Consider the relationship between the rate of growth in a growth plate, the average number of cells being produced each day, and the average amount of hypertrophy each cell experiences. Assume the following: The growth plate consists of many parallel cell columns, all growing at the same rate. The stem cell at the top of each column divides at a rate rs (divisions/year), replacing itself and producing one new chondrocyte. Each resulting chondrocyte divides, producing two new chondrocytes, which in turn divide. This mitotic sequence continues until N generations of chondrocytes are produced, all of which are aligned in a single column. Each chondrocyte in the column hypertrophies to an ultimate cell height, h.
Using the principle that the rate of growth of a growth plate is equal to the daily chondrocyte production rate for each column multiplied by the height of the maximally hypertrophied cells, we can show that the physeal growth rate is G = h • rs • 2^N.