Geometric interpretation of the Cramér-Rao Bound (CRB) of <i>T</i>₁ estimate in a linear space.

<p><b>h</b> is the signal weighting vector containing the measured signals at all acquisition times. <i>∂</i><b>h</b>/<i>∂T</i>₁ is the sensitivity vector, calculated as the derivative of the signal weighting vector with respect to <i>T</i>₁. Conceptually, increasing the norm of the sensitivity term ∥<i>∂</i><b>h</b>/<i>∂T</i>₁∥ will increase the impact of small changes in <i>T</i>₁ on the acquired signals. The orthogonality term sin <i>ϕ</i> is a consequence of the joint estimation of <i>T</i>₁ and <i>M</i>₀. The observed signal’s sensitivity for <i>M</i>₀ is <b>h</b>, while that of <i>T</i>₁ is <i>∂</i><b>h</b>/<i>∂T</i>₁. The more orthogonal these vectors are, the easier it becomes to ascribe changes in the observed signal to <i>M</i>₀ or <i>T</i>₁ unambiguously.</p

Optimized TSI pulse sequence parameters (TSI_new), compared against the original TSI pulse parameters from Table 2 of [14].

<p>Optimized TSI pulse sequence parameters (TSI_new), compared against the original TSI pulse parameters from Table 2 of [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0172573#pone.0172573.ref014" target="_blank">14</a>].</p

Comparing the <i>T</i>₁ estimates’ accuracy for four different approaches: NLSE with the new TSI sequence (blue), NLSE with the original TSI sequence (cyan), DESPOT1 (green), and NLSE with the SPGR sequence (black).

<p>The accuracy is measured in terms of the relative bias %, calculated as . This experiment uses a nominal <i>T</i>₁ value of 1500 ms. Simulated SNR levels are calibrated equivalently as 5 ≤ SNR ≤ 60 for the TSI sequences and 40 ≤ SNR ≤ 480 for the SPGR sequence. The new TSI sequence achieves the lowest overall relative bias and therefore highest accuracy among the four approaches.</p

The general pulse sequence scheme for tissue specific imaging (TSI).

<p>In each TR period, there are three imaging pulses (dark gray) followed by EPI acquisitions and interleaved by two inversion pulses (light gray) (After Fig 1 from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0172573#pone.0172573.ref014" target="_blank">14</a>]). The three imaging pulses are characterized by their flip angles <i>α</i>₁, <i>α</i>₃, <i>α</i>₅. The dashed lines indicate the times <i>t</i> when each pulse is applied. The first imaging pulse is applied at the beginning of each TR (<i>t</i>₁ = 0). There are 8 pulse parameters to optimize for in the TSI sequence: times for the two inversion pulses <i>t</i>₂, <i>t</i>₄, times for the second and third imaging pulses <i>t</i>₃, <i>t</i>₅, flip angles of the three imaging pulses <i>α</i>₁, <i>α</i>₃, <i>α</i>₅ and the sequence repetition time TR.</p

Comparing <i>T</i>₁ estimates’ precision for four different approaches: NLSE with the new TSI sequence (blue) against its theoretical lower bound (red solid), NLSE with the original TSI sequence (cyan), DESPOT1 (green), and NLSE with the SPGR sequence (black) against its theoretical lower bound (magenta dashed).

<p>The precision is measured in terms of the relative mean estimation error, calculated as the standard deviation of <i>T</i>₁ estimates normalized by the true <i>T</i>₁. The theoretical lower bound of the relative mean estimation error is the relative error, calculated as the square root of the CRB on <i>T</i>₁ estimates normalized by the true <i>T</i>₁. SNR levels equalizing for both receiver bandwidths and echo times are calibrated as SNR = 125 for the TSI sequences and SNR = 1000 for the SPGR sequence. The new TSI sequence achieves the lowest mean estimation error and therefore highest precision for tested <i>T</i>₁ values.</p

Comparison of sensitivity (top panel) and orthogonality sin <i>ϕ</i> (bottom panel) of <i>T</i>₁ estimation for the new TSI sequence (blue), the original TSI sequence (cyan), and the SPGR sequence (black).

<p>The norm of <i>T</i>₁ sensitivity is calculated as the Euclidean norm of the derivative of the signal weighting vector with respect to <i>T</i>₁. Increasing the norm of the sensitivity will increase the impact of small changes in <i>T</i>₁ on the overall signal weighting vector <b>h</b>. sin <i>ϕ</i> is the orthogonality term defined in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0172573#pone.0172573.g001" target="_blank">Fig 1</a>. The more orthogonal these vectors are, the easier it becomes to ascribe changes in the observed signal to <i>M</i>₀ or <i>T</i>₁ unambiguously. The top panel shows the new TSI sequence has the best sensitivity among the three sequences and SPGR has very poor sensitivity for <i>T</i>₁ estimation. The bottom panel shows the TSI-family sequences have greater orthogonality (above 0.7) than the SPGR sequence (equal to 0.58) for the tested <i>T</i>₁ range.</p

Results from olfactory function tests.

*<p>two-tailed.</p

Olfactory bulb volumes.

*<p>two-tailed = 0.179.</p

Smaller volumes of subcortical structures in ALL-subjects compared to controls as revealed by FIRST analysis.

*<p>two-tailed.</p>*<p>P<0.05 two-tailed.</p

Demographics of ALL-survivors and non-exposed, healthy controls (N/A = non applicable, SD = standard deviation).

<p>Demographics of ALL-survivors and non-exposed, healthy controls (N/A = non applicable, SD = standard deviation).</p