Combined volumetric T1, T2 and secular-T2 quantitative MRI of the brain: age-related global changes (preliminary results)

Magnetic Resonance Imaging 24 (2006) 877 – 887

Combined volumetric T1, T 2 and secular-T 2 quantitative MRI of the brain: age-related global changes (preliminary results) Suzuko Suzuki, Osamu Sakai, Herna´n Jara4 Boston University Medical Center, Boston University, Boston, MA 02118, USA Received 18 January 2006; accepted 3 April 2006

Abstract The combined T 1, T 2 and secular-T 2 pixel frequency distributions of 24 adult human brains were studied in vivo using a technique based on the mixed-TSE pulse sequence, dual-space clustering segmentation and histogram gaussian decomposition. Pixel frequency histograms of whole brains and the four principal brain compartments were studied comparatively and as function of age. For white matter, the position of the T 1 peak correlates with age (R 2 = .7868) when data are fitted to a quadratic polynomial. For gray matter, a weaker age correlation is found (R 2 = .3687). T 2 and secular-T 2 results are indicative of a weaker correlation with age. The technique and preliminary results presented herein may be useful for characterizing normal as well as abnormal aging of the brain, and also for comparison with the results obtained with alternative quantitative MRI methodologies. D 2006 Elsevier Inc. All rights reserved. Keywords: Volumetric mapping; Quantitative MRI; Gaussian decomposition; T 1; T 2; Brain

1. Introduction As recently reviewed [1,2], many groups have investigated 1H-proton T 1 and T 2 quantitative MRI (Q-MRI) relaxometry as tools for measuring changes caused by diseases affecting the brain, including multiple sclerosis, cerebral neoplasia, epilepsy, stroke, dementia, schizophrenia, depression, human immunodeficiency virus infection, cerebral ischemia and other conditions. Age-related changes of the mean T 1 or mean T 2 of selected brain regions have also been investigated [3 – 6]. With some exceptions [7 –9], prior research has studied changes in T 1 or T 2, but not both relaxation times at the same time. Very few Q-MRI pulse sequences [10 – 15] that allow for simultaneous and, consequently, self-co-registered T 1 and T 2 mapping with one scan have been described. Generating self-co-registered T 1 and T 2 maps could be useful for medical purposes because these two tissue parameters represent different tissue information that is largely independent of each other. Nevertheless, T 1 information and T 2 information are not fully independent of each other because all spin–lattice interactions that cause T 1 recovery also contribute to T 2 decay. The difference between the T 1 and T 2 4 Corresponding author. Tel.: +1 617 414 7478. E-mail address: [email protected] (H. Jara). 0730-725X/$ – see front matter D 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.mri.2006.04.011

relaxation rates represents the pure spin–spin interactions [16] and is known as the secular relaxation rate. The associated secular-T 2 relaxation time is given by ðsecÞ

T2

¼ T2 =ð1  T2 =2T1 Þ

ð1Þ

Secular-T 2 represents the pure spin–spin component of T 2 whereby the contribution of the spin–lattice component or nonsecular component has been removed. Here we study the combined T 1, T 2 and secular-T 2 frequency distributions (spectra) of 24 adult human brains in vivo using a Q-MRI technique based on the mixed-TSE pulse sequence that allows for combined, self-co-registered and volumetric mapping of T 1, T 2 and, consequently, secular-T 2. Pixel frequency histograms of whole brains and the four principal brain compartments (left and right cerebral and cerebellar segments) are studied comparatively. Global T 1, T 2 and secular-T 2 age dependencies of wholehead intracranial tissues are investigated and results discussed in the context of existing literature. 2. Materials and methods 2.1. Subjects Over a 4-month period (May 2005 through August 2005), 24 subjects were enrolled for this study: 2 volunteers and

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22 patients who were referred to MRI for various clinical reasons, including headache, TMJ pain, visual field defect, cerebral vascular accident, seizure, motor tics, localized paresthesia, seventh and twelfth nerve palsy, endocrinopathy and breast cancer. The average age was 47 years, and the gender composition was 14 females and 10 males. The patients were consented following NIH HIPAA guideline, and the protocol for both volunteer and patients was approved by the internal review board of our institution. 2.2. Magnetic resonance imaging scanning Imaging at 1.5 T was done with a clinical MR scanner (Philips Intera; Philips Medical Systems of North America, Andover, MA) equipped with fast imaging subsystems (a maximum gradient of 23 mT m1 and a maximum slew rate of 105 mT ms1). Standard quadrature body coil and quadrature head coil were used for radiofrequency excitation and signal detection, respectively. All subjects were imaged with the mixed-TSE pulse sequence; the key scanning parameters of this pulse sequence are listed in Table 1. Mixed-TSE is a fast multislice quadruple time point Q-MRI pulse sequence that combines the principles of T 1 weighting by inversion recovery and of T 2 weighting by multiecho sampling in a single acquisition. As its conventional precursor [12], the mixed-TSE pulse sequence begins with the application of an inversion pulse and has two inversion times (TI1 and TI2) and two effective echo times (TE1eff and TE2eff), thus, generating four self-co-registered images per slice, each with different levels of T 1 and T 2 weighting. Hence, four directly acquired images are

generated for each slice: IR1_E1 and IR1_E2 correspond to the two echoes acquired at inversion time TI1, and analogously, IR2_E1 and IR2_E2 correspond to the echoes at the second inversion time (TI2). The directly acquired images can be processed to generate Q-MRI maps portraying the T 1, T 2 and secular-T 2 distributions with the native spatial resolution and anatomic coverage of the directly acquired mixed-TSE scan. The pulse sequence interrogates two interleaved packages of slices sequentially in the same acquisition. The interslice gap of each package is equal to the slice thickness, thus, interslice cross talk artifacts are negligible. 2.3. T 1, T 2 and secular-T 2 mapping Mixed-TSE directly-acquired images were transferred in DICOM format to our image processing laboratory for anonymization and further analyses using Windows-based (Microsoft, Redmond, WA) personal computers running on Intel Pentium-4 microprocessors equipped with MathCAD2001i software (Mathsoft, Cambridge, MA). Directly acquired images were used as input to model-conforming T 1 and T 2 Q-MRI algorithms programmed in MathCAD as described below. T 1 and T 2 Q-MRI algorithms are based on the formulas in Eqs. (2) and (3); description of the mathematical steps leading to the derivation of these formulas is outside the scope of this article. T 1 and T 2 for each voxels at each (i, j, k)-position were computed as solutions to the following equations:

1

Mixed-TSE

Geometry Imaging plane Acquisition matrix Voxel dimensions Interslice gap PE percent sampling FOV(FE) FOV(PE)x mm2 Number of slices

Axial 256 192 0.94 0.94 3.00 Null (two packages) 75% 240 180 80

Contrast Effective echo time (ms) Repetition time (ms) Inversion times (ms) Echo train lengths Phase-encoding orders Fat suppression

TE1eff and TE2eff = 7.142 and 100 TR = 14,882.18 TI1,2 = 700 and 7441 ETL= 18 (9 per echo) Centric first echo and linear second echo No

Acquisition Averages SAR (W/kg) Scan time (min)

NEX = 1 2.7 9:5

pv IR1 E1 ði;j;kÞ pv IR2 E1 ði;j;kÞ



 Tl1

3

ð1E1 ðTl2Tl1TSE shot ÞÞ

6 ln6 4 ð1ð1E1 ðTRTI2TSEshot ÞÞhcos½FARFO i

Table 1 Mixed-TSE pulse sequence parameters: note that sequence interrogates two packages of slices sequentially Parameter




2

T1ði;j;kÞ ¼

slice Þ

ð2Þ

7 7 5

and

Each package has a gap equal to one slice thickness, and therefore, potential interslice cross talk errors are minimized. PE, phase encoding; FE, frequency encoding; FOV, field of view; ETL, echo train length.





T2ði;j;kÞ ¼ ln

 ðTE2eff  TE1eff Þ  ðPEÞ IR2 E2

pv ði;j;kÞ

hvsfE1 ðT 2ði;j;kÞ ÞiPE

E1 pv ðIR2 i;j;kÞ

hvsf E2 ðT 2ði;j;kÞ ÞiPE



ð3Þ

ðPEÞ

T 1 and T 2 values were then used with Eq. (1) for calculating the corresponding secular-T 2 values on a pixelby-pixel basis. Formulas in Eqs. (2) and (3) were derived by solving Bloch equations describing the magnetization dynamics during the application of the mixed-TSE pulse sequence for arbitrary inversion flip angles. In this way, the effects of imperfect inversion pulses, a major cause of T 1 inaccuracies with inversion recovery techniques [1,17,18], can be incorporated into the computation of T 1. Parameters in Eqs. (2) and (3) include the repetition time (TR), the duration of the double echo TSE readout (TSEshot), the slice average of flip angle (FARF0) of the initial inversion pulse, the two inversion times (TI1 and TI2), the two effective echo times (TE1eff and TE2eff) and the measured mixed-TSE pixel values (pv) of the

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Fig. 1. Brain segmentation procedure: bisection, bilateral dual-space clustering of the ICM tissues and subsegmentation into cerebral and cerebellar segments. This last step was performed by inspecting axial slices visually and determining the slice number that best corresponded to the superior limit of the cerebellum.

directly acquired images (IR1_E1, IR2_E1, and IR2_E2). The standard exponential notations E 1,2(t)uexp[t/T 1,2] are used. The T 2 formula also includes the effects of T 2 blur along the phase-encoding direction through the voxel sensitivity function (VSF) [19] as applicable to the centric and linear profile orders used (Table 1). Formulas in Eqs. (2) and (3)

were incorporated into model-conforming algorithms, which produce superior image quality because pixel dropout artifacts are avoided. With model-conforming Q-MRI algorithms, the quantitative physical models (i.e., Eqs. (2) and (3)) for the mixed-TSE pulse sequence are applied only to voxels that conform to the model, as conditioned by the noise level in the directly acquired images. In this way,

Fig. 2. Representative T 1, T 2 and secular-T 2 maps of two subjects: 23-year-old female (top row) and 77-year-old male. Windows settings for the T 2 and secular-T 2 images were selected for best viewing of WM and GM, and consequently, CSF pixel intensities are saturated. Note the nearly complete absence of pixel dropout artifacts resulting from using model-conforming algorithms.

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Fig. 3. Age-ordered multisubject T 1 spectra and three-gaussian spectral decomposition. Whole-brain ICM T 1 spectra of all subjects displayed as a function of increasing age from bottom to top. Also shown are the spectra of the youngest subject (bottom) and the oldest subject (top) in the standard histogram form. Also shown are the individual WM, GM and GM–CSF tissue classes’ single-gaussian curves as derived with the three-gaussian fitting algorithm: red and yellow curves are the experimental and the fitted T 1 histograms, respectively. Vertical doted lines indicate nominal WM, GM, GM–CSF interface and CSF peak maxima: visually apparent is the decreasing WM and GM peaks as a function of aging. All spectra have been normalized to one.

computation of relaxation times for voxels devoid of MR signal (e.g., bone and air) is automatically avoided, thus, leading to a significant reduction in pixel dropout artifacts. 2.4. Segmentation and spectral analysis All segmentations were performed using an in-house developed program that was written in a high-level programming environment (MathCAD 2000i). As illustrated

in Fig. 1, a bisecting plane is user defined by selecting three points in more than one slice. Then the left or the right sides of the data sets are discarded by multiplying by 0 the pixels located to the left or the right of the bisecting plane, thus, generating two whole-head hemispheres. Subsequently, these are processed with a dualspace clustering segmentation algorithm [15] to generate left and right intracranial matter (ICM) segments. These

S. Suzuki et al. / Magnetic Resonance Imaging 24 (2006) 877 – 887

were further subsegmented into cerebrum and cerebellar ICM segments. Intracranial matter tissue segmentation was done with a dual-space clustering algorithm, the operational principle of which is to interrogate each voxel in the data set as to whether it is contained in both a user-predefined Q-MRI space subvolume and also within a predefined anatomical cluster in anatomic space. With dual-space clustering, segmenting all the intracranial soft tissues, including CSF, can be accomplished in all slices of the three-dimensional data set with one set of segmentation parameter values. Furthermore, these segmentation parameter values are largely subject independent. Generated segments are inspected visually for accuracy, and this constituted the bulk of human input time required for segmentation. The user also specifies the intended segmentation side relative to specified bisecting plane. Histograms representing the T 1, T 2 and secular-T 2 frequency distributions of each tissue segment were calculated using a pixel counting algorithm. A total of 384 subsegmental spectra were generated and stored in a multisubject database. To study the whole-head ICM properties, for each subject, we computed the whole-brain T 1, T 2 and secular-T 2 spectra by adding the individual left and right hemispheric spectra. For each ICM segment and for each relaxation time, the spectra of all subjects were juxtaposed as a function of increasing subject age to form a combined multisubject

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surface plot, as illustrated in Fig. 1 (bottom). These multisubject surface plots can be displayed in any oblique perspective using either a pseudo color scheme or gray scale. Intersubject variations are best observed and compared with a top view [Fig. 1 (bottom), gray scale]. Age dependencies of the T 1 spectra were investigated using a multigaussian fitting algorithm. Each segmental T 1 spectrum was fitted to three gaussian distributions, the sum of which best fitted the experimental histogram for T 1 values less than 2 s. The fitting algorithm requires input of guess values for the peak values, standard deviations and amplitudes of the three gaussian distributions. The individual gaussian distributions represented, approximately, the white matter (WM), gray matter (GM) and GM–CSF interface segments. For each ICM segment, the three gaussian amplitudes, peak-T 1 values and standard deviations were recorded and tabulated in Excel (Microsoft) for further analyses. The same gaussian fitting algorithm with different guess values was used to fit the T 2 and secular-T 2 ICM spectra. As will be discussed in the Results section, the first gaussian distribution represented WM and GM combined, as the individual WM and GM could not be separated with this method; the second and third distributions at longer T 2 corresponded to GM–CSF interface pixels. In all cases, the resulting best-fitted distribution was visually compared with the experimental one for accuracy, and if needed, the guess values were further adjusted.

Fig. 4. Classification of T 1 spectral features. The four discernable T 1 spectral features and their associations with ICM tissue classes (WM, GM, GM–CSF interface and CSF) are shown for one slice of the left brain (27-year-old female). Analogous results are obtained for all slices. Note that tissues classified as GM–CSF interface appear as a discernable spectral feature. Also shown are the individual WM, GM and GM–CSF tissue classes’ single-gaussian curves as derived with the three-gaussian fitting algorithm: red and yellow curves are the experimental and the fitted T 1 histograms, respectively.

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3. Results 3.1. Quantitative maps Representative T 1, T 2 and secular-T 2 maps of two subjects (a 23-year-old female (top row) and a 77-year-old male) are shown in Fig. 2. Mapping image quality was comparable for all subjects at all locations (80 slices each).

Noticeable are the enlarged intra- and extraventricular CSF spaces of the 77-year-old subject relative to the 23-year-old subject, as well as the relative loss of WM-to-GM contrast in the T 1 map of the 77-year-old relative to the 23-year-old subject. Such WM-to-GM contrast loss is not visually apparent in the T 2 or the secular-T 2 maps. Also noticeable is the absence of pixel dropout artifacts, which can degrade the

Fig. 5. Age-ordered multisubject T 2 and secular-T 2 spectra and tissue classification. The WM and GM distributions show extensive overlap and are not discernable individually. Gray matter–CSF interface tissues are associated to two distinct spectral features: the long-T 2 shoulder to the (WM+GM) combined peak and a very broad shallow distribution that extends to values up to 400 ms. For all tissues, secular-T 2 values are longer than T 2, and this effect is most prominent for CSF (see Discussion). The vertical dotted line at about 75 ms is helpful for visualizing the very gradual shift toward longer relaxation time values of the (WM+GM) combined peak as function of increasing age.

S. Suzuki et al. / Magnetic Resonance Imaging 24 (2006) 877 – 887

visual appearance of Q-MRI maps when not generated with model-conforming algorithms. 3.2. T 1 spectra: whole-head ICM As shown in Fig. 3, the typical T 1 spectrum of a wholeICM segment was multimodal and consisted, as a function of increasing T 1, of a tall and narrow peak representing WM, which is adjacent to and partially overlaps with a smaller and broader peak corresponding to GM. At longer T 1 values, meninges and extraventricular CSF were represented by a comparatively smaller spectral feature that partially overlapped with the long-T 1 shoulder of the GM peak. Finally, pure CSF was represented by a nonoverlapping peak centered at about T 1 ~4 s. These associations between T 1 spectral features (peaks) and ICM tissue classes could be confirmed visually by subsegmenting an ICM segment according to selected T 1 acceptance windows, as illustrated in Fig. 4. Visually apparent is the gradual shift in the direction of longer T 1 values of the WM peak as well as the comparatively less pronounced shift of the GM matter peak in the opposite direction (i.e., toward shorter T 1 values). 3.3. T 2 and secular-T 2 spectra: whole-head ICM The whole-ICM multisubject and age-ordered T 2 and secular-T 2 spectra are displayed in Fig. 5. Individual T 2 spectra consist of a positively skewed spectral feature peaking at about 100 ms, which contains the unresolved and overlapping peaks of the WM, GM and GM–CSF

883

interface tissue classes. For each subject, the secular-T 2 and T 2 spectra were very similar in shape, differing mainly in the peak positions; as can be expected from theory, all secular-T 2 peak positions are at longer times relative to the corresponding T 2, and this effect is most pronounced for CSF (Fig. 5). Also visually noticeable is a very subtle and gradual shift toward longer relaxation time values of the (WM+GM) combined peak as function of increasing age. This aging tendency can be observed for both T 2 and secular-T 2. 3.4. Cerebral and cerebellar spectra For all subjects, bilateral multisubject T 1 spectra of the cerebral and cerebellar spectra are shown in Figs. 6 and 7, respectively, as a function of increasing age (vertical axis). T 1 spectra of the left and right cerebral segments are nearly indistinguishable of each other and also visually similar to the whole-head ICM spectra (Fig. 3). These spectra reveal a noticeable age effect consisting of a gradual shift of the WM peak toward longer T 1 values and opposite shift of the GM peaks, thus, resulting in diminishing WMto-GM T 1 differentiation with aging. The typical cerebellar segment T 1 spectrum was also multimodal, but in this case, the GM peak was most prominent (Fig. 7). Cerebral as well as cerebellar segment T 2 spectra and secular-T 2 (not shown) were primarily unimodal, which were very similar in shape to the wholeICM spectra (Fig. 5).

Fig. 6. Multisubject T 1 spectra: left (top) vs. right (bottom) cerebral segments. High degree of bilateral symmetry is observed for all subjects. Vertical dotted lines included as visual guides for assessing the gradual shift of the WM peak toward longer T 1 values as well as more gradual shift of the GM peak in opposite direction.

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Fig. 7. Multisubject T 1 spectra: left vs. right cerebellar segments. Very high bilateral symmetry is observed for all subjects, except one subject (arrows) who had a mass lesion in the left cerebellum, which was suspected as low-grade glioma; however, histologic diagnosis was not conclusive.

3.5. Global T 1 vs. age dependencies As discussed in the Materials and methods, the wholehead ICM T 1 spectra where fitted to the sum of three gaussian distributions that were individually associated with

the WM, GM and GM–CSF interface tissue classes. For each tissue class, the resulting peak T 1 values were graphed as a function of increasing age (Fig. 8), indicating the following global aging tendencies: T 1 of WM increases with aging while T 1 of GM decreases with aging.

Fig. 8. WM, GM and GM–CSF peak-T 1 values as functions of age. Vertical lengths of error bars were set equal to one SD of the corresponding fitted gaussian distribution and, therefore, are representative of the spectral width of the tissue class spectrum and do not represent peak value experimental uncertainties. Horizontal error bars are equal to 1 year. Regression analysis parameters are listed in Table 2. Squares, triangles and full circles represent WM, GM and GM–CSF interface, respectively.

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Table 2 T 1 vs. age regression analysis parameters: parameters of the T 1 model (Eq. (4)) with ranges between square parentheses as reported in Ref. [5] WM GM GM–CSF tissue interface

b 0 (ms)

b 1 (ms/year)

b 2 (ms/year2)

R2

672.98 (638.4 to 725.7) 962.7 (922.3 to 1253.9) 1658.1

1.709 (1.976 to 4.626) 0.305 (4.77 to 7.598) 2.1824

0.0305 (0.0258 to 0.0576) 0.0035 (0.0529 to 0.0886) –

.7868 .3687 .0766

Furthermore, for each tissue class, peak T 1 data were fitted as a function of age using linear (GM–CSF interface) and nonlinear (WM and GM) fitting regression analyses. White matter T 1 peak values showed strong positive correlation (R 2 =.7868) with age when data were fitted to a quadratic polynomial of the form

meters: T 2 (R 2 =.2178) and secular-T 2 (R 2 = .1534). Overall, secular-T 2 data are very similar to T 2 data, with the former being longer times by approximately 6 ms.

T1 ðageÞ ¼ b0 þ b1 age þ b2 age2

The brains of 24 adult human subjects have been analyzed with combined T 1, T 2 and secular-T 2 Q-MRI using a previously described technique [20] that provides self-co-registered and volumetric Q-MRI data sets. The research subjects were not recruited according to any specific medical criterion other than their willingness to participate in this study. This is part of a broad-scope research program of our laboratory, which has the dual objectives of Q-MRI technique development and identification of potential clinical applications of Q-MRI. Accordingly, a wide variety of medical conditions were present in the studied population, thus, potentially influencing all MR tissue properties, including T 1, T 2 and secular-T 2 studied here. Indeed, when the histograms of all subjects were juxtaposed next to each other, marked spectral differences (peak height variability and discrete shifts) were noticeable (Fig. 3). Spectral variability was most striking in the T 1 spectra compared to the transverse

ð4Þ

When fitted to a quadratic polynomial, the GM peak T 1 data showed weaker (R 2 = .3687) and negative correlation with age. The GM–CSF interface tissue class was found not to be significantly correlated (R 2 = .0052) with age. Fitting parameters are listed in Table 2. 3.6. Global T 2 and secular-T 2 vs. age dependencies The whole-head ICM T 2 and secular-T 2 spectra were fitted to the sum of three gaussian distributions that were individually associated with a tissue class that represented the bulk combination of WM and GM, and two other classes of peripheral tissues located at GM–CSF interface. The peak T 2 and secular-T 2 values of the main peak (i.e., the peak representing the bulk WM+GM) were fitted as a function of age to quadratic polynomials using nonlinear regression analyses. Weak correlation with age was found for both para-

4. Discussion and conclusion

Fig. 9. Graphs of peak-T 2 (WM+GM) and peak secular-T 2. Vertical lengths of the error bars have been set to one SD of the fitted gaussian distributions. Squares and open circles represent T 2 and secular-T 2 data points, respectively.

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relaxation times (T 2 and secular-T 2). When T 1 spectra were arranged as a function of increasing age, the observed spectral variability appeared as discrete perturbations relative to smooth age dependence. Specifically, two age tendencies were visually apparent (Fig. 3): a gradual shift in the direction of longer T 1 values of the WM peak combined with a comparatively less pronounced shift of the GM matter peak in the opposite direction (i.e., toward shorter T 1 values). Further quantitative histogram fitting analyses into individual tissue peaks showed that T 1 of WM is strongly age correlated and that the quadratic polynomial age dependence, as well as the values of the coefficients, is in agreement with the results of other researchers [3–5]. Recently, the following T 1 vs. age mathematical model has been proposed [5]. T1 ðageÞ ¼ b0 þ b1 age þ b2 age þ b3 exp½  b4 age

2

ð5Þ

This model is applicable over the full span of human life; the exponential term is significant for ages of less than about 10 years and, therefore, can be neglected for the analysis of the adult population of this work. When fitted to a quadratic polynomial, the GM peak T 1 data showed weaker and negative correlation with age. These results suggest that T 1 differentiation between WM and GM may diminish with aging, a preliminary finding that needs further confirmation with a larger study population. T 2 and secular-T 2 results are indicative of a weaker correlation with age. These preliminary results, which are representative of WM+GM, also suggest a tendency of both parameters to increase with aging. Furthermore, because the functional dependency of secular-T 2 is very similar to that of T 2 (Fig. 9), this appears to be a predominantly pure spin– spin phenomenon. T 2 brain data as a function of age are scarce; some data for humans younger than 39 years are available [6]. To the best of our knowledge, secular-T 2 brain data are not available in the literature. One study limitation stems from the limited number of subjects analyzed. Extensions of this work to include additional subjects are being planned. Nevertheless, because the presented data corresponds to 24 whole brains, the reported age tendencies here are representative of a large volume of tissue of approximately 36 L. A technique limitation relates to using a pulse sequence that interrogates the magnetization only at two time points per relaxation time measurement. Possible quantitative errors can result for voxels containing more than one tissue type where simple exponential relaxation may not accurately describe the temporal evolution of the intravoxel magnetizations [21]. The propensity of such partial volume errors diminishes as a function of decreasing voxel size. The spatial resolution used in this study is high by current clinical standards; nevertheless, partial volume effects can be significant for voxels at the interfaces between primary tissues (e.g., WM–GM interface and GM–CSF interface) and may

explain the presence of additional spectral features in the histograms. Quantitative MRI accuracy can depend also on the specific pulse sequence used [22] for image acquisition as well as on the fidelity of the theoretical Bloch equation model used for relaxation time quantification. High Q-MRI accuracy is of paramount importance to describe the more subtle tissue variations in the brain [23]. In summary, the technique and preliminary results presented herein may be useful for the characterization of normal as well as abnormal aging of the brain, and also for comparison with the results obtained with alternative Q-MRI methodologies.

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