There has been longstanding interest in the anisotropic magnetic properties of muscle tissue [1], but there has been little examination of these properties using MRI-based measurements of field perturbations. Anisotropy in the magnetic susceptibility of myocardial tissue of post-mortem mouse heart was detected in recent work [2], but investigations of skeletal muscle tissue appear to be lacking. MRI-based measurements of frequency variation in muscle could potentially provide a valuable way of probing the structure and function of muscle tissue, revealing information about its microstructure, magnetic properties and molecular composition. Here we describe an initial examination of muscle properties based on field mapping measurements carried out at 7T on phantoms containing small pieces of muscle (pork tenderloin) embedded in agar.

Initial focus was on the magnetic field perturbations generated outside the muscle pieces, since these are insensitive to microstructural effects and depend on the magnetic susceptibility of all compartments within the tissue. We assume that the magnetic properties of the muscle pieces are homogeneous so that they can be represented using a single value of isotropic/anisotropic susceptibility, χ_I/A, measured relative to the susceptibility of agar and a common direction of the principal axis of the cylindrically symmetric susceptibility tensor, assumed to run parallel to the muscle fibers [2]. χ values can be identified by a simple piecewise fit to data acquired with the sample oriented at multiple angles to the magnetic field (B₀) [3-4]. The simulated field can be described as [4]:

$$f_{sim}=f_{iso}+f_{aniso}=χ_IγΔB_I+χ_AγΔB_A$$

where $$$γ$$$=gyromagnetic ratio. $$$ΔB_I$$$ is defined as:

$$ΔB_I=B_0\text{IFT}\left\{\text{FT}(M)×\left(\frac{1}{3}-cos^2θ_k\right)\right\}$$

where $$$M$$$=sample mask, $$$θ_k$$$ defines the angle of the k-vector with respect to B₀ and IFT/FT describe the Fourier transform operators. $$$ΔB_A$$$ is defined as [4]:

$$ΔB_A=-\frac{B_0}{4}\text{IFT}\begin{Bmatrix}\text{FT}(3M×\sin2θ\cosϕ )×\frac{\sin2ϕ_k\cosϕ_k}{2} \\\text{FT}(3M×\sin2θ\cosϕ )×\frac{\sin2ϕ_k\sinϕ_k}{2} \\\text{FT}(M×(1+3(1+3\cos2θ))×(\cos^{2}θ_k-\frac{1}{3}) \end{Bmatrix}$$

where $$$ϕ_{k}$$$ is the secondary angle in spherical polar coordinates and $$$θ/ϕ$$$ describe the orientation of the principal axis of the susceptibility tensor with respect to B_0.

Three samples of pork tenderloin were studied. Each was embedded in agar (1.2% agar, 0.9% NaCl) inside a 18cm diameter Perspex sphere. Sample 3 was cut in half, with one half rotated by 90^o so the muscle fiber direction was perpendicular to that in the first half. Using a Philips Achieva 7T MR scanner, samples underwent a series of GE scans (resolution=1mm³, FOV=176mm³-sample 1; 176×176×150mm³-samples 2&3, TE₁=8ms, TE₂=20ms, TR=21.6ms, flip angle=15^o, acquisition time=572s). Samples 1&2 were scanned at 12&13 angles with respect to B₀ yielding data with the direction of the principal axis of the tensor ranging from parallel to perpendicular to B₀ Sample 3 was scanned at two orientations, so the principal axis of each piece of muscle was oriented parallel and perpendicular to B₀

A phase map was formed from the difference of the two echoes. Phase data was unwrapped/filtered using iHARPERELLA [5]. χ_I/A values were calculated for all angles simultaneously from the external field perturbations of samples 1&2 as outlined in the theory using an LSQR algorithm. Individual χ_I values were calculated for the two halves of sample 3 by a similar fitting process. The residuals after subtraction of the modelled fields from the measurements were evaluated inside and outside the muscle pieces.

Fig.1 shows the same single slice through the sample taken from co-registered field maps measured with the muscle oriented at different angles with respect to the field. The fields corresponding to the weighted forward models which best fit the external field variation are also shown along with the difference of the measured and modelled fields. Fig.2 shows similar data for sample 3 oriented at two different angles to B₀. Table.1 details the values of χ_I/A which provide the best fit to the measured external field variation, along with the average values of the residual field inside the muscle. The results show that the muscle is diamagnetic with respect to agar with a χ_I difference in the range 0.08–0.13ppm. The multiple angle measurements indicated that the muscle susceptibility was only very weakly anisotropic (and the split sample measurements Fig.2 also did not provide evidence of significant anisotropy). The χ_A values we measured are significantly smaller than those observed in [1] of 0.17ppm, however they are of a similar order to a recent study of myocardial tissue [2] where χ_A=(5.94±0.47)ppb. Examination of the residual fields in Figs.1&2 shows successful removal of external field variation with the simulated data. However, there is a significant, spatially uniform positive residual field offset of around 30ppb inside the muscle. Since this does not vary with orientation it is most likely to result from chemical exchange effects and merits further investigation [6].