Open forward and inverse problems in theoretical modeling of bone tissue adaptation

Theoretical modeling of bone tissue adaptation started several decades ago. Many important problems have been addressed in this area of research during the last decades. However, many important questions remain unanswered. In this paper, an overview of open problems in theoretical modeling of bone tissue adaptation is presented. First, the principal elements of bone tissue adaptation models are defined and briefly reviewed. Based on these principal elements, four categories of open problems are identified. Two of these categories primarily include forward problems, while two others include inverse problems. In every one of the identified categories, important open problems are highlighted and their importance is discussed. It is shown that most of previous studies on the theoretical modeling of bone tissue adaptation have been focused on the problems of the first category and not much is done in three other categories. The paper tries to highlight these potentially important problems that have been so far largely overlooked and to inspire new avenues of research.