Citation Context

...de both magnitude and phase activations. THEORY Functional Contrast of Transition-Band SSFP fMRI Unlike the contrast mechanism of T2* dephasing in conventional GRE fMRI, transition-band SSFP fMRI is based on a bulk frequency shift induced by a fractional oxygen saturation change of hemoglobin (4,5). This frequency shift is a function of vessel orientations, the fractional oxygen saturation of hemoglobin, and the magnetic field strength. If a cylindrical vessel tilted by degree with respect to the main field is assumed, the intra- (fiv) and extravascular (fev) frequency shifts are given by (18,19): fiv Hct1 YB0cos2 1/3 [1] fev Hct1 YB0R/r2sin2cos2 r, [2] where is the gyromagnetic ratio (2.678 108 rad T–1 s–1), Hct is a fractional hematocrit in blood (0.4), is the susceptibility difference between fully oxygenated and fully deoxygenated red blood cells (0.27 ppm from Ref. 1Magnetic Resonance Systems Research Laboratory, Department of Electrical Engineering, Stanford University, Stanford, California, USA. 2Department of Statistics, Stanford University, Stanford, California, USA. 3Department of Biostatistics, Harvard School of Public Health and Dan...

Citation Context

...s method more beneficial for transition-band SSFP fMRI. Since both phase and magnitude signal changes are greater in large veins, both the complex- and magnitudedata analyses will show greater signal changes in the veins. However, the signal changes from large veins are usually of no interest because they impede the localization ability of high-resolution studies. Therefore, it is desirable to remove these large signal changes from the activation maps. This can be done with the use of diffusion-weighted suppression techniques that remove intravascular signals using bipolar diffusion gradients (26,28,29), a time-series based analysis that identifies the large veins based on the time-series of a voxel (30), or a venogram approach (31). Once the large vein signals are removed, the complex-data analysis method will provide greater benefits by including more localized brain activations in the analysis. Complex Data Analysis Method When written in polar coordinates, the magnitude and phase contrasts are orthogonal to each other; therefore, a univariate test designed for testing changes in magnitude, by definition, will be insensitive to changes in phase. A change that occurs in magnitude and phase...

Citation Context

...he brain was localized with a 3D localizer sequence. An intermediate-stage anatomical scan (SPGR, FOV 16 cm, resolution 1 1 1 mm3, TR 12 ms, TE 4.2 ms, flip angle 25°, NEX 6) that helped to realign the high-resolution reference scan to the functional Complex Analysis in SSFP fMRI 907 data was performed at the same resolution and FOV as in the functional scans. To identify the locations of large vessels, a 3D spiral trajectory high-resolution venogram (GRE, FOV 16 cm, resolution 0.5 0.5 1 mm3, TR 70 ms, TE 40 ms, flip angle 25°, NEX 12) was obtained by using a flow-compensated venogram (21) sequence. Linear shimming was targeted at the occipital lobe of the brain by a custom targeted shim program before the functional scans. For the functional studies, a 3D stack-ofspirals sequence (bSSFP, FOV 16 cm, resolution 1 1 1 mm3, TR 15 ms, TE 1.5 ms, flip angle 5°, number of interleaves 10, 18 slices for subjects 1–3 and 16 slices for the others) was utilized to cover a 3D volume every 3 s (Fig. 1c). Three different center frequencies (fcenter 0 Hz, –3 Hz, and 3 Hz) were scanned consecutively to cover the wider off-resonance frequencies. The stimulus was a 10-Hz contrast-reversing ...

Citation Context

...t was tilted by /6 to the main field and occupied 50% of the voxel volume. The fractional oxygen saturation of hemoglobin (Y) was changed from 0.61 to 0.73 between the activation state and baseline state. The vessel showed a 2.2-Hz frequency shift, and the maximum signal changes were approximately 50% in magnitude and 0.60 radian in phase (the intravascular part). The resulting activation profiles are shown in Fig. 8a. The second voxel was a spherical voxel (1 mm3) consisting of small cylindrical veins (4 m radius) that were uniformly distributed according to the density P() 0.5sin, – , (24) and occupied 2% of the voxel volume (400 veins) with Y changing from 0.77 to 0.85 (Y FIG. 4. Results from the different center frequencies (fcenter –3, 0, and 3 Hz). In each center frequency a voxel shows different levels of functional contrast. Moreover, the functional contrast shifts from the magnitude to the phase and vice versa (or exists in both). See Fig. 3 for the color-coding scheme. FIG. 3. Magnitude and phase-data analysis results. a and b: Activation maps from a single-frequency acquisition study (fcenter 0, P 0.01). Red-to-yellow colors show the magnitude activations, and blue-t...

Citation Context

...s method more beneficial for transition-band SSFP fMRI. Since both phase and magnitude signal changes are greater in large veins, both the complex- and magnitudedata analyses will show greater signal changes in the veins. However, the signal changes from large veins are usually of no interest because they impede the localization ability of high-resolution studies. Therefore, it is desirable to remove these large signal changes from the activation maps. This can be done with the use of diffusion-weighted suppression techniques that remove intravascular signals using bipolar diffusion gradients (26,28,29), a time-series based analysis that identifies the large veins based on the time-series of a voxel (30), or a venogram approach (31). Once the large vein signals are removed, the complex-data analysis method will provide greater benefits by including more localized brain activations in the analysis. Complex Data Analysis Method When written in polar coordinates, the magnitude and phase contrasts are orthogonal to each other; therefore, a univariate test designed for testing changes in magnitude, by definition, will be insensitive to changes in phase. A change that occurs in magnitude and phase...

Citation Context

...i 0, and LLa Ha 2 0. These equations lead to r (XTX)1XTyr i (XTX)1XTyi, Ha 2 1 2n (yr Xr)T(yr Xr) (yi Xi)T(yi Xi)]. The same results can be derived in the magnitude and phase domain that was used as the convention in Ref. 9. Therefore, LLa can be simplified as LLa logPyHa nlog2 Ha 2 n Under the null hypothesis (Hd), we have LLd logPyHd nlog2 Hd 2 1 2 Hd 2 yr Xr) T(yr Xr) (yr Xi)T(yi Xi)] When we enforce the constraint vTr 0 and vTi 0, the constrained maximum likelihood estimates of the parameter vectors are given by (9,34): r r (XTX)1v[vT(XTX)1v]1vTr, i i (XTX)1v[vT(XTX)1v]1vTi. When LLa Hd 2 0, we have Hd 2 1 2n (yr Xr)T(yr Xr) (yi Xi)T(yi Xi)], which leads to LLd logPyHd nlog2 Hd 2 n. As a result, the likelihood ratio is given by LR PyHa PyHd Hd2 Ha2 n . This test statistic can be written as t3 LR1/n 1 Hd 2 Ha 2 Ha 2 1 Ha 2 (yr Xr) T(yr Xr) (yr Xr)T(yr Xr) (yi Xi)T(yi Xi) (yi Xi)T(yi Xi)] 916 Lee et al. After a few steps we can write (yr Xr)T(yr Xr) (yr Xr)T(yr Xr...

Citation Context

... 1m. [6] Complex Data Analysis Method To incorporate the hemodynamic response function into this T2-test, a GLM (17) is utilized to estimate the mean vectors of the activation and baseline states, as well as the covariance matrix. The complex time-series data are decomposed into real and imaginary axes. To find the mean vector of each state, one structures the design matrix (X) of the GLM by a constant vector (1 [1 1 . . .. 1]T, a real n 1 vector) and a reference waveform vector (h, a real n 1 vector, the convolution of a stimulus pattern and a hemodynamic response function). Equation [7] shows this modeling: yr Xr εr l hr1 r2T r [7] yi Xi εi l hi1 i2T i, where y yr iyi (a complex n 1 vector) is the time-series data of one voxel, r and i (a real 2 1 vector each) are the parameters of GLM, and r and i are residual errors (a real n 1 vector each). One can easily incorporate other terms, such as a linear drift, by adding more vectors and parameters into the model (see Appendix B). The least-square estimates of r and i are (XTX)1XTyr and (XTX)1XTyi, respectively. The activation level or the mean difference between the two states ...

Citation Context

...de both magnitude and phase activations. THEORY Functional Contrast of Transition-Band SSFP fMRI Unlike the contrast mechanism of T2* dephasing in conventional GRE fMRI, transition-band SSFP fMRI is based on a bulk frequency shift induced by a fractional oxygen saturation change of hemoglobin (4,5). This frequency shift is a function of vessel orientations, the fractional oxygen saturation of hemoglobin, and the magnetic field strength. If a cylindrical vessel tilted by degree with respect to the main field is assumed, the intra- (fiv) and extravascular (fev) frequency shifts are given by (18,19): fiv Hct1 YB0cos2 1/3 [1] fev Hct1 YB0R/r2sin2cos2 r, [2] where is the gyromagnetic ratio (2.678 108 rad T–1 s–1), Hct is a fractional hematocrit in blood (0.4), is the susceptibility difference between fully oxygenated and fully deoxygenated red blood cells (0.27 ppm from Ref. 1Magnetic Resonance Systems Research Laboratory, Department of Electrical Engineering, Stanford University, Stanford, California, USA. 2Department of Statistics, Stanford University, Stanford, California, USA. 3Department of Biostatistics, Harvard School of Public Health and Dan...

Citation Context

...th signals provide spatially localized information, an analysis based only on magnitude cannot fully exploit the data. Some voxels that contain phase activation without magnitude activation will not be detected, and some voxels that contain both activations will show less activation in the magnitude-only analysis. Therefore, to acquire more reliable results, a complex domain data analysis method that encompasses both magnitude- and phase-signal activations is necessary. Recently several complex-data analysis methods (7–15), most of which are based on a generalized likelihood ratio test (GLRT) (13), have been proposed. Here we propose a new method that combines a Hotelling’s T2-test (which can be derived from GLRT) (16) with a generalized linear model (GLM) (17) to calculate the statistical significance of the activation from complex data. This method is computationally efficient compared to the previously proposed methods, and generates full activation maps that include both magnitude and phase activations. THEORY Functional Contrast of Transition-Band SSFP fMRI Unlike the contrast mechanism of T2* dephasing in conventional GRE fMRI, transition-band SSFP fMRI is based on a bulk frequen...

Citation Context

...voxels that contain phase activation without magnitude activation will not be detected, and some voxels that contain both activations will show less activation in the magnitude-only analysis. Therefore, to acquire more reliable results, a complex domain data analysis method that encompasses both magnitude- and phase-signal activations is necessary. Recently several complex-data analysis methods (7–15), most of which are based on a generalized likelihood ratio test (GLRT) (13), have been proposed. Here we propose a new method that combines a Hotelling’s T2-test (which can be derived from GLRT) (16) with a generalized linear model (GLM) (17) to calculate the statistical significance of the activation from complex data. This method is computationally efficient compared to the previously proposed methods, and generates full activation maps that include both magnitude and phase activations. THEORY Functional Contrast of Transition-Band SSFP fMRI Unlike the contrast mechanism of T2* dephasing in conventional GRE fMRI, transition-band SSFP fMRI is based on a bulk frequency shift induced by a fractional oxygen saturation change of hemoglobin (4,5). This frequency shift is a function of vessel ...

Citation Context

... the total acquisition time to increase the statistical power. Since our experiment was relatively short (2 min 15 s), increasing the total scan time by a factor of 4 (9 min) is still a reasonable approach. Another method is to use a higher-field-strength system. The bulk frequency shift of vessels increases linearly with the field strength, resulting in increased phasesignal changes. In addition to this increased contrast, the SNR also increases linearly, resulting in a quadratic increase of the detectability. A third method is using a realtime, respiration-compensation technique. Lee et al. (27) demonstrated a significant increase in the z-score by reducing the respiration-induced the SSFP profile shift. This respiration compensation is especially effective for increasing the contrast and reducing the noise interference because the respiration-induced B0 field modulates the SSFP transition profile, causing a large signal interference and time-varying functional contrasts in transition-band SSFP fMRI. By combining these methods, one can obtain much more localized activation information from the phase signal, which makes the proposed complex data analysis method more beneficial for tra...

Citation Context

...z) of subject 5 showed significant movements (1 mm) and were therefore discarded from further analysis. A small shift (one voxel) between the functional scans was found in subject 3, which was fixed by aligning the data to the first functional scan. The intermediate-stage anatomical images were also aligned to the first functional scan. The signal attenuation in this intermediate-stage anatomical image, induced by the surface coil sensitivity, was removed with the use of a custom program. The high-resolution reference scan was then aligned to the intermediate-stage anatomical data using SPM5 (22). The alignment was further refined manually. The gray matter (GM) regions were identified from the reference scan. The venogram result was aligned to the high-resolution reference scan. We identified the locations of large veins from both the magnitude and phase venogram results by carefully tracking the vessel geometries from all of the slices. To display the results, the reference scan and z-score maps were enlarged to match the resolution with the venogram. The magnitude and phase data were generated from the complex functional data. The phase data were unwrapped in the time-series for eac...

Citation Context

... setting (P 0.01 and n 45) was 0.041 radian. This minimum threshold agrees with the histogram result of the signal changes from the phase activation voxels whose minimum detected signal level was 0.031 radian (Fig. 11). These results are still greater than the simulation result (a 0.013 radian change in the capillary geometry), but are not substantially different. Hence, it is plausible that the phase activation would provide a certain degree of localized information. Moreover, it has been suggested that at 1.5T most of the magnitude signal changes originate from larger veins than capillaries (26). These results, together with the aforementioned venogram results and the fact that the number of FIG. 8. Simulation results of the magnitude (solid line) and phase (dashed line) contrasts depending on the off-resonance frequency. a: A voxel with a large vein (radius 0.4 mm) case. b: A voxel with 400 small veins (radius 4 m) distributed by 0.5 sin(). FIG. 7. Maximum z-score projected results in the complex data analysis. A total of six slices (slices 2, 5, 8, 11, 14, and 17 from bottom left to top right) from 18 slices are shown. A higher threshold (P 0.005) is applied to reduce the false po...

Citation Context

...RY Functional Contrast of Transition-Band SSFP fMRI Unlike the contrast mechanism of T2* dephasing in conventional GRE fMRI, transition-band SSFP fMRI is based on a bulk frequency shift induced by a fractional oxygen saturation change of hemoglobin (4,5). This frequency shift is a function of vessel orientations, the fractional oxygen saturation of hemoglobin, and the magnetic field strength. If a cylindrical vessel tilted by degree with respect to the main field is assumed, the intra- (fiv) and extravascular (fev) frequency shifts are given by (18,19): fiv Hct1 YB0cos2 1/3 [1] fev Hct1 YB0R/r2sin2cos2 r, [2] where is the gyromagnetic ratio (2.678 108 rad T–1 s–1), Hct is a fractional hematocrit in blood (0.4), is the susceptibility difference between fully oxygenated and fully deoxygenated red blood cells (0.27 ppm from Ref. 1Magnetic Resonance Systems Research Laboratory, Department of Electrical Engineering, Stanford University, Stanford, California, USA. 2Department of Statistics, Stanford University, Stanford, California, USA. 3Department of Biostatistics, Harvard School of Public Health and DanaFarber Cancer Institute, Boston, Massach...

Citation Context

...n, R is the radius of the vessel, and r is a vector from the center axis of the vessel on an orthogonal plane of the vessel. The magnitude and phase signals of a voxel are determined by the intra- and extravascular frequency shifts, the fractional volume of the vessels, and the off-resonance frequency distribution. If a voxel contains n veins whose volumes are small (and the veins are distant from each other), and the off-resonance frequency distribution of the voxel is assumed to be uniform, then the magnetization of the voxel (M) becomes M 1 Pfoff i 0 n i Pfoff fidi, [3] where is the total volume of all veins (including extravascular spaces), foff is the off-resonance frequency of the voxel, i is the volume of the ith vein (including the extravascular space), fi is the fractional frequency shift from the off-resonance frequency induced by the ith vein in the di space, and P is the magnetization profile of balanced SSFP (bSSFP; Fig. 1a and b). If a vessel is located near the resonance frequency, the sharp phase transition will create a large phase-signal change in accordance with the bulk frequency shift. As a result, a task-correlated phase-signal change...

Citation Context

... the sample (i.e., m 2 in the complex data) and n is the number of samples). This T2 statistic can FIG. 1. Small-flip-angle bSSFP (a) magnitude and (b) phase profiles at three different TEs (TE 0.1TR, 0.5TR, and 0.9TR). The frequency sensitivity of these profiles provides the functional contrasts of transition-band SSFP fMRI. c: 3D interleaved stack-of-spirals sequence for the functional scan. 906 Lee et al. be derived from a likelihood ratio test (a full derivation can be found in Ref. 16). For a given significance level , the null hypothesis is rejected when T2 n 1mn m Fm,nm. [5] A P-value can be obtained from the cumulative distribution function (CDF) of Fm,n-m evaluated at T2n m/n 1m. p 1 CDF of Fm,nmT2 n mn 1m. [6] Complex Data Analysis Method To incorporate the hemodynamic response function into this T2-test, a GLM (17) is utilized to estimate the mean vectors of the activation and baseline states, as well as the covariance matrix. The complex time-series data are decomposed into real and imaginary axes. To find the mean vector of each state, one structures the design matrix (X) of the GLM by a constant vector (1 [1 1 . . .. 1]T, a real n ...

Citation Context

...t magnitude activation will not be detected, and some voxels that contain both activations will show less activation in the magnitude-only analysis. Therefore, to acquire more reliable results, a complex domain data analysis method that encompasses both magnitude- and phase-signal activations is necessary. Recently several complex-data analysis methods (7–15), most of which are based on a generalized likelihood ratio test (GLRT) (13), have been proposed. Here we propose a new method that combines a Hotelling’s T2-test (which can be derived from GLRT) (16) with a generalized linear model (GLM) (17) to calculate the statistical significance of the activation from complex data. This method is computationally efficient compared to the previously proposed methods, and generates full activation maps that include both magnitude and phase activations. THEORY Functional Contrast of Transition-Band SSFP fMRI Unlike the contrast mechanism of T2* dephasing in conventional GRE fMRI, transition-band SSFP fMRI is based on a bulk frequency shift induced by a fractional oxygen saturation change of hemoglobin (4,5). This frequency shift is a function of vessel orientations, the fractional oxygen saturat...

Citation Context

... complex- and magnitudedata analyses will show greater signal changes in the veins. However, the signal changes from large veins are usually of no interest because they impede the localization ability of high-resolution studies. Therefore, it is desirable to remove these large signal changes from the activation maps. This can be done with the use of diffusion-weighted suppression techniques that remove intravascular signals using bipolar diffusion gradients (26,28,29), a time-series based analysis that identifies the large veins based on the time-series of a voxel (30), or a venogram approach (31). Once the large vein signals are removed, the complex-data analysis method will provide greater benefits by including more localized brain activations in the analysis. Complex Data Analysis Method When written in polar coordinates, the magnitude and phase contrasts are orthogonal to each other; therefore, a univariate test designed for testing changes in magnitude, by definition, will be insensitive to changes in phase. A change that occurs in magnitude and phase simultaneously can only be captured fully by a complex bivariate test. On the other hand, if the effect truly exists only in the ma...