Modelling Creep (Relaxation) of the Urinary Bladder

Open access


We first present the results of an experiment in which the passive properties of the urinary bladder were investigated using strips of rabbit bladder. Under the assumption that the urinary bladder had orthopaedic characteristics, the strips were taken in the longitudinal and in the circumferential directions. The material was subjected to uniaxial tension, and stress-stretch curves were generated for various rates of deformation. We found that the rates did not have a significantly effect on the passive response of the material. Additionally, the stress-stretch dependence during relaxation of the material when exposed to isometric conditions was determined experimentally.

Next, we measured nonlinear stress-stretch dependence to determine the coefficients for this dependence in analytical form using a standard fitting procedure. The same approach was used to obtain the coefficients for the relaxation curves from the experimental data. Two constitutive laws, the nonlinear model for passive response and the creep model, were introduced within the shell finite element for geometrically and materially nonlinear analysis. We provide descriptions of the numerical procedures that were performed by considering the urinary bladder as a thin-walled shell structure subjected to pressure loading.

The developed numerical algorithm for the incremental-iterative solution was implemented into the finite element program, PAK. The response of the urinary bladder was calculated for continuous filling, and the numerical and experimental results were compared through cystometrograms (pressure-volume relationships). We also present comparisons of the shapes and volumes of the urinary bladder obtained numerically and experimentally. Finally, the numerical results of the creep response, when placed under constant internal pressure, are provided for various stages of deformation.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • 1. Alexander R. S. Mechanical properties of urinary bladder. Am J Physiol. 1971; 220(5): 1413-1421.

  • 2. Bathe K. J. Finite Element Procedures. Prentice-Hall Englewood Cliffs N. J. 1996.

  • 3. Coolsaet B. L. R. A. Van Duyl W. A. Van Mastright R. and Van Der Zwart A. Visco-elastic properties of the bladder wall. Urol. Int. 1975; 30:16-26.

  • 4. Cvetkovic A. Milasinovic D. Peulic A. Mijailovic N. Filipovic N. and Zdravkovic N. Numerical and experimental analysis of factors leading to suture dehiscence after Billroth II gastric resection. Computer Methods and Programs in Biomedicine. 2014; 117(2):71-79

  • 5. Damaser M. S. and Lehman S. L. The effect of the urinary bladder shape on its mechanics during filling. Journal of Biomechanics. 1995; 28(6): 725-732.

  • 6. Fung Y. C. Biomechanics-Mechanical Properties of Living Tissues. Springer-Verlag New York 1981. pp. 355-381.

  • 7. Griffiths D. J. Van Mastright R. Van Duyl W. A. and Coolsaet B. L. R. A. Active mechanical properties of the smooth muscle of the urinary bladder. Medical & Biological Engineering & Computing. 1979; 17: 281-290.

  • 8. Kojic M. Mijailovic S. Zdravkovic N. A numerical algorithm for stress integration of a fiber-fiber kinetics model with Coulomb friction for connective tissue. Computational Mechanics 1998; 21(2): 189-198.

  • 9. Kojic M. Mijailovic S. Zdravkovic N. Modeling of muscle behavior by the finite element method using Hill’s three-element model. Int. J. Num. Meth. Engng. 1998; 43: 941-953.

  • 10. Kojic M. Zdravkovic N. Mijailovic S. A numerical stress calculation procedure for a fiber-fiber kinetics model with Coulomb and viscous friction of connective tissue. Computational Mechanics. 2003; 30(3):185-195.

  • 11. Van Mastright R. Coolsaet B. L. R. A. and Van Duyl W. A. Passive properties of the urinary bladder in the collection phase. Medical & Biological Engineering & Computing. 1978; 16: 471-481.

  • 12. Uvelius B. Isometric and isotonic length-tension relations and variations in cell length in longitudinal smooth muscle from rabbit urinary bladder. Acta Physiol. Scand. 1976; 97: 1-12.

Journal information
Impact Factor

CiteScore 2018: 0.13

SCImago Journal Rank (SJR) 2018: 0.118
Source Normalized Impact per Paper (SNIP) 2018: 0.079

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 228 109 2
PDF Downloads 102 53 4