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2D and 3D refer to the actual dimensions in a computer workspace. 2D is "flat", using the horizontal and vertical (X and Y) dimensions, the image has only two dimensions and if turned to the side becomes a line. 3D adds the depth (Z) dimension. This third dimension allows for rotation and visualization from multiple perspectives. It is essentially the difference between a photo and a sculpture.
The key difference between 2D and 3D echocardiography is the volumetric approach to data acquisition (Figure 1), visualization (Figure 2 and 3), and quantitation (Figure 4). 
Figure 1. Two-dimensional echocardiography is a tomographic technique which provides "flat" views of the heart and great vessels which thickness is fixed and related to the piezoelectric element vertical dimension. Three-dimensional echocardiography is based on real-time volumetric imaging that allows acquisition of pyramidal data sets.
Figure 2. Imaging of the mitral valve with 2D (left panel) and 3D (right panel) echocardiography) from the ventricular perspective. 2D imaging allows visualization mitral valve leaflet margins and left ventricular wall only. 3D volume rendering of the same valve allows appreciation of the whole leaflets, commissures and relationships with surrounding structures (e.g. left ventricular outflow tract) in a realistic anatomic display.
Figure 3. In contrast with 2D technique, 3D echocardiography allows the visualization of the structure of interest from virtually any desired perspective. For example, by 2D echocardiography the mitral valve can be seen from the ventricular perspective only, while by 3D echocardiography the mitral valve can be visualized both from the ventricular and the atrial ("surgical view") perspectives.
Figure 4. Quantitative analysis with 2D echocardiography is based on geometric assumptions about cardiac structure shape, spatial interpolation among available views and calculations using fixed mathematical formulas irrespective of the actual shape of the cardiac structure of interest. Quantitative analysis with 3D echocardiography is based on voxel count in a volume which has been identified by semi-automated or automated border identification without geometric assumptions about structure shape.
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