Final answer:
The most appropriate method to quantify the patient's edema is volumetric measurements, as it accurately measures the volume of the swollen hand by the displacement of water and is less influenced by changes in tissue composition.
Step-by-step explanation:
To quantify the patient's edema most appropriately, volumetric measurements should be used. This method involves submerging the affected hand in water and measuring the displaced volume, which directly corresponds to the volume of the hand and any edema present. Volumetric measurements are considered one of the most accurate techniques for assessing changes in limb volume, including the presence of edema. Other methods, such as circumferential measurements, girth measurements, and anthropometric measurements, provide valuable data but are less precise than volumetric measurements for edema because they are influenced by changes in tissue composition and distribution, which can occur with injury and rehabilitation.