Apparatus and method for providing breathing gases to a subject employs an exchanger taking up a quantity of a given component, such as CO₂, from expiratory breathing gases passing through the exchanger and thereafter releasing the given component in inspiratory breathing gases subsequently passing through the exchanger. The exchanger may be selectively inserted in a flow path for the breathing gases for this purpose. Or, the breathing gases may be selectively passed through and bypassed around the exchanger. The apparatus and method may be used for non-invasive determination of the functional cardiac output of a patient using the differential form of the Fick equation.