The invention relates to methods of using an apparatus to sequester thrombi (including emboli) from blood of an animal such as a human. The apparatus comprises a stepped or sloped separation element interposed between an inlet region and an outlet region of a void that can be filled with fluid. The void can be enclosed within a cover and fluid flow through the void engages cells and thrombi/emboli in a blood sample with the separation element. Only particles (e.g., blood cells) which have or can deform to have a characteristic dimension smaller than or equal to the distance between a step and the cover or body can pass onto or past a step. By selecting dimensions which permit blood cells, but not thrombi or emboli, to pass onto or past a step and passing fluid through the apparatus, thrombi/emboli can be sequested from the blood sample. The thrombi can be observed, removed, or treated to effect their degradation or lysis.
