SupportingInformation
Materials and Methods
Example of Omni-directional Pressure integration
Fig. S1 shows a schematic of the integration paths used to calculate the pressure fields from the pcMRI data. Integration follows the lines similar to the ones shown, integrating from voxel to voxel in the velocity field within the left ventricle of the heart. Vectors are colored by the magnitude of the velocity and the background image depicts the image intensity during that instantaneous frame for reference. In the figure, the symbols “At,” “Mi,” “MV,” and “Ap” denote the approximate locations of the left atrium, mitral valve, mid ventricle, and LV apex, respectively.
Proper Orthogonal Decomposition (POD) energy spectrum
After POD has been performed, the modes are sorted by energy, and those below a threshold can be excluded to limit the influence of noise from a final smoothed reconstruction. Fig. S2 shows the energy spectrum from the POD reconstruction of the patient shown in Fig. 1. Here, as discussed in the main paper, for each reconstruction at least 10 modes were taken for a minimum of 95% of the total energy of all modes. For this patient, 10 modes were determined to preserve approximately 97.0% of the total energy of the flow field, with the 10th mode contributing only 0.4%.
Additional Detailed Patient Information and Results
Some readers might find more complete information on the clinical status of each of the patients in this study useful. Since the participants were drawn from patients already undergoing clinically-indicated MRI procedures, it was not possible in all cases to obtain full information about their filling performance because a full echocardiographic workup was not performed near the date of their MRI. However, the available data has been provided in Table S1, with missing values marked.
Additionally, a complete list of pressure and circulation values for each patient is tabulated in Table S2. For the pressures, “total” indicates a measurement between the top of the left atrium and the apex of the left ventricle, “atrial” means the pressure difference between the top of the atrium and the mitral valve, and “ventricular” is defined as the difference between the mitral valve and the apex. The atrial and ventricular values do not always sum to equal the total because the contribution of each sometimes peaks at a different time than the overall gradient in the left heart.
The patients selected as representative examples for the “normal,” “diastolic dysfunction,” and “LVDD with dilated cardiomyopathy” groups are each listed first in their respective categories in Table S1 and Table S2
Results
Movies of pcMRI velocities, pressure, and Vortices
Movies S1-S3 show the smoothed velocity vectors for the three representative patients discussed in the main text. Movie S1 and Movie S2 show the patients with normal and diastolic dysfunction filling patterns from Fig. 1 and Fig. 2 in the main text. Movie S3 shows the patient with dilated cardiomyopathy. In each, the velocity vectors are plotted in black over the instantaneous pressures relative to the mitral valve. A representative swirling strength contour from the vortex ID process is also plotted in red. In the background, the raw MRI image fields are shown for reference. Below each movie, a line plot of the relative pressure differences between the top border of the atrium, the mitral valve, and the ventricular apex a given with a moving marker to help orient the viewer as to what part of the heart cycle is currently shown. The still image from each movie was taken at approximately the time of peak early filling (for Movie S1 and Movie S2 this is the same time instants as Fig. 1D and Fig. 2D, respectively).
Movies of FTLE values and Lagrangian coherent structures
Movies S4-S6 show the movies of the FTLE values calculated for the same three patients. The movies were created by integrating forward in time one complete period starting from each frame of the pcMRI cine, and so always include a complete systole and diastole. As such, the FTLE fields are slightly different from those shown in Fig. 4 in the main text, which were integrated through early or late filling only to emphasize motions that occurred during that period of the heartbeat. In each movie, the dark areas indicate regions of high spreading rates, with red areas being the peak values. The motion of these boundaries over a complete cycle clearly shows how different regions of blood within the heart move back and forth, and how some areas are not ejected from the left ventricle during each beat. In particular for the dilated cardiomyopathy patient inMovie S6, the swirling motion of the blood leaves a region in the center of the ventricle nearly stationary during each beat. The still image from each movie was taken at the beginning of diastole, which corresponds to the top images in Fig. 4 (and for Movie S4 and Movie S5 this is the same time instants as Fig. 1C and Fig. 2C respectively).
Table S1: Extended clinical data for the study participants
age / sex / E (cm/s)1 / A(cm/s)2 / lat. E' (cm/s)3 / sep. E' (cm/s)4 / E/A / E/E'5 / echo EF (%EDV)6 / MRI EF (%EDV)7 / HR
(bpm)8 / Additional comments
normal filling:
19 / M / * / * / * / * / * / * / * / * / 83 / --
18 / M / * / * / * / * / * / * / * / * / 97 / --
24 / M / 102 / 78 / 12.3 / 12.4 / 1.3 / 8.3 / 45 / 48 / 88 / chemotherapy patient
52 / F / 90 / 84 / 7.9 / 5.6 / 1.1 / 13.3 / 67 / 67 / 77 / chemotherapy patient
left ventricular diastolic dysfunction:
66 / F / * / * / * / * / * / * / * / * / 74 / coronary artery disease and bypass surgery
73 / F / * / * / * / * / * / * / 46 / 55 / 46 / bypass surgery
61 / M / * / * / * / * / * / * / * / * / 51 / hypertensive
61 / M / * / * / * / * / * / * / * / * / 51 / --
60 / F / 68 / 80 / 10.6 / 7.7 / 0.9 / 7.4 / 69 / * / 60 / --
38 / F / 69 / bad signal / 7.4 / 7.7 / -- / 9.1 / 48 / 54 / 83 / uncontrolled hypertension, left ventricular hypertrophy
71 / F / 46 / 58 / 4 / 4.6 / 0.8 / 10.7 / 47 / 59 / 56 / recent Takutsubo's syndrome, now normalized
54 / F / 58 / 76 / 7 / 3.2 / 0.8 / 11.4 / 60 / 61 / 82 / --
52 / M / 39 / 43 / 4.3 / 5.5 / 0.9 / 8.0 / 30 / * / 88 / acute anterior MI
LVDD with dilated cardiomyopathy:
40 / F / fused signal / * / * / * / * / 25 / 21 / 87 / non-ischemic DCM with recovered LV function, severe asthma
*No contemporaneous measurement was performed; 1 peak early mitral filling velocity from pulsed-wave Doppler at the leaflet tips; 2 peak late mitral filling velocity from pulsed-wave Doppler at the leaflet tips; 3 motion of the lateral side of the mitral annulus using tissue Doppler in an apical 4-chamber view; 4 motion of the septal side of the mitral annulus using tissue Doppler in an apical 4-chamber view; 5 calculated from average of lateral and septal E'; 6 ejection fraction as per cent of end diastolic volume from apical 4-chamber echocardiography; 7 ejection fraction as per cent of end diastolic volume from MRI; 8Heart rate as estimate from the MRI scan.
Table S2: List of peak circulation and pressure difference measurements for each patient.
peak circulation (m2/s) / early Ppeak(mmHg) / late Ppeak
(mmHg)
Early / Late / total / atrial / ventricular / total / atrial / ventricular
normal filling:
268 / 89 / 4.9 / 1.9 / 3.3 / 1.5 / 0.5 / 0.9
242 / 137 / 5.2 / 3.9 / 2.0 / 1.9 / 1.2 / 0.7
320 / 279 / 3.6 / 2.6 / 1.8 / 1.3 / 0.8 / 0.5
387 / 215 / 4.2 / 1.4 / 2.9 / 3.3 / 1.7 / 1.6
left ventricular diastolic dysfunction:
78 / 146 / 1.0 / 0.4 / 0.5 / 2.9 / 1.1 / 1.8
111 / 65 / 2.0 / 1.5 / 0.7 / 0.9 / 0.6 / 0.4
147 / 184 / 1.7 / 0.8 / 1.0 / 2.7 / 1.9 / 1.1
84 / 91 / 0.7 / 0.9 / 0.1 / 1.0 / 0.8 / 0.3
89 / 144 / 1.6 / 0.6 / 1.0 / 1.2 / 0.8 / 0.5
93 / 103 / 1.6 / 1.1 / 0.5 / 0.2 / 0.5 / -0.4
60 / 116 / 0.6 / 0.4 / 0.2 / 1.8 / 1.1 / 0.7
113 / 129 / 1.8 / 1.2 / 0.9 / 0.5 / 0.6 / -0.1
111 / 123 / 2.5 / 0.7 / 1.9 / 3.3 / 1.0 / 2.4
LVDD with dilated cardiomyopathy:
192 / 192 / 0.9 / 0.5 / 0.4 / 1.4 / 1.1 / 0.5
Supporting Information Figures
Fig. S1. Idealized schematic of the omni-directional pressure integration superimposed on a snapshot of pcMRI data. Integrations are performed within the segmented fluid domain between all possible combination of points on the virtual boundary. For clarity, only a limited subset of these paths is shown.
Fig. S2. Representative POD energy spectrum. After POD analysis has been performed, the energy per mode and cumulative contribution of each mode to the total can be calculated. The energy spectrum is plotted in by the blue solid line with open circles, and the selected mode (mode 10) is marked by a dashed red line.
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