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Origins of R2 Orientation Dependence in Gray and White Matter

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Origins of R2 Orientation Dependence in Gray and White Matter R* PNAS PLUS Origins of 2 orientation dependence in gray and white matter David A. Rudkoa,b, L. Martyn Klassenb, Sonali N. de Chickerac, Joseph S. Gatib, Gregory A. Dekabanc,d, and Ravi S. Menona,b,1 aDepartment of Physics and Astronomy, University of Western Ontario, London, ON, Canada N6A 3K7; bCenter for Functional and Metabolic Mapping and cMolecular Brain Research Group, Robarts Research Institute, London, ON, Canada N6A 5B7; and dDepartment of Microbiology and Immunology, University of Western Ontario, London, ON, Canada N6A 5C1 Edited by Marcus E. Raichle, Washington University in St. Louis, St. Louis, MO, and approved November 27, 2013 (received for review April 5, 2013) R* Estimates of the apparent transverse relaxation rate ( 2) can be orientations and (ii) magnitude-regularized dipole inversion (14). used to quantify important properties of biological tissue. Surpris- The difference between these two estimates represents the local R* ingly, the mechanism of 2 dependence on tissue orientation is not frequency shift due to a cylindrical, axon geometry and is a marker well understood. The primary goal of this paper was to character- of axonal integrity. R* ize orientation dependence of 2 in gray and white matter and Having modeled the orientation dependence, we next exam- relate it to independent measurements of two other susceptibility ined the effect of myelin and iron on both Rp and Δχ.We f 2 based parameters: the local Larmor frequency shift ( L) and quan- demonstrated a linear correlation between these quantities and titative volume magnetic susceptibility (Δχ). Through this compar- R′ optical density (OD) derived from diaminobenzidine (DAB)- ative analysis we calculated scaling relations quantifying 2 (reversible contribution to the transverse relaxation rate from lo- enhanced Perls stain (sensitive to ferritin-based iron) for cortical cal field inhomogeneities) in a voxel given measurements of the gray matter. Similarly, using OD derived from solochrome cya- R′ nine-R (ScR)–stained slides in rat brain major white matter fiber local Larmor frequency shift. 2 is a measure of both perturber geometry and density and is related to tissue microstructure. Ad- regions, we showed strong positive correlations between the ′ ditionally, two methods (the Generalized Lorentzian model and transverse relaxation constants, R2 and R2, and myelin density. Δχ p iterative dipole inversion) for calculating were compared in Taken together, our results demonstrate that observed R2 values gray and white matter. The value of Δχ derived from fitting the in ex vivo brains can be explained by a sinusoidal dependence on Generalized Lorentzian model was then connected to the ob- tissue microstructure orientation in conjunction with a linear R* served 2 orientation dependence using image-registered optical dependence on the myelin concentration in cortical gray and density measurements from histochemical staining. Our results white matter. In deeper gray matter structures with no preferred R* f demonstrate that the 2 and L of white and cortical gray matter symmetry axis, Rp does not have an orientation dependence but are well described by a sinusoidal dependence on the orientation 2 retains a linear dependence on iron concentration. of the tissue and a linear dependence on the volume fraction of myelin in the tissue. In deep brain gray matter structures, where NEUROSCIENCE * Theory there is no obvious symmetry axis, R and fL have no orientation 2 Orientation Dependence of R* in White Matter. Recently, Lee et al. dependence but retain a linear dependence on tissue iron concen- 2 Δχ (12) used a theoretical model developed by Yablonskiy and tration and hence . p Haacke (15) to fit an orientation-dependence curve to R2 data MRI contrast mechanisms | grey matter | cellular architecture | from ex vivo, fixed human corpus callosum at 7 T. The model p relaxation times assumes that the orientation dependence of R2 in groups of close-packed, parallel white matter fibers can be approximated n many neurological diseases such as multiple sclerosis, Alz- with the following equation: Iheimer’s, and Parkinson, and in conditions following traumatic brain injury, microstructural changes occur in gray and white matter (1–4). One method for quantifying these microstructural Significance changes is the mapping of the effective transverse relaxation rate p Differences in the apparent transverse relaxation rate (R*) be- (R2). Along with the longitudinal relaxation rate (R1) and 2 p tween tissues are exploited in numerous magnetic resonance transverse relaxation rate (R2), R2 has been viewed as a funda- mental MRI tissue parameter, affected by several factors in- imaging (MRI) techniques from functional MRI to susceptibility cluding myelin content (5, 6), endogenous ferritin-based (Fe3+) weighted imaging. Recent results show a surprising dependence R* iron (7, 8), tissue microstructure (6), and paramagnetic, blood of tissue 2 on orientation. This study demonstrates that the R* deoxyhemoglobin (9). However, a number of recent studies have orientation dependence of 2 in both white and cortical gray p matter has a sinusoidal dependence on tissue orientation and reported a somewhat surprising dependence of R2 on tissue ori- entation, at least in white matter (10–12). The purpose of this a linear dependence on the perturber volume fraction (measured paper was to investigate the mechanisms that could contribute to by quantitative histology). A biophysical model is used to relate this orientation dependence of Rp in both gray and white matter. the observed orientation dependence to the local Larmor fre- p 2 quency shift and volume magnetic susceptibility of the tissue. Because R2 is influenced by magnetic field perturbations, we ex- amined the role of local Larmor frequency shift (fL) and quanti- Δχ Author contributions: D.A.R. and R.S.M. designed research; D.A.R., L.M.K., S.N.d.C., J.S.G., tative magnetic susceptibility ( ), parameters that relate field and G.A.D. performed research; G.A.D. contributed new reagents/analytic tools; D.A.R. and frequency. Through this analysis we identified unique scaling and R.S.M. analyzed data; and D.A.R. and R.S.M. wrote the paper. ′ relations that relate R2 to the local Larmor frequency shift cal- The authors declare no conflict of interest. culated after removal of macroscopic field inhomogeneities. Ad- This article is a PNAS Direct Submission. ditionally, we compared two methods for computing Δχ in gray 1To whom correspondence should be addressed. E-mail: [email protected]. and white matter: (i) fitting the Generalized Lorentzian (GL) This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. model of field perturbers (13) to fL measured at multiple brain 1073/pnas.1306516111/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1306516111 PNAS | Published online December 27, 2013 | E159–E167 Downloaded by guest on September 24, 2021 p direction. The local Larmor frequency shift of water molecules R ðθÞ¼C þ C sinð2θ þ ψ Þ; [1] 2 0 1 0 moving inside parallel axons of the external capsule bundle rel- where C , C , and ψ are constants and θ is the angle of the ative to the external gray matter can be calculated using the 0 1 0 Lorentzian cylinder approximation of He and Yablonskiy (13). longitudinal axis of the fiber tract relative to the B0 field. Eq. 1 is an extension of the standard relationship for Rp: In this approximation, a model Lorentzian cylinder surrounds 2 the white matter bundle and has a diameter larger than that of p ¼ þ ′: [2] the bundle. The nuclei of water molecules inside the axon bundle R2 R2 R2 experience a frequency shift that is the summation of the con- The C0 constant in Eq. 1 represents the conventional transverse tributions from point magnetic dipoles which exist either (i) in- ′ relaxation rate, R2, as well as any contributions to R2 that are not side or (ii) outside a Lorentzian cylinder. The magnetic field ′ angularly dependent (e.g., R2 shifts due to endogenous ferritin- experienced by nuclei due to dipoles existing inside the Lor- based iron). For white matter fiber bundles, the constant C1 is entzian cylinder averages to 0 because the average magnetic field defined as around a point dipole is 0. Consequently, the frequency shifts of the nuclei inside the external capsule are influenced by point ¼ πω ζ Δχ; [3] C1 2 0 dipoles in the medium outside the cylinder of Lorentz. Along the anterior–posterior direction, the external capsule ζ where the variable represents the volume fraction of field per- bundle can be considered as an infinite circular cylinder with Δχ turbers and represents the magnetic susceptibility difference a length significantly larger than its diameter. In this regime, we between a fiber bundle and the medium surrounding the bundle. can write the frequency shift for external capsule white matter as In this paper, we validated the orientation-dependence model of Eq. 1 (specifically, the relation C =2πω ζ Δχ) by comparing 1 0 fL;WM 1 the fitted parameters from the linear Rp model to the value of Δχ ¼ − 2πðχ − χ Þ · cos2 θ − ; [5] 2 f ae WM calculated from the GL model of field perturbers (further dis- 0 3 cussed in Orientation Dependence of f in White Matter). To per- L where f is the local frequency shift in the white matter rel- form this comparison, the OD of myelin obtained from L,WM ative to the surrounding, isotropic gray matter medium, χ histochemical staining and slide registration was used as a surro- ae ζ (ppm) is the magnetic susceptibility of the isotropic medium gate for the volume fraction ( ). Throughout this paper we de- χ ′ surrounding the axon bundle, WM = 0.067 ppm is the magnetic fine the R2 value as being the same as C1. According to the θ ′ susceptibility of myelin in white matter (13), and is the orien- original derivation (15), the true value of R2 for a network of πω ζ Δχ θ tation angle of an axon bundle relative to the B0 field.
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