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Dynamic vortical flow profile quantitatively characterizes mitral valvular-left ventricular hemodynamic coupling: In vivo analysis by dynamic 3D enstrophy mapping from 4D Flow MRI

Vortical blood flow in the human left ventricular (LV) inflow initiates from the mitral valve (MV) and evolves within the LV during diastolic E-filling. Hence, vortical flow links MV and LV hemodynamics. This study sought to elucidate and quantitatively characterize the in vivo 3D dynamics of LV vortical flow over E-filling and relation to MV-LV hemodynamic coupling using 4D Flow MRI flow field. 34 healthy volunteers and 5 example patients underwent 4D Flow MRI. Vortical blood flow evolution was mapped in the LV over E-wave using enstrophy density. A new dimensionless profile PMV-LV was derived as a function of both MV vortex formation time (VFT) and LV volumetric enstrophy density. Results reveal that 3D vortical flow evolution in the healthy LV follows a bi-phasic behavior with a vortical growth phase followed by a vortical decay phase. In healthy LVs studied, the PMV-LV profile showed that the vortical growth and decay phases are characterized by a vortical growth time T_growth= 1.23+/-0.25, growth rate {\alpha}=0.80+/-0.17, decay time T_decay= 0.96+/-0.39 and decay rate \b{eta}=-1.02+/-0.49. Distinctly altered parameters were found in the pilot patients studied. The derived PMV-LV profile quantitatively characterizes MV-LV hemodynamic coupling by vortical flow dynamics. Results herein unravel new insights into cardiac physiology and could enable a novel standardized methodology to study MV-LV hemodynamic coupling and association to cardiac function in health and disease.


Introduction
In-vivo and in-vitro studies have shown that the inflow of blood into the human heart's left ventricle (LV) during E-filling provokes a swirling motion forming distinct vortical flow patterns (1)(2)(3)(4)(5)(6). LV vortical flow is thought to help to preserve momentum, minimize kinetic energy loss and to help redirecting mitral inflow blood towards the aortic outflow tract (2,6,7).
The formation of vortical flow in the human heart has been extensively studied in-vivo and invitro (2-5, 7, 10-13). Altered vortical flow formation was reported in patients with congenital and acquired heart disease (1,5,8,9) and was recently associated to elevated levels of intracardiac viscous energy loss (7,10). Nevertheless, the role of vortical blood flow in cardiac (patho)physiology is not yet fully understood and remains a subject of debate in the literature (11)(12)(13).
Earlier studies have shown that diastolic vortical flow initiates, with the start of the Efilling, from the shear layers distal to the mitral valve (MV) leaflets as a result of MV inflow interaction with the MV geometry. Thus, vortical flow formation has been characterized as a function of MV geometry and inflow dynamics (1,5,14,15). However, such characterization implies that LV vortical flow is uni-phasic dominated by vortical flow formation from the MV and does not take into account the impact of the dynamic LV geometry on vortical flow. Recent studies have shown that the formed vortical flow continues to evolve within the dynamic LV geometry over diastole resulting in time-varying vortical flow patterns (3,4,16,17). Thus, suggesting an impact of the dynamic LV geometry on the evolution of vortical flow. While previous studies have provided a better understanding of the LV vortical flow formation phenomenon (1, 4-6, 16, 17), there is currently a lack of quantitative methods for characterizing or mapping of the time-evolution of vortical flow within the dynamic LV geometry of healthy subjects and patients. As a result, the actual in vivo evolution of vortical flow in the LV over Efiling remains unclear.
Given that vortical flow, during E-filling, emerges from MV inflow dynamics but progresses inside the LV bounded by its dynamics geometry (1,3,4), we hypothesized that vortical flow evolution would be determined as a function of both MV and LV dynamics (i.e. is a reflection of the coupled dynamics between MV and LV). Therefore, characterization of the 3D intra-cardiac vortical flow evolution during E-filling could allow deriving a novel method to assess MV-LV hemodynamic coupling in the presence of normal and pathologic valvular and ventricular dynamics.
In this work, we aimed to employ 4D Flow MRI to 1) Elucidate the dynamics of vortical flow within the human LV over E-filling in healthy subjects 2) Derive a standardized quantitative profile characterizing the MV-LV hemodynamic coupling during E-filling using 3D vortical flow evolution. 3) Probe the feasibility of the derived profile in detecting differences between healthy subjects and five pilot patients with various MV and LV abnormalities.

Study Population
The study was conducted across two centers, Leiden University Medical Center, the Netherlands and University of Leeds, UK, and was approved by the institutional Medical Ethical Committee in Leiden and the National Research Ethics Service in Leeds. Written informed consents were obtained from all participants or their parents.
A total of 39 subjects were retrospectively enrolled in this study; 34 healthy volunteers (age 27±16 years) and 5 example patients as representatives of valvular and/or ventricular disease: a hypertrophic cardiomyopathy (HCM) patient, a patient with restricted MV opening, a patient with remodeled LV manifested in LV dilation after myocardial infarction (MI), a patient with a presentation of both MV restriction and LV dilation, and a dilated cardiomyopathy (DCM) patient.
These patients were chosen to show the feasibility of the derived method in detecting differences in the presence of example MV and LV abnormalities compared to the studied healthy volunteers.

MRI acquisition
All subjects underwent whole-heart 4D Flow MRI on a 3T or 1.5T MRI scanner (Philips Healthcare, Best, The Netherlands) using a combination of FlexCoverage Posterior coil in the table top with a dStream Torso coil, providing up to 32 coil elements for signal reception.
Retrospective ECG-gating was used and 30 cardiac phases were reconstructed to represent one average heartbeat. To accelerate acquisition, parallel imaging SENSE with factor 2 was used and echo planar imaging with factor 5. To allow a reasonable acquisition time (8-10 minutes), free breathing was allowed for both patients as well as controls. Standard short-axis anatomical MRI cine data was as also acquired. A typical volume for a whole-heart 4D Flow MRI acquisition was 396 mm (right-left) × 336 mm (anterior-posterior) × 117 mm (feet-head).
Concomitant gradient correction and local phase correction were applied using the software available on the MRI system. For more details on the MRI protocol, readers are referred to our previous publications (4,7,8).

Image analysis workflow
Using in-house developed MASS software (Leiden University Medical Center), the LV endocardial contours were segmented from 4D Flow MRI as previously described (7). In short, to tackle the typical low contrast in 4D Flow MRI that makes its LV segmentation challenging, LV contours were first manually traced on anatomical short-axis slices over all acquired time phases. Contours were then projected on the whole-heart 4D Flow data. To reduce possible translation and rotation errors between cine short-axis and whole-heart 4D Flow acquisitions, automated image registration by mutual information using Elastix (18) was performed between cine short-axis data and velocity magnitude reconstructed images of the 4D Flow data using a single phase that visually showed the best depiction of the LV in the velocity magnitude 4D Flow image. Registration was restricted to translation and rotation. The resulted transformation matrix was then propagated to all 4D Flow phases. The 3D velocity field data within the segmented 4D Flow LV volume was then used to compute enstrophy parameters as described below.
Segmented LV endocardial boundaries were also used to compute the LV end-diastolic volume (EDV), end-systolic volume (ESV), stroke volume (SV) and ejection fraction.
Retrospective mitral valve tracking was used to quantify inflow and derive flow-time curves from the 4D flow data as previously described (19). The time points corresponding to start of E-filling, peak early filling (E-peak) and end of E-filling were defined from the flow-time curves. For further details on our used image analysis framework and workflow, readers are referred to our previous publications (4,7). With as the image width, as the image height and as the number of slices. This provides an enstrophy map at time instance over the segmented LV volume.

Computation of instantaneous total enstrophy in the LV (TED LV ) over E-filling
To quantify the overall evolution of LV vortical flow patterns, we introduce the instantaneous non-dimensional Total (volume-integrated) Enstrophy Density (TED LV ) derived as follows: The total enstrophy ( ) at time instance over the 3D segmented LV volume of voxels and with voxel size is computed as: such that 0 ∶ correspond to the acquired 4D Flow MR time frame that are spanning from the start of E-filling 0 to the end of E-filling by the end of diastasis . This results in a profile curve representing the dynamic evolution of total enstrophy in the LV over E-filling. Since our control volume (the LV volume) changes dynamically over the cardiac cycle, we use the spatially-averaged enstrophy density to account to this volumetric variability (20). Accordingly, volume-normalized enstrophy density ( ) is defined as: 1/s 2 [3] such that is the volume of the segmented LV region of interest at acquired time frame . Of note, computation involves normalization by instantaneous LV volumes. Therefore, it accounts for the potential difference in LV size between different subjects and also takes into consideration the LV size change over the diastolic filling of the same subject.
To further enable a standardized analysis over different subjects, it is best to evaluate vortical flow profile in a standardized dimensionless means. Therefore, to account for subject-specific variability of the vorticity field, the so obtained enstrophy integral ( ) is normalized by the timepeak enstrophy for this individual over the entire E-filling process (i.e. instantaneous TED LV values are time-normalized relative to time-peak TED LV -time-peak TED LV has normalized to 1): , 0: , [dimensionless] [4] is number of acquired E-filling phases as described above. Using this normalization approach allows standardized comparison of between different patients.

Construction of standardized MV-LV vortical flow evolution profile (P MV-LV )
To quantify vortical flow dynamics in the LV over E-filling and to link to both MV and LV hemodynamics, we constructed a temporal vortical flow profile (P MV-LV ) as a function of both MV and LV vorticity dynamics over E-filling. The dimensionless profile P MV-LV is constructed from Equation 4 and 5 by plotting LV enstrophy density evolution (TED LV ) as the y-axis relative to the temporal vorticity discharge rate from MV by means of the dimensionless temporal vortex formation time ( ) as the X-axis. Following (15), is computed as: , * , t 0: T [dimensionless] [5] is the temporal resolution of acquired 4D Flow MRI, is the instantaneous inflow velocity through the MV and as maximum diameter of mitral inflow opening. D was computed at Epeak from the area of the MV flow on retrospective valve tracking (19) at peak inflow velocity level (i.e., approximately at the tip of the valves), assuming a circular inflow area. In the original definition, D=constant. However in our case, we use D = D(t) since the valve opens and closes over E-filling. This is similar to the concept used by Gharib et al in (1) with D defined as the maximum MV inflow diameter over E-wave. We used the maximum diameter (D max ) instead of average diameter as in (1) because we estimate MV dimeter from flow data in which MV region can be unclear near to diastasis when little or no inflow is present. As such, using D max assures more reliable measurement of MV diameter derived from 4D Flow MRI.
As such, P MV-LV characterizes the MV and LV hemodynamic coupling through vortical flow dynamics by linking the enstrophy density derived from LV vorticity dynamics to the vortex formation time derived from MV vorticity dynamics. Note that P MV-LV is a dimensionless profile.
Thus, facilitates standardized comparison of MV-LV hemodynamic coupling between different patients.
All enstrophy analyses were performed using an in-house software module developed using MATLAB (MathWorks Inc.).

Statistical Analysis
Data analysis was performed using SPSS Statistics (version 20.0 IBM SPSS, Chicago, IL).
Variables were tested for normal distribution using the Shapiro-Wilk test. P<0.05 was considered statistically significant. Continuous variables are expressed as mean ± standard deviation (SD) or as median with inter-quartile range (IQR) where appropriate.

Clinical Characteristics
Clinical characteristics of the studied subjects are summarized in Table 1. into a ring-like structure near to the moment of the peak E-filling (1,(3)(4)(5)14). However, following peak E-filling, this vortex ring propagates at an inclined angle towards the LV free wall giving rise to vortex-wall interaction. At a time point past-peak E-filling, the vortex ring flow starts to decay becoming disorganized as it gradually loses its distinct ring-like shape. We note that this apparent decay phase of the vortex ring emanating from the MV has not been reported before in-vivo though it has been postulated by numerical simulation (3). impacts its growth (1,3,4) while the LV wall dynamics governs its subsequent decay.

Bi-phasic vortical flow process regulated by MV-LV hemodynamic coupling
Therefore, this supports our hypothesis that vortical flow evolution in the LV is not only a function of MV inflow but rather regulated by a hemodynamic coupling between MV inflow and LV wall geometry dynamics.  Table 2 presents the results of the derived characteristic parameters over all studied healthy subjects. In    Figure 2b shows the P MV-LV profiles corresponding to the 5 representative patients as compared to P MV-LV profiles of all studied 34 healthy volunteers. Figure 3 presents the computed enstrophy maps of these patients in a standard four chambers cross-sectional view of the heart at five sample time points over E-filling (Supplementary videos 3-7 show evolution over complete E-filling). Table 2 presents a summary of the vortical profile's characteristic parameters for each of the individual patients studied. As hypothesized, results reveal distinct and readily quantifiable differences in the P MV-LV vortical profiles between patients and healthy volunteers.

Discussion
Using in-vivo 4D Flow MRI-derived dynamic enstrophy mapping, this study elucidates a biphasic vortical flow evolution over the E-filling in the healthy LV. This bi-phasic behavior is characterized by a vortical growth phase followed by a vortical decay phase. To our knowledge this is the first in vivo study to use enstrophy to characterize vortical flow evolution in the LV. A

Bi-phasic vortical flow profile and relation to MV-LV hemodynamic coupling in healthy volunteers
Previous studies showed that vortical flow emerges from the MV (1,2,14,21,22) and progresses inside the LV over E-filling (3,4,6,11,16,17,23). As such, vortical flow dynamics over E-filling could serve as a linkage between MV and LV hemodynamics. Therefore, in this work, we aimed to derive a dimensionless profile that links both MV and LV hemodynamics has retained in the ventricle at end-systole which might contribute to increased levels of hemodynamic energy losses (7,9).
While our feasibility results are clearly encouraging, caution need to be taken in interpreting such early results or extrapolating them to other patients. Follow-up cohort-based studies are needed to further confirm such results and to understand the link to cardiac function.

Potential Clinical implications
Altered LV or MV geometrical or dynamic properties due to heart disease would impact the vortical flow evolution as reflected in altered characteristics of the derived PMV-LV profile relative to that of the healthy heart. Mitral valvular impairments or deformations would adversely impact the characteristic of vortical growth parameters in the PMV-LV profile in a similar manner to that exemplified in the pilot patients studied herein i.e. the HCM patient and the two patients with restricted MV opening ( Figure 3). Meanwhile, LV geometry deformations including myocardial stiffness, impaired relaxation or wall motion abnormalities such as those seen in cardiomyopathy (27), physiological LV remodeling as in healthy athletes or pathological remodeling such as in patients after myocardial infarction or LV hypertrophy (28)  for cardiac diseases (e.g. Mitral valve repair) (32,33). Future studies are needed, however, to reveal how specific pathophysiological events in different cardiac diseases affect vortical flow evolution and association to cardiac function. Moreover, our revealed bi-phasic vortical flow dynamics can be an important step to guide the design of accurate in-vitro experiments and numerical in-silico patient-specific simulations that resemble realistic cardiac hemodynamics (33).

Limitations
A limitation of this study is relatively small number of subjects. However, our results show consistent behavior with a narrow band of variability in all studied healthy subjects which could further emphasize the reliability of our results. While only five example patients were studied, the aim was not to provide health outcomes of these patients. Instead, these patients were carefully chosen with various MV and LV abnormalities to experimentally illustrate the feasibility of the method to pave the way for future cohort-specific studies using our methodology for investigating MV-LV hemodynamic coupling and its relation to cardiac function.
The derived P MV-LV profile can be considered as a global quantification method i.e. it shows that different enstrophy density is present but does not identify the spatial distribution of enstrophy within the LV. However, for a localized analysis, the global-based analysis by P MV-LV profile could be readily accompanied by the presented enstrophy maps to identify enstrophy density in different regions of the heart. 4D Flow MRI was acquired without respiratory gating to allow a reasonable acquisition time (8-10 minutes). We have used this protocol in several of our previously published work (4,7,8). It should be acknowledged, however, that lack of respiratory gating could potentially result in blurring in the acquired flow field and related errors.
We have visually inspected the data and we have not identified any significant blurring.
Furthermore, a recent publication showed that 4D flow MRI acquired without respiratory gating yields comparable quantitative measurements of vortex formation to 4D flow MRI with respiratory gating (34).
4D Flow MRI includes averaging the flow field data over several cardiac cycles. This time-averaging would potentially smooth out the small-scale flow features and does not, generally, adjust for flow deviations resulting from beat to beat variability. However, it was the aim of this study to evaluate large-scale cardiac vortical flow patterns defined as being with larger size than the acquired voxels and with a longer time-span than the acquired temporal resolution from 4D Flow MRI (in this study a spatial resolution of 2.3mm×2.3mm×3mm-4.2 mm and a temporal resolution of 31ms were used). Vortical flow features beyond acquired resolution might not be negligible but could not be captured and therefore not included in the provided analysis.
In conclusion, using 4D Flow MRI, we derived a standardized profile that quantitatively characterizes MV-LV hemodynamic coupling through vortical flow dynamics by means of LV enstrophy mapping and MV vorticity discharge. This profile shows consistent bi-phasic vortical evolution behavior in healthy subjects characterized by a growth phase followed by a decay phase. Distinct quantifiable alterations were found in the derived profile of the pilot example patients studied with MV and LV abnormalities. These findings unravel new insights into human heart's physiology and could enable a novel method to understand the coupling between the valvular and ventricular hemodynamics and its association with different heart diseases. Future studies with large cohorts are needed to reveal how specific pathophysiological events in different cardiac diseases affect vortical flow evolution and association to cardiac function.