Teddy Xuke Cai1,2, Nathan Hu Williamson1,3, Velencia Witherspoon1, Rea Ravin1,4, and Peter Basser1
1Section on Quantitative Imaging and Tissue Sciences, Eunice Kennedy Shriver National Institute of Child Health and Human Development, Bethesda, MD, United States, 2Wellcome Centre for Integrative Neuroimaging, University of Oxford, Oxford, United Kingdom, 3National Institute of General Medical Sciences, Bethesda, MD, United States, 4Celoptics, Inc., Rockville, MD, United States
1Section on Quantitative Imaging and Tissue Sciences, Eunice Kennedy Shriver National Institute of Child Health and Human Development, Bethesda, MD, United States, 2Wellcome Centre for Integrative Neuroimaging, University of Oxford, Oxford, United Kingdom, 3National Institute of General Medical Sciences, Bethesda, MD, United States, 4Celoptics, Inc., Rockville, MD, United States
Instantaneous diffusivity curves from 50 – 500 microseconds are recovered in 1 minute using a static gradient, time-incremented echo train acquisition (SG-TIETA) framework. Measured curves on yeast suspensions are consistent with the expected behavior for micron length-scale structures.
SG-TIETA decays and inverted $$$\textbf{X}$$$ for D6, yeast, and water. (a) Decays analyzed as described in the text. Err. bars = $$$\pm1$$$ SD for, in legend order, $$$38, 3, 4, 25$$$ repetitions truncated at $$$n = 34, 17, 17, 15$$$, respectively. (b) $$$\textbf{X}$$$ solutions. Inversion parameters were identical to Fig. 2 other than $$$\Delta t(k)$$$ for D6. Again, $$$D_0$$$ and $$$D_\infty$$$ (dashed lines) were given as initial $$$\textbf{X}$$$ guesses. Zoomed plot compares experimental results to the presented theoretical short-time $$$D_{\mathrm{inst}}(t)$$$.
Example SG-TIETA sequence. (a) Timings: $$$m_j = \{1, 3, 1, 2, 1\}$$$, $$$\tau = 4\delta$$$, and $$$\delta = 14\; \mu$$$s $$$= 1$$$ dash. $$$\pi$$$-pulses occur at $$$t_n$$$ and echoes form at $$$T_n$$$. Magenta line indicates timing behavior: $$$T_n = t_{n} + h_n$$$, where $$$h_n$$$ is the $$$|F(t)|/\gamma g$$$ "height" at $$$t_n$$$, given recursively by $$$h_1 = \tau$$$ and $$$h_{n} = 2\tau + m_n\delta -h_{n-1}$$$ for $$$n > 1$$$. (b) Direct echo $$$F(t)$$$ drawn along with other coherence pathways that refocus (red, dash-dot) or do not refocus (gray, dotted).