Myocardial deformation imaging can provide valuable insights in myocardial mechanics and help in the diagnosis, prognosis and follow-up of cardiac diseases. However, extracting these indices in 3D is challenging due to the limitations in spatial and temporal resolution of the current volumetric ultrasound systems. For this purpose, we developed an anatomical free-form deformation image registration framework which is locally adapted to the anatomy of the heart. In this work we explored whether incorporating a myocardial volume conservation regularizer would improve strain estimates. We evaluated our technique on in silico echo sequences featuring realistic speckle textures and showed the volume conservation regularizer to be beneficial in reducing strain errors further when used in combination with a smoothness penalty. This combination led to more physiological boundary conditions. It also made distinguishing ischemic from normal segments easier in clinical images.