Multiscale in Silico Models of Fracture Healing: Providing an Integrative Framework to Understand the Influences of Defect Size, Sex Differences, and Inflammation

Bone healing is a well-coordinated process involving numerous biological entities. While successful healing typically occurs within weeks, fracture severity, anatomical location and host factors can lead to delayed or non-healing. Critical-size defects require intervention to promote healing, with healing depending on the defect's location and its surroundings. Among host factors, the role of sex differences remains poorly understood, as most preclinical research has focused primarily on male subjects. Consequently, treatments may affect men and women differently. The use of (sex-specific) in silico models offers an interesting methodology to investigate the biological mechanisms underlying fracture healing and the influences of external factors, as well as to propose patient-specific treatment strategies. Following existing bioregulatory models we developed multiscale in silico models of bone healing to investigate normal and impaired sex-specific healing in long bone, mandibular and calvarial defects. These geometries were derived from in vivo experimental set-ups in rabbits and rodents. Our in silico models describe the spatiotemporal evolution of biochemical factors, cells and tissues, from the early inflammatory response to hard callus formation, incorporating sprouting angiogenesis with lateral inhibition of endothelial cells via Dll4-Notch1 signaling. The models were parameterized with sex-specific values informed by literature, focusing on young males and females of reproductive age. Finally, we explored the influence of a scaffold produced by melt electrowriting (MEW), coated (or not) with cells and/or growth factors (GF) as a treatment strategy. The models were implemented in MATLAB and FreeFEM and validated against in vivo data from the literature and in-house experiments. For normal healing in long bone defects, our model predicted a stronger inflammatory response in females and a stronger repair response in males, in alignment with literature data (results not shown). The predicted healing outcomes were similar between both sexes, matching experimental observations both qualitatively and quantitatively. For critical-sized craniofacial defects, our in silico predictions of a non-union matched the in vivo results at 4 and 12 weeks. We used our models to investigate adequate GF concentrations to load onto the MEW scaffold to achieve (delayed) healing. In summary, our in silico models predict realistic healing patterns that align with experimentally observed behavior, enhancing our understanding of bone defect healing mechanisms under different conditions, a first step towards the implementation of patient-specific in silico models of bone regeneration.