title: Mathematical modeling of collagen turnover in biological tissue.
abstract: We present a theoretical and computational model for collagen turnover in soft biological tissues. Driven by alterations in the mechanical environment, collagen fiber bundles may undergo important chronic changes, characterized primarily by alterations in collagen synthesis and degradation rates. In particular, hypertension triggers an increase in tropocollagen synthesis and a decrease in collagen degradation, which lead to the well-documented overall increase in collagen content. These changes are the result of a cascade of events, initiated mainly by the endothelial and smooth muscle cells. Here, we represent these events collectively in terms of two internal variables, the concentration of growth factor TGF-β and tissue inhibitors of metalloproteinases TIMP. The upregulation of TGF-β increases the collagen density. The upregulation of TIMP also increases the collagen density through decreasing matrix metalloproteinase MMP. We establish a mathematical theory for mechanically-induced collagen turnover and introduce a computational algorithm for its robust and efficient solution. We demonstrate that our model can accurately predict the experimentally observed collagen increase in response to hypertension reported in literature. Ultimately, the model can serve as a valuable tool to predict the chronic adaptation of collagen content to restore the homeostatic equilibrium state in vessels with arbitrary micro-structure and geometry.
authors.affiliation: Department of Mechanical Engineering, Stanford University, Stanford, CA, 94305, USA, psaez@unizar.es.
authors.forename: Pablo
authors.initials: P
authors.lastname: Sáez
authors.forename: Estefanía
authors.initials: E
authors.lastname: Peña
authors.forename: Miguel
authors.initials: M
authors.lastname: Ángel Martínez
authors.forename: Ellen
authors.initials: E
authors.lastname: Kuhl
mesh_terms: D000465:Algorithms; D001696:Biomechanical Phenomena; D003094:Collagen / Q000378:metabolism*; D006801:Humans; D006973:Hypertension / Q000378:metabolism; D020782:Matrix Metalloproteinases / Q000235:genetics / Q000378:metabolism*; D008954:Models, Biological; D009130:Muscle, Smooth / Q000166:cytology / Q000378:metabolism*; D019714:Tissue Inhibitor of Metalloproteinases / Q000235:genetics / Q000378:metabolism*; D016212:Transforming Growth Factor beta / Q000235:genetics / Q000378:metabolism*; D015854:Up-Regulation / Q000502:physiology
chemical_list: D019714:Tissue Inhibitor of Metalloproteinases; D016212:Transforming Growth Factor beta; D003094:Collagen; D020782:Matrix Metalloproteinases