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The Collaborative International Dictionary
Vesical tenesmus

Tenesmus \Te*nes"mus\, n. [NL., fr. Gr. ?, fr. ? to stretch: cf. L. tenesmos.] (Med.) An urgent and distressing sensation, as if a discharge from the intestines must take place, although none can be effected; -- always referred to the lower extremity of the rectum.

Vesical tenesmus, a similar sensation as to the evacuation of urine, referred to the region of the bladder.

Wikipedia
Vesical tenesmus

Vesical tenesmus refers to the feeling of incomplete emptying of the bladder following urination. When the word tenesmus is used without modification, it usually refers to rectal tenesmus.