In hyperthyroid sympathetic activity is more so it wil not increase gastric motility then how diarrhea occurs
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You are right. In hyperthyroid state sympathetic activity is more. Thats why there is tachycardia. But still the reason for diarrhoea in hyperthyroidism is increased gastro-intestinal motility. The exact mechanism is not known yet. But as you know gastro-intestinal motility not only depends on autonomic nervous system, but also on enteric nervous system (called as the brain of alimentary tract), and various local hormones have effect on the motility like motilin. So all these in total contribute to increase the motility so that the food transits in less time. Though double blind studies confirm this fact, exact mechanism has not been established.