Brain functional BOLD perturbation modelling for forward fMRI and inverse mapping

<div><p>Purpose</p><p>To computationally separate dynamic brain functional BOLD responses from static background in a brain functional activity for forward fMRI signal analysis and inverse mapping.</p><p>Methods</p><p>A brain functional activity is represented in terms of magnetic source by a perturbation model: χ = χ₀ +δχ, with δχ for BOLD magnetic perturbations and χ₀ for background. A brain fMRI experiment produces a timeseries of complex-valued images (T2* images), whereby we extract the BOLD phase signals (denoted by δP) by a complex division. By solving an inverse problem, we reconstruct the BOLD δχ dataset from the δP dataset, and the brain χ distribution from a (unwrapped) T2* phase image. Given a 4D dataset of task BOLD fMRI, we implement brain functional mapping by temporal correlation analysis.</p><p>Results</p><p>Through a high-field (7T) and high-resolution (0.5mm in plane) task fMRI experiment, we demonstrated in detail the BOLD perturbation model for fMRI phase signal separation (<i>P</i> + δ<i>P</i>) and reconstructing intrinsic brain magnetic source (χ and δχ). We also provided to a low-field (3T) and low-resolution (2mm) task fMRI experiment in support of single-subject fMRI study. Our experiments show that the δχ-depicted functional map reveals bidirectional BOLD χ perturbations during the task performance.</p><p>Conclusions</p><p>The BOLD perturbation model allows us to separate fMRI phase signal (by complex division) and to perform inverse mapping for pure BOLD δχ reconstruction for intrinsic functional χ mapping. The full brain χ reconstruction (from unwrapped fMRI phase) provides a new brain tissue image that allows to scrutinize the brain tissue idiosyncrasy for the pure BOLD δχ response through an automatic function/structure co-localization.</p></div

Task-evoked brain functional mappings in different dataspaces: (a1, a2, a3) T2* magnitude image dataspace <i>A</i>[r,t]; (b1,b2,b3) the reconstructed χ[r,t] source dataspace (including static background); (c1,c2,c3) the reconstructed δχ[r,t] source dataspace (pure BOLD χ responses).

<p>In (c2), the ROI_act defines a task-evoked active region of interest, and the ROI_inact defines a task-irrelevant region of interest.</p

(a1,b1,c1) T2* phase processing and χ[r,t] reconstruction; (a2,b2,c2) SNR and CNR characterizations.

<p>The SNR CNR values were calculated according to the definition in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0191266#pone.0191266.e014" target="_blank">Eq (14)</a>, with the ROI_act and ROI_inact defined retrospectively in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0191266#pone.0191266.g005" target="_blank">Fig 5(c2)</a>, in a small size of 5 × 5 × 3 voxels. The task* is included to observe the dynamics of SNR and CNR with respect to the stimuli. The <u>SNR</u> and <u>CNR</u> denote time averages.</p

Visualization of magnitude- and susceptibility-depicted brain <i>fmap</i>s (on the reconstructed χ motor cortex image).

<p>(a1,a2) Magnitude-based <i>fmap</i> (A_tcorr); (b1, b2) BOLD χ-depicted <i>fmap</i> (δχ_tcorr). The magnified insets are for scrutinizing function/structure associations. The numbers in (a1,a2) denote the z-scored <i>tcorr</i> values at the activation blobs.</p

Overview diagram of BOLD perturbation model for brain imaging and functional mapping.

<p>Overview diagram of BOLD perturbation model for brain imaging and functional mapping.</p

T2* magnitude and phase image acquisition under a task paradigm.

<p>The ON states are defined by task*[t] ≥ 0.5 and the OFF states by task*[t] < 0.5.</p

A low-field (3T) and low-resolution (2mm) brain task fMRI experiment (finger tapping) with task function analyses in different dataspaces: (a1,b1,c1) fMRI magnitude, (a2,b2,c2) reconstructed susceptibility (χ), and (a3,b3,c3) reconstructed temporal susceptibility change (δχ).

<p>A brain snapshot state (at a timepoint t₁) was displayed with an axial slice (z₀ = 14mm from brain top) in (a1) magnitude, (a2) reconstructed χ, and (a3) reconstructed δχ. Correspondingly, task correlation <i>fmap’</i>s were displayed in (b1,b2,b3); and the maximal (red) and minimal (black) task-correlated voxel timecourses were plotted in (c1,c2,c3). Note that the functional <i>tcorr</i> maps (b1,b2,b3) were displayed over the reconstructed brain χ image (a2). Display units: <i>a</i>.<i>u</i>., arbitrary unit (dimensionless); <i>corr</i>, correlation value in range [–1, 1] (dimensionless); <i>ppm</i>, parts per million 10⁻⁶ (dimensionless).</p

Summary of classifier performance.

<p>Performance metrics (sensitivity, specificity, and best cross validation accuracy (CVA)) and proportion of noise components in data for model of all comprehensive noise (All Noise, M1) built with Data A and tested with ten -fold cross validation on three novel datasets: Data B (same institution, same scanner, different subject population), Data C (different institution, same scanner), Data D (different institution, different scanner).</p

“Signatures” of Component Groups.

<p>Top 10 Chosen Features for classifiers M1, M2, M3, and M4 built using Data A (top), and associated weights (bottom). Gray Matter (GM), white matter (WM), cerebral spinal fluid (CSF). complete set of results included as <b><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095493#pone.0095493.s001" target="_blank">Tables S1</a></b>.</p

An individual and group model of “all noise types” (M1)(M5) was built using Data A, to be tested on three other datasets, Data B, C, and D.

<p>Specific noise types (M2)(M3)(M4) were successfully built with Data A, and then extended to Data B. Models of functional networks (M6)(M7)(M8) were not successful, and were not extended to other datasets. Ten-fold cross validation was used for evaluation of all models.</p