Fourier Decomposition (FD) MRI was previously introduced as a non-invasive contrast agent free approach for MRI based functional imaging. By acquiring a set of time-resolved images it is possible to separate pixels showing signal changes at the ventilation and cardiac frequency, respectively. While it is a promising approach, using Fourier analysis poses challenges when confronted with signal irregularities such as arrhythmia. A drawback with FD is its dependency on signal stability which limits the accuracy of frequency estimation. Human ventilation and perfusion frequencies lie on average between 0.22-0.33 Hz and 1.00-1.33 Hz. As seen in figure 1 FD ideally produces a peak at the ventilation frequency followed by harmonics, then the cardiac frequency with its harmonics. Yet, the maximal image acquisition rate is limited so the cardiac signal’s harmonics might be folded in due to aliasing. In this work we present wavelet decomposition (WD) as an alternative approach to generate frequency peaks. WD displays frequency over time and is not constrained to the signal stability. One can also choose window scaling and thus optimize frequency resolution.

The image sequence consisted of 300 pre-processed[1],[2] images representing 47.6s recording time. Pulse sequence was TrueFISP 2d Sequence (TR/TE=1.1ms/0.4ms, TA=175ms, FoV=500x500mm, fa=27.5 degrees, TI=106ms, slice thickness=15 cm, imaging matrix=128x128,) on a 1.5T full-body (Siemens MEGNETOM Aera) MR scanner. The highest possible measured frequency for a given sample was $$$\frac{1}{2*TA} =2.86Hz$$$ . The first 20 images in the series were discarded for signal stability purposes, DC values were then subtracted and divided from every pixel. The signal was then split into perfusion and ventilation frequency by applying a low and high pass filter, respectively. Wavelet analysis was performed in every pixel along with FFT for comparison. The Paul wavelet[3] was chosen, due to its visual similarity to the acquired signal. The polynomial order of the wavelet was optimized with respect to the highest Signal-to-Noise-Ratio (SNR) and Contrast-to-Noise-Ratio (CNR).Figure 2 presents ventilation- (VW) and perfusion-weighted (QW) images in coronal view using WD (Fig.2a/c) and FD (Fig.2b/d). Figures 2(a-d) show homogenous signal distribution within the lung area. Residual diaphragmic movement is correlated with ventilation frequency and thus generates a signal outside the lung area in the VW images. Table 1 displays all images’ calculated SNR and CNR, showing WD as the superior method for this image sequence. In the VW-images WD produces 23 % higher SNR and 26% higher CNR than FD while the QW-images show similar SNR for both methods and an increase of CNR by 10% for WD-MRI. Using WD when evaluating perfusion and ventilation frequency shows a promising improvement of image quality. WD removed the dependency on signal stability and showed better results whilst remaining completely non-invasive, free-breathing and contrast-agent-free. Although the numerical improvement is smaller in the QW-images, comparing WD- and FD-images visually, one can observe more pixelated noise embedded in the FD images. The diaphragm’s signal would likely be improvable by using a suitable registration algorithm which excludes movement to a larger extent. Similar to Bauman et al.[4], the perfusion signal’s largest artefact is the aorta’s pulsation. Since the wavelet scaling can be arbitrarily chosen, further possibilities for SNR- and CNR-optimization exist.In conclusion, we demonstrated Wavelet Decomposition-MRI as a further development of Fourier Decomposition-MRI. Future work will concentration on optimizing the parameters of the method and validation on additional patient data.