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These coughing fits are a <a class="bbc_url" href='http://www.mayoclinic.org/diseases-conditions/pulmonary-embolism/basics/symptoms/con-20022849'>symptom of pulmonary emboli </a>being released into the circulation and entering the lungs. It’s usually a dry cough, but it turns into hemoptysis (coughing up blood) it’s a real problem. Cerebral venous thromboses of size have the potential to <a class="bbc_url" href='http://www.hopkinsmedicine.org/healthlibrary/conditions/nervous_system_disorders/cerebral_venous_sinus_thrombosis_134,69/'>cause strokes or infarcts of the brain</a>. Venal circulation returns blood to the heart, which directs it to the lungs for re-oxygenation via the pulmonary artery. Arteries bring blood to organs, veins take it away from organs. If a clot of sufficient size blocks the pulmonary artery, it’s lights out, and quickly. Such clots usually result from <a class="bbc_url" href='http://www.mayoclinic.org/diseases-conditions/deep-vein-thrombosis/basics/definition/con-20031922'>deep vein thrombosis</a>. It’s not common, but CVST’s (cerebral venous sinus thrombosis) can lead to pulmonary emboli. If small clots form or dislodge from the wall of a vein they travel to the heart and then to the lung where they can get lodged in the alveoli and causes irritation and subsequent coughing.For more see <a class="bbc_url" href='http://qjmed.oxfordjournals.org/content/95/3/137'>here</a>, <a class="bbc_url" href='http://www.neurology.org/content/65/7/1136.short'>here</a>, and <a class="bbc_url" href='http://www.clinph-journal.com/article/S1388-2457%2812%2900296-9/abstract?cc=y='>here</a>. In Clinton’s case it may be that she is still forming clots at the site of the injury or she may be having bits separate from a not fully resolved clot.