Background and Objective. B-spline interpolation (BSI) is a popular technique in the context of medical imaging due to its adaptability and robustness in 3D object modeling. A field that utilizes BSI is Image Guided Surgery (IGS). IGS provides navigation using medical images, which can be segmented and reconstructed into 3D models, often through BSI. Image registration tasks also use BSI to align pre-operative data to intra-operative data. However, such IGS tasks are computationally demanding, especially when applied to 3D medical images, due to the complexity and amount of data involved. Therefore, optimization of IGS algorithms is greatly desirable, for example, to perform image registration tasks intra-operatively and to enable real-time applications. A traditional CPU does not have sufficient computing power to achieve these goals. In this paper, we introduce a novel GPU implementation of BSI to accelerate the calculation of the deformation field in non-rigid image registration algorithms. Methods. Our BSI implementation on GPUs minimizes the data that needs to be moved between memory and processing cores during loading of the input grid, and leverages the large on-chip GPU register file for reuse of input values. Moreover, we re-formulate our method as trilinear interpolations to reduce computational complexity and increase accuracy. To provide pre-clinical validation of our method and demonstrate its benefits in medical applications, we integrate our improved BSI into a registration workflow for compensation of liver deformation (caused by pneumoperitoneum, i.e., inflation of the abdomen) and evaluate its performance. Results. Our approach improves the performance of BSI by an average of 6.5x and interpolation accuracy by 2x compared to three state-of-the-art GPU implementations. We observe up to 34% acceleration of non-rigid image registration.