The presented work proposes a Fourier analysis approach to measuring temporal periodicity and spatial coherence of ventricular wall motion in real-time CMR images over a series of sequential cardiac cycles. We have demonstrated that the temporospatial evaluation of LV and RV wall motion can detect the difference of ventricular performance in healthy volunteers and in patients with HF, providing a proof-of-concept of real-time CMR Fourier analysis for quantitative assessment of cardiac function.
Rationales for real-time CMR Fourier analysis
Real-time CMR permits the visualization of ventricular wall motion over a series of cardiac cycles for quantitative assessment of LV and RV myocardial function. Due to the lack of sufficient SNR and resolution, however, it is difficult to identify the anatomy of ventricular walls and track the wall motion directly in real-time images. The presented work seeks to assess myocardial function in the ventricles by analyzing real-time CMR signals arising from the ventricular wall motion. As illustrated in Figure 1, we can identify LV and RV ventricular anatomy in real-time images and define two ROIs (LV-ROI and RV-ROI) which gives an estimate of the range of ventricular wall motion during systolic contraction and diastolic relaxation. Although the real-time CMR signals within the ROIs are associated with both ventricular walls and pericardial tissues, their dynamic changes depend primarily on the systolic and diastolic motion of ventricular walls. By characterizing the temporospatial behaviors of real-time CMR signals within the ROIs, real-time CMR Fourier analysis provides an indirect approach to quantitative assessment of ventricular wall motion.
It is known that ventricular motion spread spatially through the ventricular walls during every heartbeat [28, 29], allowing the ventricular wall motion to be synchronized at different spatial locations. Due to the synchronization, there should exist a common motion pattern along the time across the anatomy of ventricular walls. This common motion pattern should dominate the dynamic changes of real-time CMR signals arising from the ventricular wall motion. In the presented work, a reference CMR signal was calculated from the spatial average of real-time CMR signals over an ROI (LV-ROI or RV-ROI in Figure 1), providing an estimate of the common motion pattern in the ventricular walls. The measurements of temporal periodicity and spatial coherence are both based on the calculation of the reference CMR signal.
Temporal periodicity is a traditional engineering concept for the study of periodic signals along the time. This concept has been introduced for characterizing the temporal patterns of a reference CMR signal. We believe that, to maintain a consistent cardiac output, a healthy heart should exhibit periodicity globally in the LV and RV contraction and relaxation over a series of sequential cardiac cycles. This periodic pattern, which can be measured quantitatively with temporal periodicity from the reference CMR signal, is expected to be stronger when there is a need for higher cardiac output. As demonstrated in our exercise stress CMR study (Figure 4), the reference CMR signal showed a periodic pattern that follows the heartbeats. The temporal periodicity became higher during exercise when ventricular wall motion increased. These findings validate the physiological relevance of temporal periodicity in real-time CMR Fourier analysis.
Spatial coherence (Equation 2) provides the spatial characterization of ventricular wall motion over a series of sequential cardiac cycles. Motion may spread along the ventricular walls [28, 29], and also from the ventricular walls to the around tissues inside or outside the ventricles during contraction and relaxation. We believe that ventricular performance should be dependent on how widely ventricular wall motion would spread over the entire ventricular anatomy. In the presented work, Fourier cross spectra (Equation 2) were used to calculate the temporal correlation between the reference CMR signal and every real-time CMR signal at different spatial locations in the ventricular anatomy. A spatial coherence map was generated from the Fourier cross spectra to investigate spatial spread of the primary temporal patterns of LV and RV wall motion. To globally assess the spatial spread of LV and RV wall motion, spatial coherence was evaluated by calculating the average of a spatial coherence map within the ventricular anatomy.
In the presented work, the measurements of temporal periodicity and spatial coherence were found to be lower in the HF patients than those in the healthy volunteers. This suggests that both temporal aperiodicity and spatial spread of the ventricular wall motion should contribute to the reduced myocardial contractility. The spatial coherence maps indicate that the LV and RV wall motion is spread less widely over the ventricular anatomy in the HF patients, suggesting that abnormal myocardium may suffer from the impediment of motion spread (Figure 5). These findings provide a validation of the ability of real-time CMR Fourier analysis to quantitatively assess ventricular performance in the healthy subjects and HF patients.
Real-time CMR Fourier analysis and volumetric measurements
We have found that temporal periodicity and spatial coherence are correlated strongly (R>0.5) with EF and ESV, moderately (0.5>R>0.3) with EDV, and weakly (R<0.3) with SV (Figure 6). These findings further evidence the physiological relevance of real-time CMR Fourier analysis. Especially, the temporospatial indices were found to be most correlated to EF (R>0.6), indicating that they should be related to both systolic contraction and diastolic preload in a cardiac cycle. This strong correlation may be partially explained by the fact that both temporospatial indices and EF are normalized. Because of normalization, real-time CMR Fourier analysis provides inter-subject comparability.
Despite the correlation, real-time CMR Fourier analysis and volumetric measurements extract different information from the CMR images. Volumetric measurements give an estimate of the change of blood volume from the end of diastole to that of systole in a cardiac cycle and are thereby insensitive to dynamic events in the midst of ventricular filling and ejection. In contrast, real-time CMR Fourier analysis characterizes the ventricular wall motion temporarily and spatially throughout the systole and diastole over a series of sequential cardiac cycles. As Fourier transform is dependent on the data measurements at every time point, temporal periodicity and spatial coherence can evaluate how ventricular performance may be affected by the temporal variation of ventricular wall motion within each cardiac cycle and across different cardiac cycles. With more information, real-time CMR Fourier analysis can provide better assessment of the difference of ventricular performance between the healthy volunteers and the HF patients than that given by volumetric measurements. This explains why the HF patients and healthy volunteers are clearly separated in the scanner plots of spatial coherence against temporal periodicity and while they are mixed in those of ESV against EF (Figure 6b). Our findings suggest that spatial coherence and temporal periodicity may provide the metrics of ventricular performance that are superior to the conventional estimates in detecting change of myocardial performance that is independent of ventricular size. Therefore, real-time CMR Fourier-analysis has the potential to be complementary to the traditional volumetric measurements.
Potential applications
Potential applications for real-time CMR Fourier analysis include quantitative assessment of left ventricular function during stress (exercise or pharmacological) MRI; measurement of left atrial functional performance parameters; assessment of left ventricular diastolic function; and assessment of the right ventricle in various disease states (including pulmonary hypertension and congenital heart disease). They may also have the potential to allow effective assessment of therapeutic response in patients with cardiomyopathy.
It should be mentioned that Fourier analysis offers a SNR gain over time-domain analysis because a spectral peak in Fourier transform arises from temporal summation that may suppress noise [18, 20, 30]. This SNR gain can compensate for the relatively low image quality in real-time CMR (Figure 2). This gain may be beneficial to clinical applications of real-time CMR Fourier analysis.
Study limitations
The presented work is a proof-of-concept study on real-time CMR Fourier analysis for temporospatial characterization of ventricular wall motion. As ventricular wall motion is the cause of many mechanic events in a cardiac cycle, such as pressure, volume and flow velocity changes as well as the response to the change of electrical conduction, this characterization may provide information about the intricacy of wall motion in normal subject and in patients with a number of different cardiac diseases. Accordingly, a small group of HF patients is not sufficient for a comprehensive evaluation of the clinical potential of real-time CMR Fourier analysis. The follow-up studies should expand into an experimental work on a wider range of cardiac diseases with a larger number of human subjects. Additional future work should also address inter-operator, intra-operator, and inter-exam reproducibility; comparison with other left ventricular functional parameters and techniques; and improving the reconstruction time of radial MRI data.