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High-resolution quantification of myocardial perfusion using spatial correlations

Judith Lehnert¹, Christoph Kolbitsch^1,2, Gerd Wübbeler¹, Amedeo Chiribiri², Cian Scannell², Tobias Schafffter^1,2, and Clemens Elster¹

¹Physikalisch-Technische Bundesanstalt (PTB), Berlin, Germany, ²King’s College London, School of Biomedical Engineering and Imaging Sciences, London, United Kingdom

Synopsis

Pixel-wise quantification of myocardial perfusion by dynamic contrast-enhanced magnetic resonance imaging allows for a non-invasive, observer independent and reproducible evaluation of the perfusion with high spatial resolution. The method suggested here, exploits the spatial smoothness of the perfusion using a spatial Tikhonov regularization to cope with the low signal-to-noise ratio of the data. This allows us to obtain quantitative perfusion values with high spatial resolution to detect small ischemic regions. The parameter regulating the strength of regularization is determined from the L-curve criterion and does not require any manual adjustments. The feasibility of the method is demonstrated in three patients.

Introduction

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a well-established non-invasive technique to identify ischemic regions by visual assessment¹. Quantitative estimation of myocardial perfusion would allow for observer independent and reproducible evaluation. Due to the low signal-to-noise ratio (SNR) of the images, most studies have used segment-wise quantification (Fig.1a) entailing the risk of missing small perfusing defects. Temporal and/or spatial filtering of the data have been suggested to increase the SNR as a preprocessing step of a pixel-wise quantification^2,3. Inherently, this decreases the spatial resolution of the results. Furthermore, no objective criterion for the choice of the filter parameters exists. Here, we propose a method based on a spatial Tikhonov regularization to stabilize the pixel-based quantification⁴ by exploiting the characteristics of neighboring pixels (Fig.1b). The required regularization parameter is determined by means of the L-curve criterion⁵. The performance of the method is studied in a numerical phantom with ground truth values. Its feasibility is shown in motion-corrected dynamic MR-perfusion data of three patients. It is demonstrated that it reliable recovers the perfusion defects previously diagnosed by a clinician.

Methods

Perfusion estimation: After motion-correction⁶, segmentation and baseline subtraction, data were approximated by the first four modes of a truncated singular-value decomposition (SVD). To this end, the myocardial signal was written as a matrix with the first dimension denoting time and the second one space. From the approximated data, a first estimation of perfusion parameters on the pixel-level was calculated with the Fermi method⁷. The employed model is linearized around this estimate and the Tikhonov regularization term is added. When solving the linearized problem, we use the non-SVD-approximated data such that the approximation in the first step has no direct influence on the results. The regularization term increases as the spatial heterogeneity of the parameters rises. Note that this is in contrast to other authors who use a temporal Tikhonov regularization when fitting the data⁸. The degree of regularization $$$\lambda$$$ is obtained from an L-curve (Fig.2) as the point of maximal curvature where both the regularization term and the residuum of the fit are small.

Numerical phantom: The method was investigated in a numerical phantom that includes a realistic distribution of parameters from clinical scans to simulate dynamic MR-signals by convoluting the arterial input function with the Fermi function. The numerical phantom was used to validate the optimal regularization chosen by the L-curve approach. Furthermore, the root mean square error (RMSE) between calculated and true perfusion values was investigated for different SNRs.

Data acquisition: Clinical MR-perfusion data were obtained from patients with angina symptoms. Dynamic contrast enhanced MRI were acquired on a 3T MR-scanner (Philips Medical Systems, the Netherlands) using a spoiled gradient echo with TE=1.1ms, TR=2.5ms, a flip angle of 15° on three short-axis slices (apical, mid-ventricular and basal) with a spatial resolution of 1.1x1.1x10mm³, and a FOV of 356 x 356mm². Informed consent was obtained in all patients (ethics approval number 15/NS/0030).

Results

Figure 2e shows the L-curve for simulated data. For $$$\lambda_L=0.25$$$ (Fig.2c) chosen by the L-curve criterion a precise estimate with an root mean square error (RMSE) of 0.2 ml/(min ml) was obtained. $$$\lambda=2.5\cdot10^{-4}$$$ (Fig.2b) and $$$\lambda=2.5\cdot10^{2}$$$ (Fig.2d) yield larger RMSEs of 1.0 and 0.4 ml/(min ml) as the regularization is too weak and too strong, respectively. $$$\lambda_L=0.25$$$ is located close to the minimum of the RMSE (Fig.2f) confirming the viability of choosing $$$\lambda$$$ by this criterion. Figure 3 depicts the RMSE in the defect, the healthy myocardium and the total myocardium for different SNRs demonstrating that our method significantly decreases the RMSE compared to an unregularized single-pixel-fit. Figure 4 shows the perfusion and L-curves for two different patients. In Fig.5, three different slices of the same patient are depicted. Affected segments are visually assessed by a clinician and marked with a red arrow. Depicted is the parameter $$$F$$$ of the Fermi model, where the perfusion is given by $$$F/2$$$.

Discussion

In contrast to prefiltering in time and space, the Tikhonov regularization achieves fitting and regularization simultaneously and, therefore, balances the effects of these two procedures (Fig.1b). The strength of the filtering effect of the regularization is not global but varies between pixels finding locally the best compromise between the smoothness of the perfusion and the fit to the data.

Conclusion

We demonstrated the pixel-wise quantification of myocardial perfusion with a spatial Tikhonov regularization in both, simulated and patient data. The overall strength of the regularization can be determined objectively with the L-curve criterion. In patient data, the method provided perfusion maps which corresponds well with visual assessment by a clinician.

Acknowledgements

This work was supported by the EMPIR project 15HLT05 PerfusImaging. The EMPIR initiative is co-funded by the European Union’s Horizon 2020 research and innovation programme and the EMPIR Participating States.

References

1. Jerosch-Herold M "Quantification of myocardial perfusion by cardiovascular magnetic resonance." Journal of Cardiovascular Magnetic Resonance 12 (2010): 57.

2. Zarinabad N, Chiribiri A, Hautvast GL, et al. "Pixel‐wise quantification of myocardial perfusion by cardiac magnetic resonance. Feasibility and methods comparison." Magnetic resonance in medicine 68 (2012): 1994-2004.

3. Kellman P, Hansen MS, Nielles-Vallespin S, et al. "Myocardial perfusion cardiovascular magnetic resonance: optimized dual sequence and reconstruction for quantification." Journal of Cardiovascular Magnetic Resonance 19 (2017): 43.

4. Lehnert J, Wübbeler G, Kolbitsch C, et al. "Pixel-wise quantification of myocardial perfusion using spatial Tikhonov regularization." Physics in Medicine and Biology 63 (2018):215017

5. Hansen PC, O’Leary DP "The use of the L-curve in the regularization of discrete ill-posed problems." SIAM Journal on Scientific Computing 14 (1993): 1487-1503.

6. Scannell C, Lee J, Villa ADM, et al. “Fully-automated motion correction and probability-based segmentation of myocardial perfusion MRI data” Proceedings of the Joint Annual Meeting of the ISMRM/ESMRMB (2018).

7. Jerosch‐Herold M, Wilke N, Stillman AE, et al. "Magnetic resonance quantification of the myocardial perfusion reserve with a Fermi function model for constrained deconvolution." Medical physics 25 (1998): 73-84.

8. Calamante F, Gadian DG, Connelly A "Quantification of bolus‐tracking MRI: Improved characterization of the tissue residue function using Tikhonov regularization." Magnetic resonance in medicine 50 (2003): 1237-1247.

Figures

Schematic of different methods to quantify perfusion. (a) Standard method. MR images are segmented into 4 (apical slice) or 6 (basal and mid-ventricular slice) segments. Averaged myocardial signal intensities are fitted in each segment. (b) New method proposed here: Pixel-wise quantification of unfiltered data. Fitting and Tikhonov regularization are carried out simultaneously.

Quantification of perfusion in simulated data with an SNR of 5. (a) True $$$F$$$ values. $$$\hat F$$$ in ml/(ml min) for (b) $$$\lambda=2.5\cdot10^{-4}$$$ , (c) $$$\lambda_L=0.25$$$ as obtained with the L-curve criteria, and (d) $$$\lambda=2.5\cdot10^{2}$$$ . (e) Corresponding L-curve. Due to the different scaling of x- and y-axis, the maximum curvature appears visually different to $$$\lambda_L$$$ selected by the L-curve criterion. (f) RMSE in ml/(ml min) versus $$$\lambda$$$. Green dot marks $$$\lambda_L$$$ as obtained with the L-curve criterion. Orange dot marks minimum of the RMSE.

Root mean square error (RMSE) in ml/(ml min) of $$$F$$$ vs. SNR in (a) an extended defect as marked by the red arrow in Fig. 2a, (b) the healthy myocardium, and (c) the total myocardium, respectively. Blue bars: unregularized single-pixel fit. Red bars: Tikhonov regularized fit. Data were obtained from 100 realizations of the numerical phantom.

Quantification of perfusion in patient data. (a) and (d) Myocardial signal of the mid-ventricular slice of two different patients at $$$t=81$$$ s and $$$t=66s$$$ , respectively. Ischemic segments were visually assessed by a clinician and are marked by red arrows. (b) and (e) $$$\hat F$$$ values in ml/(ml min) obtained with the proposed approach. (c) and (f) Corresponding L-curves with $$$\lambda_L$$$ chosen by the L-curve criterion marked with a green dot. Due to the different scaling of x- and y-axis, the maximum curvature appears visually different to $$$\lambda_L$$$ selected by the L-curve criterion.

Quantification of perfusion in patient data. (a) - (c) Myocardial signal at $$$t=70$$$ for the (a) basal, (b) mid-ventricular, and (c) apical slice of the same patient. Ischemic segments which were visually assessed by a clinician are marked with red arrows. (d) - (f) $$$\hat F$$$ values in ml/(ml min) obtained with the proposed method.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)

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