Multi-component T2∗ relaxation modelling in human Achilles tendon: Quantifying chemical shift information in ultra-short echo time imaging

Abstract

Purpose: To examine multi-component relaxation modelling for quantification of on- and off-resonance relaxation signals in multi-echo ultra-short echo time (UTE) data of human Achilles tendon (AT) and compare bias and dispersion errors of model parameters to that of the bi-component model.

Theory and methods: Multi-component modelling is demonstrated for quantitative multi-echo UTE analysis of AT and supported using a novel method for determining number of MR-visible off-resonance components, UTE data from six healthy volunteers, and analysis of proton NMR measurements from ex vivo bovine AT. Cramer-Rao lower bound expressions are presented for multi- and bi-component models and parameter estimate variances are compared. Bias error in bi-component estimates is characterized numerically.

Results: Two off-resonance components were consistently detected in all six volunteers and in bovine AT data. Multi-component model exhibited superior quality of fit, with a marginal increase in estimate variance, when compared to the bi-component model. Bi-component estimates exhibited notable bias particularly in $R_{2,1}^{\ast }$ in the presence of off-resonance components.

Conclusion: Multi-component modelling more reliably quantifies tendon matrix water components while also providing quantitation of additional non-water matrix constituents. Further work is needed to interpret the origin of the observed off-resonance signals with preliminary assignments made to chemical groups in lipids and proteoglycans.

Keywords: Cramer Rao lower bound; Multi-exponential; multi-echo UTE; quantitative MRI; tendinopathy; ultrashort echo time.