TAC stands for Tooth Agenesis Code (van Wijk & Tan, 2006). The TAC methodology is a procedure to obtain values that represent specific patterns of missing teeth. One value is obtained for each quadrant (q1, q2, q3, q4) that specifies the number and location of missing teeth in each quadrant.
The basic idea
Each quadrant of the human dentition normally contains 8 teeth. The teeth are numbered 1–8, according to the FDI system (Peck & Peck, 1996). Associated with each tooth is a tooth value. The tooth value can be determined by calculating 2(n-1), in which n equals the tooth number (i.e. the value for tooth number 4 is 2(3) = 8). To assign a unique value to any possible pattern, simply take the sum of the values associated with the missing teeth in that pattern. Eight teeth that can be absent or present give 28 = 256 unique combinations. As each combination is associated with one value ranging from 0 to 255, it becomes obvious that each combination is assigned a unique value. With 32 possible teeth, the number of different patterns equals 4,294,967,296 (232), or more than 4 billion combinations, which would be inefficient to work with. Therefore, we propose to apply this procedure to each quadrant separately.
Figure 1 shows a schematic representation of the human dentition with 32 teeth. It becomes apparent that any pattern of tooth agenesis can be described using four values (ranging from 0 to 255) corresponding to each quadrant. The latter is referred to as the Tooth Agenesis Code (TAC) and simply consists of the unique values assigned to each of the quadrants (q1, q2, q3, q4), called the TAC values.
Thousand separators
So, the dentition is divided into four quadrants. The obvious advantage of this, is that it gives four values (ranging from 0 - 255) which are still interpretable without a computer. This in contrast to a number that ranges from 0 - 4,294,967,296 (232). The disadvantage is that the TAC leaves us with 4 variables to worry about, which is inconvenient when you are interested in the upper, or lower jaw, or the entire dentition. There is a solution to this. Creton et al. (2007) suggested to take the four TAC values (or two for each jaw), and to connect them using thousand separators. The general procedure for the overall TAC is as follows:
For example, consider the following TAC for casei= [1, 128, 8, 16].
| 1 * | 1.000.000.000 | = | 1.000.000.000 | |
| 128 * | 1.000.000 | = | 128.000.000 | |
| 8 * | 1.000 | = | 8.000 | |
| 16 * | 1 | = | 16 | |
| + | ||||
| Overall TAC | = | 1.128.800.016 | ||
Important! One should keep in mind that a ZERO in q1 (and subsequent quadrants) leads to a "strange" looking overall TAC. For instance, the TAC = [0, 0, 1, 128] leads to an overall TAC = 1.128. Although one can logically deduct that this must be caused by q1 and q2 being zero, it is not as clear as it could be. For that reason, on this website the overall tac is presented by using 3 numbers for each quadrant, for instance overall TAC = 000.000.001.128.
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