An analytic study on nonlinear radius change for hyperelastic tubular organs under volume expansion

Tubular organs with multilayers are common in human bodies and important for maintaining normal lives by transporting fluid, nutrient, or waste throughout the bodies. The inner layers of the organs are usually soft and can easily increase their volume under various adverse physiological effects such as edema and plaque growth. The volume expansion can also alter the stiffness of the organ tissues. The corresponding finite deformation of the tubular organs may significantly modify the size of the inner opening determining transportation capability. Deep understanding of the pattern of the luminal radius change is vital for treating related diseases incurred by the volume expansion. For this purpose, a two-layered tubular organ is modeled by generalized hyperelasticity, and the modeling is analyzed mathematically to more thoroughly demonstrate the nonlinear patterns of radius change under volume expansion and corresponding stiffness alteration. This article serves as an exemplary study for other tubular organs with more complicated structure and volume expansion characteristics.