Physiological tissue dynamics following breast compression offer new contrast mechanisms for evaluating breast health and disease with near infrared spectroscopy. We monitored the total hemoglobin concentration and hemoglobin oxygen saturation in 28 healthy female volunteers subject to repeated fractional mammographic compression. The compression induces a reduction in blood flow, in turn causing a reduction in hemoglobin oxygen saturation. At the same time, a two phase tissue viscoelastic relaxation results in a reduction and redistribution of pressure within the tissue and correspondingly modulates the tissue total hemoglobin concentration and oxygen saturation. We observed a strong correlation between the relaxing pressure and changes in the total hemoglobin concentration bearing evidence of the involvement of different vascular compartments. Consequently, we have developed a model that enables us to disentangle these effects and obtain robust estimates of the tissue oxygen consumption and blood flow. We obtain estimates of 1.9+/-1.3 micromol/100 mL/min for OC and 2.8+/-1.7 mL/100 mL/min for blood flow, consistent with other published values.