Two Dimensional Magnetic Recording (TDMR) is a promising technology for next generation magnetic storage systems based on a systems level framework involving sophisticated signal processing at the core. The TDMR channel suffers from severe jitter noise along with electronic noise that needs to be mitigated during signal detection and recovery. Recently, we developed noise prediction based techniques coupled with advanced signal detectors to work with these systems. However, it is important to understand the role of harmful patterns that can be avoided during the encoding process. In this paper, we investigate into the Voronoi based media model to study the harmful patterns over multi-track shingled recording systems. Through realistic quasi micromagnetic simulations studies, we identify 2D data patterns that contribute to high media noise. We look into the generic Voronoi model and present our analysis on multi-track detection with constrained coded data. We show that two dimensional (2D) constraints imposed on input patterns result in an order of magnitude improvement in the bit error rate for TDMR systems. The use of constrained codes can reduce the complexity of 2D intersymbol interference (ISI) signal detection since lesser 2D ISI span can be accommodated at the cost of a nominal code rate loss. However, a system must be designed carefully so that the rate loss incurred by a 2D constraint does not offset the detector performance gain due to more distinguishable readback signals.Index Terms-TDMR systems, 2D no isolated bit constraint, multi-track detection, bit error rate, GBP algorithm.