Purpose: Tensor-valued diffusion encoding can probe more specific features of tissue microstructure than what is available by conventional diffusion weighting. In this work, we investigate the technical feasibility of tensor-valued diffusion encoding at high b-values with q-space trajectory imaging (QTI) analysis, in the human heart in vivo. Methods: Ten healthy volunteers were scanned on a 3T scanner. We designed time-optimal gradient waveforms for tensor-valued diffusion encoding (linear and planar) with second-order motion compensation. Data were analyzed with QTI. Normal values and repeatability were investigated for the mean diffusivity (MD), fractional anisotropy (FA), microscopic FA (μFA), isotropic, anisotropic and total mean kurtosis (MKi, MKa, and MKt), and orientation coherence (Cc). A phantom, consisting of two fiber blocks at adjustable angles, was used to evaluate sensitivity of parameters to orientation dispersion and diffusion time. Results: QTI data in the left ventricular myocardium were MD = 1.62 ± 0.07 μm2/ms, FA = 0.31 ± 0.03, μFA = 0.43 ± 0.07, MKa = 0.20 ± 0.07, MKi = 0.13 ± 0.03, MKt = 0.33 ± 0.09, and Cc = 0.56 ± 0.22 (mean ± SD across subjects). Phantom experiments showed that FA depends on orientation dispersion, whereas μFA was insensitive to this effect. Conclusion: We demonstrated the first tensor-valued diffusion encoding and QTI analysis in the heart in vivo, along with first measurements of myocardial μFA, MKi, MKa, and Cc. The methodology is technically feasible and provides promising novel biomarkers for myocardial tissue characterization.@en