Network Modeling Approach for the Nonlinear Dynamics of the Osseous Bio-Physics and Bio-Mathematics

Bone is termed the smart material, and its modeling is of great interest in biomechanics, biochemistry, endocrinology, and oncology. The bone health of cancer patients is directly affected by hormonal imbalances, receptor-mediated tumor-targeted processes, and disturbed bone mineral density. Researchers have used different therapeutic approaches to monitor bone health during and after cancer treatment. This paper describes a reverse process of bone rebuilding after the resorption of bone via cancer treatment. A detailed model is used for hormonal therapy, which leads to the physical changes in trabecular structure. These changes are demonstrated with the aid of artificial neural networks and Petri nets. This paper connects the structural modeling of the bone trabecula with chemical kinetics. The main goal of this study is to provide a PN model of bone metastasis and an analysis of its structural properties. These properties are very helpful in demonstrating the complex dynamics of bone metastasis. Although both ANNs and PNs are well organized in the areas of machine learning and network modeling, neither technique is without limitations. ANNs, for example, are very efficient machine-learning applications, but their utter lack of explanation capabilities classifies them as a “black-box” technique. On the other hand, PNs are an effective modeling technique, but their theory does not include machine learning. This paper provides a hybrid approach to address the two approaches in a novel manner.