This paper presents a common stochastic modelling framework for physiological signals which allows patient simulation following a synthesis-by-analysis approach. Within this framework, we propose a general model-based methodology able to reconstruct missing or artifacted signal intervals in cardiovascular monitoring applications. The proposed model consists of independent stages which provide high flexibility to incorporate signals of different nature in terms of shape, cross-correlation and variability. The reconstruction methodology is based on model sampling and selection based on a wide range of boundary conditions, which include prior information. Results on real data show how the proposed methodology fits the particular approaches presented so far for electrocardiogram (ECG) reconstruction and how a simple extension within the framework can significantly improve their performance.