Optimized filter and method

In a blood filtration system comprising

• a hollow fiber membrane device for separating filtrate from blood comprising a housing having a blood inlet port, a blood outlet port, and a filtrate outlet port, the membrane device including a preselected number (N) of hollow fiber membrane elements carried within the housing, each element having a preselected length (L) and a preselected internal diameter (D), and
• apparatus associated with the hollow fiber membrane device for conveying blood having a determinable hematocrit (H.sub.i) and viscosity (.mu.) from a source through the blood inlet and outlet ports of the membrane device to therein separate filtrate from the blood and for conveying the filtrate from the filtrate outlet port of the membrane device, the apparatus including
• first means for establishing a flow rate (Q.sub.i) of blood through the blood inlet port of the membrane device,
• second means for establishing a flow rate (Q.sub.i) of filtrate from the filtrate outlet port of the membrane device, and
• third means for conveying filtrate-poor blood from the blood outlet port of the membrane device,
• a method of operating the system subject to a selected safety factor for red blood cell hemolysis (HSF) comprising the step of simultaneously obtaining the following performance relationships:
• Performance Relationships(1) Q.sub.f =K.sub.1, Q.sup.x N.sup.(1-x) L.sup.(1-y) D.sup.(1-3x)
• where
• K.sub.1 =0.0002206 [ln (95/Hi)].sup.z II.sup.(1-x) (8/15).sup.x and
• x=0.9141;
• y=0.3619;
• z=0.8528;
• Q is the average blood flow rate through the device defined as the blood flow rate through the blood inlet port (Q.sub.i) minus one-half the filtrate flow rate through the filtrate outlet port, or Q.sub.i -Q.sub.f/2 ;
• and
• H.sub.i is the hematocrit (expressed in %) of the blood entering the blood inlet port of the device;
• ##EQU14## where .mu. is the blood viscosity function=3.236206/[(1-H.sub.i)/100.sup.1.440442 ;
• L.sub.p is the potting length of the fibers, expressed in cm;
• P is the pressure drop across the device expressed in mmHg;
• and ##EQU15## and ##EQU16## r.sub.p is the average pore radius of the membrane;
• (-20 mmHg) is the assumed filtrate collection chamber pressure;
• and ##EQU17## is the shear rate for hemolysis.