Error model for reduction of cardiac and respiratory motion effects in quantitative liver DW-MRI

Diffusion-weighted images of the liver exhibit signal dropout from cardiac and respiratory motion, particularly in the left lobe. These artifacts cause bias and variance in derived parameters that quantify intravoxel incoherent motion. Many models of diffusion have been proposed, but few separate attenuation from diffusion or perfusion from that of bulk motion. The error model proposed here (Beta*LogNormal) is intended to accomplish that separation by modeling stochastic attenuation from bulk motion as multiplication by a Beta-distributed random variate. Maximum likelihood estimation with this error model can be used to derive intravoxel incoherent motion parameters separate from signal dropout, and does not require a priori specification of parameters to do so. Liver intravoxel incoherent motion parameters were derived for six healthy subjects under this error model and compared with least-squares estimates. Least-squares estimates exhibited bias due to cardiac and respiratory gating and due to location within the liver. Bias from these factors was significantly reduced under the Beta*LogNormal model, as was within-organ parameter variance. Similar effects were appreciable in diffusivity maps in two patients with focal liver lesions. These results suggest that, relative to least-squares estimation, the Beta*LogNormal model accomplishes the intended reduction of bias and variance from bulk motion in liver diffusion imaging.