We present an adaptive algorithm which uses a fast electrophysiological (EP) model to estimate apparent electrical conductivity and local conduction velocity from noncontact mapping of the endocardial surface potential. Development of such functional imaging revealing hidden parameters of the heart can be instrumental for improved diagnosis and planning of therapy for cardiac arrhythmia and heart failure, for example during procedures such as radio-frequency ablation and cardiac resynchronisation therapy. The proposed model is validated on synthetic data and applied to clinical data derived using hybrid X-ray/magnetic resonance imaging. We demonstrate a qualitative match between the estimated conductivity parameter and pathology locations in the human left ventricle. We also present a proof of concept for an electrophysiological model which utilizes the estimated apparent conductivity parameter to simulate the effect of pacing different ventricular sites. This approach opens up possibilities to directly integrate modelling in the cardiac EP laboratory.