Mathematical reflections on acupoint combinations in the traditional meridian systems

The meridian system is a systematic order of empirical knowledge functioning as a rational ground for a balanced treatment by combining meridians. In TCM theory, a continuous circulation of Qi through 12 meridians is postulated, described as the Chinese clock (CC). On this basis, combinations of meridians and acupoints had been described in historical writings. The most common is the interior/exterior system beside the neighbouring system, the opposite clock system, and three systems, developed out of the theory of the six stages. All of these represent symmetrical combinations, which were defined by the steps in the CC. We calculated the possible combinations that fit into the systematics of the historical descriptions, leading to 19 systems. Merging the data of the 19 systems, possible steps in the CC clock for balancing a meridian are 1, 2, 3, and 6. Step 4 is not possible. Step 5 is a combinatory possibility but has no widespread tradition except for activating the yin extraordinary vessels. These possibilities can be plotted on the CC as a powerful tool for daily practice. Only two meridians might be excluded as potentially balancing meridians, so it seems almost impossible to define noneffective acupuncture points as controls in clinical trials.