{\displaystyle (x,y,z)=((R+P\sin v)\cos u,(R+P\sin v)\sin u,P\cos v).} If R and P in the above flat torus parametrization form a unit vector (R, P) = (cos(η), sin(η)) then u, v, and 0 < η < π/2 parameterize the unit 3-sphere as Hopf coordinates. In particular, for certain very specific choices of a square flat torus in the 3-sphere S3, where η = π/4 above, the torus will partition the 3-sphere into two congruent solid tori subsets with the aforesaid flat torus surface as their common boundary.
Low blood pressure is initially treated with fluids along with bicarbonate to reverse metabolic acidosis (if present), if the blood pressure remains low despite fluids then further measures such as the administration of epinephrine, norepinephrine, or dopamine can be used to increase blood pressure.Another potentially severe symptom is seizures: Seizures often resolve without treatment but administration of a benzodiazepine or other anticonvulsive may be required for persistent muscular overactivity. There is no role for physostigmine in the treatment of tricyclic toxicity as it may increase cardiac toxicity and cause seizures. In cases of severe TCA overdose that are refractory to conventional therapy, intravenous lipid emulsion therapy has been reported to improve signs and symptoms in moribund patients with toxicities involving several types of lipophilic substances, therefore lipids may have a role in treating severe cases of refractory TCA overdose. Dialysis
Tricyclic antidepressants are highly protein bound and have a large volume of distribution; therefore removal of these compounds from the blood with hemodialysis, hemoperfusion or other techniques are unlikely to be of any significant benefit. Epidemiology
Studies in the 1990s in Australia and the United Kingdom showed that between 8 and 12% of drug overdoses were following TCA ingestion. TCAs may be involved in up to 33% of all fatal poisonings, second only to analgesics. Another study reported 95% of deaths from antidepressants in England and Wales between 1993 and 1997 were associated with tricyclic antidepressants, particularly dothiepin and amitriptyline.