Fig. 1

Circulatory inflammation mediating carbon black exposure induced ex vivo hACEC activation. In mediation analysis (a), the c coefficient denotes the direct effect of carbon black exposure on hACEC activation, without controlling for circulatory inflammation (mediator). The c’ coefficient denotes the direct effect of carbon black exposure on hACEC activation, controlling for circulatory inflammation (mediator). The proportion mediated is equal to delta c (i.e., c-c’) divided by c. We used a permutation-based method to assess if the proportion mediated was statistically significant (b). The relationship between biosensor PC1 and the vector of independent variables was permuted for 500 times. Each permutated dataset allowed for the association analysis of biosensor PC1 with carbon black exposure and other covariates without and with including TNF-α to calculate the c and c’. Permutation was conducted for 500 times to generate the distribution of c-c’ under null hypothesis of no mediation. Value of c-c’ calculated using observed data (− 0.768) was compared to the distribution generated by permutation and Pperm was calculated as the number of permuted databases generating a c-c’ that is smaller than observed value (n = 0 for TNF-α) divided by 500. CB = carbon black; pHCAEC = primary human coronary artery endothelial cell