Bone tissue and porous media: common features and differences studied by NMR relaxation

Despite significant differences between bone tissues and other porous media such as oilfield rocks, there are common features as well as differences in the response of NMR relaxation measurements to the internal structures of the materials. Internal surfaces contribute to both transverse (T2) and longitudinal (T1) relaxation of pore fluids, and in both cases the effects depend on, among other things, local surface-to-volume ratio (S/V). In both cases variations in local S/V can lead to distributions of relaxation times, sometimes over decades. As in rocks, it is useful to take bone data under different conditions of cleaning, saturation, and desaturation. T1 and T2 distributions are computed using UPEN. In trabecular bone it is easy to see differences in dimensions of intertrabecular spaces in samples that have been de-fatted and saturated with water, with longer T1 and T2 for larger pores. Both T1 and T2 distributions for these water-saturated samples are bimodal, separating or partly separating inter- and intratrabecular water. The T1 peak times have a ratio of from 10 to 30, depending on pore size, but for the smaller separations the distributions may not have deep minima. The T2 peak times have ratios of over 1000, with intratrabecular water represented by large peaks at a fraction of a ms, which we can observe only by single spin echoes. CPMG data show peaks at about a second, tapering down to small amplitudes by a ms. In all samples the free induction decay (FID) from an inversion-recovery (IR) T1 measurement shows an approximately Gaussian (solid-like) component, exp[−12 (T/TGC)2], with TGC ≈ 11.7 ± 0.7 μs (GC for “Gaussian Component”), and a liquid-like component (LLC) with initially simple-exponential decay at the rate-average time T2-FID for the first 100 μs. Averaging and smoothing procedures are adopted to derive T2-FID as a function of IR time and to get T1 distributions for both the GC and the LLC. It appears that contact with the GC, which is presumed to be 1H on collagen, leads to the T2 reduction of at least part of the LLC, which is presumed to be water. Progressive drying of the cleaned and water-saturated samples confirms that the long T1 and T2 components were in the large intertrabecular spaces, since the corresponding peaks are lost. Further drying leads to further shortening of T2 for the remaining water but eventually leads to lengthening of T1 for both the collagen and the water. After the intertrabecular water is lost by drying, T1 is the same for GC and LLC. T2-FID is found to be roughly 320/α μs, where α is the ratio of the extrapolated GC to LLC, appearing to indicate a time τ of about 320 μs for 1H transverse magnetization in GC to exchange with that of LLC. This holds for all samples and under all conditions investigated. The role of the collagen in relaxation is confirmed by treatment to remove the mineral component, observing that the GC remains and has the same TGC and has the same effect on the relaxation times of the associated water. Measurements on cortical bone show the same collagen-related effects but do not have the long T1 and T2 components.