The coagulation cascade is a series of different clotting factors which results in the formation of fibrin, fibrin causes blood to clot by arranging fibrous chains causing the coagulation of red blood cells.
The image below displays 3 different pathways is involved in the formation of fibrin.
Tissue damage causes FXII to become its active form, this is denoted by the a at the end of the factors, FXIIa. FXIIa then acts as a coenzyme which activates FXI into FXIa, FXIa then acts as a coenzyme to activate FIX into FIXa. FIXa is vital in activating FX into FXa
Tissue factor is released from adventitia of vessels, it is an enzyme which activates FVII into FVIIa. Similar to FXa, FVIIa activates FXa.
FXa then activates prothrombin which is currently in its inactive form of FII into its active form of thrombin, FIIa. Thrombin activates fibrinogen into fibrin. Finally fibrin has been product which is able to clot and coagulate blood.
There are a some vitamins which is essential in coagulation;
Prothrombin is vitamin K dependent, therefore with a vitamin K deficiency less prothrombin is produced and consequently less thrombin can be produced (thrombin is the active form of prothrombin). This results in a greater clotting time. This deficiency can be tested for by doctors using the partial thromboplastin time test.