Circulating tumor cells (CTCs) play a key role during the metastatic process of human cancers and their reliable detection and characterization could enable new and effective ways of cancer diagnosis, monitoring and treatment. However, due to their ultralow concentration in patient blood, the CTCs must first be enriched before such analysis can be performed. Classical microfiltration is an important and widely used method for the mechanical enrichment of CTCs. This method exploits that CTCs are generally larger than the accompanying blood cells, however, does not differentiate the cells in other ways. In an affinity filtration, selectivity is added by functionalizing the membrane with specific antibodies against a CTC-characteristic surface protein such as the epithelial cell adhesion molecule (EpCAM). A common shortcoming of both filtration approaches is that there is still a poor understanding of the enrichment process and the systems developed so far are frequently operated under non-optimized conditions. To address this, systematic filtration experiments are performed in this work using the EpCAM+ cell line MCF-7 as CTC-model and standard track-etched membranes modified with or without antibodies against EpCAM. The influences of the key filtration parameters time and applied pressure are studied and it is found that in all cases the extent of cell recovery is limited by a lysis process which occurs on the membrane surface. Counterintuitively, it is found that filtration at rather high pressures is advantageous to ensure high recovery rates. To describe the pressure-induced lysis process a biophysical model is developed. This model allows the determination of optimum filtration conditions to achieve both high cancer cell recovery and large blood sample throughput. It is demonstrated that this way practically 100% of spiked cancer cells can be recovered from milliliters of undiluted whole blood within seconds.