A patient support, such as a mattress, includes a plurality of inflatable bladders. Depth sensors are included in the support that measure the degree of penetration of a patient into the mattress. An air pressure sensor is also included that measures the pressure inside at least one bladder. A suitable inflation level of the mattress is determined by monitoring the rate of change of the depth with respect to air pressure as the bladder is either inflated or deflated. By detecting an inflection point in the graphical relationship of the depth and pressure outputs, a suitable inflation point for the bladders is determined that reduces interface pressures experienced by the patient, yet does not overly sink the patient into the mattress to a degree of discomfort. Analyzing the outputs of the depth and pressure sensors can also be used to detect a patient's heart rate and respiration rate.