Page:Fabella prevalence rate increases over 150 years, and rates of other sesamoid bones remain constant - a systematic review.pdf/4

4 Fabella: more common than it once was, M. A. Berthaume et al. exact P-values were performed to identify the relationship between fabella presence, age, and height.

Systematic review

Published studies report on both knee and individual prevalence rates. We chose to transform all prevalence rates to knee prevalence rates for two reasons. First, several studies prior to 1950, reported knee and not individual prevalence rates, and it is not possible to know how many individuals were in the sample, especially considering some samples had an odd number of knees. Secondly, some studies were carried out on single legs and on whole individuals (e.g. X-rays taken of just one knee, or only one knee was available for dissection). Studies in which this transformation could not be performed were excluded.

A Bayesian mixed effects generalized linear model was executed to investigate temporal changes in prevalence rate while accounting for the random effects of country and method for data collection using the rethinking package in R (McElreath, 2016). A logistic regression was utilized to ensure prevalence rates were between 0 and 1. The model predicts the number of fabellae present for a given sample size, allowing the regression to take study sample size into account, which varied greatly, from 12 to 2340 knees. ‘Country’ was the country in which the study was conducted, unless the study specified the race of the sample used. If more than one race was specified, each race was treated as an individual data point (Miaśkiewicz & Partyka, 1984). ‘Method’ was the method for data collection, either X-ray, CT scans, MRI or anatomical dissection. If more than one method was used, each method was treated as an individual data point (Chew et al. 2014; Hedderwick et al. 2017).

The Bayesian model followed protocol set out by McElreath (2016). The map2stan function was used to create a binomial distribution using the number of knees and fabellae in the published studies. The probability that a fabella would be present was defined as follows:

logit(probability) = α+αcountry+αmethod+β*Year

where broad, weakly regularizing priors were used for the fixed (α, β) and random (αcountry, αmethod) effects (see Data S1 for further details). Markov-chain Monte Carlo (MCMC) estimation was used to estimate the posterior probability distribution (4 chains, 10 000 iterations, 1000 iterations warmup).

To determine whether there were any outliers, a Pearson’s linear regression was run between the natural log of knee and fabella count. A log transformation was used, as the density plot of study sample sizes were non-normally distributed. If any study had an unusually high or low variance (i.e. an unusually high or low number of fabellae for that sample size), it was considered an outlier and removed from further analyses. After outliers were removed, the missing data concerning ‘method for data collection’ was imputed using the mice package in R (van Buuren & Groothuis-Oudshoorn, 2011). Two methods were used to impute the data, ‘pmm’ and ‘lmer,’ to create 20 imputed datasets (10/method). The consensus results were used for further analysis.

Results and Discussion

Korean dataset

Fabellae were present in 56/106 individuals (52.83%) and 94/212 knees (44.34%). All fabellae were located in the lateral heads of the gastrocnemius: other than the patella, no other sesamoid bones were observed in the knees. Of the 56 individuals with fabellae, bilateral cases were more prevalent than unilateral ones (bilateral = 38/56, unilateral = 18/56, χ2 = 7.1429, P = 0.0107). Of the 32 female cases, bilateral cases were as prevalent as unilateral (bilateral = 20/32, unilateral = 12/32, χ2 = 2, P = 0.2110), but of the 24 male cases, bilateral cases were more prevalent than unilateral ones (bilateral = 18/24, unilateral = 6/24, χ2 = 6, P = 0.0238). Our prevalence rate of 67.86% falls slightly below the prevalence rate of ~ 80% bilateral cases reported by other studies (Sutro et al. 1935; Pritchett, 1984), but rates of ~ 50–66% have been reported (Houghton-Allen, 2001; Phukubye & Oyedele, 2011; Piyawinijwong et al. 2012; Egerci et al. 2017). The relatively high prevalence rates of fabellae in this sample were comparable to those reported in other Asian samples (e.g. 28.50–86.69% in Chinese and 15.29–85.85% in Japanese samples; Table 2).

There were no differences between males and females in terms of knee (f = 52/110, m = 42/102, χ2 = 0.7970, P = 0.4059) or individual (f = 32/55, m = 24/51, χ2 = 1.3138, P = 0.3341) prevalence rates (Table 3). Both men and women were equally likely to have bilateral (f = 20/55, m = 18/51, χ2 = 0.0132, P = 1) or unilateral (f = 12/55, m = 6/51, χ2 = 1.8972, P = 0.2087) fabellae. These results are in agreement with other fabella studies, in which no sex-based differences in fabella presence/absence were observed (Parsons & Keith, 1897; Chew et al. 2014; Ortega & Olave, 2018). Within unilateral cases, fabellae were equally likely to be present in the right or left knee (right = 8/18, left = 10/18, χ2 = 0.222, P = 0.8177).

Height was not correlated to individual prevalence rate (rpbi = −0.0245, t = −0.2502, df = 104, P = 0.8029), or the likelihood of having bilateral (rpbi = 0.0574, t = 0.5867, df = 104, P = 0.5587) or unilateral (rpbi = −0.106, t = −1.0869, df = 104, P = 0.2796) fabellae (Table 4). These results are supported by the substantiated knowledge that the number of ossification centres is not correlated to adult height in humans.

Similarly, individual prevalence rate was not correlated to age (rpbi = 0.0601, t = 0.6143, df = 104, P = 0.5404), or the likelihood of having bilateral (rpbi = −0.0136, t = −0.1384, df = 104, P = 0.8902) or unilateral (rpbi = 0.0973, t = 0.9967, df = 104, P = 0.3212) fabellae. This is not surprising as all individuals in this study were skeletally mature (age 21+ years), and new ossifications do not typically occur during adulthood. Three studies on human foetuses reported the fabella to be common (Jin et al. 2017), rare (Minowa et al. 2005) or completely absent (Oransky et al. 1989) at early stages of development, suggesting fabella initiation time is variable in humans.

One study investigating prevalence rates in a Japanese population identified a correlation between fabella prevalence rate and age, finding a lower prevalence rate in younger (< 50 years, 31%) than older individuals (> 50 years, 47%) (Kato et al. 2012). In our dataset, individuals < © 2019 Anatomical Society