Limitations of using logarithmic transformation and linear fitting to estimate relaxation rates in iron-loaded liver

Abstract

MRI is being increasingly used to evaluate tissue relaxation in the setting of iron overload. Diagnostic accuracy is strongly dependent upon the acquisition and analysis methods employed. Typically, a multi-echo train of relaxation data is acquired, the resulting curve is fit using a non-linear (exponential) function, and the derived relaxation time is converted to iron concentration by a calibration formula derived from paired MRI-biopsy samples. A theoretically valid processing alternative is to fit a straight line to the relaxation data after logarithmic transformation (log-linear). This log-linear method is more computationally efficient, allowing a full relaxation map to be generated in near real time. This method is present on all scanner platforms and has been published for use in assessing iron concentration. These factors imply methodological validity. To use in vivo and simulation data to show that log-linear fitting can generate highly erroneous relaxation results in iron-loaded tissues. After IRB approval, exponential and linear fitting were compared in a cohort of 20 patients being evaluated for hepatic iron overload. Simulation analyses were performed to characterize the main factors impacting derived results. In human subjects, log-linear analyses demonstrated gross deviation from exponential results at a moderate relaxation shortening (T2* ~5 ms). Simulation analyses demonstrated that the discrepancy was caused by noise effects and additional signal components violating mono-exponential function shape. Log-linear processing results in increasingly erroneous estimation of T2* with iron-loading. Therefore, this method should not be employed for measurement of relaxation behavior in clinical samples.