MRI-guided laser-induced interstitial thermal therapy (LITT) is a form of laser ablation and a potential alternative to craniotomy in treating glioblastoma multiforme (GBM) and epilepsy patients, but its effectiveness has yet to be fully evaluated. One way of assessing short-term treatment of LITT is by evaluating changes in post-treatment MRI as a measure of response. Alignment of pre- and post-LITT MRI in GBM and epilepsy patients via nonrigid registration is necessary to detect subtle localized treatment changes on imaging, which can then be correlated with patient outcome. A popular deformable registration scheme in the context of brain imaging is Thirion's Demons algorithm, but its flexibility often introduces artifacts without physical significance, which has conventionally been corrected by Gaussian smoothing of the deformation field. In order to prevent such artifacts, we instead present the Anisotropic smoothing regularizer (AnSR) which utilizes edge-detection and denoising within the Demons framework to regularize the deformation field at each iteration of the registration more aggressively in regions of homogeneously oriented displacements while simultaneously regularizing less aggressively in areas containing heterogeneous local deformation and tissue interfaces. In contrast, the conventional Gaussian smoothing regularizer (GaSR) uniformly averages over the entire deformation field, without carefully accounting for transitions across tissue boundaries and local displacements in the deformation field. In this work we employ AnSR within the Demons algorithm and perform pairwise registration on 2D synthetic brain MRI with and without noise after inducing a deformation that models shrinkage of the target region expected from LITT. We also applied Demons with AnSR for registering clinical T1-weighted MRI for one epilepsy and one GBM patient pre- and post-LITT. Our results demonstrate that by maintaining select displacements in the deformation field, AnSR outperforms both GaSR and no regularizer (NoR) in terms of normalized sum of squared differences (NSSD) with values such as 0.743, 0.807, and 1.000, respectively, for GBM.