C H A P T E R I1

Urethral Resistance

Hydrodynamics in the bladder and urethra follow the ordinary physical laws for the movement of fluids, but the processes in the urethra are so complex that the hydro- dynamics of micturition have not yet been accurately defined, although the subject has been tackled in recent years by an increasing number of authors, int. al. by

& MILLER (1964), RITTER et coll. (1964), SMITH (1964 & 1966), NUNN (1965), ZATZ (1965), WHITAKER & JOHNSTON (1966), BACKMANN (1966), and GLEASON et coll. (1 967).

BRYNDORF & S A N D ~ E (1960), like SCHWARZ & BRENNER (1922), assumed that the urinary flow through the urethra was turbulent and that urethral resistance, therefore, was porportional to the square of flow.

HOLM (1964) expressed the conductivity of the urethra by means of the so-called standard flow. RITTER et coll. (1964) preferred calculating the urethral diameter to indicate the resistance in the urethra, and this method was later elaborated by BACK-

SMITH (1964 & 1966) as well as WHITAKER & JOHNSTON (1966) (cf. Chapter 1V)

BRYNDORF & SANDBE (1960), ARBRUCKLE & PAQUIN (1963), HOLM (1964), HINMAN

MANN (1 966).

calculated urethral resistance from the formula

intravesical pressure - exit pressure flow2

R =

which in the simpler form intravesical pressure R = -

flow?

has frequently been described, int. al. by CLARIDGE (1965) and by LEVIN et coll. (1966 and 1967).

GLEASON et coll. (1967) maintained that the area of the vena contracta as well as the intravesical pressure and urinary flow had to be known to calculate the urethral resistance - except in cases with a stable flow.

HOLM (1964) and BACKMANN (1966) found Reynolds’ number to be 13,000 for men and 14,000 for women, i. e. far beyond the critical value of 2000 (JOHANSEN 1938) and that therefore it had to be interpreted as a sign of turbulence.

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Now, it is generally assumed that the urinary flow in normal adults is turbulent (RITTER et coll. 1964, SMITH 1964, HUFFMANN & KEITZER 1965), and presumably this also applies to normal children as soon as they have reached a certain age. Possibly, the ratio between length and radius in girls does not, during the first years of life, en-

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tirely fulfill the necessary demand - (JOHANSEN 1938, BACKMANN 1966) to obtain

complete turbulence. BACKMANN felt that presumably this source of error was of little importance, but it goes to show how difficult it is to assess the hydrodynamics of micturition. The transport of the urine through the urethra depends not only upon the intravesical pressure, but also upon the length and radius of the urethra, the mucosal surface, the configuration of the lumen, the curvatures of the urethra, and the elasticity of the urethral wall. All these factors vary to a major or minor degree during micturition. Accordingly, all formulae for calculating urethral resistance are approximate, a number of these complex factors in the bladder neck and urethra usu- ally having been disregarded.

If the urethra is considered as a smooth, straight, and inelastic tube, the ratio between the intravesical pressure P and the urinary flow F may be expressed, according to JOHANSEN (1 938) and HOLM (1 964), as :

P F

K = - 7/4 (1)

where K is a constant, or with approximation, as stated by.ZATz (1965),

11 P F

R = - (2)

where R indicates urethral resistance or urethral conductivity. ZATZ (1965) is one of the few authors who has reported the detailed results of micturition studies in a sizeable material of children, using a method of a principle similar to the present one (cf. Chapter IV). Therefore, formula (2) was chdsen here to express the conductivity in the urethra or urethral resistance R.

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