An internal combustion engine fluidly coupled to an exhaust aftertreatment system that includes an exhaust purifying device is described. A pressure monitoring device is disposed to monitor a pressure differential between an inlet and an outlet of the exhaust purifying device. A method of monitoring the exhaust purifying device includes monitoring a pressure differential between an inlet and an outlet thereof, and determining an exhaust gas flowrate associated with operation of the internal combustion engine. A raw flow resistance is dynamically determined based upon the pressure differential and the exhaust gas flowrate, and an estimated flow resistance is determined based upon the raw flow resistance. The exhaust purifying device is evaluated based upon the estimated flow resistance.