Characterization of anomalous relaxation using the time-fractional Bloch equation and multiple echo T2 *-weighted magnetic resonance imaging at 7T

PURPOSE To study the utility of fractional calculus in modeling gradient-recalled echo MRI signal decay in the normal human brain. METHODS We solved analytically the extended time-fractional Bloch equations resulting in five model parameters, namely, the amplitude, relaxation rate, order of the time-fractional derivative, frequency shift, and constant offset. Voxel-level temporal fitting of the MRI signal was performed using the classical monoexponential model, a previously developed anomalous relaxation model, and using our extended time-fractional relaxation model. Nine brain regions segmented from multiple echo gradient-recalled echo 7 Tesla MRI data acquired from five participants were then used to investigate the characteristics of the extended time-fractional model parameters. RESULTS We found that the extended time-fractional model is able to fit the experimental data with smaller mean squared error than the classical monoexponential relaxation model and the anomalous relaxation model, which do not account for frequency shift. CONCLUSIONS We were able to fit multiple echo time MRI data with high accuracy using the developed model. Parameters of the model likely capture information on microstructural and susceptibility-induced changes in the human brain.

Context-based assessment: Creating opportunities for resonance between classroom fields and societal fields

There is on-going international interest in the relationships between assessment instruments, students’ understanding of science concepts and context-based curriculum approaches. This study extends earlier research showing that students can develop connections between contexts and concepts – called fluid transitions – when studying context-based courses. We provide an in-depth investigation of one student’s experiences with multiple contextual assessment instruments that were associated with a context-based course. We analyzed the student’s responses to context-based assessment instruments to determine the extent to which contextual tests, reports of field investigations, and extended experimental investigations afforded her opportunities to make connections between contexts and concepts. A system of categorizing student responses was developed that can inform other educators when analyzing student responses to contextual assessment. We also refine the theoretical construct of fluid transitions that informed the study initially. Implications for curriculum and assessment design are provided in light of the findings.