simulations using Gaussian noise with zero mean and different SD ranging from 0 to 23.5%.

Additionally, we conducted an experiment in which all vials in the numerical phantom were assigned non‐zero fat fraction and velocity values. This setup was designed to further demonstrate the proposed method's ability to separate fat and water while accurately capturing velocity. Detailed results of this experiment are provided in Appendix 1.

2.3.2. In Vivo Experiments

We conducted MRI scans on 14 healthy volunteers using a 1.5 T Achieva system (Philips, Best, The Netherlands). We acquired 2D axial neck images to analyze water‐fat components and measure blood velocity in the carotid arteries. Informed consent was obtained from all volunteers prior to their participation in the study. Authors elect to not share data.

To enable water‐fat separation and velocity encoding, we designed and implemented a 2D gradient‐echo IDEAL acquisition sequence. This sequence involved incorporating bipolar gradients before the multi‐echo sequences. Both sequences were equipped with velocity‐compensated readout gradients. Given that the PC T2*‐IDEAL method necessitates two IDEAL acquisitions, we introduced a temporal shift in the second acquisition. Consequently, we had data from six different echo times (TEs) with customizable echo spacing for water‐fat separation. The first IDEAL acquisition had TEs of 1.9, 4.2, and 6.5 ms, while the second IDEAL acquisition, featuring bipolar gradients of opposite polarity and a 0.6 ms shift, had TEs of 2.5, 4.8, and 7.1 ms. We experimentally tested various time shifts and found that a shift of 0.6 yielded the best results.

We compared the measurements obtained from PC IDEAL with those from standard IDEAL and 2D PC‐MRI acquisitions, keeping all parameters constant. We acquired a single 8‐mm‐thick slice, spatial resolution of $0.83\times 0.83$ mm, with an in‐plane matrix size of $240\times 240$, capturing 20 cardiac phases and using a variable VENC of $110\pm 10$ cm/s, dependent on the volunteer. PC IDEAL, 2D PC‐MRI, and standard IDEAL acquisitions all shared the same temporal resolution (20 cardiac phases). For the standard IDEAL acquisition, data from each TEs were recorded during each cardiac phase, and the bipolar gradient was turned off, i.e., without velocity encoding. Water‐fat components were compared using images captured during a representative peak systolic cardiac phase. Flow measurements were compared by calculating the blood flow in the carotid arteries of volunteers, obtained by summing over the artery area.

The acquisition times for each acquisition where 119 s for PC T2*‐IDEAL, 120 s for standard T2*‐IDEAL, and 120 s for standard 2D PC‐MRI. Fully sample data were acquired without using any parallel imaging acceleration during the scans. Table 1 shows a summary of the MRI acquisition parameters of the pulse sequence implementation of PC T2*‐IDEAL.

TABLE 1.

The MRI acquisition parameters.

Parameter
Voxel size, mm	0.83 × 0.83 × 8.0
Cardiac phases	20
VENC, cm/s	$100\pm 10$
Resolution	240 × 240
Echo time, ms
PC T2*‐IDEAL and T2*‐IDEAL
Acquisition 1	1.9, 4.2, and 6.5
Acquisition 2	2.3, 4.6, and 6.9
2D PC‐MRI	2.04
Acquisition time, s PC T2*‐IDEAL T2*‐IDEAL 2D PC‐MRI	119 120 120

2.4. Statistical Assessment

We quantitatively compared the PC T2*‐IDEAL method to the standard T2*‐IDEAL method. We reported mean absolute error (MAE $={\sum }_{i=1}^n\left|x_1-x_0\right|/n$) and the structural similarity index (SSIM).

In the phantom, we defined 16 regions of interest (ROIs), each encompassing an entire vial. The fat fraction in the phantom was reported as the median and range across the vials, and the MAE was calculated for all ROIs simultaneously.

In in vivo data, we manually delineated three ROIs in muscle, spine, and subcutaneous fat. Fat fraction errors were assessed using median values. To compare velocity estimation, we calculated blood flow in the carotid arteries for each cardiac phase and the total blood flow per cardiac cycle in PC T2*‐IDEAL and standard 2D PC‐MRI images. ROIs were drawn in the standard PC images and then translated to the PC T2*‐IDEAL method. In the case of motion, manual adjustments to the ROI were required. Subsequently, we performed a Wilcoxon signed rank test for blood volume estimation in a cardiac cycle for both carotid arteries, considering a p value < 0.05 as significant.

3. Results

3.1. Monte Carlo Simulations

We conducted Monte Carlo experiments to compare velocity bias across varying velocity values using both PC T2*‐IDEAL and standard PC methods (Figure 3A). Additionally, we assessed velocity estimation for different fat fraction values (Figure 3B). Figure 3A provides a comparative analysis of velocity bias across different velocity values derived from Monte Carlo simulations comparing PC T2*‐IDEAL against standard PC. Similarly, Figure 3B shows the VNR derived from Monte Carlo simulations across different fat fraction values.

FIGURE 3.

Monte Carlo simulations, comparison of PC T2*‐IDEAL, and standard 2D PC‐MRI. (A) Velocity bias (cm/s) vs velocity ground truth. Colors in this plot indicate the fat fraction used in each simulation. Plots show the range $\pm 15$ cm/s of velocity bias to easily compare velocity bias for lower values of fat fraction. (B) Velocity‐to‐noise ratio (VNR) vs fat fraction. Colors in this plot indicate the velocity used in each simulation.

Our findings revealed that PC T2*‐IDEAL outperformed standard PC in velocity estimation, particularly in the presence of fat. Notably, the PC T2*‐IDEAL method showed errors close to zero for fat fractions between 0 and 0.5, across almost all velocities. In contrast, standard 2D PC‐MRI exhibited an increasing velocity bias as fat content increased, with the bias also growing at higher velocities. Standard 2D PC‐MRI displayed a high VNR for fat fractions below 0.4 for velocities under 90% of the VENC; however, our method exhibited a high SNR for fat fractions up to 0.9.

3.2. Numerical Phantom Experiments

Numerical phantom experiments showed accurate water‐fat separation and velocity estimation results for several scenarios of Gaussian noise and T2* decay using the PC T2*‐IDEAL method as the solver. The phase of both water components obtained preserve the velocity encoding information with opposed polarities. This allow us to compute the velocity information in the codified direction using standard 2D PC‐MRI techniques over those water‐only images.

Figure 4 shows qualitative comparisons between the PC T2*‐IDEAL method and standard methods obtained from numerical simulations. Water‐fat components and field maps were compared to the standard T2*‐IDEAL method, and the velocities were compared to standard 2D PC‐MRI.

FIGURE 4.

(A) Scheme of the numerical in silico phantom showing the fat fraction and velocity (cm/s) encoded in each of the vials. (B) Water‐fat magnitude (‐), phase (rad), field map of inhomogeneities (Hz), velocity images (cm/s), and T2* decay (ms) comparison between PC T2*‐IDEAL method and standard T2*‐IDEAL acquisition to compare water and fat components, and standard 2D PC‐MRI to compare velocity images in the numerical phantom.

Figure 5A illustrates the median fat fraction, and its range obtained from the vials within the numerical phantom, which contains varying water and fat compositions. The estimated error, median, and range for fat fraction estimation was 0.00 and [0.00, 0.11] for PC T2*‐IDEAL, compared to 0.00 and [0.00, 0.08] for standard T2*‐IDEAL. The MAE was 2.69% for PC T2*‐IDEAL, whereas it was 2.54% for standard T2*‐IDEAL. Regarding velocity estimation, the percentage error was 0.10 and [0.09, 0.11]% for PC T2*‐IDEAL and 0.10 and [0.05, 0.12]% for standard 2D PC‐MRI. The MAE for velocity estimation was 2.69 cm/s for PC T2*‐IDEAL and 2.68 cm/s for standard 2D PC‐MRI. It is important to note that these MAE values were calculated using all pixels within the region of interest.

FIGURE 5.

(A) A quantitative comparison illustrating the estimation error based on the median values of fat fraction within the tubes of the numerical phantom. This comparison contrasts the water‐fat separation performance of PC T2*‐IDEAL against the standard T2*‐IDEAL method. (B) Estimation error values were calculated by comparing the fat fractions obtained under varying levels of Gaussian noise, ranging from 0 to 23.5% SD. (A,B) The error was computed as the absolute difference between each method and ground truth values.

Our noise analysis (Figure 5B) revealed that standard T2*‐IDEAL performs slightly better than PC T2*‐IDEAL with differences less than 1.00% comparing the estimated error in the quantification of the fat fractions for levels of noise lower than SD = 12.5% of Gaussian noise.

3.3. In Vivo Experiments

In Figure 6A, we present images of water and fat fractions, a field map of inhomogeneities, and velocity estimation for a representative volunteer. We employed the three‐chemical element T2*‐IDEAL method to compare PC T2*‐IDEAL and the standard T2*‐IDEAL method for water‐fat separation. Figure 6B displays plots of blood flow estimated in each carotid artery across the cardiac cycle for this representative volunteer.

FIGURE 6.

(A) Comparison of water‐fat components and velocity images acquired through the PC T2*‐IDEAL and standard T2*‐IDEAL acquisition methods for assessing water and fat components. Standard 2D PC‐MRI images served as the benchmark for evaluating velocity estimation in a representative volunteer. We show images of magnitude (‐), water and fat fractions (‐), phase (rad), field map of inhomogeneities (Hz), and velocity images (cm/s). (B) Velocity estimation profiles throughout the 20 cardiac phases in both carotid arteries for a representative volunteer. The blue lines represent blood flow estimates obtained using our proposed PC T2*‐IDEAL method.

When analyzing the fat fractions across all volunteers, we determined the median and range of differences between methods was 0.01 $\pm$ 0.03 for ROIs in muscle, 0.01 $\pm$ 0.06 for ROIs in the spine, and 0.01 $\pm$ 0.03 for ROIs in subcutaneous fat. Muscle and Spine ROIs showed no significant differences in a Wilcoxon signed rank test to compare the median values of fat fractions within the ROIs between the PC T2*‐IDEAL and standard T2*‐IDEAL methods (p values of 0.22 and 0.67). The test revealed significant differences in the subcutaneous fat ROIs (p value of 1.22e−4). Figure 7A displays a Bland Altman plot illustrating the median values of fat fractions for PC T2*‐IDEAL and standard T2*‐IDEAL. Bland–Altman plot shows a mean difference between ROIs of 0.01.

FIGURE 7.

(A) A comparison of blood flow estimation in each carotid artery over the cardiac cycle across the 14 volunteers. This comparison contrasts the results obtained using the PC T2*‐IDEAL method with those acquired through standard 2D PC‐MRI. (B) Bland–Altman plot illustrating the comparison of fat fraction estimates between the PC T2*‐IDEAL method and the standard T2*‐IDEAL method. Three distinct ROIs were employed for each volunteer in the evaluation.

The median and range MAE values, comparing fat fractions between PC T2*‐IDEAL and standard T2*‐IDEAL across all volunteers, were 0.06 $\pm$ 0.02. Additionally, the median and range of SSIM values for fat fraction comparison between PC T2*‐IDEAL and standard T2*‐IDEAL were 0.84 $\pm$ 0.07. It is worth noting that MAE and SSIM values were computed based on all pixels within the acquired region of the neck.

To quantitatively compare velocity estimation, we computed blood flow per cardiac cycle in each carotid artery across the 14 volunteers. Figure 7B shows a Bland–Altman plot comparing blood flow estimates obtained using the PC T2*‐IDEAL method versus standard 2D PC‐MRI. The median and range of velocity obtained with our technique was 8.44 and [6.23, 10.6] mL, compared to 7.16 and [4.79, 8.78] mL obtained by 2D PC‐MRI. We performed a Wilcoxon signed rank test to compare blood volume estimations, revealing significant differences in blood volume estimations of 1.45 mL per cardiac cycle between the PC T2*‐IDEAL method and standard 2D PC‐MRI, with a p value of 3.79e−6.

4. Discussion

We introduced a novel approach that combines 2D PC‐MRI and T2*‐IDEAL acquisitions to simultaneously obtain water‐fat components and velocity images. Monte Carlo simulations have provided strong evidence that PC T2*‐IDEAL surpasses standard 2D PC‐MRI methods in the presence of fat. The velocity bias in standard 2D PC‐MRI grows as the fat fraction increases, whereas T2*‐IDEAL maintains a consistently low‐velocity bias. Moreover, unlike standard 2D PC‐MRI methods, the VNR plot demonstrates consistent values across various fat fraction scenarios.

Numerical phantom experiments revealed similar quantification of water‐fat components between PC T2*‐IDEAL and standard T2*‐IDEAL methods. The estimation error, median, and range for fat fraction estimation was 0.0028 and [0.00, 0.11] for PC T2*‐IDEAL, compared to 0.0016 and [0.00, 0.08] for standard T2*‐IDEAL. Additionally, our comparison of MAE results for fat fraction quantification under different water‐fat components showed minor discrepancies between PC T2*‐IDEAL and standard T2*‐IDEAL methods.

Assessing noise performance through fat fraction estimation errors demonstrated minimal differences between PC T2*‐IDEAL and standard T2*‐IDEAL methods for low noise levels (below 10% SD in Gaussian noise).

In our volunteer studies, water‐fat components obtained from PC T2*‐IDEAL acquisitions exhibited similar results compared to standard T2*‐IDEAL and 2D PC‐MRI acquisitions. By employing the three‐chemical element T2*‐IDEAL method, we successfully recovered velocity encoding information using only water components.

Statistical analysis of fat fraction estimations indicated no significant differences between the PC T2*‐IDEAL and standard T2*‐IDEAL methods in assessing water‐fat components for muscle and spine ROIs, though subcutaneous fat ROIs showed significant differences according to the Wilcoxon signed rank test, likely due to challenges in consistently selecting ROIs in the neck's subcutaneous fat region for certain volunteers. Quantitative comparisons of fat fractions from volunteers, shown in the Bland–Altman plot (Figure 7A), revealed variations of less than 6% between the two methods, with a mean difference of 1.07%, indicating that both methods provided comparable water‐fat separation. These results were further supported by MAE and SSIM values.

Velocity estimation demonstrated similar results in PC T2*‐IDEAL and 2D PC‐MRI simulations. However, in volunteer studies, we observed a difference in the estimated velocity. The Bland–Altman plot in Figure 7B illustrated a difference of 1.49 mL per cardiac cycle in blood flow estimation. Statistical analysis of blood flow estimations confirmed these results, revealing significant differences between the PC T2*‐IDEAL method and standard 2D PC‐MRI. These differences warrant further investigation, as they diverged from our simulation results. While the implementation of the sequence was examined through multiple runs, we were unable to identify any issues. One key distinction between our approach and standard 2D PC‐MRI is that, in our method, each water component is unaffected by field inhomogeneity. Consequently, we did not apply phase correction, which is necessary for standard 2D PC‐MRI, and it was done directly on the MR scanner software. Another potential issue is related to our use of pre‐processed DICOM images. The data acquisition involved multiple coil elements, but we worked with DICOM data that had already undergone coil combination. A possible source of these differences could be that the coil combination process did not perform a weighted sum across the individual coil elements. However, this would likely have affected fat measurements as well, which we did not observe in the volunteer results. Unfortunately, we did not record the raw data, which would have allowed us to implement our own reconstruction and investigate further. Future work will address this limitation. However, since the scanner was operating on an older release version that is no longer supported for research, we were unable to acquire additional data.

In the volunteer acquisitions, both PC T2*‐IDEAL and standard 2D PC‐MRI methods were completed in an average of 119 s and 120 s respectively, as they were conducted under cardiac gating. PC T2*‐IDEAL acquisitions have the advantage of obtaining water‐fat components and velocity information within the same time frame as a standard 2D PC‐MRI acquisition. We used a thick slice (8 mm) in our acquisitions; however, this value can be adjusted to smaller sizes to suit different requirements. No acceleration techniques were used during the scans.

Previous research has demonstrated using readout gradients for velocity encoding in velocity measurement [29]. Nonetheless, multi‐echo gradient readouts restrict velocity measurement to in‐plane velocities, and the VENC setup poses challenges due to gradient amplitude and bandwidth constraints. Incorporating bipolar gradients allows for velocity measurement in customizable directions, effectively addressing these limitations.

The signal model assumes that all water has the same velocity. Incorporating a non‐moving tissue component could enhance the model's realism. However, we assume that any stationary water contribution is already accounted for within the existing model framework. That said, the model cannot handle water with different velocities within the same pixel. Future work could refine this approach by explicitly integrating a third, non‐moving component to better represent tissue contributions with varying velocities. This study has some limitations. We assumed no phase‐wrapping artifacts in the proposed PC T2*‐IDEAL technique in the water‐fat separation process, although we did not see phase‐wrapping artifacts in volunteers. We introduced an arbitrary shift between the two multi‐echo acquisitions (0.6 ms). This shift was chosen to create a difference between the sets of TEs acquired, and longer shifts increase the length of the last TE reducing the SNR; however, this TE is shorter than in a traditional 6 echoes acquisition that is usually required for the IDEAL technique. Finally, the sample size of volunteers is limited, and the resolution of the images acquired do not allow measuring the performance of the proposed method in a water‐fat interface.

5. Conclusion

We introduced a novel approach that enables concurrently acquiring water‐fat components and velocity images by merging 2D PC‐MRI and T2*‐IDEAL imaging techniques. Through a comprehensive evaluation, we have substantiated the efficacy of this approach through both numerical phantom experiments and imaging of healthy volunteers. Our findings demonstrated that the PC T2*‐IDEAL method, compared to the conventional T2*‐IDEAL method, delivers similar results in imaging water‐fat components and velocity measurements in simulations. However, when estimating velocity information from in vivo experiments, our results indicated differences between the PC T2*‐IDEAL method and the standard 2D PC‐MRI method, which require further investigation.

Supporting information

Figure S1 Water‐fat magnitude (‐), phase (rad), field map of inhomogeneities (Hz), velocity images (cm/s), and T2* decay (ms) comparison between PC T2*‐IDEAL methods and a standard T2*‐IDEAL acquisition to compare water and fat components, and a standard 2D PC‐MRI to compare velocity images in the numerical phantom.

Figure S2 Quantitative comparison of error obtained from the fat fraction in the tubes of the numerical phantom. We compared PC T2*‐IDEAL and standard T2*‐IDEAL results.

Data Availability Statement

Research data are not shared.