Comparison of compressed sensing and conventional 4D flow MRI for turbulent kinetic energy assessment in healthy participants and patients with aortic stenosis

Abstract

This study aims to evaluate the feasibility of turbulent kinetic energy (TKE) assessments using compressed sensing (CS)-accelerated three-dimensional time-resolved phase-contrast magnetic resonance imaging (4D flow MRI) in patients with aortic stenosis (AS). Conventional and CS 4D flow MRI (R = 2 with GRAPPA and R = 7.7 with CS, respectively) were sequentially acquired for voxel-wise comparison in healthy participants and patients. Total TKE was measured in both the ascending aorta (AAo) and the whole aortic region. The difference between GRAPPA and CS was expressed as the ratio of (CS 4D flow - Conventional 4D flow) to (Conventional 4D flow). A two-tailed paired t-test was used to assess statistical significance. In healthy participants, the maximum total TKE (TKE_max) measured by CS 4D flow MRI was substantially higher than that obtained with conventional 4D flow MRI, showing a 95.4% increase in the AAo region (0.74 ± 0.43 mJ by GRAPPA vs. 1.17 ± 0.72 mJ by CS; P = 0.053) and a 207.7% increase in the whole aortic region (1.13 ± 0.73 mJ by GRAPPA vs. 2.13 ± 0.95 mJ by CS; P = 0.006). In patients with AS, CS 4D flow MRI showed good agreement with conventional imaging, with only a 5.0% difference in TKE_max at the AAo (14.0 ± 4.6 mJ by GRAPPA vs. 14.8 ± 5.5 mJ by CS; P = 0.129) and a 7.4% difference in the whole region (16.3 ± 5.5 mJ by GRAPPA vs. 17.6 ± 6.5 mJ by CS; P = 0.050). CS 4D flow MRI demonstrated agreement, showing insignificant differences in total TKE measurements specifically within the AAo for AS patients. In healthy participants, CS-based TKE assessment showed larger relative differences compared with conventional 4D flow MRI, likely reflecting a low-TKE effect.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-55843-9.

Introduction

Three-dimensional time-resolved phase-contrast magnetic resonance imaging (MRI), also known as 4D flow MRI, has emerged as a powerful tool for assessing complex 3D blood flow dynamics in vivo. While conventional modalities, such as 2D phase-contrast (PC) MRI and Doppler echocardiography, have been established for flow quantification^1,2, 4D flow MRI offers a unique capability for the retrospective quantification of blood flow at any analysis plane within volumetric data^3,4. This innovation extends beyond flow quantification, enabling the evaluation of advanced metrics, including flow energetics, wall shear stress (WSS), and turbulent kinetic energy (TKE)^5–7. In particular, TKE estimation provides valuable insights into the energy dissipation of blood flow, offering crucial information for conditions such as bicuspid aortic valves and dilated ascending aortic geometries, which current echocardiography methods are likely unable to assess⁸.

However, conventional 4D flow MRI is associated with long scan times due to the acquisition of multidimensional data and the necessity for respiratory motion compensation, which is crucial for minimizing cardiothoracic motion artifacts. In addition, achieving accurate TKE estimation often requires a signal magnitude ratio, ( and represent the magnitude of MR signal at the flow-encoded and the reference scans, respectively), to approach ~0.6. Consequently, velocity-encoding (VENC) values are typically set below the maximum velocity to obtain ~0.6⁹. This can potentially lead to velocity aliasing in MR phase images. Thus, additional MR scans are required to obtain appropriate velocity data from MR phase images without aliasing, using a VENC value comparable to the maximum velocity. These repeated MR scans pose practical challenges to test TKE assessments in patients with aortic valve diseases, and further hinder the clinical applicability of TKE estimation.

Recent advancements in 4D flow MRI have introduced compressed sensing (CS)-accelerated MRI imaging, leveraging the inherent compressibility of MR data^10–14. Ma et al. have demonstrated substantial reductions in scan time, with CS 4D flow MRI scans taking only 2 minutes¹⁵. Moreover, key hemodynamic parameters such as V_max and Q_max obtained from CS 4D flow MRI are in good agreement with those from conventional 4D flow MRI. As the clinical feasibility of CS 4D flow MRI with reduced scan times has been established, it was also observed that CS-accelerated image reconstruction can lead to the underestimation of hemodynamic parameters, such as flow rate and WSS, by approximately 10% in a parallel comparison with conventional 4D flow¹⁶.

Despite extensive research on CS 4D flow MRI and its impact on various hemodynamic parameters, including velocity and WSS, the effect of CS acceleration on TKE estimation remains largely unexplored. Therefore, this study aimed to evaluate the performance of TKE assessment using CS 4D flow MRI, specifically in patients with aortic stenosis (AS), through a parallel comparison with conventional 4D flow MRI commonly used in clinical settings.

Methods

Study cohort

Conventional and CS 4D flow MRI scans were prospectively acquired from thirteen healthy participants (mean age = 29 ± 5; range = 21 to 38; 7M/6F) and retrospectively from twenty-five patients with AS. Three patient datasets were further excluded: two due to poor signal-to-noise ratio caused by motion artifacts, and one due to partial coverage of the aorta (age = 78 ± 5; range = 66 to 85; 8M/14F; n = 2 with bicuspid aortic valve and n = 20 with tricuspid aortic valve). The demographics of healthy participants and AS patients are summarized in Table 1. All AS patients were diagnosed with moderate severity of AS by echocardiography (Table 2), and no valve replacement had been performed. Human studies were conducted after obtaining approval from the Institutional Review Board (IRB) of Daegu Gyeongbuk Medical Innovation Foundation (approval number: DGMIF-20210721-HR-001-01) for healthy participants and Eunpyeong St. Mary’s Hospital (IRB No. PC20OCSI0133) for AS patients, following the relevant guidelines and regulations. This study adhered to the principles of the Declaration of Helsinki. Written informed consent was obtained from all participants.

Table 1.

Demographics and MRI scan parameters for healthy participants and AS patients.

	Healthy participants		AS patients.
N (m/f)	13 (7/6)		22 (8/14)
BAV (%)	0 (0)		2 (9.1)
Age [y]	29 ± 5 [21‒38]		78 ± 5 [66‒85]
Weight [kg]	69.4 ± 15.5 [46‒90]		66.3 ± 10.9 [50‒90]
Height [cm]	171.4 ± 10.6 [151‒190]		159.3 ± 7.9 [150‒175]
BSA [m2]	1.8 ± 0.2 [1.4‒2.2]		1.7 ± 0.2 [1.4‒2.1]
Scan parameters	Conventional	CS	Conventional	CS
Scan time [s]	420 ± 90 (336‒582)	144 ± 36 (96‒210)	390 ± 72 (270‒534)	144 ± 30 (102‒198)
Acceleration Rate, R	2	7.7	2	7.7
Echo time [ms]	2.58‒3.34	3.02‒3.31	2.25‒2.48
Repetition time [ms]	4.9‒5.2		4.6‒4.7
Field of view [mm3]	271‒320 × 231‒256 × 54‒64		400 × 320 × 70
Spatial resolution [mm3]	1.7‒2.0		2.5
Interpolated temporal resolution [ms]	27.6‒45.6	28.2‒42.7	25.1‒49.6	25.0‒49.6
Bandwidth [Hz/voxel]	495	560	558
Flip angle [°]	7‒15	8	7 (12 with contrast)
VENC [cm/s]	70‒90		188‒300
Cardiac time frames	25		25

Table 2.

Echocardiographic biomarkers for AS patients.

Echocardiography	AS patients
Aortic valve area [cm2]	1.2 ± 0.1
Peak velocity [m/s]	3.4 ± 0.2
Mean pressure gradient [mmHg]	26.6 ± 4.6
Left-ventricular ejection fraction [%]	61.9 ± 6.7
Left-ventricular mass index [g/m2]	91.6 ± 18.0

4D flow MRI image acquisitions

4D flow MRI scans for healthy participants and AS patients were conducted on two different 3T MRI systems: the MAGNETOM Skyra (Siemens Healthcare) at the Daegu Gyeongbuk Medical Innovation Foundation and the MAGNETOM Vida (Siemens Healthcare) at Eunpyeong St. Mary’s Hospital, respectively. 4D flow MRI scans were added to the clinical scans of AS patients to supplement the AS diagnosis process and were not part of their routine clinical assessments. Out of 22 AS patients, 16 received an infusion of the contrast agent gadoterate meglumine (0.2 mmol/kg) as part of their clinical procedure. The accuracy of TKE estimation can vary according to the magnitude signal attenuation ratio (), which is optimized when approaching ~0.6 (analytically e^-1/2)⁹. Thus, a VENC scout was first performed to determine the peak velocity. The acquisition order was fixed across all participants and not randomized. CS 4D flow (R = 7.7) was then acquired using a VENC set to approximately 75% of the peak velocity to optimize sensitivity for IVSD-based TKE estimation. Subsequently, conventional 4D flow (GRAPPA, R = 2) was acquired in the same imaging session using the same VENC setting (approximately 75% of the peak velocity) to ensure physiological consistency. All 4D flow scans were retrospectively ECG-gated during free breathing using navigator gating, whereby the scan time broadly varied depending on heart rate and respiratory navigator efficiency. For example, in AS patients, heart rate was 69.1 ± 13.4 bpm [range, 48.4–95.7] for GRAPPA and 69.4 ± 13.4 bpm [range, 48.4–96.0] for CS, while respiratory navigator efficiency was 64.0 ± 17.2% [range, 25.0–90.0] for GRAPPA and 63.2 ± 20.0% [range, 24.7–94.0] for CS. The sequence parameters between conventional and CS 4D flow scans are summarized in Table 1.

CS reconstruction

The CS reconstruction technique has been well described in the previous references^15,16. In brief, the CS reconstruction involved solving the optimization problem represented by equation (1):

1

where t denotes a time point; represents the frames that need to be reconstructed for all t; and and are the system matrix and the measured data for each t, respectively. Spatial and temporal L1 regularization was conducted by employing a Haar wavelet transform where and are the spatial and temporal Wavelet transforms, respectively; and and are the spatial and temporal regularization parameters, respectively¹⁷. A FISTA optimization¹⁸ with 30 iterations resolved Equation (1) using = 0.0015 and = 5 , while considering a maximum image magnitude intensity of 1.

4D flow MRI data analysis

For velocity estimation, post-processing was performed to apply eddy-current correction, noise filtering, and anti-aliasing to MR images, acquired at lower VENC comparable to peak velocity¹⁹. As significant aliasing was observed throughout systole phases, anti-aliasing process was rigorously employed. This process was semi-automatically executed using our in-house MATLAB codes (Mathworks, Natick, MA)¹⁹. Subsequently, 3D phase-contrast magnetic resonance angiography (PC-MRA) images were generated from conventional 4D flow MRI to segment fluid and non-fluid regions, utilizing 3D Slicer (Version 5.4.0) software. The same segmentation of the fluid region was used for CS 4D flow MRI, enabling voxel-by-voxel comparison for velocity and TKE parameters without employing any co-registration methods. A noise filter, based on the method of the 99^th percentile maximum value²⁰, was applied to prevent capturing increased noise within a region of interest (ROI). Peak velocity was obtained within the ROI, which was selected to extend from just behind the coarctation to the end of the jet. Peak flow rate was also obtained behind the coarctation and averaged along the ROI to minimize the noise effect.

For TKE estimation, an intravoxel standard deviation of velocity (IVSD), which is associated with turbulence-induced signal attenuation in MR magnitude images^9,21, was initially quantified using the following equation (2):

2

where represents the standard deviation at i-direction, represents the net motion sensitivity, which equals π / VENC. and represent MR magnitude signal of reference and flow-encoded scans, respectively.

TKE per unit volume was subsequently estimated from as follows:

3

where ρ is the density of blood and is the standard deviation at i-direction. It is important to note that the presence of both positive and negative noise contributions in the logarithm term, , eliminates the need to take the square root when calculating total TKE [mJ]^22,23. The obtained TKE values near the vessel edges, extracted by eroding one pixel, were further filtered using a 3×3 median filter to reduce border noise, in line with methods reported in previous studies^24,25.

Total TKE was volumetrically calculated by summing TKE per unit volume within the ROI. The maximum of total TKE and the sum of total TKE values during the systole (total TKE_max and total TKE_sys) were obtained. TKE parameters were regionally assessed at the AAo and whole aortic region. Velocity and TKE distributions at peak systole were visualized as MIPs, with representative images displayed as velocity streamlines, along with TKE and velocity colormaps. Voxel-by-voxel comparisons were employed based on the sequential acquisition of conventional and CS 4D flow MRI scans, and Bland-Altman analysis was also conducted to assess mean bias and limits of agreement (bias ± 1.96×SD) between conventional and CS 4D flow MRI. Change for CS [%] (% for CS) was defined as the ratio of (CS 4D flow – Conventional 4D flow) to (Conventional 4D flow). A two-tailed paired t-test was employed to evaluate statistical differences in peak velocity, peak flow rate, total TKE_max, and total TKE_sys. A p-value < 0.05 was considered statistically significant. For each timeframe, a two-tailed paired t-test was performed, and P-values were adjusted using the Benjamini-Hochberg method to control the false discovery rate across all timeframes.

In vitro 4D flow MRI acquisitions

A coarctation phantom model was used to evaluate % for CS, as observed in healthy participants and AS patients, by assessing total TKE within regions with and without jet flow. The 4D flow scans were performed on a 3T MRI system (MAGNETOM Skyra, Siemens Healthcare, Erlangen, Germany) at the Daegu Gyeongbuk Medical Innovation Foundation, with acceleration factors of R = 2 for conventional 4D flow MRI and R = 7.7 for CS 4D flow MRI. For a parallel comparison of CS and conventional 4D flow, images were sequentially acquired with a VENC of 375 cm/s, corresponding to approximately 75% of the peak velocity, and retrospectively gated using an external triggering signal from an in-house pulsatile pump²⁶. Change for CS was evaluated using voxel sizes of 1.5 mm, 2.0 mm, and 2.5 mm.

Results

Comparisons between conventional and CS 4D flow in healthy participants

CS 4D flow with R = 7.7 had a large reduction in scan time compared to conventional 4D flow in healthy participants (420 ± 90 s for conventional vs. 144 ± 36 s for CS). Fig. 1IA depicts the representative differences in TKE patterns by CS-accelerated 4D flow, particularly in the proximal region of the aortic jet flow (indicated by arrows in the velocity stream with the TKE colormap in Fig. 1IB). However, the locations where TKE patterns were different varied when compared to the velocity colormap (Insets in the Fig. 1IB), where higher velocity intensity was observed at the sides of the jet flow and in the descending aorta.

Fig. 1.

Representative comparisons of velocity and TKE parameters between a healthy participant (I) and an AS patient (II). (A) MIPs of conventional 4D flow (R = 2) and CS 4D flow MRI (R = 7.7) are shown at peak systole. A black diamond indicates the location of maximum TKE. ROIs (I.A, top left) are used to quantify the total TKE in the ascending aorta (total TKE_AAo) and the whole region (total TKE_whole). (B) The differences in TKE distributions between conventional and CS 4D flow are compared using velocity streamlines with a TKE colormap, shown alongside a velocity colormap (inset). Arrows indicate the locations of distinct differences in TKE and velocity patterns between conventional and CS 4D flow MRI. (C) Temporal variations of peak velocity, total TKE_AAo, and total TKE_whole are compared. Voxel-by-voxel Bland-Altman (D) and orthogonal regression (E) analyses are conducted to compare TKE values across the whole region.

The total TKE curves at the AAo (TKE_AAo) and the whole region (TKE_whole), plotted against cardiac time frames, showed increase in total TKE during systole (Fig. 1IC), while the velocity curve remained nearly identical, except during late diastole. Voxel-by-voxel Bland-Altman and orthogonal regression analyses further demonstrated a mean bias of 7.8 mJ, along with a low correlation (ICC = 0.42) throughout the whole region during systole (Fig. 1ID, 1IE). Orthogonal regression analysis for all healthy participants also showed a low correlation, with an ICC of 0.21 (Supplementary Fig S1).

Additionally, the total TKE_AAo and the total TKE_whole​ for all healthy participants demonstrated significant increases, particularly during systole (Fig 2). Bland-Altman analysis also revealed that the mean biases were -0.00 m/s for peak velocity, 0.43 mJ for total TKE_max​ at the AAo, and 1.00 mJ for total TKE_max​ in the whole region. We also observed that total TKE_max and total TKE_sys significantly increased, especially at the whole region, by 207.7 ± 286.4% (P = 0.006) and 720.8 ± 1008.6% (P = 0.004), respectively (Table 3). Our in vitro 4D flow MRI experiment also revealed substantial increases in % for CS within the non-jet flow region, ranging from 122.1% to 352.7% for total TKE_max and from 54.4% to 421.4% for total TKE_sys (Supplementary Fig. S2 and Supplementary Table S1).

Fig. 2.

(A) Temporal variations of peak velocity, total TKE_AAo, and total TKE_whole for all 13 healthy participants. Solid and dashed lines indicate mean and standard deviation for conventional 4D flow and CS 4D flow MRI, highlighted in blue and red colors, respectively. (B) Bland-Altman comparisons using the maximum of corresponding parameters. Mean biases and 95% limits of agreement (±1.96 SD) are shown by solid and dashed black lines, respectively. (*) denotes statistical differences (P < 0.05) between conventional 4D flow and CS 4D flow MRI after Benjamini-Hochberg correction for multiple comparisons across timeframes.

Table 3.

Comparisons of peak velocity, peak flow rate, total TKE_max, and total TKE_sys between conventional 4D flow (R = 2) and CS 4D flow MRI (R = 7.7) in healthy participants and AS patients. TKE parameters were obtained at the ascending aorta (AAo) and the whole region. (*) denotes the significant difference between conventional 4D flow and CS 4D flow MRI with *p<0.05, **p<0.01.

		Healthy participants (n = 13)				Patients (n = 22)
		GRAPPA	CS	% for CS	P-value	GRAPPA	CS	% for CS	P-value
Peak velocity [m/s]		1.38 ± 0.25	1.38 ± 0.24	0.5 ± 9.7	0.981	3.65 ± 0.99	3.47 ± 0.85	-3.6 ± 11.1*	0.029
Peak flow rate [mL/s]		269.3 ± 61.5	266.7 ± 61.4	-0.7 ± 7.0	0.623	245.5 ± 69.7	240.6 ± 71.5	-2.4 ± 9.2	0.263
Total TKEmax [mJ]	AAo	0.74 ± 0.43	1.17 ± 0.72	95.4 ± 127.4	0.053	14.0 ± 4.6	14.8 ± 5.5	5.0 ± 19.3	0.129
	Whole	1.13 ± 0.73	2.13 ± 0.95	207.7 ± 286.4**	0.006	16.3 ± 5.5	17.6 ± 6.5	7.4 ± 19.3*	0.050
Total TKEsys [mJ]	AAo	2.10 ± 1.44	4.21 ± 2.60	212.0 ± 293.3*	0.016	51.9 ± 19.3	56.5 ± 25.1	6.5 ± 20.7	0.056
	Whole	3.46 ± 3.13	7.99 ± 3.53	720.8 ± 1008.6**	0.004	61.4 ± 23.2	68.8 ± 29.6	10.9 ± 21.2*	0.017

Comparisons between conventional and CS 4D flow in patients with AS

The scan times of conventional and CS 4D flow in AS patients were 390 ± 72 s and 144 ± 30 s, respectively. Fig. 1IIA shows representative MIPs for conventional and CS 4D flow MRI, displaying a similar TKE distribution in contrast to the healthy participant shown in Fig. 1IA. However, CS 4D flow tended to provide a somewhat blunted TKE distribution at the AAo. Two distinct differences, indicated by arrows, are shown in the velocity stream with the TKE colormap in Fig 1IIB. The locations showing differences in TKE patterns appeared nearly identical to those showing differences in velocity patterns, as visualized in the streamlines with velocity colormaps (insets in Fig. 1IIB).

The total TKE_max curves demonstrated the distinct increases both in the AAo and the whole region (Fig. 1IIC). Voxel-by-voxel Bland-Altman analysis showed a mean bias of 16.5 mJ (Fig. 1IID). Orthogonal regression analyses exhibited good correlations of ICC = 0.81 for the representative AS patient (Fig. 1IIE) and 0.70 for all AS patients (Supplementary Fig. S1).

No statistically significant differences were observed across all timeframes in AS patients for velocity, total TKE_AAo and total TKE_whole, except for a single diastolic phase in total TKE_whole (Fig. 3). In addition, Bland-Altman analysis for all AS patients revealed mean biases of -0.18 m/s for peak velocity, 0.84 mJ for total TKE_max at the AAo, and 1.31 mJ for total TKE_max in the whole region. We also observed small percentage changes for CS, with -3.6% for peak velocity (P = 0.029), 5.0% for total TKE_max at the AAo (P = 0.129), and 6.5% for total TKE_sys at the AAo (P = 0.056) (Table 3), suggesting good agreement between conventional and CS 4D flow MRI. Our in vitro findings also showed that % for CS in the jet flow region was relatively small compared to that in the region without jet flow, ranging from -0.22% to 15.8% for total TKE_max and from 9.9% to 22.7% for total TKE_sys (Supplementary Fig. S2 and Supplementary Table S1).

Fig. 3.

(A) Temporal variations of peak velocity, total TKE_AAo, and total TKE_whole for all 22 AS patients. Solid and dashed lines indicate mean and standard deviation for conventional 4D flow and CS 4D flow MRI, highlighted in blue and red colors, respectively. (B) Bland-Altman comparisons using the maximum of corresponding parameters. Mean biases and 95% limits of agreement (±1.96 SD) are shown by solid and dashed black lines, respectively. (*) denotes statistical differences (P < 0.05) between conventional 4D flow and CS 4D flow MRI after Benjamini-Hochberg correction for multiple comparisons across timeframes.

Discussion

In this study, we demonstrated that CS 4D flow significantly increased total TKE parameters compared to conventional 4D flow in healthy participants, with differences ranging from 2 to 8 folds for CS. For AS patients, CS resulted in relatively small differences in total TKE_max at the AAo and whole region by 5.0% and 7.4%, respectively. These findings suggest that CS 4D flow may be useful for estimating TKE within AS patients, where elevated turbulent flow was observed. However, because healthy participants and AS patients were scanned on different MRI systems and differed in age and sequence parameters, the present findings should be interpreted primarily as within-group comparisons between conventional and CS 4D flow MRI rather than direct between-group comparisons. This approach may facilitate clinical assessment of turbulent energy dissipation in AS patients while significantly reducing scan time.

The CS-based approach has been associated with the underestimation of MRI-derived velocity parameters^11,27. This underestimation is likely due to both spatial and temporal undersampling, as well as regularization¹⁵. However, our study demonstrates that peak velocity and peak flow rate were not significantly different between conventional and CS 4D flow for healthy participants. This may be attributed to the relatively low VENC setting used for TKE assessment in the present study compared with the VENC settings used in previous CS 4D flow MRI studies, which were generally selected to capture peak velocity. Since this study was aimed to test feasibility of CS 4D flow MRI for TKE assessment, a lower VENC than peak velocity is required (typically, 150 cm/s is used for healthy participants from the 4D flow MRI consensus²⁸). It is well-known that a higher VENC can lead to a lower velocity-to-noise ratio, ultimately resulting in poor signal quality in low-flow regions²⁹. In addition, a recent study also demonstrated that a low VENC could more accurately capture peak velocity than a higher VENC³⁰. Thus, the low VENC setting in this study may improve the velocity-to-noise ratio, leading to better agreement in peak velocity between CS and conventional 4D flow.

We observed that CS 4D flow increased total TKE at the AAo and whole aortic region during both systole and diastole in healthy participants. The prior CFD study demonstrated that TKE increases at a lower VENC of 0.5 m/s, where total TKE_max in the whole region increased to 5.4, 6.3, and 7.6 at R ≈ 1.9, 9.1, and 18.1, respectively, suggesting that undersampling itself may contribute to the observed increase in total TKE during systole in healthy participants³⁰. However, when the underlying TKE level is low, as expected in relatively non-turbulent or non-jet flow regions, small absolute differences or noise contributions may produce large relative percentage differences. This interpretation is supported by our in vitro experiment, in which larger percentage changes with CS were observed in the non-jet flow region than in the jet-flow region (Supplementary Fig. S2 and Supplementary Table S1). Therefore, the larger relative differences observed in healthy participants should be interpreted primarily as a low-TKE effect.

In AS patients, CS 4D flow showed a generally similar TKE distribution compared with conventional 4D flow, although a blunted TKE region was observed in the AAo (Fig. 1IIA). This region was visually observed in a similar anatomical location to differences in the velocity-field appearance between conventional and CS 4D flow (Fig. 1IIB), but not to imply a direct relationship between the IVSD-based TKE distribution and velocity-field appearance.

In addition, AS patients exhibited increases of total TKE_max and total TKE_sys with CS 4D flow, ranging from 5.0% to 10.9% (Table 3), with significant differences observed when analyzing the whole aortic region. This suggests that CS 4D flow allows consistent TKE assessments within AAo region, whereas inclusion of the arch and DAo further introduces additional bias. Previous work with conventional 4D flow demonstrated that TKE parameters across whole aortic region could discriminate between dilated AAo and bicuspid aortic valve from normal controls⁸. Our findings therefore highlight that whole-aorta TKE assessment using CS 4D flow should be interpreted with caution, as it may be subject to potential biases.

Our CS 4D flow detected relatively small differences in peak velocity and peak flow rate, both ranging from -4% to -2% across conventional and CS 4D flow, which was less pronounced than the ~10% underestimation reported in previous studies^15,16. This discrepancy may be also related to the lower VENC setting used in our study, which, similar to the healthy cohort, allowed for more accurate peak velocity capture³⁰. These findings suggest that CS 4D flow performance may be influenced by both acceleration rate and velocity-to-noise ratio across different VENC settings.

A recent study demonstrated that a multi-VENC approach provides reliable estimation of both velocity and TKE simultaneously, as low VENC optimizes sensitivity to IVSD while high VENC ensures peak velocity measurement without aliasing in the phase images of 4D flow data³⁰. Although conventional multi-VENC increases scan time, CS acceleration may mitigate this limitation by enabling reliable acquisition of both velocity and TKE within practical scan durations. In addition, machine learning-based anti-aliasing strategies could be applied during post-processing to correct for velocity aliasing at lower VENC, further enhancing the feasibility of CS-based TKE assessment³¹.

The current study has several limitations: (1) A systematic investigation of TKE estimation across varying acceleration rates would be beneficial, as the acceleration rate affects both TKE and flow-derived parameters. (2) A recent study demonstrated that the parameter λ used in CS reconstruction governs the strength of CS regularization and contributes to the discrepancies observed between conventional and CS 4D flow MRI³². Therefore, further studies are warranted to delineate its impact on TKE estimation. (3) The differences between the Skyra scanner used for healthy participants and the Vida scanner used for AS patients may have contributed to systematic biases, as different scanners from the same vendor or from different vendors can serve as major confounders³³. However, this study compares TKE values between conventional and CS 4D flow within each scanner, thereby not directly resulting from this issue. Future studies that might compare TKE values in AS patients acquired from Skyra and Vida both, then caution may be considered for systemic biases.

(4) CS-accelerated TKE distribution may be affected differently by the spatial and temporal evolution of flow patterns. However, the current study did not include a systematic analysis of the effects of blood flow structures. An in-depth investigation into the relationship between complex blood flow and the corresponding CS-accelerated signal changes in MR magnitude images may be necessary to better understand CS reconstruction. (5) Clinical parameters such as peak velocity, mean pressure gradient, and aortic valve area were not widely distributed among AS patients diagnosed with moderate AS. While the current study demonstrated the feasibility of using CS-accelerated TKE estimation, larger cohorts are needed to evaluate the % for CS across a wide range of pathophysiological conditions. (6) Inconsistencies in age and sequence parameters, including voxel size, between healthy participants and AS patients can affect TKE estimation. Therefore, future studies using comparable cohorts and standardized sequence parameters would be valuable for systematically comparing TKE parameters.

Conclusion

This study demonstrated the feasibility of using CS 4D flow MRI for TKE estimation, particularly in AS patients. Given the predominance of turbulent flow in AS, CS 4D flow showed good voxel-by-voxel agreement in TKE estimation. Larger relative TKE differences were observed when the underlying TKE level was low, suggesting that CS-based TKE assessment should be interpreted with caution in low-TKE or non-jet flow regions. These findings provide valuable insights into assessing AS severity through the energy dissipation of blood flow, with the potential to substantially reduce scan times in routine clinical practice.

Author contributions

S. Park, J.-E. Yi, A.J. Barker, and H. Huh participated in the study design. S. Park and J.-E. Yi analyzed the data. S. Park and J.-E. Yi drafted the manuscript. Others participated in editing and reviewing the manuscript. All authors read and approved the final version of the submitted manuscript.

Funding

This research was supported by NRF grant funded by the Korea government (MSIP) (RS-2021-NR061225, RS-2024-00451584), supported by Commercialization Promotion Agency for R&D Outcomes (COMPA) funded by the Ministry of Science and ICT (MSIT) Grant No. 2710086063 (RS-2025-02653196), supported by a grant of the Korea Health Technology R&D Project through the Korea Health Industry Development Institute (KHIDI) funded by the Ministry of Health & Welfare, Republic of Korea (RS-2025-02263007), supported by the Korean Cardiac Research Foundation (202002-01), and supported by the Regional Innovation System & Education (RISE) program through the Gangwon RISE Center, funded by the Ministry of Education (MOE) and the Gangwon State (G.S.), Republic of Korea (2026-RISE-10-002).

Data availability

The datasets used and or analyzed during the current study are available from the corresponding author upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.