The phase 1 clinical trial of systemic Targeted Alpha Therapy for metastatic melanoma has shown that solid tumours can be regressed by alpha radiation. However, patient blood vessels and lymphocytes inevitably received a background radiation from non-targeted alpha decays in the blood circulation. To determine the toxicity of alpha particle to normal tissue capillaries and peripheral blood lymphocytes, capillary and lymphocyte models were established with Geant4 Monte Carlo microdosimetry technique. The specific energy deposited in a capillary endothelial cell nucleus or lymphocyte nucleus per radioactive decay and the cell survival rates were calculated for the source constrained in the vessel. The specific energy to lymphocytes depends on the type of blood vessels, with survival rates between 89% and 98%. The relationship between calculated specific energy and micronuclei data obtained in a clinical trial was determined, further establishing this technique as a biological dosimeter for Targeted Alpha Therapy. The 2 cGy dose to the capillary endothelial cell nucleus was found to be negligible. These results show that systemic Targeted Alpha Therapy is safe for the function of lymphocytes and normal tissue capillaries.