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Urine flow curves of healthy males: a mathematical model of bladder and urethal function during micturition

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Abstract

Previously isolated clinical and experimental observations on bladder and urethra are drawn together into a mathematical model of micturition. The urethra is treated as passively distensible, while the course of the flow rate is determined by the changing geometry of the actively contracting bladder. Numerical solution of the resulting equations, using independent clinical estimates of the majority of the parameters, shows that they can account for the observed features of the urine flow rate curves of healthy males. It appears that the series elasticity of the bladder muscle is important in maintaining a high flow rate down to low bladder volumes. A mechanical explanation of the peculiar character of micturitions from high initial bladder volumes is put forward. The bases of two clinical methods of assessing bladder function are clarified.

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Abbreviations

F :

force in bladder (strip or whole), N

F iso :

isometric value ofF, N

k :

small-strain elastic constant of series elastic component, N/m

L :

length of bladder strip or circumference, m

L o :

rest value ofL, m

P c :

cutoff pressure of urethral resistance relation, cm H2O or Pa

P dct :

detrusor pressure, cm H2O or Pa

P iso :

isometric detrusor pressure, cm H2O or Pa

P o :

isometric detrusor pressure at small bladder volume, cm H2O or Pa

Q :

volume flow rate out of bladder, ml/s or m3/s

Q * :

flow parameter of bladder output relation, ml/s or m3/s

Q o :

flow rate calculated from model, neglecting series elastic component, ml/s or m3/s

t :

time, s

V :

volume within bladder, ml or m3

v :

contraction velocity of bladder strip or circumference, (m)m/s

v c :

contribution tov from contractile component alone, (m)m/s

v * :

velocity parameter of strip force/velocity relation or of bladder output relation, (m)m/s

α:

slope of urethral resistance relation, ml s−1/cm H2O or m3s−1/Pa

γ:

fractional rate of decrease ofp iso withV, ml−1 or m−3

Δl :

extension of series elastic component, m

μ:

elasticity exponent of series elastic component, m−1

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Author notes

  1. D. J. Griffiths

    Present address: Department of Physics, Exeter University, Exeter, England

Authors and Affiliations

  1. Department of Biological and Medical Physics, Erasmus University, Rotterdam, The Netherlands

    D. J. Griffiths & H. J. Rollema

  2. Department of Urology, University Hospital, Groningen, The Netherlands

    D. J. Griffiths & H. J. Rollema

Authors
  1. D. J. Griffiths
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  2. H. J. Rollema
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Griffiths, D.J., Rollema, H.J. Urine flow curves of healthy males: a mathematical model of bladder and urethal function during micturition. Med. Biol. Eng. Comput. 17, 291–300 (1979). https://doi.org/10.1007/BF02443813

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  • DOI: https://doi.org/10.1007/BF02443813

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