Emerging mathematical approaches to blood coagulation and clot formation under flow: From constitutive biophysical laws to integrative multiscale models

Blood clotting disorders can lead to a wide range of serious and life-threatening medical conditions. Effective control of coagulation remains a major clinical challenge due to the complexity of the coagulation process, its sensitivity to local physiological and biophysical factors, and significant inter-individual variability. Mathematical and computational models have been developed to study various physiological and clinical aspects of blood coagulation. The field is experiencing a rapid growth nowadays, fueled by the increased data availability, the advances in computational power, the integration of clinical practice with biophysical methods and modeling, and the emergence of novel approaches, including machine learning and artificial intelligence. In this review, we highlight recent innovations and emerging approaches in coagulation modeling, with a focus on clinically relevant scenarios and their underlying physiological and biophysical principles.