Mapping of the Magnetic-Field Distribution in Cancellous Bone

aging sequence, with the 1807 refocusing pulse shifted relaThe incremental transverse relaxation time, T *2 , of protons tive to its appearance in the regular spin-echo imaging sein regions of human vertebral cancellous bone closely correquence, such that the time interval between the 907 and 1807 lates with trabecular structural arrangement (1) , comprespulses is (TE 0 t) /2 and that between the 1807 pulse and sive elastic modulus (2) , and fracture risk (3, 4) . The phethe gradient-echo is (TE / t) /2, where TE is the time of nomena are believed to arise from the magnetic-field perturoccurrence of the gradient echo. The refocusing times for bation due to differences in diamagnetic susceptibility of the spin echo and the gradient echo therefore differ by an mineralized bone and surrounding marrow constituents (5– amount t. In the presence of local magnetic-field perturba9) . In this paper, a modified Dixon technique (10) was tions, due to the presence of adjacent diamagnetic trabeculae, implemented on a 9.4 T NMR microimaging system to investhe resulting change in the Larmor frequency of the proton tigate the effects of the trabecular network on the proton causes a net phase shift relative to a regular spin-echo image. NMR signal, providing direct evidence for the T *2 behavior The phase shift Df(x , y) is given by observed clinically (3, 11) . The results indicate a volume susceptibility of the trabeculae of about 00.3 to 00.5 ppm Df(x , y) A g DBz(x , y) t, 1 (SI units) relative to water, and further that the local magnetic-field effect is only sensitive to trabeculae oriented perwhere DBz(x , y) represents the local magnetic-field perturbapendicular to the external field. Therefore, in most MRI tion, which can be computed from the phase image Df(x , y). systems widely used clinically, T *2 of the human vertebral The imaging experiments were performed on a Bruker body is sensitive only to the number density of horizontal AMX-400 9.4 T spectrometer equipped with microimaging trabeculae, the preferential loss of which is known to inaccessory. Spin-echo images were acquired using the pulse crease vertebral fracture incidence by causing buckling of sequence shown in Fig. 1 with tA 0 and 1 ms at a resolution load-bearing vertical trabeculae (12–14) . The findings in of 29 1 29 1 250 mm. The choice of t A 1 ms allows this work thus have clinical implications for the early detecmapping of local magnetic fields of{0.06 G without causing tion of loss of horizontal trabeculae, corroborating the ratioaliasing. TR was 2000 ms and TE was 20 ms with a 512 1 nale for using T *2 measurements as a clinical tool to diagnose 512 image matrix. Both real and imaginary parts of the mild to severe vertebral osteoporosis. Further investigation reconstructed data were stored. Magnitude images showing of the magnetic-field distribution within this heterogeneous the trabecular structure were generated from the t A 0 data. material also explains the voxel size dependence of T *2 reThe corresponding field maps were then obtained by taking ported previously (7, 15) . the phase difference of the images acquired at t A 0 and 1 Cancellous bone specimens from human lumbar vertebrae ms, and phase wrapping problems were reduced by em(L4–L5) were obtained at autopsy and kept frozen until ploying complex division instead of using phase differences used. Cylindrical cores parallel to the spinal axis were drilled (16) . All the image calculations were performed on Silicon to about 1 cm in volume and marrow was subsequently Graphics workstations using Matlab software. removed. Air bubbles were carefully removed following susFollowing the generation of the magnetic-field map for pension of the cleaned specimens in distilled water. the bone specimens, a simple model of a diamagnetic cylinA modified Dixon technique (10) (Fig. 1) was used to der was used to estimate the susceptibility of mineralized investigate microscopically the local magnetic-field distributrabeculae. Assuming an infinitely long diamagnetic cylinder tion within cancellous bone. It is basically a spin-echo imoriented along the y axis, perpendicular to an external magnetic field Bo along the z direction, the local field outside the cylinder is given by (17) * To whom correspondence should be addressed. † MRI/S Laboratory, Institute of Biomedical Sciences, Academia Sinica, Nankang, Taipei, Taiwan 11529, Republic of China. ‡ Department of Radiology, University of Pennsylvania Medical Center, DBz(x , z) A Dx 2 B0R 2 (z 2 0 x ) (x 2 / z ) 2 , 2 Philadelphia, Pennsylvania 19104.