Post-valvular energy exchange in bicuspid aortic valve with regurgitation and stenosis and its association with left ventricular workload: a 4D flow magnetic resonance imaging cross-sectional study

Abstract

Background

Bicuspid aortic valve (BAV) regurgitation and stenosis considerably alter post-valvular flow dynamics and impose additional energetic load on the left ventricle (LV). We therefore sought to determine whether 4D Flow MRI-derived ascending-aortic kinetic energy (KE) and viscous energy loss (EL), can differentiate BAV subtypes and healthy controls, and are associated with LV remodeling markers.

Methods

Seventy-one participants (19 BAV without valve dysfunction, 17 with isolated aortic regurgitation (BAV-AR), 15 with isolated aortic stenosis (BAV-AS), and 20 healthy controls) underwent 3.0 T magnetic resonance imaging (MRI), including cine balanced SSFP and 4D‐Flow. Post valvular KE, viscous EL, and the dimensionless EL index were computed from the 4D Flow velocity fields. Global 3D LV strain metrics were derived via cine SSFP feature-tracking technique. Between‐group differences were assessed with one‐way ANOVA or Kruskal–Wallis tests, and associations were evaluated using Spearman’s rank correlation.

Results

Average ascending aortic KE rose progressively from controls (3.3[2.3–4.3]) to uncomplicated BAV (6.7[5.3–9.1]), to BAV-AS (15.4[12.2–29.5]) and peaked in the BAV-AR (19.4[14.9–21.3], p < 0.001). Peak-systolic viscous EL was significantly elevated in both the stenotic (16.2 [9.1–24.4] mW) and regurgitant (11.4 [9.5–17.6] mW) groups compared to controls (4.1 [3.4–5.7] mW), but not in the uncomplicated BAV (6.4 [5.1–8.0] mW). Over the entire systole, viscous EL in the uncomplicated BAV (3.3 [2.5–4.1] mW) was also statistically increased compared to controls (1.7 [1.3–2.3] mW). KE correlated more strongly with regurgitation severity (rho = 0.50, p < 0.001), and EL with stenosis severity (rho = 0.48, p < 0.001). Aortic surgery referral was more closely associated with elevated KE (rho = 0.65, p < 0.001) and viscous EL (rho = 0.64, p < 0.001) than with aortic diameter (rho = 0.50, p < 0.001). Left ventricular Mass index and peak diastolic strain rate circumferential were correlated but more strongly with KE than viscous EL.

Conclusions

4D Flow MRI-derived post-valvular KE and viscous EL may serve as sensitive early biomarkers of LV dysfunction, and might outperform aortic diameter in risk stratification, and guide optimal intervention timing in BAV diseases while they need to be validated in broader populations.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12880-025-02026-z.

Introduction

Bicuspid aortic valve (BAV) is the most prevalent congenital valve defect associated with the development of aortic stenosis, aortic regurgitation, either in isolation or in combination [1]. Altered aortic blood flow patterns are common in BAV disease, even in the absence of secondary complications [2]. Both aortic stenosis (AS) and regurgitation (AR) increase left ventricular (LV) workload, prompting compensatory remodeling and, over time, potential LV dysfunction and heart failure [3–5]. This LV deterioration can contribute to substantial cumulative alterations in post-valvular flow patterns in this cohort [6]. As the proximal conduit for left ventricular ejection, the ascending aorta (AAo) plays a pivotal role in modulating LV afterload [7]. Traditional cardiac catheterization, the gold standard for measuring LV load associated with aortic valve pathologies, is an invasive procedure and susceptible to pressure recovery error [8, 9]. Hence, deriving non-invasive biomarkers that quantify the energetic load on the LV resulting from BAV-induced aortic flow alterations is promising [10]. Mechanical energy exchange in the case of idealized blood flow is assumed to be conserved within the circulatory system. (i.e., a decrease in pressure from one location to another may be balanced by an increase in the blood flow kinetic energy). Under non-ideal flow conditions, part of the kinetic and potential energy is permanently lost as thermal and acoustic energy, commonly referred to as frictional energy loss (EL) [10, 11]. EL is a well-established hemodynamic concept rooted in fluid dynamics, can be used to assess the influence of valvular performance on adjacent cardiovascular structures and function [10]. Four-dimensional flow magnetic resonance imaging (4D Flow MRI) has emerged as a powerful technique for capturing in-vivo, time-resolved three-dimensional velocity fields [12, 13]. This advancement underscores the need to re-evaluate the utility of EL as a marker of cardiac performance in the setting of valvular lesions. Viscous EL, which is sensitive to abnormal laminar or complex nonturbulent flow patterns such as vortex or helix formation, is commonly observed in conditions like aortic valve disease or dilation. It can be directly calculated from the 3D velocity field by solving the incompressible Navier-Stokes energy equations [14].

Recent MRI advancements also enable the simultaneous capture of cardiac structure and function through feature-tracking of routine cine MRI. This approach allows retrospective quantification of myocardial strain as a highly sensitive biomarker of myocardial deformation, fibrosis, and remodeling [15]. Hence, understanding how post-valvular mechanical energy can be derived from velocity data provides valuable insights into cardiac workload. Post-valvular kinetic energy (KE) reflects the work required to accelerate blood to its instantaneous velocity, whereas viscous energy loss (EL) represents the conversion of kinetic energy into heat due to viscous friction within the blood flow. These parameters characterize the efficiency of energy transfer across the aortic valve and may offer additional markers of LV workload and cardiac risk assessment [10].These quantifications are particularly overlooked in pathological BAV cases and those with isolated aortic valve lesions. Therefore, this study aimed to employ cardiovascular MRI techniques to determine if post-valvular KE and viscous EL can differentiate between BAV subgroups with and without lesions, as well as from healthy controls. Additionally, we sought to investigate whether these hemodynamic parameters could serve as indicators of increased LV myocardial workload associated with BAV lesions.

Materials and methods

Study cohorts

We retrospectively identified a total of 51 BAV patients with varying degrees of stenosis and regurgitation as a subgroup from a prospective observational registry with a clinical focus from our local Cardiovascular Imaging Registry of Calgary (CIROC). Aortic regurgitation was assessed using through-plane 2D phase-contrast flow imaging by placing the analysis plane at the aortic valve and contouring throughout the cardiac cycle. The regurgitation fraction (RF) was calculated as the ratio of backward to forward flow in the plane at the aortic valve [16]. Aortic stenosis was graded based on the peak velocity at the aortic valve plane. Both regurgitation and stenosis were graded according to American Heart Association (AHA) guidelines [17]. BAV patients were classified into three groups: 19 BAV patients without or with trivial regurgitation or stenosis (BAV-No VD); 17 BAV patients with isolated aortic regurgitation (BAV-AR) by grouping moderate to severe aortic valve regurgitation; and 15 BAV patients with isolated aortic stenosis by grouping moderate to severe aortic stenosis (BAV-AS). Isolated aortic valve stenosis and regurgitation means excluding cases with combined moderate to severe regurgitation and stenosis. Our BAV cohort was also free of mitral valve deficiencies. Additionally, 23 healthy controls with tricuspid aortic valves (TAV) were recruited specifically for research purposes. All the subjects were required to have no contraindications for MRI. All the subjects underwent routine cardiovascular magnetic resonance imaging (MRI) followed by 4D Flow MRI. Left ventricular function and flow measurements were evaluated using post-processing commercial software (cvi42 v5.11.5, Circle Cardiovascular Imaging Inc., Calgary, AB, Canada). This study received ethics approval from the Conjoint Health Research Ethics Board (CHREB) at the University of Calgary. The CHREB functions in accordance with the Tri-Council Policy Statement: Ethical Conduct for Research Involving Humans (TCPS 2), Health Canada Food and Drug Regulations Division 5, Part C, ICH Guidance E6: Good Clinical Practice, and the provisions and regulations of the Health Information Act (RSA 2000, c H-5). All subjects invited to participate in the research study were required to complete an informed consent form.

Magnetic resonance imaging

Cardiovascular MRI was conducted on 3.0 Tesla Siemens scanners (Skyra or Prisma, Erlangen, Germany) equipped with a 32-channel body coil. Approximately 5–10 min after the administration of gadolinium contrast (Gadovist, Bayer, Canada), 4D flow MRI was performed using free-breathing with diaphragmatic navigator gating and retrospective electrocardiogram (ECG) gating. Acquisition parameters were configured as follows: velocity encoding (VENC) range in all directions = 150–400 cm/s, flip angle (FA) ∼ 15° with, ∼7° without gadolinium, acquired spatial resolution (row × column × slice) = 2.0-2.5 × 2.0-2.5 × 2.5-3 mm³, field of view (FOV) with sagittal slab = 240–350 × 320–400 mm², temporal resolution = 25–35 ms, timeframe = 30, bandwidth (BW) = 455–495 Hz/Pixel, echo time (TE) = 2.01–2.35 ms, and pulse repetition time (TR) = 4.53–5.07 ms, k-t generalized autocalibrating partially parallel acquisition (k-t GRAPPA), R = 4 [18, 19]. Total scan time ranged from 8 to 12 min, influenced by physiological factors, selected imaging parameters, and the efficiency of respiratory gating.

Standard analyses of LV volume, function, and structure were performed using segmented ECG-gated, time-resolved cine balanced steady-state free precession (bSSFP) imaging in four-, three-, and two-chamber views, and short-axis views, covering the entire heart at end-expiration. Scan parameters included: FA = 40–55°, TE = 1.5 ms, TR = 37.3 ms, spatial resolution (row × column × slice) = 1.0 × 1.0 × 8.0 mm³, FOV = 256 × 200 mm², and BW = 975 Hz/Pixel. The same sequences were executed on both scanners.

Data analysis

4D flow MRI

Figure 1 illustrates the workflow of the data analysis strategy. Initially, 4D Flow MRI underwent preprocessing steps to correct for eddy currents and Maxwell terms, as well as velocity aliasing, if necessary [20]. Following preprocessing, a phase-contrast magnetic resonance angiogram (PC-MRA) over the entire cardiac cycle was generated to segment the thoracic aorta, using a previously reported method [20]. Furthermore, the sinotubular junction and the takeoff of the brachiocephalic artery served as anatomical landmarks for the automatic delineation of the AAo. Then, flow-time curves were computed for each subject using the AAo mask to define the peak systolic time point. Ascending aortic KE at a given time instance was computed in joules, on a voxel-by-voxel basis, and the individual voxel values were then integrated over the segmented AAo volume. Non-turbulent energy loss was estimated noninvasively using viscous dissipation, reflecting internal fluid friction. Instantaneous power (in watts) was calculated by multiplying blood viscosity with the integrated dissipation across each voxel within the segmented AAo volume, based on the incompressible Navier-Stokes equations. To focus on intraluminal flow features such as vortices and helical patterns, and to avoid boundary shear–related dissipation, near-wall voxels were excluded from the viscous dissipation calculation by masking them as NaN (‘not a number’). 4D Flow MRI enabled the calculation of viscous EL over the full cardiac cycle by integrating the instantaneous losses, resulting in the total energy dissipated due to viscosity in joules. This value was then normalized by the integrated KE in the AAo during the heartbeat to derive the viscous EL index. EL index is a dimensionless parameter representing the proportion of KE lost to friction throughout the cardiac cycle, Fig. 1b.

Fig. 1.

Workflow illustration (a) MRI acquisitions including cine bSSFP and 4D Flow data, (b) thoracic aorta segmentation and calculation of KE, viscous EL, and EL index in the AAo, and (c) calculation of LV strain parameters using long- and short-axis bSSFP imaging. 4D Flow MRI, four-dimensional flow magnetic resonance imaging; KE, kinetic energy; EL, energy loss; AAo, ascending aorta; AAo, ascending aorta; bSSFP, balanced steady-state free precession; PCMRA, phase contrast magnetic resonance angiogram; SAX, short axis view; LAX, long axis view

A detailed explanation of the mathematical methods is provided in the Supplementary Data. All the data analysis was performed in MATLAB (R2024b, The MathWorks, Inc., Natick, MA, USA).

Myocardial strain

Three-dimensional feature-tracking myocardial strain analysis was conducted by a single trained observer (SA, with four years of research experience) on LV long- and short-axis cine bSSFP images. Analysis was performed with the commercial software cvi42^® (version 6.0.1, Circle Cardiovascular Imaging, Calgary, Canada) (Fig. 1c). The LV endocardial and epicardial borders were semi-automatically traced at end-systole and end-diastole on the image planes. The software then tracked myocardial motion throughout all cardiac phases. A nearly incompressible 3D deformable model of the myocardium was created to derive the deformation gradient and Lagrangian strain tensors, following previously established methods [21]. Global longitudinal strain and strain rate were extracted from long-axis images, whereas circumferential and radial strain and strain rates were obtained from short-axis slices at the basal, mid, and apical levels. Strain parameters were calculated across all 17 segments defined by the AHA model and averaged to determine global values. Intra-observer reproducibility of this strain analysis method, using the same software, has been validated in earlier work [22].

Statistical analysis

Normality of each parameter’s distribution was assessed using the Shapiro–Wilk test. As most variables did not follow a normal distribution, non-parametric data are presented as median [25th, 75th percentiles], while normally distributed variables are shown as mean ± standard deviation. Group comparisons across the four cohorts were performed using either the Kruskal–Wallis test or one-way ANOVA, depending on data distribution. Spearman’s correlation coefficients (rho) were used to assess relationships between hemodynamic measures and both LV function and myocardial strain parameters. Bonferroni correction was applied to adjust for multiple comparisons among the four groups, resulting in six pairwise comparisons. Each p-value was therefore multiplied by six to control for the family-wise error rate, while maintaining the overall significance threshold at p < 0.05. All analyses were performed using IBM SPSS Statistics, version 29.0.1.1 (Armonk, NY).

Results

Study cohorts

The clinical characteristics of the study cohorts are summarized in Table 1. BAV-AR and BAV-AS were statistically older than those in the healthy TAV group. Stroke volume (SV) was elevated in the BAV-AR compared to the other cohorts. LV ejection fraction (EF) was statistically lower in BAV-AR compared with healthy TAV and BAV-AS, yet remained within the preserved range. Left ventricular mass was higher in BAV patients with valvular lesions, with the greatest values observed in the BAV-AR group. The indexed mid-ascending aortic diameter was increased in all BAV groups relative to healthy controls, with BAV-AS showing the largest diameter.

Table 1.

Demographic and clinical characteristics

Parameters	TAV	BAV			p-value
		No VD	AR	AS
n (female%)	20 (35%)	19 (31%)	17 (0%)	15 (40%)	-
Age (years)	37 ± 12.3	46.3 ± 17.3	49.1 ± 11.4	52.2 ± 12.7	0.01b, e
HR (bpm)	64.5 ± 11.8	61.3 ± 11	65 ± 9.5	65.8 ± 8	0.58
SBP (mmHg)	109 ± 13.8	112.3 ± 20	115.3 ± 12	110.8 ± 13	0.69
DBP (mmHg)	61.5 ± 12.8	66.3 ± 11.3	60.7 ± 8.4	69.6 ± 11.4	0.08
BSA (m2)	1.8 ± 0.3	1.9 ± 0.3	2 ± 0.1	2 ± 0.3	0.03b
LVEDV (ml)	155 ± 40.5	171.3 ± 47	279 ± 62.7	161 ± 27.4	< 0.001b, c,d
LVESV (ml)	60.4 ± 19	74 ± 29.2	124.6 ± 35.2	58.9 ± 9.8	< 0.001b, c,d
LVEF (%)	62 ± 4.9	57.7 ± 8.1	56 ± 7.7	63.2 ± 3.9	0.005b, d
SV (ml)	95.3 ± 25	97.3 ± 24.5	154.6 ± 35.1	102.2 ± 20.8	< 0.001b, c,d
CO (l/min)	6 ± 1.5	6 ± 1.6	9.8 ± 2	6.6 ± 1.3	< 0.001 b, c,d
LV Mass (gr)	92.7 ± 30.1	123.5 ± 39.8	189.1 ± 40.2	137.5 ± 49.8	< 0.001b, c,d, e
MAAD (mm/m2)	14.9 ± 2.4	19.2 ± 3.8	21.1 ± 3.1	22.4 ± 3.7	< 0.001a, b,e
BAV phenotypes
RL	-	12	14	7	-
RN	-	1	2	4	-
Type 0	-	6	1	4	-

Aortic diameters were obtained from cardiovascular magnetic resonance imaging. BSA stands for body surface area; HR, heart rate; SBP, systolic blood pressure; DBP, diastolic blood pressure; LVEDV, left ventricular end diastolic volume; LVESV, left ventricular end systolic volume; SV, stroke volume; LVEF, left ventricular ejection fraction; CO, cardiac output; MAAD, mid ascending aorta; RL, right and left coronary cusps fusion; RN, right and non-coronary cusps fusion, values are shown as mean ± standard deviation

^a Differences between TAV and BAV-No VD, ^b TAV and BAV-AR, ^c BAV-AR with BAV-No VD, ^d BAV-AR with BAV-AS, ^e TAV with BAV-AS

Ascending aortic hemodynamics

Significant differences in ascending aortic hemodynamics were observed across the four study groups (TAV, BAV-No VC, BAV-AR, BAV-AS) when evaluating both KE and viscous EL at peak systole and throughout systole (Fig. 2).

Fig. 2.

Peak systolic (a) KE and (c) viscous EL, systolic average (b) KE and (d) viscous EL in BAV patients without valvular complications (BAV-No VC), with regurgitation (BAV-AR), with stenosis (BAV-AS), and healthy TAV controls. Stars indicate a significant difference between two groups (*p < 0.05, **p < 0.01, **p < 0.001). KE, kinetic energy; EL, energy loss; BAV, bicuspid aortic valve; TAV, tricuspid aortic valve

Kinetic energy

At peak systole (Fig. 2a), KE was significantly elevated in all BAV subgroups compared to TAV. Median KE in TAV was lowest, while BAV-AR and BAV-AS showed markedly increased values (9.4 [6.6–12.4] vs. 36.1 [27.8–50.1] and 26.5 [18.1–50.3], p < 0.001). Notably, KE in BAV-AR was significantly higher than BAV-No VC (36.1 [27.8–50.1] vs. 13.5 [12.1–21.9], p = 0.003).

Across the entire systole (Fig. 2b), a similar trend persisted. Additionally, KE was significantly elevated in both BAV-AR and BAV-AS compared to BAV-No VC (19.4 [14.9–21.3], 15.4 [12.2–29.5], vs. 6.7 [5.3–9.1], p = 0.01 and 0.03). These findings highlight the increased flow-related energy in BAV phenotypes, particularly in those with regurgitation and stenosis.

Viscous Energy Loss: At peak systole (Fig. 2c), viscous EL was significantly higher in BAV-AR and BAV-AS compared to healthy TAV (11.4[9.5–17.6], 16.2[9.1–24.4] and 4.1[3.4–5.7] respectively, p < 0.001) with BAV-AS showing the highest overall values. However, no significant difference was observed between BAV-No VC and TAV, suggesting preserved viscous efficiency in BAV patients without valvular complications during the peak systolic instant. Figure 3 further illustrates this disparity: BAV-AR and BAV-AS subjects exhibit focal hotspots of energy dissipation along the inner curvature of the ascending aorta, co-localizing with exaggerated helical flow formations, while healthy TAV anatomy shows uniformly low EL and predominantly laminar streamlines.

Fig. 3.

Representative flow streamlines and viscous energy loss heat maps in a BAV patient with regurgitation (BAV-AR), a BAV patient with stenosis (BAV-AS), and a TAV healthy control. Areas exhibiting pronounced secondary flow structures coincide with regions of elevated viscous energy loss. BAV, bicuspid aortic valve; TAV, tricuspid aortic valve

In contrast, when assessed over the entire systolic phase (Fig. 2d), viscous EL was also significantly increased in BAV-No VC compared to TAV (3.3[2.5–4.1] and 1.7 [1.3–2.3] respectively, p < 0.03), indicating subtle but measurable inefficiencies across systole even in the absence of overt valvular disease. The computed viscous EL in the AAo in our study falls within the range reported in a previous study with age-matched cohorts [14, 23].

Viscous EL index

The viscous EL index differed significantly across the study groups (Fig. 4). The BAV-AR group demonstrated a significantly lower EL index compared to TAV (0.32 [0.28–0.41] vs. 0.47 [0.41–0.53], p = 0.001), BAV-No VC (0.44 [0.33–0.51], p = 0.03), and BAV-AS (0.48 [0.38–0.55], p = 0.009). There was no significant difference between TAV and BAV-No VC, nor between TAV and BAV-AS. Further details are provided in Table 2.

Fig. 4.

Comparison of the viscous EL index in BAV patients without valvular complications (BAV-No VC), with regurgitation (BAV-AR), with stenosis (BAV-AS), and healthy TAV controls. Stars indicate a significant difference between two groups (*p < 0.05, **p < 0.01, ***p < 0.001). EL, energy loss; BAV, bicuspid aortic valve; TAV, tricuspid aortic valve

Table 2.

Quantitative analysis of hemodynamic parameters

	TAV	BAV			p-value
		No-VC	AR	AS
KE Peak−Sys(mJ)	9.4 [6.6–12.4]	13.5[12.1–21.9]	36.1[27.8–50.1]	26.5[18.1–50.3]	< 0.001a, b,c, e
KE Avg−Sys (mJ)	3.3[2.3–4.3]	6.7[5.3–9.1]	19.4[14.9–21.3]	15.4[12.2–29.5]	< 0.001a, b,c, e,f
KE Cardiac−Cyc(mJ.s)	1.7[1.3–2.3]	2.8[2.3–4.8]	8.2[6.2–11.4]	7.9[5.6–12.7]	< 0.001a, b,c, e,f
EL Peak−Sys(mW)	4.1[3.4–5.7]	6.4[5.1- 8]	11.4[9.5–17.6]	16.2[9.1–24.4]	< 0.001b, c,e
EL Avg−Sys (mW)	1.7[1.3–2.3]	3.3[2.5–4.1]	6.7[4.5- 9]	8.5[6.3–14.5]	< 0.001a, b,e, f
EL Cardiac−Cyc(mJ)	0.82[0.6–1.1]	1.4[1.1–2.1]	2.8[2.3–4.7]	4.1[2.8–5.8]	< 0.001a, b,e, f
EL index	0.47[0.41–0.53]	0.44[0.33–0.51]	0.32[0.28–0.41]	0.48[0.38–0.55]	< 0.001b, c,d

BAV, stands for bicuspid aortic valve; BAV No-VC, BAV patients without valve disease; AR, aortic regurgitation; AS, aortic stenosis; TAV, healthy controls with tricuspid aortic valve; Sys, systole; Cyc, cycle; Avg, average; KE, kinetic energy: EL, energy loss. Values are presented as median with interquartile range (IQR)

^a Differences between TAV and BAV-No VD, ^b TAV and BAV-AR, ^c BAV-AR with BAV-No VD, ^d BAV-AR with BAV-AS, ^e TAV with BAV-AS, ^f BAV-AS with BAV-No VD

Myocardial strain

Left ventricular strain analysis revealed that peak circumferential strain was significantly reduced in the BAV-AR group compared with healthy TAV controls (-18.4 [-19.9- -16.4] vs. -21.3 [-22.5- -19.6], p = 0.01), while peak longitudinal strain was likewise attenuated in both BAV‐AR and BAV-No VC (-14.3 ± 2.1 and − 14 ± 2.7 vs. -16.7 ± 2.1, p = 0.01). Although peak systolic strain rate longitudinal was decreased in BAV-AS relative to other groups, it was not statistically significant. Diastolic function was most affected circumferentially, indicating peak diastolic circumferential strain rate fell in BAV‐AR and BAV-No VC compared to healthy TAV (0.63 [0.5–0.7], 0.91 [0.6- 1], vs. 1.1 [1- 1.1] respectively, p < 0.001, p = 0.01), with BAV‐AR exhibiting the greatest impairment. This reduction was interestingly significant between BAV-AR and BAV-AS (0.63 [0.5–0.7] vs. 0.96 [0.8- 1], p = 0.02). Peak diastolic longitudinal strain rate was also lower in BAV‐AR versus TAV (0.59 [0.5–0.7], 0.66 [0.5–0.8], and 0.83 [0.7- 1] respectively, p = 0.003, and p = 0.04) (Table 3).

Table 3.

Left ventricular strain parameters

	TAV	BAV			p-value
		No-VC	AR	AS
Peak strain-radial,%	38[32.9–44.6]	32.2[26–38]	34.3[30.8–39]	35.6[32- 42.1]	0.13
Peak strain-circumferential,%	-21.3[-22.5- -19.6]	-19.4[-20.8- -17.1]	-18.4[-19.9- -16.4]	-21.2[-22.3- -18.7]	0.007b
Peak strain-longitudinal,%	-16.7 ± 2.1	-14.3 ± 2.1	-14 ± 2.7	-14.7 ± 2.8	0.003a, b
Time to peak strain-radial, 1/s	326 ± 36.3	332.1 ± 36.4	307.7 ± 48.7	355.7 ± 40.8	0.01d
Time to peak strain- circumferential, 1/s	328.6 ± 36.1	336.6 ± 40.6	324.8 ± 48.5	340 ± 48.7	0.7
Time to peak strain-longitudinal, 1/s	335.6[306.5- 355.1]	346.4[313.4- 400.7]	345.3[309.9- 357.9]	355.3[315.6- 417.9]	0.20
Peak systolic strain rate-radial, 1/s	2[1.7–2.5]	1.8[1.4–2.2]	2[1.6- 3.]	2.2[1.7–3.2]	0.27
Peak systolic strain rate-circumferential, 1/s	-1[-1.1- -0.9]	-0.95[-1.1- -0.9]	-0.96[-1- -0.8]	-0.95[-1- -0.8]	0.16
Peak systolic strain rate-longitudinal, 1/s	-0.83[-0.9- -0.7]	-0.76[-0.8- -0.6]	-0.76[-0.9- -0.6]	-0.74[-0.8- -0.6]	0.13
Peak diastolic strain rate-radial, 1/s	-2.2[-2.6- -1.8]	-1.9[-2.8- -1.4]	-1.6[-2.3- -0.5]	-1.9[-2.3- -1.6]	0.21
Peak diastolic strain rate-circumferential, 1/s	1.1[1- 1.1]	0.91[0.6- 1]	0.63[0.5–0.7]	0.96[0.8- 1]	< 0.001a, b,d
Peak diastolic strain rate-longitudinal, 1/s	0.83[0.7- 1]	0.66[0.5–0.8]	0.59[0.5–0.7]	0.71[0.6–0.8]	0.003a, b

BAV, stands for bicuspid aortic valve; BAV No-VC, BAV patients without valve disease; REG, regurgitation; STEN, stenosis; TAV, healthy controls with tricuspid aortic valve

For normally distributed variables, ANOVA (significant for p < 0.05) and for skewed variables, equivalent non-parametric tests were used. Values are presented as mean ± standard deviation or median with interquartile range (IQR)

^a Differences between TAV and BAV-No VD, ^b TAV and BAV-AR, ^c BAV-AR with BAV-No VD, ^d BAV-AR with BAV-AS, ^e TAV with BAV-AS, ^f BAV-AS with BAV-No VD

Global LV, hemodynamic parameters, and aortic surgery outcome

Systolic KE and systolic viscous EL were almost collinear (rho = 0.96, p < 0.001), indicating that the most significant energy-dissipative burden occurs in subjects with the highest intraluminal kinetic energy. KE showed a stronger correlation with regurgitation severity (rho = 0.50, p < 0.001) than with stenosis severity (rho = 0.40, p < 0.001). Correlations of regurgitation severity with LV mass index (rho = 0.55, p < 0.001) and LV mass with systolic KE (rho = 0.57, p < 0.001) indicate that elevated LV load is more pronounced in regurgitation than stenosis cases. Although systolic KE and viscous EL showed no significant correlation with the mid ascending aortic diameter (MAAD) index in cohorts without valvular lesions (healthy TAV and BAV-No VC), they correlated strongly with BAV cohorts with valvular lesions (BAV-AR and BAV-AS; rho = 0.61 and 0.59, respectively; p < 0.001) Fig. 5. EL index was inversely correlated with cardiac output (rho = -0.56, p < 0.001) as a hallmark of LV hypertrophy. Systolic KE was correlated but not strongly with peak diastolic strain rate circumferential (rho = -0.37, p = 0.002).

Fig. 5.

Scatter plots illustrating relationships between (a) systolic KE and MAAD index and (b) systolic viscous EL and MAAD index. No significant associations were observed in healthy TAV and BAV without valvular complications (BAV-No VC). KE, kinetic energy; EL, energy loss; MAAD, mid ascending aortic diameter, BAV, bicuspid aortic valve; TAV, tricuspid aortic valve

Referral for aortic surgery was most strongly associated with a larger MAAD-index diameter (rho = 0.50, p < 0.001) and a higher LV mass index (rho = 0.42, p < 0.001). On the haemodynamic side, elevated systolic KE (rho = 0.65, p < 0.001) and systolic viscous EL (rho = 0.63, p < 0.001) showed the largest associations (Table 4).

Table 4.

Correlations between post valvular hemodynamic and LV parameters

Parameters	KE sys		Viscous EL sys
	rho	p-value	rho	p-value
AR	0.50	< 0.001	0.39	< 0.001
AS	0.40	< 0.001	0.48	< 0.001
Age	0.40	< 0.001	0.39	< 0.001
MAAD Ind	0.61	< 0.001	0.59	< 0.001
Aortic Surgery Ref	0.65	< 0.001	0.64	< 0.001
Left Ventricular
Mass Ind	0.57	< 0.001	0.47	< 0.001
SV	0.43	< 0.001	0.43	< 0.001
PDS Rate Circ	-0.37	0.001	-0.28	0.02

Sys, systole; AR, aortic regurgitation; AS, aortic stenosis; MAAD, mid ascending aortic diameter; LV, left ventricle; Ind, index; Ref, referral; SV, stroke volume; PDS, peak diastolic strain; Circ, circumferential

Pearson correlation used when both variables were parametric, Spearman’s correlation used when at least 1 variable was non-parametric

Discussion

Our results indicate that 4D Flow–derived hemodynamic parameters, and their associations with left ventricular function, may offer additional insights beyond traditional measures in identifying subtle alterations that could be relevant to BAV management. BAV patients with normally functioning valves have LV parameters and function comparable to healthy TAV controls, whereas those with stenosis or regurgitation exhibit LV functional abnormalities. 4D Flow MRI–derived kinetic energy and viscous energy loss were computed in AAo to characterize altered flow characteristics. Since AAo serves as the primary buffer for the generated LV energy wave and accounts for most of the thoracic-aortic energy dissipation [7, 14], we focused our study on this region. Our findings show that AAo hemodynamics are markedly altered in BAV patients with stenosis and regurgitation and, to a lesser degree, in those without valvular complications at peak systole and over systolic timepoints. This indicates that a persistent hemodynamic burden exists even in BAV patients with normally functioning valves [2, 24]. A previous study suggested that even in BAV without secondary complications, local hemodynamic shear forces, captured through flow-derived markers, play a pivotal role in shaping the continuum of BAV-related aortopathy beyond geometric metrics [25].

A marked increase of peak systolic viscous EL in BAV patients with valvular lesions compared to BAV-No VD and healthy TAV and more considerably in BAV-AS is consistent with the higher irreversible pressure loss in post-stenotic flow [11]. The marked increase in viscous EL in our stenotic cohort can be attributed to flow changes induced by rapid contraction, throat obstruction, and expansion of the outflow tract geometry [10], which may be further exacerbated in BAV phenotypes characterized by eccentric or directional jets [26]. Hence, the contribution of secondary flow structures such as helices and vortices are likely outweighed. These secondary flow structures are typically associated with greater irreversible energy loss compared with direct flow paths [20]. Elevated average systolic viscous EL in the BAV-No VC group, coupled with the absence of a diameter-energy relationship despite a significantly larger MAAD index compared with healthy TAV, indicates that aortic dilation by itself does not substantially alter the viscous EL in the AAo. Similarly, research focusing on patients with congenital Tetralogy of Fallot also reported no correlation between aortic diameter and viscous EL in the AAo [27]. This finding is inconsistent with a previous study, which reported associations between aortic dilation (but not BAV subjects), helical and vortical flow, and irreversible viscous EL [14, 28]. Therefore, our findings, in agreement with previous studies, suggest that the congenital bicuspid morphology itself generates subclinical secondary systolic flow disturbances unique to each fusion pattern [26]irrespective of indexed aortic size. This intrinsic effect of BAV is further supported by prior work showing that flow abnormalities and elevated wall shear stress are more pronounced in stenotic BAV than in stenotic TAV patients [29].

The novelty of this study lies in demonstrating that the isolated BAV-AR cohort also indirectly increases post-valvular KE and viscous EL, exhibiting the highest KE among all cohorts. Stroke volume was highest in BAV-AR, resulting in higher flow velocities and, consequently, greater KE within the ascending aorta, as KE is proportional to both blood mass and the square of velocity. The increased SV also contributes to elevated viscous EL, since the larger blood volume moving through the aorta generates more internal friction and energy dissipation.

Valvular regurgitation imposes volume overload on the ventricle, subjecting the myocardium to additional diastolic stress. This mechanical burden triggers mechanotransduction pathways [30], leading to cellular and interstitial remodeling within the myocardial tissue as evidenced by a marked reduction in both circumferential and longitudinal PDS rates in the BAV-AR. In this cohort, increased KE in AAo tied to increased LV mass and reduced diastolic strain rates, highlighting KE as a potential marker of left-ventricular remodeling, hypertrophy, and functional impairment. This is aligned with the fact that BAV with aortic regurgitation are at higher risk for cardiac events [31–33]. The wide variability in viscous EL and KE measurements may also reflect their respective associations, with the former primarily correlating with stenosis severity and the latter mainly linked to regurgitation severity.

Although the BAV-AS cohort exhibited a lower peak longitudinal systolic strain rate than the other groups, this reduction did not reach statistical significance, likely because our sample included predominantly moderate stenosis cases. This mirrors findings from speckle-tracking studies, which have shown that global longitudinal strain rate does not significantly decline until pressure overload exceeds the compensatory concentric hypertrophy response typical of more severe stenosis [34, 35]. PDS rate circumferential was preserved in the BAV-AS group but markedly reduced in BAV-AR, highlighting the greater diastolic dysfunction imposed by volume overload versus pressure overload [36]. Similar to the study of Geiger et al. more interstitial fibrosis was revealed in patients with AR compared with AS using the T1-mapping technique [37].

The exploratory part of this study demonstrates that the viscous EL index provides a normalized, dimensionless measure of energy dissipation independent of absolute kinetic energy. Similar EL index values in TAV and BAV-No VC indicate that bicuspid morphology alone does not elevate viscous losses, preserving hemodynamic efficiency despite known geometric and flow-pattern differences. A markedly reduced viscous EL index in BAV-AR indicates that regurgitant flow redirects much of the kinetic energy backward rather than allowing it to dissipate through viscosity. This occurs even when total EL or KE is high, highlighting the EL index’s ability to characterize the efficiency of energy dissipation. On the other hand, the elevated EL index in BAV-AS, comparable to TAV and BAV-No VC, likely arises from increased energy losses driven by the high shear and turbulent jets characteristic of stenosis. Overall, the EL index offers complementary insight into flow inefficiency patterns, uniquely distinguishing BAV-AR by its low viscous dissipation ratio from both healthy TAV and the other BAV cohorts.

While echocardiography remains the mainstay for assessing valvular disease severity, they primarily quantify instantaneous flow and pressure differences across the valve [38]. In contrast, 4D Flow MRI–derived parameters such as KE and viscous EL provide volumetric, time-resolved insight into the energetic efficiency of blood flow throughout the cardiac cycle. By quantifying both the energy imparted by the LV and the fraction dissipated through viscous losses, these biomarkers can reveal subtle hemodynamic inefficiencies and early remodeling processes not evident on conventional ultrasound measures. This added sensitivity is exemplified in our BAV-NoVC group, classified as having no regurgitation or stenosis yet showing significant hemodynamic differences from healthy controls. Thus, KE and EL may offer complementary value for early risk stratification and comprehensive assessment of congenital BAV.

Our findings appear to be consistent with recent work suggesting that 4D Flow MRI–derived parameters may unmask high-risk flow patterns and improve risk stratification beyond traditional clinical criteria [39].

Despite the advantages of 4D Flow MRI over other imaging modalities and the potential of theses flow-derived biomarkers, the clinical implementation of KE and viscous EL remains constrained by several challenges. Data acquisition and post-processing are still inconsistent and time-intensive, and limitations in spatial and temporal resolution can affect measurement accuracy, thereby reducing confidence in individual patient decision-making. Additionally, the lack of standardized analysis protocols and established reference ranges for these biomarkers continues to hinder their widespread clinical adoption [40].

Limitations

This study has several limitations. First, our BAV cohorts were relatively small due to stringent inclusion criteria, which limit statistical power. Future multicenter studies with larger sample sizes are needed to validate these findings. Second, our healthy TAV controls were not perfectly age-matched to the BAV groups, as secondary valvular lesions in BAV typically emerge later in life. Prior study shows that with ageing and increasing aortic diameter, hemodynamic parameters such as systolic velocity and consequently KE tend to decline [41]. Our data suggested that the hemodynamic changes we observed were driven more by disease-related factors and ventricular function (for example, increased SV in AR) than by age alone. However, more rigorous age-matching in follow-up studies would strengthen comparative analyses. Third, the finite spatiotemporal resolution of 4D Flow MRI and the smoothing kernel applied during viscous EL quantification may underestimate true laminar dissipation. Likewise, variability in VENC settings, especially the higher VENC required for stenotic and regurgitant valves, can introduce noise into velocity measurements and affect the EL and KE calculations. However, these intraluminal flow-derived biomarkers are expected to be less affected by the reduced velocity-to-noise ratio associated with higher VENC settings compared to wall shear stress. Fourth, cine MRI–derived strain metrics are susceptible to variations in image quality and algorithm performance. To minimize these technical sources of bias, all scans and post-processing were performed at a single center using consistent acquisition parameters and software versions.

Conclusion

Post-valvular KE and viscous EL, quantified via 4D Flow MRI, may help characterize hemodynamic patterns across BAV without and with distinct valvular complications, including aortic stenosis and regurgitation, and reveal early signs of LV remodeling. The observed increase in post-valvular KE in BAV-AR, along with its associations with LV functional and structural parameters, suggests potential compensatory mechanisms and increased myocardial workload as adaptive responses to maintain functional efficiency. Integrating these energy-based parameters into clinical workflows might therefore refine risk stratification and optimize the timing of intervention in BAV diseases. However, validation of these markers in larger and more diverse populations is warranted.

Supplementary Information

Below is the link to the electronic supplementary material.

Abbreviations

BAV

Bicuspid aortic valve

TAV

Tricuspid aortic valve

AR

Aortic regurgitation

AS

Aortic stenosis

AAo

Ascending aorta

LV

Left ventricle

4D Flow MRI

Four-dimensional flow magnetic resonance imaging

bSSFP

Balanced steady-state free procession

MAAD

Mid ascending aortic diameter

SV

Stroke volume

EF

Ejection fraction

EL

Energy loss

KE

Kinetic energy

Author contributions

SA: Conception and design, Collection and assembly of data, Data analysis and interpretation, Writing original draft. JW: Provision of study materials or patients, Final approval of manuscript. DL: Provision of study materials or patients, Final approval of manuscript. SR: Provision of study materials or patients, Final approval of manuscript. JG: Supervision, Provision of study materials or patients, Review and editing, Administrative support, Final approval of manuscript.

Funding

This work was supported by the University of Calgary; J.G. start-up funding (#11022618 and #11021988); Calgary Health Foundation; Alberta Innovates Health Solutions (AIHS); and the Canadian Institutes for Health Research (CIHR). We acknowledge the support of the Natural Science and Engineering Research Council of Canada/Conseil de recherche en science naturelles et en génie du Canada (#RGPIN-2020-04549 and #DGECR-2020-00204), and the support of NSERC Alliance – Alberta Innovates Advance Program (#232403115). The study was also supported by the University of Calgary, Department of Biomedical Engineering, Graduate Program, and Libin Cardiovascular Institute (Kenneth M Stephenson Graduate Scholarship in Cardiovascular Research to S.A.).

Data availability

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

This study received ethics approval from the Conjoint Health Research Ethics Board (CHREB) at the University of Calgary. The CHREB functions in accordance with the Tri-Council Policy Statement: Ethical Conduct for Research Involving Humans (TCPS 2), Health Canada Food and Drug Regulations Division 5, Part C, ICH Guidance E6: Good Clinical Practice, and the provisions and regulations of the Health Information Act (RSA 2000, c H-5). Informed consent was obtained from all participants invited to take part. Our study was conducted in accordance with the Declaration of Helsinki.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.