 This is a non-randomised Phase ll feasibility study to assess i whether Rituximab with PEX decreases the time to remission of patients with acute TTP, ii the mortality of TTP patients assessed at 3 months from presentation, iii the safety and toxicity of Rituximab in conjunction with standard therapy for acute TTP, iv the effect of Rituximab on B cell function, v the effect of Rituximab on ADAMTS 13 activity and antibody production and time to relapse. The study design and methodology has been devised to specifically address questions regarding the use of Rituximab with PEX to further improve the treatment of TTP patients with the least disruption and inconvenience to their standard and local treatment and care to decrease TTP patient mortality. 