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Physics-based-theoretical models have been used to predict developmental patterning processes such as branching morphogenesis for over half a century. While such techniques are quite successful in understanding the patterning processes in organs such as the lung and the kidney, they are unable to accurately model the processes in other organs such as the submandibular salivary gland. One possible reason is the detachment of these models from data that describe the underlying biological process. This hypothesis coupled with the increasing availability of high quality data has made discrete, data-driven models attractive alternatives. These models are based on extracting features from data to describe the patterns and their time evolving multivariate statistics. These discrete models have low computational complexity and comparable or better accuracy than the continuous models. This paper presents a case study for coupling continuous-physics-based and discrete-empirical-models to address the prediction of cleft formation during the early stages of branching morphogenesis in mouse submandibular salivary glands (SMG). Given a time-lapse movie of a growing SMG, first we build a descriptive model that captures the underlying biological process and quantifies this ground truth. Tissue-scale (global) morphological features are used to characterize the biological ground truth. Second, we formulate a predictive model using the level-set method that simulates branching morphogenesis. This model successfully predicts the topological evolution, however, it is blind to the cellular organization, and cell-to-cell interactions occurring inside a gland; information that is available in the image data. Our primary objective via this study is to couple the continuous level set model with a discrete graph theory model that captures the cellular organization but ignores the forces that determine the evolution of the gland surface, i.e. formation of clefts and buds. We compared the prediction accuracy of our model to an on-lattice Monte-Carlo simulation model which has been used extensively for modeling morphogenesis and organogenesis. The results demonstrate that the coupled model yields comparable simulations of gland growth to that of the Monte-Carlo simulation model with a significantly lower computational complexity.
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