Sodium MRI can act as a biomarker for heart tissue viability^1,2. As it suffers from low signal-to-noise ratio (SNR), many techniques have been recently developed using 3D ultra-short echo time (UTE) sequences with anisotropic resolution and retrospective electrocardiogram gating³. In sodium heart MRI, several aspects (blurring behavior of radial sequences, blurring because of heart motion, small myocardial infarction (MI) regions) complicate MI detection due to resolution reasons. Optimal sequence parameters are difficult to find since many subject parameters (e.g., relaxation times, heart motion) must be considered. In this study, a beating heart was simulated to find optimal acquisition parameters dependent on physiological parameters.

Simulations were performed on an analytical heart model (short-axis) using Matlab (The MathWorks Inc., Natick, MA). The heart was modeled by ellipsoidal shapes only, since raw data can be generated analytically⁴$$F(k_x,k_y,k_z)=\rho abc\frac{\sin{(2\pi K)}-2\pi K\cos{(2\pi K)}}{2\pi^2K^3},$$with signal scaling factor ρ, semi-principal axes of lengths a, b, c and$$K=\left((ak_x)^2+(bk_y)^2+(ck_z)^2\right)^{1/2}.$$Figure 1a shows the heart model with geometric dimensions and relative signal for heart chambers (RV, LV), myocardium and assumed MI. A 3D density-adapted radial UTE sequence³ was used for simulated acquisition with additional complex pseudorandom Gaussian noise (Fig. 1b) with following parameters: 30,000 projections with golden angle distribution, 160 samples per projection, readout time of 10 ms, in-plane resolution of 2.5 mm and anisotropy factor of 2 (i.e., 5 mm). Data were averaged 10 times and regridded for a field-of-view of 300 mm with a Kaiser-Bessel kernel⁵, oversampling ratio⁶ of 1.375 and iterative sample density estimation⁷. A scale factor between 0.84 (maximum contraction) and 1.0 (diastole) for the heart dimensions was applied according to the function shown in Figure 1c to simulate heart motion. A repetition time of 20 ms was used at a simulated random heartbeat of 55-65 min^-1.

Simulations were performed with different temporal window sizes (called assumed systole length), within which the projections were not considered for reconstruction. In a second simulation, the resolution was continuously reduced to consider signal loss because of fewer projections used. The resolution was adapted to maintain SNR for increasing window sizes:$$\Delta x(w)=\left[\left(\frac{mCCL-w}{mCCL}\right)^{-1/2}\right]^{1/3}\cdot\Delta x(w=0),$$where mCCL is the mean cardiac cycle length and w is the window length of projections that are not considered for reconstruction.

If all projections of the heart cycle are considered for reconstruction, blurring due to heart motion is clearly visible (Fig. 2a) compared to measurements at longer window sizes (Fig. 2b: 400 ms, Fig. 2c: 800 ms) with less motion/blurring. In Figure 2d, the signal profile (dotted line in Fig. 2a) is shown for the three different window sizes. It can be observed that the MI is better delineated at a window length of 400 ms compared to 0 ms and 800 ms. More blurring occurs at signal transitions if all projections are considered (black line). The SNR in the MI region shows an optimum at about 380 ms assumed for the systole length (Fig. 2e). The same simulation was performed but the resolution was adapted for same SNR values (Fig. 3). Maximum SNR in MI is obtained at a longer window size of about 500 ms (Fig. 3e) compared to the former case.

It could be demonstrated that sequence parameter optimization is very important especially in case of any kind of motion. The window length of retrospectively chosen projections with golden angle increments and the resolution can be optimized by the use of the presented beating heart model. Parameters like relaxation times, heart motion, dimensions, etc. are considered. The choice of the window length after heart contraction (in which projections are not considered for reconstruction) is a trade-off between the proportions of motion artifacts and SNR/resolution. In this study, an optimal window length could be found for MI detection assuming a certain parameter set. Since resolution cannot be changed (without modifying the readout time and SNR) after the measurement, it is advisable to know optimal and SNR-efficient sequence parameters by simulation of the actual parameter set. The main drawback of this study is that heart motion is modeled only by a scale factor for the heart dimensions, whereas heart rotation and density changes are not considered. Future work should improve the heart model by integrating a more realistic heart motion, which can be incorporated after evaluation of a large cohort. Furthermore, other acquisition schemes (e.g., flexTPI⁸) should be investigated.

The presented simulation model of a beating heart can be used to optimize sequence parameters, among other things, for better visualization of MI and can be adapted to any kind of motion and to different subject parameters.