Introduction: In clinical care, structural images of the patient are often available. A major question is therefore how to integrate this information in order to drive ECGI. The most common approach to compute ECGI problem is based on the model of the torso as a passive volume conductor, outside the heart. The method of fundamental solutions (MFS) with Tikhonov regularization is commonly used to solve this problem. It is limited because it cannot easily take into account scars inside the heart volume, and also because it assumes that cardiac sources are only distributed on the epicardium. In this work, we propose a methodology to take into account the location of scars in ECGI problem. Methods: We considered the torso as a volume conductor including the intracavitary blood, the heart and the remaining torso volume, in which only the heart volume behaves as an electrical current source field. We could take into account a different electrical conductivity in each of the regions, and in particular in the scar. We identified the source best matching a given body surface potential map, by solving the classical quadratic optimization problem with a Tikhonov regularization term. In order to account for scars, the regularization parameter was increased, but also the conductivity was decreased in the scar. Datasets computed on a realistic human-based anatomical model were used. The activation times (ATs) recovered by the standard MFS and this method were compared to the reference ATs obtained from the model. Conclusion: In this study, the method performed better than the MFS method in presence of a scar. The correlation coefficients of the activation times around the scar are improved up to 10% on the epicardium, and 7% on the endocardium, by adapting the Tikhonov regularization parameter and conductivity coefficient in the scar.