Fig. 1.

Undeformed voxel (green) is mapped by the displacement vectors to create the deformed voxel (purple). Equation (10) describes how the ventilation metric varies when $\mathbf{d}({\mathbf{x}}_k)$ is perturbed by a vector with magnitude $∥\mathbf{h}∥$. The perturbation implies that the mapped position $\mathbf{y}={\mathbf{x}}_k+\mathbf{d}({\mathbf{x}}_k)-\mathbf{h}$ lies within the red ball of radius of $∥\mathbf{h}∥$ centered on the unperturbed position, denoted $B_{∥\mathbf{h}∥}(\mathbf{y})$