Filtration devices for collection and filtration of biological samples are disclosed. Devices having a filtration element oriented in a generally vertical orientation are provided, as well as filtration devices that incorporate a cooling mechanism to reduce the temperature of collected solids. Tissue collection devices, such as aspiration assemblies, tissue sampling devices, and the like incorporating filtration devices are disclosed. Methods of collecting biological samples and separating biological solids from a liquid/solids mixture are also disclosed, together with analytical techniques and protocols for analyzing biological samples.