Calculation of deformation models of the urinary bladder

Deformation models of the human bladder are calculated based on known literature data. The results of uniaxial mechanical tests of bladder wall samples obtained from autopsy and surgical material were used. The models were calculated using the Mathcad 15.0 computer algebra system and the ANSYS 2022 R2 software package. The accuracy of the modeling was assessed using the descriptive statistics parameters: SD, Δ, δmax, R. Formal approximation models (linear, bilinear, trilinear, and exponential) and hyperelastic deformation models (Neo – Hookean, Mooney – Rivlin, Ogden, polynomial, Yeoh, and Veronda – Westmann) were investigated. Among the first, the best results in modeling the mechanical behavior of the bladder wall were shown by the trilinear model (SD = 0,012 MPa, R = 0,9947), for hyperelastic models – Veronda – Westmann and polynomial (SD = 0,0014 MPa, R = 0,9999 and SD = 0,0015 MPa, R = 0,9999, respectively). However, it has been established that, based on additional indicators, the Ogden model is best suited to describe the mechanical properties of the bladder wall. Young's modulus of the human bladder in the linear model in the direction from the base to the apex E = 0,47 MPa, in the transverse direction – 0,214 MPa, the elastic anisotropy coefficient is 2,19. When averaging hyperelastic models – 0,53 MPa, 0,22 MPa and 2,41, respectively. The results obtained can be useful both in the development of methods for restoring the structure of the bladder using artificial materials and tissue engineering, and for a better understanding of the biomechanics of the urinary system.