This paper presents first results on the dynamics of filaments of scroll waves of myocardium excitation obtained for personalized models of the left ventricle of the human heart. The paper describes a mathematical model of the left ventricle of the human heart and its electrical activity, numerical methods for the model calculation within the framework of computer implementation, and also the method of personalization of the model according to data of ultrasound examination. We found that regardless of the starting point of wave the filaments of wave drift along a spiral to the attractor located near the apex of the ventricle. The attractor position was essentially different in models constructed from the data of patients without identified pathology and those for patients with an increased left ventricular cavity.