A mathematical model is presented for growth and remodeling of arteries. The model is a thick-walled tube composed of a constrained mixture of smooth muscle cells, elastin and collagen. Material properties and radial and axial distributions of each constituent are prescribed according to previously published data. The analysis includes stress-dependent growth and contractility of the muscle and turnover of collagen fibers. Simulations were conducted for homeostatic conditions and for the temporal response following sudden hypertension. Numerical pressure-radius relations and opening angles (residual stress) show reasonable agreement with published experimental results. In particular, for realistic material and structural properties, the model predicts measured variations in opening angles along the length of the aorta with reasonable accuracy. These results provide a better understanding of the determinants of residual stress in arteries and could lend insight into the importance of constituent distributions in both natural and tissue-engineered blood vessels.
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Acknowledgments This research was supported by NIH grant R01 HL64347 (LAT), NIH grants R01 HL64372 and HL80415 (JDH) and by NIH Training Grant T32 HC007916 (PI: Dr. Frank C.-P. Yin).