Modeling of Hypertrophy and Hyperplasia in Porcine Adipose Tissue

Adipocyte sizes from adult adipose tissue are distributed bimodally. Thus, the standard metric reported, mean cell size, could be misleading. The objectives of this study were to develop a novel method for testing bimodality of adipocytes in porcine adipose tissue, describe the size distribution with a more informative metric, and statistically test hypertrophy and hyperplasia. Testing distribution bimodality was done by describing two bins with bin 1 (adipocytes 25.0 ‐ 40.1 µm in diameter) containing the suspected minor mode and bin 2 (adipocytes 50.2 ‐ 65.4 µm in diameter) containing a region assumed to separate major and minor modes. For the k th cell, we defined the event [ X k = 1] with probability p = Pr[ X k = 1] if that cell's diameter falls in bin 1, and the event [ X k = 0] with probability 1 ‐ p = Pr[ X k = 0] if it falls in bin 2. The following natural estimator of ( p ) was used:Bins 1 and 2 were chosen to have approximately the same width and bin 2 was scaled to match the width of bin 1 so the hypothesis test for distribution bimodality was: H 0 : p = 0.5 versus H 1 : p > 0.5. Because the sample size, N , associated with the number of cells falling in either bin was on average 6,600 adipocytes counted for a given test, the Central Limit Theorem applies and results in the following standard normal test statistic:Increased adiposity is correlated positively with an adipocyte being found in the minor mode ( r = .46) and correlated negatively with an adipocyte being found in the major mode (adipocytes larger than 65.4 µm ( r = ‐.22)), providing evidence of hyperplasia. Additionally, as adiposity increases, the mode of the major distribution of cells occurs at a larger diameter of adipocyte, indicating hypertrophy.