The present study was designed to assess the relationships between QUS parameters and bone density or microarchitecture on samples of human femoral trabecular bone. The normalized slope of the frequency-dependent attenuation (nBUA), the speed of sound (SOS) and the broadband ultrasound backscatter coefficient (BUB) were measured on 37 specimens of pure trabecular bones removed from upper parts of fresh human femurs. Bone mineral density (BMD) was assessed using a clinical scanner. Finally, 8 mm diameter cylindrical cores were extracted from the specimens and their microarchitecture was reconstructed after synchrotron radiation microtomography experiments (isotropic resolution of 10 microm). A large number of microarchitectural parameters were computed, describing morphology, connectivity and geometry of the specimens. BMD correlated with all the microarchitectural parameters and the number of significant correlations was found among the architectural parameters themselves. All QUS parameters were significantly correlated to BMD (R=0.83 for nBUA, R=0.81 for SOS and R=0.69 for BUB) and to microarchitectural parameters (R=-0.79 between nBUA and Tb.Sp, R=-0.81 between SOS and Tb.Sp, R=-0.65 between BUB and BS/BV). Using multivariate model, it was found that microstructural parameters adds 10%, 19%, and 4% to the respective BMD alone contribution for the three variables BUA, SOS and BUB. Moreover, the RMSE was reduced by up to 50% for SOS, by up to 21% for nBUA and up to 11% when adding structural variables to BMD in explaining QUS results. Given the sample, which is not osteoporosis-enriched, the added contribution is quite substantial. The variability of SOS was indeed completely explained by a multivariate model including BMD and independent structural parameters (R(2)=0.94). The inverse problem on the data presented here has been addressed using simple and multiple linear regressions. It was shown that the predictions (in terms of R(2) or RMSE) of microarchitectural parameters was not enhanced when combining 2 or 3 QUS in multiple linear regressions compared to the prediction obtained with one QUS parameter alone. The best model was found for the prediction of Tb.Th() from BUA (R(2)=0.58, RMSE=17 microm). Given the high values of RMSE, these linear models appear of limited clinical value, suggesting that appropriate models have to be derived in order to solve the inverse problem. In this regard, a very interesting multivariate model was found for nBUA and BUB with Tb.Th and Tb.N, in agreement with single scattering theories by random medium. However, the source of residual variability of nBUA and BUB (15% and 45% respectively) remained unexplained.