Calibration allows accurate estimation of the axonal volume fraction with diffusion MRI

Biophysical models enable the non-invasive estimation of microstructural tissue features of the central nervous system such as the axonal volume fraction using diffusion weighted imaging (DWI)-data. However, these models trade accuracy with complexity and demands for time-efficient data acquisition. In this study, we hypothesise that their accuracy can be improved substantially through biophysically motivated, linear calibration. We test this hypothesis in the context of axonal volume fraction estimation in four different DWI-models of different complexity using multi-modal data including ex-vivo diffusion MRI- and electron microscopy (EM)-data in mice with broad dynamic range, whereby the latter served as gold standard. We found that two calibration parameters, an offset accounting for the fraction of unmyelinated axons in severely hypomyelinated mice and a scaling accounting for the compartment-specific relaxation, substantially improved the accuracy of axonal volume fraction. Furthermore, we theoretically predict the scaling parameter, and demonstrate that similar accuracy improvement can be achieved for a subset of DWI-models, if the scaling parameter is fixed to the predicted value instead of estimating it on basis of data. This is of practical relevance because it allows to estimate the remaining offset calibration parameter from a limited amount of multi-modal data and thus makes the proposed method usable in human brain data.