Numerical models consisting of two-dimensional (2D) and three-dimensional (3D) uniform grid meshes for the Transmission Line Matrix Method (TLM), use sqrt(2) and sqrt(3), respectively, to compensate for the apparent sound speed. In this work, new compensation factors are determined from a priori simulations, performed without compensation, in 2D and 3D TLM one-section cylindrical waveguide acoustic models. The mistuned resonance peaks obtained from these simulations are substituted in the corresponding equations for the resonance frequencies in one-section cylindrical acoustical waveguides to find the mesh apparent sound speed and, thus, the necessary compensation. The TLM meshes are constructed over the voxels (Volumetric Picture Elements) of segmented MRI volumes, so that the extracted mesh fits the segmented object. The TLM method provides a direct simulation approach instead of solving a PDE by variational methods that must consider the plane wave assumption to run properly. Results confirm the improvement over the conventional compensation factors, particularly for frequencies above 4 kHz, providing a concrete reduction of the topology-dependent numerical dispersion for both 2D and 3D TLM lattices. Since this dispersion problem is common to all TLM applications using uniform grids, investigators in other areas of wave propagation can also benefit from these findings.