Prazosin mechanism of action
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Prazosin blocks alpha-1 adrenergic receptors. Normally, norepinephrine from the hypogastric nerves raises smooth-muscle tone at the bladder neck and proximal urethra. Blocking this signal lowers outlet tone and allows that smooth muscle to relax.
The note calls this the internal urethral sphincter. It is a functional smooth-muscle outlet, rather than a separate anatomical ring. The external urethral sphincter is striated muscle and receives somatic pudendal input.
Phenoxybenzamine is a less selective alpha blocker, while prazosin is more selective for alpha-1 receptors. Prazosin also has a faster onset than phenoxybenzamine. Alpha blockade can affect vascular smooth muscle too, so hypotension can occur. Lowering urethral pressure is a pharmacological effect; clinical benefit depends on the cause of the voiding problem.
References
Chris Wood’s ACVS notes; Johnston & Tobias, Veterinary Surgery: Small Animal, 2nd ed., ch.32,116,118; Fischer, Lane & Cribb, Can J Vet Res 2003;67:30–38.