This paper presents a new method to estimate left ventricle deformations using variational data assimilation that combines image observations from cine MRI and a dynamic evolution model of the heart. The main contribution of the model is that it embeds parameters modeling the contraction / relaxation process. It estimates myocardial motion and contraction parameters simultaneously, providing accurate complementary information for diagnosis. The method was applied to synthetic datasets with known ground truth motion and to 47 patients MRI datasets acquired at three slice locations (base, mid-ventricle and apex). Radial and circumferential strain components were compared to those obtained with a reference tag tracking software, exhibiting good agreement with intraclass correlation coefficients (ICC) above 0.8. Results were also evaluated against wall motion score indices used to assess cardiac kinetics in clinical practice. The assimilation process overcame issues caused by temporal artifacts as a result of the dynamic model, compared to using the observation term alone. Moreover we found that the new dynamic model, consisting of a piecewise transport model acting independently on systole and diastole performed better than the standard continuous transport model, which oversmooths temporal variations. Estimated strain and contraction parameters significantly correlated to clinical scores, making them promising features for diagnosing not only hypokinesia but also dyskinesia.