Numerical Analysis of Deformation and Flow in the Proximal Area of the Urethra

R. Rudyk 1 , M. Malinowski 1 , A. Mackiewicz 1 , R. Bedzinski 1 , A. Noszczyk-Nowak 2 , J. Skonieczna 2  and J.P. Madej 2
  • 1 University of Zielona Góra, , 65-516, Zielona Góra, Poland
  • 2 Wroclaw University of Environmental and Life Sciences, , Wroclaw, Poland

Abstract

Pathological conditions of a male urethra, including fibrosis, have a mechanical background along the entire length of the urethra. They may be caused by excessive deformation of the urethra locally or globally. The condition of prolonged overload causes abnormal tissue remodelling and, consequently, the formation of a thick layer of scar tissue differentiated from the connective tissue of the urethra. This tissue, which has higher mechanical properties, is not highly deformable and therefore, causes a decrease in the diameter of the urethra, which results in conditions that disturb the natural flow of urine. In this paper, it was decided to determine the deformation conditions in the proximal part of the urethra. The study was conducted in three main stages. Transverse sections of the animal urethral tissues were prepared in order to examine mechanical properties and perform histological examinations. On the basis of these examinations, material models which fitted best for the experimental results were sought. Material constants of the Mooney-Rivlin material model with the best fit ratio were determined for further research. On the basis of histological photographs, a geometrical and numerical model of the urethra was developed. The urethra was tested in a flat state of deformation. The strain and stress fields of the Caucha tensor were examined. The methodology of testing the dynamics of the urine flow in the highly deformable urethra was proposed. This is important for the analysis of the influence of at excessive pressure on pathological tissue remodelling leading to fibrosis.

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

  • [1] Boselli F., Freund J.B. and Vermot J. (2015): Blood flow mechanics in cardiovascular development. − Cell Mol Life Sci., vol.72, No.13, pp.2545-2559.

  • [2] Halpern D. and Grotberg J.B. (2003): Nonlinear saturation of the Rayleigh instability in a liquid-lined tube due to oscillatory flow. − J. Fluid Mech., vol.492, pp.251-270.

  • [3] Dixon J.B., Gashev A.A., Zawieja D.C., Moore J.E. and Cote G.L. (2007): Image correlation algorithm for measuring lymphocyte velocity and diameter changes in contracting microlymphatics. − Ann Biomed Eng., vol.35, pp.387-396.

  • [4] Ishii T., Bys Y. and Ach Y. (2017): Vector flow visualization of urinary flow dynamics in a bladder outlet obstruction model. − Ultrasound Med Biol., vol.43, No.11, pp.2601-2610.

  • [5] Zamir M., Moore J.E., Fujioka H. and Gaver D.P. (2010): Biofluid mechanics of special organs and the issue of system control. − Ann Biomed Eng., vol.38, No.3, pp.1204-1215.

  • [6] Natali A.N., Carniel E.L., Fontanella C.G., Frigo A., Todros S., Rubini A., De Benedictis G.M., Cerruto M.A. and Artibani W. (2017): Mechanics of the urethral duct: tissue constitutive formulation and structural modeling for the investigation of lumen occlusion. − Biomechanics and Modeling in Mechanobiology, vol.16, No.2, pp.439-447.

  • [7] Hampel C., Thuroff J.W. and Gillitzer R. (2010): Epidemiology and etiology of male urinary incontinence. − Urologe, vol.49, pp.481-488.

  • [8] Mathur R., Aggarwal G., Satsangi B., Khan F. and Odiya S. (2011): Comprehensive analysis of etiology on the prognosis of urethral strictures. − International Braz. J. Urol., vol.37, No.3, pp.362-70.

  • [9] Nitti V.W. (2005): Pressure flow urodynamic studies: the gold standard for diagnosing bladder outlet obstruction. − Rev Urol., vol.7, Suppl 6, pp.S14-21.

  • [10] Cho K.S., Kim J.H., Kim D.J., Choi Y.D., Kim J.H. and Hong S.J. (2008): Relationship between prostatic urethral angle and urinary flow rate: its implication in benign prostatic hyperplasia pathogenesis. − Urology, vol.71, No.5, pp.858-62.

  • [11] Tritschler S., Roosen A., Füllhase C., Stief Ch.G. and Rübben H. (2013): Urethral stricture: etiology. investigation and treatments. − Dtsch Arztebl Int., vol.110, No.13, pp.220-226.

  • [12] Djordjevic, M. (2016), Treatment of urethral stricture disease by internal urethrotomy, dilation and stenting. − European Urology, Suppl 15, pp. 7-12.

  • [13] Natali A., Carniel E., Fontanella C., Frigo A., Todros S., Rubini A., Benedictis G., Cerruto M. and Artibani W. (2016): Mechanics of the urethral duct: tissue constitutive formulation and structural modeling for the investigation of lumen occlusion. − Exp. Physiol., vol.101, No.5, pp.641-56.

  • [14] Chung E. (2014): A state-of-the-art review on the evolution of urinary sphincter devices for the treatment of post-prostatectomy urinary incontinence: past, present and future innovations. − J. Med. Eng. Technol., vol.38, pp.328-332.

  • [15] Ramesh M.V., Raj D., Sanjeevan Kalavampra V. and Dilraj N. (2014): Design of wireless real time artificial sphincter control system for urinary incontinence. − IEEE Int. Symp. Technology Management and Emerging Technologies (ISTMET), Bandung, Indonesia, pp.44-49.

  • [16] Zhao L. (2017): Male urethral reconstruction and the management of urethral stricture disease. − Urologic Clinics of North America, vol.44, No.1, pp.1-146.

  • [17] Cohen A.J., Baradaran N., Mena J., Krsmanovich D. and Breyer B.N. (2019): Computational fluid dynamic modeling of urethral strictures. − J. Urol., vol.202, No.2, pp.347-353.

  • [18] Jin Q., Zhang X., Li X. and Wang J. (2010): Dynamics analysis of bladder-urethra system based on CFD. − Front. Mech. Eng., vol.5, No.3, pp.336-340.

  • [19] Bonfanti M., Balabani S., Alimohammadi M., Agu O., Homer-Vanniasinkam S. and Díaz-Zuccarini V. (2018): A simplified method to account for wall motion in patient-specific blood flow simulations of aortic dissection: comparison with fluid-structure interaction. − Medical Engineering and Physics, vol.58, pp.72-79.

  • [20] Zheng J., Pan J., Qin Y., Huang J., Luo Y., Gao X. and Zhou X. (2015): Role for intravesical prostatic protrusion in lower urinary tract symptom: a fluid structural interaction analysis study. − BMC Urology, vol.15, Article No.86.

  • [21] Tuccitto G., Benjamin F., Maccatrozzo L., Santoro G.A., Wieczorek A.P. and Bartram C.I. (2010): Urodynamics Edoardo Ostardo. − Pelvic Floor Disorders Springer-Verlag Italia.

  • [22] Zhang K., Fu Q., Yoo J., Chen X., Chandra P., Moc X., Song L., Atala A. and Zhao W. (2016): 3D bioprinting of urethra with PCL/PLCL blend and dual autologous cellsin fibrin hydrogel: An in vitro evaluation of biomimetic mechanicalproperty and cell growth environment. − Acta Biomaterialia, vol.43, pp.154-164.

  • [23] Zinner R., Sterling A.M., Ritter R.C., Harris J.H., Gessner B.F., Reid J.M., Hedges J., Chow D. and Barber E.F. (1973): The Velocity Profile of the Human urethra: Measurement and Significance N., Urodynamics © Springer-Verlag Berlin Heidelberg.

  • [24] Bréaud J., Baqué P., Loeffler J., Colomb F., Brunet C. and Thollon L. (2012): Posterior urethral injuries associated with pelvic injuries in young adults: computerized finite element model creation and application to improve knowledge and prevention of these lesions. − Surg. Radiol. Anat., vol.34, No.4, pp.333-339.

  • [25] Spirka T., Kenton K., Brubaker L. and Damaser M.S. (2013): Effect of material properties on predicted vesical pressure during a cough in a simplified computational model of the bladder and urethra. − Ann Biomed Eng., vol.41, No.1, pp.185-194.

  • [26] Bush M.B., Lied B. and Petros P.R. (2014): A finite element model validates an external mechanism for opening the urethral tube prior to micturition in the female. − World J. Urol., vol.33, No.8, pp.1151-1157.

  • [27] Shi L.B., Cai H.X., Chen L.K., Wu Y., Zhu S.A., Gong X.N., Xia Y.X., Ouyang H.W. and Zou X.H. (2014): Tissue engineered bulking agent with adipose-derived stem cells and silk fibroin microspheres for the treatment of intrinsic urethral sphincter deficiency. − Biomaterials, vol.35, No.5, pp.1519-1530.

  • [28] Tai H., Yin J-H., Huang Z-H. and Tsao T-Y. (2015): Penile-preserving surgery for primary urothelial carcinoma of male urethra. − Urological Science, vol.26, No.2, pp.131-133.

  • [29] Jia W., Tang H., Wu J., Hou X., Chen B., Chen W., Zhao Y., Shi C., Zhou F., Yu W., Huang S., Ye G. and Dai J. (2015): Urethral tissue regeneration using collagen scaffold modified with collagen binding VEGF in a beagle model. − Biomaterials, vol.69, pp.45-55.

  • [30] Skonieczna J., Madej J.P. and Będziński R. (2019): Accessory genital glands in the New Zealand white rabbit: A morphometrical and histological study. − J. Vet. Res., vol.63, No.2, pp.251-257.

  • [31] Holzapfel G.A. (2001): Biomechanics of soft tissue. − In: Lemaitre J (ed) Handbook of Materials Behavior Models. Academic Press, USA, pp.1057-1070.

  • [32] Müller B., Ratia J.G, Marti F., Leippold T. (2008), Mechanical properties of tissue urethral − Journal of Biomechanics, 41 Supplement 1, pp. S61.

  • [34] Horák M. and Kren J. (2003): Mathematical model of the male urinary tract. − Mathematics and Computers in Simulation, vol.61, pp.573-581.

  • [35] Kumar N. and Rao V. (2016): Hyperelastic Mooney-Rivlin Model: Determination and physical interpretation of material constants. − MIT International Journal of Mechanical Engineering, vol.6, No.1, pp.43-46.

  • [36] Barzegari M., Vahidi B. and Safarinejad M.R. (2017): A Clinical and Finite Elements Study of Stress Urinary Incontinence in Women Using Fluid-Structure Interactions. − Project: Computational Analysis of Stress Urinary Incontinence.

  • [37] Zheng Q., Ding Ch., Sun B., Li Y., Sun X. and Zhao Ch. (2013): Establishment of a stable urethral stricture model in New Zealands rabbits. − Actas Urológicas Españolas, vol.37, No.3, pp.162-166.

  • [38] Andersen H.L., Duch B.U., Gregersen H., Nielsen J.B. and Ørskov H.(2003): The effect of the somatostatin analogue Lanreotide on the prevention of urethral strictures in a rabbit model. − Urol. Res., vol.31, pp.25-31.

  • [39] Natali A., Carniel E., Frigo A., Pavan P., Todros S., Pachera P., Fontanella C., Rubini A., Cavicchioli L., Avital Y. and Benedictis G. (2016): Experimental investigation of the biomechanics of urethral tissues and structures. − Exp. Physiol, 101.5, pp.641-656.

  • [40] Kaczmarek-Pawelska A. (2019): Based hydrogels in regenerative medicine. − In Alginates, ed. L. Pereira. J. Cotas, IntechOpen Limited, pp.1-16.

  • [41] Bagi P., Thind P., Colstrup H. and Kristensen J.K. (1993): The dynamic pressure response to rapid dilatation of the resting urethra in healthy women: an in vivo evaluation of visco-elastic properties. − Urol. Res., vol.21, No.5, pp.339-43.

  • [42] Todros S., Pavan P.G. and Natali A.N. (2016): Biomechanical properties of synthetic surgical meshes for pelvic prolapse repair. − J. Mech. Behav. Biomed. Mater., vol.55, pp.271-285.

  • [43] Yao F., Laudano M.A., Seklehner S., Chughtai B. and Lee R.K. (2015): Image-based simulation of urethral distensibility and flow resistance as a function of pelvic floor anatomy. − Neurourol. Urodyn., vol.34, No.7, pp.664-668.

  • [44] Jankowski R.J., Prantil R.L., Fraser M.O., Chancellor M.B., De Groat W.C., Huard J. and Vorp D.A. (2004): Development of an experimental system for the study of urethral biomechanical function. − Am J. Physiol. Renal. Physiol, vol.286, No.2, pp.225-322.

  • [45] Korkmaz I. and Rogg B. (2007): A simple fluid-mechanical model for the prediction of the stress-strain relation of the male urinary bladder. − J. Biomech., vol.40, No.3, pp.663-668.

  • [46] Jankowska M.A., Bartkowiak-Jowsa M. and Będziński R. (2015): Experimental and constitutive modeling approaches for a study of biomechanical properties of human coronary arteries. − Journal of the Mechanical Behavior of Biomedical Materials, vol.50, pp.1-12.

  • [47] Bartkowiak-Jowsa M., Będziński R., Szaraniec B. and Chlopek J. (2011): Mechanical, biological, and microstructural properties of biodegradable models of polymeric stents made of PLLA and alginate fibers. − Acta of Bioengineering and Biomechanics, vol.13, pp.21-28.

OPEN ACCESS

Journal + Issues

Search