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Bone tissue and porous media: common features and differences studied by NMR relaxation
Magnetic Resonance Imaging 21 (2003) 227–234
Bone tissue and porous media: common features and differences studied by NMR relaxation Paola Fantazzinia*, Robert James Sidford Brownb, Giulio Cesare Borgiac a
Univ. of Bologna, Dept. of Physics, Viale Berti Pichat 6/2, 40127 Bologna, Italy b 953 W. Bonita Ave., Claremont CA 91711-4193 c Univ. of Bologna, Dept. of ICMA, Viale Risorgimento 2, 40136 Bologna, Italy
Abstract 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 inversionrecovery (IR) T1 measurement shows an approximately Gaussian (solid-like) component, exp[⫺1⁄2 (T/TGC)2], with TGC ⬇ 11.7 ⫾ 0.7 s (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 s. 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/␣ s, where ␣ is the ratio of the extrapolated GC to LLC, appearing to indicate a time of about 320 s 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. © 2003 Elsevier Science Inc. All rights reserved. Keywords: NMR relaxation; Bone; Spin exchange; Trabecular porosity; Gaussian FID component
1. Introduction 1.1. Premise The potentialities of water 1H nuclei Magnetic Resonance Relaxation (MRR) in the study of properties of po* Corresponding author. Tel.: ⫹39 051 2095119; fax: ⫹39 051 2090457. E-mail address: [email protected] (P. Fantazzini).
rous media was first realized in the early 1950s [1-2], when the unanticipated “surface effects” were revealed. Not only can the relaxation times of the exponential process of return to equilibrium of the nuclear magnetization be many orders of magnitude shorter than the corresponding times in bulk water, but they can also show distributions of relaxation times many decades wide. Early studies include oil industry work on relating MRR parameters to reservoir properties of oilfield rocks and also work in the universities on the nature
0730-725X/03/$ – see front matter © 2003 Elsevier Science Inc. All rights reserved. doi:10.1016/S0730-725X(03)00129-2
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of water in the vicinity of solid surfaces. In the mid-1980s a resurgence of interest in this subject was probably helped by the rapid growth of the field of medical Magnetic Resonance Imaging. Then a huge explosion of work in NMR in porous media, including MRR, took place, as one can see by comparing the ratio of contributions to the Fifth International Meeting on Magnetic Resonance in Porous Media (MRPM5, Bologna-2000) [3] to those of MRPM1 (Bologna-1990). We will show how the corpus of theories, experiments, algorithms for relaxation data processing, and interpretation, established in the broad field of Magnetic Resonance for fluids in porous media can successfully be applied to the study of a very particular and important porous material: bone tissue [4-5]. 1.2. The “surface effects” Major assumptions are usually required for the interpretation of MRR data from porous media. Relaxation at pore walls increases the relaxation rate because of the high S/V of the pore and is often represented by the simple relationship 1/T1,2 ⫽ 1,2 S/V ⫹ 1/T1,2-bulk. The surface relaxivity is the velocity at which the magnetization in the pore in the vicinity of the surface flows out of the pore. If is constant and diffusion in the pore fluid is fast enough to maintain magnetization nearly constant throughout the pore (fast diffusion regime), then is a macroscopic parameter as used in the equation above. In this regime need not be microscopically constant, but may be considered an average over surfaces within distances of diffusion in a local relaxation time, that is, within the local diffusion cell. Likewise, S/V is averaged over this local volume, which may be larger than a single “pore”; if the sample is heterogeneous in and/or S/V on a scale larger than local diffusion lengths, multiexponential relaxation will be observed. If diffusion is not in the fast regime, gives the boundary condition for application of the diffusion equation. A microscopic picture gives the interpretation ⫽ h/(Ts⫹r) in the Torrey model [6], where h is the thickness of the surface layer, in which the local relaxation time is Ts, and r is the residence time of water molecules in this layer. It is important to note that the results of many measurements on porous media depend strongly on length scales involved. S/V measurements by gas adsorption can give values many times higher than those by Hg injection or optical scanning, and the corresponding values of vary accordingly. Methods of measurement and forms of “average” relaxation times used to represent distributions of times, as well as types of S/V measurement, can greatly affect the values obtained, so care is necessary in comparing values. It should be noted that the volume over which S/V is averaged by diffusion depends on local relaxation time and local (restricted) diffusion. This volume may be larger than a single pore, and the relaxation time for this volume may be an average over a range of pore sizes. However, with very small pores, relaxation times may be
short and diffusion restricted, giving small regions averaged. Although may vary both within a sample and from sample to sample, there is usually not much choice but to assume it constant, taking its value from some related measurements. There is no obvious reason that should be constant even over all surfaces of a single porous material. Nevertheless, there is enough similarity of values for many materials, that MRR measurements have been useful for applications where estimates of the length V/S are needed. In a recent paper [7] the observation of relatively constant surface relaxivity is explained as the result of consistently high surface concentration of paramagnetic materials [8]. Examples of the application of MRR to porous materials are estimation of capillary pressure (inversely proportional to a length) [9], and residual fluid content after drainage at a given pressure [10-13]. Another is the estimation of the permeability to fluid flow in response to a pressure gradient [14-17]. Results will now be presented of the application of these procedures to the study of bone tissue. As in rocks, it is useful to take bone data under different conditions of cleaning, saturation, and desaturation.
2. Materials and methods Bones of pigs and cows were stored in the slaughterhouse refrigerator immediately after slaughter. Cylindrical samples of cortical and trabecular bone, 7 mm in diameter and in height, were cored from different regions of the femurs. All samples were preserved at 4°C up to the time of the NMR measurement. All the measurements on fresh samples were accomplished within a few days after slaughter. Then some samples were defatted and saturated with distilled water. NMR measurements were performed at 20 MHz (0.47 T) (at 30°C for fresh samples and 20°C for cleaned and hydrated samples), by means of a Bruker Minispec P20 (Karlsruhe, Germany) equipped with NMR data station (Stelar, Pavia, Italy). The measurements began after the temperature of the sample had equilibrated with that of the probe. Add/subtract phase-cycled sequences were used in all the measurements, and measurements were accumulated for signal averaging. Relaxation delay was adequate for full magnetization to be reached after each sequence. T1 relaxation data are taken by inversion-recovery (IR) sequences, and for each of 127 IR times the free induction decay (FID) signal is sampled and recorded at 2-s intervals from 14 to 266 s. The shortest IR time is usually 100 s, with successive times increased by fixed factors, giving maximum recovery times of about 5 s in fresh samples and 10 s in defatted and hydrated samples. T2 data were taken from FID’s and by Carr-Purcell-Meiboom-Gill (CPMG) and single-Spin-Echo (SE) sequences. For details see Ref. [4]. Quasi-continuous relaxation time distribution analysis of
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the data were by UPEN [18], which is based on a UniformPENalty (UPEN) inversion algorithm, using a regularizing or smoothing coefficient varying with relaxation time and determined by iterative negative feedback in such a way that the smoothing penalty, rather then the coefficient, is roughly uniform. This can give sharp lines that are not broadened more than is consistent with the noise and in the same distribution show a tail decades long without breaking it up into several peaks not required by the data to be separate, which might be misinterpreted as physically meaningful resolved compartments. The performance of the relaxometer and data processing were tested by repeating the whole set of measurements for doped water samples, where longitudinal and transverse relaxation were expected to be single-exponential. In all cases single-exponential behavior was observed.
3. Results and discussion 3.1. Solid-like and liquid-like contribution to the free induction decay Despite the fact that the FID signal was not reliably usable before 14 s, there is clearly an approximately Gaussian Component (GC) to the FID, a “solid-like” component probably coming from 1H nuclei in collagen. It is long known that macromolecular protons can contribute to the FID signal from biologic tissues [19], and such a GC has been observed also in normal cartilage [20-21]. The GC decay has the form exp[⫺1⁄2 (T/TGC)2], where T is time after the end of the 90° pulse, and TGC is the Gaussian decay time. The remaining “Liquid-Like” Component (LLC) signal has initially simple exponential form, in some cases becoming clearly multiexponential by about the middle of the 266 s recorded interval. It has been possible to separate the GC from LLC in a reasonably stable and reproducible manner, giving separate T1 distributions and also giving the two extrapolated amplitudes and the two time constants, TGC and T2-FID, where T2-FID is the rate-average T2, that is, the T2 corresponding to the initial slope of the FID decay curve (without GC). The ratio ␣ of the GC and LLC will be a useful parameter in the following. Fig. 1 shows a plot of the average of the first 10 FID’s from an IR sequence, together with the fitted curves, for a sample of trabecular bone that has been defatted, water saturated, and vacuum dried. The insert shows the GC plotted against T2. As can be seen, the fit is reasonably good, and the separated GC is reasonably close to Gaussian in form. TGC averages 11.7 s (s.d. 0.7 s) for the cortical and trabecular bone samples reported here, regardless of treatment (as fresh, defatted and water-saturated, dried, vacuum dried, and even demineralized) and are not clearly different for samples from different types (from cow and pig femurs, rat vertebrae). The extrapolation for the GC FID is more than a factor of two and is very sensitive to the TGC value
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Fig. 1. Average of ten FID’s from an inversion recovery (IR) T1 sequence, fit by the sum of a Gaussian Component (GC) and an exponential LiquidLike Component (LLC). The differences between the input points and the fitted exponential are plotted against T2 in the insert.
used. For this reason, TGC is not allowed to vary within the set of FID’s for a series of IR times used to determine a T1 distribution. By picking a mean TGC value for a sample for which data are taken for a sequence of treatments one may hope to compare GC component amplitudes without scatter due to extrapolation with different TGC values. 3.2. Relaxation time distributions in the fresh and dried trabecular samples Distributions (not shown) of T1 and T2 for a group of femur samples before and after desiccation at 37°C for many days at constant weight without defatting show that the high T1 peaks or shoulders present for the fresh samples are lost in drying [4-5], making it clear that they are due to water. The rest of the distributions are shifted to slightly shorter times; progressive drying decreases the tails toward short times. T2 distributions also show the shift to shorter times 3.3. Surface effects in defatted and fully water saturated trabecular bone samples Fig. 2 shows examples of quasi-continuous T1 distributions for carbonate rocks (bottom), and trabecular bone samples (top) from different sources (pig and cow femur, rat vertebrae), defatted and fully saturated with water. In almost all fully saturated trabecular bone samples we found bimodal distributions, with two T1 peaks, resolved or partly resolved, and also a small tail going down to about 1 ms. Peaks on the right at longer times indicate larger pores. The results of a cryoporometry study [22] and the comparison with rocks suggests that the two peaks come from two compartments not well connected on the NMR time scale. The long T1 peak is due to water in the largest cavities, in slow exchange with the remaining water. The known morphology of trabecular bone and the known classes of porosities in the bone [23] lead one to conclude
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Fig. 2. T1 distributions for several trabecular bone samples, defatted and saturated with water, and for several rock samples. The ordinate is (dS)/(dlnT), where S is percent of total signal, T is T1, and per Neper is per factor of e (for bone only LLC is represented). Equal areas correspond to equal percentages of total signal.
that the long T1 peak should correspond to inter-trabecularporosity and the short T1 peak to intra-trabecular porosity. 3.4. Solid-like and liquid-like T1 distributions in trabecular bone for different treatments and various degrees of drying In order to check this picture and to understand better what is reflected by the whole distribution, defatted and water-saturated samples were progressively dried. In the defatting, the macromolecular components, including the collagen fibers, are not lost. These, along with the mineral apatite, are the structural components of the trabeculae [23]. Fig. 3 shows an example of the T1 distributions for a trabecular sample at different degrees of drying, from full saturation to nearly complete desiccation under vacuum. The dashed curves at the top of the figure are for GC, the solid lines at the bottom for LLC. By imposing a mean value of TGC ⫽ 11.7 s we get the same amplitude for the GC signal within a few percent. The areas under the dashed curves are the same, indicating that the amount of 1H contributing to the GC signal did not change on drying. The solid curve for full saturation and for the first degree of drying show two nearly separated peaks. The one at longer times disappears with progressive drying. It is worth noting that, after the peak at longest times is lost, continued drying does not greatly change the T1 of the remaining component exclusive of the tail, except that the times get somewhat longer at extreme drying. All this confirms that the peak at longer times represents water in the intertrabecular spaces. The GC is presumably due to macromolecular protons of restricted mobility, for which a Gaussian line shape is usually assumed [20-21]. In order to test this hypothesis a sample of bone was treated to remove the mineral components. The FID for also this sample could be separated into a GC, with TGC close to the above value of 11.7 s, and a LLC. Fig. 4 (upper part) shows GC (dashed line) and LLC
Fig. 3. T1 curves for a sample of trabecular bone from a cow femur, defatted and saturated with water and subject to progressive degrees of drying. The dashed curves are for the GC and have all about the same area. The curve with the peak shifted to the right is for the most extreme drying. The solid curves are for LLC, with amplitudes clearly showing the progressive drying, giving the lowest curve barely above the baseline. The ordinate is (dS)/(d lnT), where now S is extrapolated signal, here and in the remaining figures. Data are taken and processed with regard to various gains, numbers of accumulations, etc., so that comparisons of absolute amplitudes are meaningful.
(solid line) distributions for this demineralized sample as prepared and after two progressive degrees of drying, with the lowest solid line barely distinguishable from the baseline. The results are compared (lower part) with GC and LLC distributions for the sample of Fig. 3 in the two extreme conditions: fully saturated and after desiccation under vacuum. It appears that hydrated collagen has T1 of about 70 ms, and that this value tends to increase with severe drying. The GC of the trabecular sample shows the same behavior, which was observed in both components of all samples examined. The drying process in trabecular bone confirms that the LLC peak at long times is entirely due to water and that no fat was present in the cleaned samples, since it disappears completely with drying. The long T1 peak of LLC is water in inter-trabecular spaces, as it disappears first; while the shorter T1 peak is due to water in intra-trabecular spaces. The GC, present also in the demineralized sample, does not disappear, confirming that it is due to the collagen. Moreover, it appears clear that water in the short T1 peak and collagen have the same T1. 3.5. Solid-like and liquid-like 1H T1 distributions in cortical bone The picture is further supported by the results for cortical bone samples, where intertrabecular spaces do not exist. Fig. 5 shows GC (top) and LLC (bottom) for four samples, all measured fresh and two of them measured dried in one
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Fig. 5. T1 curves for GC (top) and LLC (bottom) for four samples of cortical bone from a pig femur, all measured fresh and two of them measured dried in one or more stages. Dashed curves are GC, again with nearly constant area and with shift to the right with extreme drying. The same shift is shown in the lowest solid curves for LLC (bottom).
Fig. 4. Progressive drying of demineralized trabecular bone (top) and defatted and water-saturated trabecular bone (bottom). Dashed curves are for GC and solid for LLC. Area under GC remains the same, and the peak moves to the right at the most extreme drying. The solid curves for the most severe drying are barely distinguishable from the baseline.
or more stages. In all samples examined the same characteristics were observed: no peak for either GC or LLC at long T1, a peak for each component a little below 100 ms, except with severe drying, in which case both components are well over 100 ms.
s or so. Even for the de-fatted and hydrated samples, the SE data can give the peak at a few hundred s meaningfully resolved from the long component if, in UPEN, the data are used only up to about 8 ms (to avoid diffusion effects) and the program is allowed to compute T2’s up to about 300 ms. The times for the long component are not covered by the data, but the times for the component under a ms should be good, and the integrated signal in the long peak should be meaningful, since the baseline is known to be zero. 3.7. Quantification of intertrabecular porosity, bonevolume-fraction and trabecular porosity If the picture outlined up to now is correct, the data at our disposal allow one to estimate several kinds of porosities in
3.6. Comparison of T2 distributions in trabecular and cortical bone Fig. 6 compares T2 distributions in cortical bone and in cleaned, defatted and hydrated trabecular bone. CPMG measurements at TE as short as 300 s in cortical bone do not give enough signal to determine T2 distributions. For these samples our only usable T2 measurements were single-Spin-Echo (SE) and FID. A single peak at about 400 s is observed. CPMG measurements in defatted and watersaturated trabecular bone show wide distributions and suggest a large T2 peak at times shorter than 1 ms, here best seen by SE. SE T2 data work well for T2’s over about 100 s, especially when the measurements go to echo times down to 10
Fig. 6. T2 curves by single-Spin-Echo (SE) for 4 cortical and 3 trabecular bone samples. Diffusion effects prevent processing the SE data beyond about 8 ms, but the area under the extrapolated peaks should be meaningful. See text. The peaks for the cortical samples are all at slightly shorter times than those for the trabecular. The insert shows CPMG curves for the trabecular samples, not measurable for the cortical.
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3.8. Solid-liquid coupling
Fig. 7. Division of signal between intra- and intertrabecular space in defatted and water saturated trabecular bone at the minima in the T1 distributions. Bone Volume Fraction and trabecular porosity may be computed. See text.
the bone [23-25]. Fig. 7 shows T1 distributions for LLC of three fully saturated trabecular bone samples (experimental curves in the insert). The total porosities ⌽, obtained by weight differences and volumes, for samples a, b, and c are 44, 62 and 66%, respectively. As the LLC T1 distributions of de-fatted and water-saturated trabecular samples are bimodal and the peaks are due to signal from water in intertrabecular spaces (Sinter, large T1) and in intratrabecular spaces (Sintra, short T1), the fractions of intertrabecular and intratrabecular pore volumes can be estimated by dividing the distribution at the minimum. Estimated ratios of intratrabecular and intertrabecular pore volumes to total pore volume are  ⫽ Sintra/(Sinter⫹Sintra) and 1⫺ ⫽ Sinter/ (Sinter⫹Sintra), respectively. The intertrabecular porosity ⌽inter ⫽ ⌽Sinter/(Sinter⫹Sintra) ⫽ ⌽(1⫺), the intratrabecular porosity ⌽intra ⫽ ⌽⫺⌽inter ⫽ ⌽, and the Bone Volume Fraction (BVF) ⫽ 1⫺⌽inter ⫽ 1⫺⌽(1⫺). For samples a, b, and c (coarse, fairly coarse, and fine, respectively) we obtained  ⫽ 0.63, 0.33 and 0.29, giving BFV ⫽ 0.84, 0.58 and 0.53, respectively. These parameters can be determined also by other methods, such as CT, MRI, and crosssection analysis. By combining the previous volume ratios, it is easy to compute also the internal porosity of the trabeculae, defined as the ratio between the pore space inside the trabeculae and the volume of the trabeculae themselves ⌽trabec ⫽ ⌽Sintra/[(Sinter⫹Sintra)BVF] ⫽ ⌽/(1⫺⌽⫹⌽). For samples a, b, and c we obtained ⌽trabec ⫽ 0.33, 0.35 and 0.36, respectively, values which are remarkably similar considering the wide range of the other parameters. We do not know any other method to determine ⌽trabec in a nondestructive way. These values are consistent with the only data available, the porosity ⌽ of cortical bone, where there is no intertrabecular space, where we found ⌽ ⫽ 24% and 28% for two samples. Following Cowin [23], the vascular porosity, the lacunar-canalicular porosity and the collagen-apatite porosity are located within the cortical bone and within the trabeculae of trabecular bone.
All these results suggest that the LLC peak, at shorter T1, is due to water confined in regions where it is in some kind of spin exchange with GC, presumably the collagen. There is evidence [19,21,26] that water and collagen exchange longitudinal magnetization by a cross-relaxation process that produces a common T1, as shown in Figs. 3-5. Our results suggest that there is transverse magnetization exchange. If we assume that the very short T2-FID values we observe are due to transverse magnetization exchange between the collagen and collagen-associated water, we find what appears to be a remarkably small range of times , of the order of a few hundred s, for 1H transverse magnetization exchange from GC to LLC, holding for a wide range of bone types and degrees of cleaning, hydration, drying, and even demineralization. We have seen that the GC FID decays with a Gaussian time of about 11.7 s, making the signal negligible for our purposes in about 35 s. This is not to say that there is no phase memory that might permit refocusing within GC; however, exchange with neighboring water molecules is probably random, not transferring any refocusable transverse magnetization to the water at FID times greater than about 35 s. Our measured T2-FID range is from 43.4 to 1260 s, so transverse magnetization exchange between GC and LLC is effective only in the direction from LLC to GC. Since the T2 of the collagen-associated water is shortened by contact with the collagen, we do not directly know its inherent T2. However, T1 is about 70 ms. For many porous media T2 is not much less than half of T1, and if this applies here, for our range of T2-FID values the inherent transverse relaxation in LLC is probably negligible. With negligible inherent transverse relaxation and negligible inflow on exchange with GC, the initial FID decay rate in LLC is simply the reciprocal of its exchange time with GC, since magnetization is uniform throughout LLC and GC at the beginning of the FID, even if parts of LLC (intertrabecular water and fat) do not exchange with the collagen-associated water. Here ␣ is the ratio of amounts of hydrogen in GC and LLC (ratio of extrapolated signals), is exchange time from GC to LLC, and /␣ is the exchange time from LLC to GC. Thus, we have T2-FID ⫽ /␣. Fig. 8 shows T2-FID as a function of 1/␣, with all the data falling close to the line for ⫽ 320 s for the variables over a range of one and a half decades. There are points from cow and pig femurs and rat vertebrae; both cortical and trabecular samples are included, and many combinations of cleaning, saturation, and drying are represented. There are also two points from demineralized bone. The common feature of these systems is the collagen, which seems to have values ranging over a factor of only about 2.2 including measurement uncertainties.
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References
Fig. 8. T2-FID, the T2 of LLC computed from the initial slope of the FID, is approximately 320 s divided by ␣, suggesting a nearly uniform time of about 320 s for exchange of transverse 1H magnetization in the collagen with that in water. This applies for cortical and trabecular bone from cow and pig femurs and for rat vertebrae and demineralized bone, all in various conditions (fresh, dried, defatted and saturated, dried further).
4. Conclusions The separation of the solid-like and liquid-like components, the quasi-continuous distribution analysis by UPEN, the evolution of the distributions with the drying process, the results on demineralized samples, and the known structural differences between cortical and trabecular bone allow us to conclude that: - In water-saturated trabecular bone samples, where UPEN identifies two T1 peaks, the longer peak is due to water in intertrabecular spaces and shows surface effects. - The shorter T1 peak (at about 70 ms) associated with the 300-500 s T2 peak, present also in cortical bone, is due to water inside the solid material of the bone whether trabecular or cortical. - The shorter T1 peak (at about 70 ms) for water has the same T1 as the solid-like signal from the collagen. - Some kind of exchange appears between solid- and liquid-like 1H, with an exchange time for collagen of the order of 300 s, and it is independent, or nearly so, of the kind or condition of the samples. - Several kinds of porosities can be quantified, including the trabecular porosity, and we do not know any other method to estimate ⌽trabec in a non-destructive way.
Acknowledgments The instrumentation and the data processing were funded by MURST (5% Multimedialita`) and by University of Bologna (Funds for selected research topics). The authors wish to thank Mara Camaiti for cleaning and demineralizing the bone samples; C. Garavaglia, F. Peddis, B. Ravaglia, and C. Vescogni for technical assistance.
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[25] Ferretti M, Muglia MA, Remaggi F, Cane` V, Palumbo C. Histomorphometric study on the osteocyte lacuno-canalicular network in animals of different species: II Parallel-fibered and lamellar bones. Ital J Anat Embryol 1999;104:121–31. [26] Tzou D-L, Lee S-M, Yeung HN. Temperature dependence and phase transition of proton relaxation of hydrated collagen in intact beef tendon specimens via cross-relaxation spectroscopy. Magn Reson Med 1997;37:359–65.
Bone tissue and porous media: common features and differences studied by NMR relaxation Paola Fantazzinia*, Robert James Sidford Brownb, Giulio Cesare Borgiac a
Univ. of Bologna, Dept. of Physics, Viale Berti Pichat 6/2, 40127 Bologna, Italy b 953 W. Bonita Ave., Claremont CA 91711-4193 c Univ. of Bologna, Dept. of ICMA, Viale Risorgimento 2, 40136 Bologna, Italy
Abstract 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 inversionrecovery (IR) T1 measurement shows an approximately Gaussian (solid-like) component, exp[⫺1⁄2 (T/TGC)2], with TGC ⬇ 11.7 ⫾ 0.7 s (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 s. 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/␣ s, where ␣ is the ratio of the extrapolated GC to LLC, appearing to indicate a time of about 320 s 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. © 2003 Elsevier Science Inc. All rights reserved. Keywords: NMR relaxation; Bone; Spin exchange; Trabecular porosity; Gaussian FID component
1. Introduction 1.1. Premise The potentialities of water 1H nuclei Magnetic Resonance Relaxation (MRR) in the study of properties of po* Corresponding author. Tel.: ⫹39 051 2095119; fax: ⫹39 051 2090457. E-mail address: [email protected] (P. Fantazzini).
rous media was first realized in the early 1950s [1-2], when the unanticipated “surface effects” were revealed. Not only can the relaxation times of the exponential process of return to equilibrium of the nuclear magnetization be many orders of magnitude shorter than the corresponding times in bulk water, but they can also show distributions of relaxation times many decades wide. Early studies include oil industry work on relating MRR parameters to reservoir properties of oilfield rocks and also work in the universities on the nature
0730-725X/03/$ – see front matter © 2003 Elsevier Science Inc. All rights reserved. doi:10.1016/S0730-725X(03)00129-2
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of water in the vicinity of solid surfaces. In the mid-1980s a resurgence of interest in this subject was probably helped by the rapid growth of the field of medical Magnetic Resonance Imaging. Then a huge explosion of work in NMR in porous media, including MRR, took place, as one can see by comparing the ratio of contributions to the Fifth International Meeting on Magnetic Resonance in Porous Media (MRPM5, Bologna-2000) [3] to those of MRPM1 (Bologna-1990). We will show how the corpus of theories, experiments, algorithms for relaxation data processing, and interpretation, established in the broad field of Magnetic Resonance for fluids in porous media can successfully be applied to the study of a very particular and important porous material: bone tissue [4-5]. 1.2. The “surface effects” Major assumptions are usually required for the interpretation of MRR data from porous media. Relaxation at pore walls increases the relaxation rate because of the high S/V of the pore and is often represented by the simple relationship 1/T1,2 ⫽ 1,2 S/V ⫹ 1/T1,2-bulk. The surface relaxivity is the velocity at which the magnetization in the pore in the vicinity of the surface flows out of the pore. If is constant and diffusion in the pore fluid is fast enough to maintain magnetization nearly constant throughout the pore (fast diffusion regime), then is a macroscopic parameter as used in the equation above. In this regime need not be microscopically constant, but may be considered an average over surfaces within distances of diffusion in a local relaxation time, that is, within the local diffusion cell. Likewise, S/V is averaged over this local volume, which may be larger than a single “pore”; if the sample is heterogeneous in and/or S/V on a scale larger than local diffusion lengths, multiexponential relaxation will be observed. If diffusion is not in the fast regime, gives the boundary condition for application of the diffusion equation. A microscopic picture gives the interpretation ⫽ h/(Ts⫹r) in the Torrey model [6], where h is the thickness of the surface layer, in which the local relaxation time is Ts, and r is the residence time of water molecules in this layer. It is important to note that the results of many measurements on porous media depend strongly on length scales involved. S/V measurements by gas adsorption can give values many times higher than those by Hg injection or optical scanning, and the corresponding values of vary accordingly. Methods of measurement and forms of “average” relaxation times used to represent distributions of times, as well as types of S/V measurement, can greatly affect the values obtained, so care is necessary in comparing values. It should be noted that the volume over which S/V is averaged by diffusion depends on local relaxation time and local (restricted) diffusion. This volume may be larger than a single pore, and the relaxation time for this volume may be an average over a range of pore sizes. However, with very small pores, relaxation times may be
short and diffusion restricted, giving small regions averaged. Although may vary both within a sample and from sample to sample, there is usually not much choice but to assume it constant, taking its value from some related measurements. There is no obvious reason that should be constant even over all surfaces of a single porous material. Nevertheless, there is enough similarity of values for many materials, that MRR measurements have been useful for applications where estimates of the length V/S are needed. In a recent paper [7] the observation of relatively constant surface relaxivity is explained as the result of consistently high surface concentration of paramagnetic materials [8]. Examples of the application of MRR to porous materials are estimation of capillary pressure (inversely proportional to a length) [9], and residual fluid content after drainage at a given pressure [10-13]. Another is the estimation of the permeability to fluid flow in response to a pressure gradient [14-17]. Results will now be presented of the application of these procedures to the study of bone tissue. As in rocks, it is useful to take bone data under different conditions of cleaning, saturation, and desaturation.
2. Materials and methods Bones of pigs and cows were stored in the slaughterhouse refrigerator immediately after slaughter. Cylindrical samples of cortical and trabecular bone, 7 mm in diameter and in height, were cored from different regions of the femurs. All samples were preserved at 4°C up to the time of the NMR measurement. All the measurements on fresh samples were accomplished within a few days after slaughter. Then some samples were defatted and saturated with distilled water. NMR measurements were performed at 20 MHz (0.47 T) (at 30°C for fresh samples and 20°C for cleaned and hydrated samples), by means of a Bruker Minispec P20 (Karlsruhe, Germany) equipped with NMR data station (Stelar, Pavia, Italy). The measurements began after the temperature of the sample had equilibrated with that of the probe. Add/subtract phase-cycled sequences were used in all the measurements, and measurements were accumulated for signal averaging. Relaxation delay was adequate for full magnetization to be reached after each sequence. T1 relaxation data are taken by inversion-recovery (IR) sequences, and for each of 127 IR times the free induction decay (FID) signal is sampled and recorded at 2-s intervals from 14 to 266 s. The shortest IR time is usually 100 s, with successive times increased by fixed factors, giving maximum recovery times of about 5 s in fresh samples and 10 s in defatted and hydrated samples. T2 data were taken from FID’s and by Carr-Purcell-Meiboom-Gill (CPMG) and single-Spin-Echo (SE) sequences. For details see Ref. [4]. Quasi-continuous relaxation time distribution analysis of
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the data were by UPEN [18], which is based on a UniformPENalty (UPEN) inversion algorithm, using a regularizing or smoothing coefficient varying with relaxation time and determined by iterative negative feedback in such a way that the smoothing penalty, rather then the coefficient, is roughly uniform. This can give sharp lines that are not broadened more than is consistent with the noise and in the same distribution show a tail decades long without breaking it up into several peaks not required by the data to be separate, which might be misinterpreted as physically meaningful resolved compartments. The performance of the relaxometer and data processing were tested by repeating the whole set of measurements for doped water samples, where longitudinal and transverse relaxation were expected to be single-exponential. In all cases single-exponential behavior was observed.
3. Results and discussion 3.1. Solid-like and liquid-like contribution to the free induction decay Despite the fact that the FID signal was not reliably usable before 14 s, there is clearly an approximately Gaussian Component (GC) to the FID, a “solid-like” component probably coming from 1H nuclei in collagen. It is long known that macromolecular protons can contribute to the FID signal from biologic tissues [19], and such a GC has been observed also in normal cartilage [20-21]. The GC decay has the form exp[⫺1⁄2 (T/TGC)2], where T is time after the end of the 90° pulse, and TGC is the Gaussian decay time. The remaining “Liquid-Like” Component (LLC) signal has initially simple exponential form, in some cases becoming clearly multiexponential by about the middle of the 266 s recorded interval. It has been possible to separate the GC from LLC in a reasonably stable and reproducible manner, giving separate T1 distributions and also giving the two extrapolated amplitudes and the two time constants, TGC and T2-FID, where T2-FID is the rate-average T2, that is, the T2 corresponding to the initial slope of the FID decay curve (without GC). The ratio ␣ of the GC and LLC will be a useful parameter in the following. Fig. 1 shows a plot of the average of the first 10 FID’s from an IR sequence, together with the fitted curves, for a sample of trabecular bone that has been defatted, water saturated, and vacuum dried. The insert shows the GC plotted against T2. As can be seen, the fit is reasonably good, and the separated GC is reasonably close to Gaussian in form. TGC averages 11.7 s (s.d. 0.7 s) for the cortical and trabecular bone samples reported here, regardless of treatment (as fresh, defatted and water-saturated, dried, vacuum dried, and even demineralized) and are not clearly different for samples from different types (from cow and pig femurs, rat vertebrae). The extrapolation for the GC FID is more than a factor of two and is very sensitive to the TGC value
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Fig. 1. Average of ten FID’s from an inversion recovery (IR) T1 sequence, fit by the sum of a Gaussian Component (GC) and an exponential LiquidLike Component (LLC). The differences between the input points and the fitted exponential are plotted against T2 in the insert.
used. For this reason, TGC is not allowed to vary within the set of FID’s for a series of IR times used to determine a T1 distribution. By picking a mean TGC value for a sample for which data are taken for a sequence of treatments one may hope to compare GC component amplitudes without scatter due to extrapolation with different TGC values. 3.2. Relaxation time distributions in the fresh and dried trabecular samples Distributions (not shown) of T1 and T2 for a group of femur samples before and after desiccation at 37°C for many days at constant weight without defatting show that the high T1 peaks or shoulders present for the fresh samples are lost in drying [4-5], making it clear that they are due to water. The rest of the distributions are shifted to slightly shorter times; progressive drying decreases the tails toward short times. T2 distributions also show the shift to shorter times 3.3. Surface effects in defatted and fully water saturated trabecular bone samples Fig. 2 shows examples of quasi-continuous T1 distributions for carbonate rocks (bottom), and trabecular bone samples (top) from different sources (pig and cow femur, rat vertebrae), defatted and fully saturated with water. In almost all fully saturated trabecular bone samples we found bimodal distributions, with two T1 peaks, resolved or partly resolved, and also a small tail going down to about 1 ms. Peaks on the right at longer times indicate larger pores. The results of a cryoporometry study [22] and the comparison with rocks suggests that the two peaks come from two compartments not well connected on the NMR time scale. The long T1 peak is due to water in the largest cavities, in slow exchange with the remaining water. The known morphology of trabecular bone and the known classes of porosities in the bone [23] lead one to conclude
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Fig. 2. T1 distributions for several trabecular bone samples, defatted and saturated with water, and for several rock samples. The ordinate is (dS)/(dlnT), where S is percent of total signal, T is T1, and per Neper is per factor of e (for bone only LLC is represented). Equal areas correspond to equal percentages of total signal.
that the long T1 peak should correspond to inter-trabecularporosity and the short T1 peak to intra-trabecular porosity. 3.4. Solid-like and liquid-like T1 distributions in trabecular bone for different treatments and various degrees of drying In order to check this picture and to understand better what is reflected by the whole distribution, defatted and water-saturated samples were progressively dried. In the defatting, the macromolecular components, including the collagen fibers, are not lost. These, along with the mineral apatite, are the structural components of the trabeculae [23]. Fig. 3 shows an example of the T1 distributions for a trabecular sample at different degrees of drying, from full saturation to nearly complete desiccation under vacuum. The dashed curves at the top of the figure are for GC, the solid lines at the bottom for LLC. By imposing a mean value of TGC ⫽ 11.7 s we get the same amplitude for the GC signal within a few percent. The areas under the dashed curves are the same, indicating that the amount of 1H contributing to the GC signal did not change on drying. The solid curve for full saturation and for the first degree of drying show two nearly separated peaks. The one at longer times disappears with progressive drying. It is worth noting that, after the peak at longest times is lost, continued drying does not greatly change the T1 of the remaining component exclusive of the tail, except that the times get somewhat longer at extreme drying. All this confirms that the peak at longer times represents water in the intertrabecular spaces. The GC is presumably due to macromolecular protons of restricted mobility, for which a Gaussian line shape is usually assumed [20-21]. In order to test this hypothesis a sample of bone was treated to remove the mineral components. The FID for also this sample could be separated into a GC, with TGC close to the above value of 11.7 s, and a LLC. Fig. 4 (upper part) shows GC (dashed line) and LLC
Fig. 3. T1 curves for a sample of trabecular bone from a cow femur, defatted and saturated with water and subject to progressive degrees of drying. The dashed curves are for the GC and have all about the same area. The curve with the peak shifted to the right is for the most extreme drying. The solid curves are for LLC, with amplitudes clearly showing the progressive drying, giving the lowest curve barely above the baseline. The ordinate is (dS)/(d lnT), where now S is extrapolated signal, here and in the remaining figures. Data are taken and processed with regard to various gains, numbers of accumulations, etc., so that comparisons of absolute amplitudes are meaningful.
(solid line) distributions for this demineralized sample as prepared and after two progressive degrees of drying, with the lowest solid line barely distinguishable from the baseline. The results are compared (lower part) with GC and LLC distributions for the sample of Fig. 3 in the two extreme conditions: fully saturated and after desiccation under vacuum. It appears that hydrated collagen has T1 of about 70 ms, and that this value tends to increase with severe drying. The GC of the trabecular sample shows the same behavior, which was observed in both components of all samples examined. The drying process in trabecular bone confirms that the LLC peak at long times is entirely due to water and that no fat was present in the cleaned samples, since it disappears completely with drying. The long T1 peak of LLC is water in inter-trabecular spaces, as it disappears first; while the shorter T1 peak is due to water in intra-trabecular spaces. The GC, present also in the demineralized sample, does not disappear, confirming that it is due to the collagen. Moreover, it appears clear that water in the short T1 peak and collagen have the same T1. 3.5. Solid-like and liquid-like 1H T1 distributions in cortical bone The picture is further supported by the results for cortical bone samples, where intertrabecular spaces do not exist. Fig. 5 shows GC (top) and LLC (bottom) for four samples, all measured fresh and two of them measured dried in one
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Fig. 5. T1 curves for GC (top) and LLC (bottom) for four samples of cortical bone from a pig femur, all measured fresh and two of them measured dried in one or more stages. Dashed curves are GC, again with nearly constant area and with shift to the right with extreme drying. The same shift is shown in the lowest solid curves for LLC (bottom).
Fig. 4. Progressive drying of demineralized trabecular bone (top) and defatted and water-saturated trabecular bone (bottom). Dashed curves are for GC and solid for LLC. Area under GC remains the same, and the peak moves to the right at the most extreme drying. The solid curves for the most severe drying are barely distinguishable from the baseline.
or more stages. In all samples examined the same characteristics were observed: no peak for either GC or LLC at long T1, a peak for each component a little below 100 ms, except with severe drying, in which case both components are well over 100 ms.
s or so. Even for the de-fatted and hydrated samples, the SE data can give the peak at a few hundred s meaningfully resolved from the long component if, in UPEN, the data are used only up to about 8 ms (to avoid diffusion effects) and the program is allowed to compute T2’s up to about 300 ms. The times for the long component are not covered by the data, but the times for the component under a ms should be good, and the integrated signal in the long peak should be meaningful, since the baseline is known to be zero. 3.7. Quantification of intertrabecular porosity, bonevolume-fraction and trabecular porosity If the picture outlined up to now is correct, the data at our disposal allow one to estimate several kinds of porosities in
3.6. Comparison of T2 distributions in trabecular and cortical bone Fig. 6 compares T2 distributions in cortical bone and in cleaned, defatted and hydrated trabecular bone. CPMG measurements at TE as short as 300 s in cortical bone do not give enough signal to determine T2 distributions. For these samples our only usable T2 measurements were single-Spin-Echo (SE) and FID. A single peak at about 400 s is observed. CPMG measurements in defatted and watersaturated trabecular bone show wide distributions and suggest a large T2 peak at times shorter than 1 ms, here best seen by SE. SE T2 data work well for T2’s over about 100 s, especially when the measurements go to echo times down to 10
Fig. 6. T2 curves by single-Spin-Echo (SE) for 4 cortical and 3 trabecular bone samples. Diffusion effects prevent processing the SE data beyond about 8 ms, but the area under the extrapolated peaks should be meaningful. See text. The peaks for the cortical samples are all at slightly shorter times than those for the trabecular. The insert shows CPMG curves for the trabecular samples, not measurable for the cortical.
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3.8. Solid-liquid coupling
Fig. 7. Division of signal between intra- and intertrabecular space in defatted and water saturated trabecular bone at the minima in the T1 distributions. Bone Volume Fraction and trabecular porosity may be computed. See text.
the bone [23-25]. Fig. 7 shows T1 distributions for LLC of three fully saturated trabecular bone samples (experimental curves in the insert). The total porosities ⌽, obtained by weight differences and volumes, for samples a, b, and c are 44, 62 and 66%, respectively. As the LLC T1 distributions of de-fatted and water-saturated trabecular samples are bimodal and the peaks are due to signal from water in intertrabecular spaces (Sinter, large T1) and in intratrabecular spaces (Sintra, short T1), the fractions of intertrabecular and intratrabecular pore volumes can be estimated by dividing the distribution at the minimum. Estimated ratios of intratrabecular and intertrabecular pore volumes to total pore volume are  ⫽ Sintra/(Sinter⫹Sintra) and 1⫺ ⫽ Sinter/ (Sinter⫹Sintra), respectively. The intertrabecular porosity ⌽inter ⫽ ⌽Sinter/(Sinter⫹Sintra) ⫽ ⌽(1⫺), the intratrabecular porosity ⌽intra ⫽ ⌽⫺⌽inter ⫽ ⌽, and the Bone Volume Fraction (BVF) ⫽ 1⫺⌽inter ⫽ 1⫺⌽(1⫺). For samples a, b, and c (coarse, fairly coarse, and fine, respectively) we obtained  ⫽ 0.63, 0.33 and 0.29, giving BFV ⫽ 0.84, 0.58 and 0.53, respectively. These parameters can be determined also by other methods, such as CT, MRI, and crosssection analysis. By combining the previous volume ratios, it is easy to compute also the internal porosity of the trabeculae, defined as the ratio between the pore space inside the trabeculae and the volume of the trabeculae themselves ⌽trabec ⫽ ⌽Sintra/[(Sinter⫹Sintra)BVF] ⫽ ⌽/(1⫺⌽⫹⌽). For samples a, b, and c we obtained ⌽trabec ⫽ 0.33, 0.35 and 0.36, respectively, values which are remarkably similar considering the wide range of the other parameters. We do not know any other method to determine ⌽trabec in a nondestructive way. These values are consistent with the only data available, the porosity ⌽ of cortical bone, where there is no intertrabecular space, where we found ⌽ ⫽ 24% and 28% for two samples. Following Cowin [23], the vascular porosity, the lacunar-canalicular porosity and the collagen-apatite porosity are located within the cortical bone and within the trabeculae of trabecular bone.
All these results suggest that the LLC peak, at shorter T1, is due to water confined in regions where it is in some kind of spin exchange with GC, presumably the collagen. There is evidence [19,21,26] that water and collagen exchange longitudinal magnetization by a cross-relaxation process that produces a common T1, as shown in Figs. 3-5. Our results suggest that there is transverse magnetization exchange. If we assume that the very short T2-FID values we observe are due to transverse magnetization exchange between the collagen and collagen-associated water, we find what appears to be a remarkably small range of times , of the order of a few hundred s, for 1H transverse magnetization exchange from GC to LLC, holding for a wide range of bone types and degrees of cleaning, hydration, drying, and even demineralization. We have seen that the GC FID decays with a Gaussian time of about 11.7 s, making the signal negligible for our purposes in about 35 s. This is not to say that there is no phase memory that might permit refocusing within GC; however, exchange with neighboring water molecules is probably random, not transferring any refocusable transverse magnetization to the water at FID times greater than about 35 s. Our measured T2-FID range is from 43.4 to 1260 s, so transverse magnetization exchange between GC and LLC is effective only in the direction from LLC to GC. Since the T2 of the collagen-associated water is shortened by contact with the collagen, we do not directly know its inherent T2. However, T1 is about 70 ms. For many porous media T2 is not much less than half of T1, and if this applies here, for our range of T2-FID values the inherent transverse relaxation in LLC is probably negligible. With negligible inherent transverse relaxation and negligible inflow on exchange with GC, the initial FID decay rate in LLC is simply the reciprocal of its exchange time with GC, since magnetization is uniform throughout LLC and GC at the beginning of the FID, even if parts of LLC (intertrabecular water and fat) do not exchange with the collagen-associated water. Here ␣ is the ratio of amounts of hydrogen in GC and LLC (ratio of extrapolated signals), is exchange time from GC to LLC, and /␣ is the exchange time from LLC to GC. Thus, we have T2-FID ⫽ /␣. Fig. 8 shows T2-FID as a function of 1/␣, with all the data falling close to the line for ⫽ 320 s for the variables over a range of one and a half decades. There are points from cow and pig femurs and rat vertebrae; both cortical and trabecular samples are included, and many combinations of cleaning, saturation, and drying are represented. There are also two points from demineralized bone. The common feature of these systems is the collagen, which seems to have values ranging over a factor of only about 2.2 including measurement uncertainties.
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References
Fig. 8. T2-FID, the T2 of LLC computed from the initial slope of the FID, is approximately 320 s divided by ␣, suggesting a nearly uniform time of about 320 s for exchange of transverse 1H magnetization in the collagen with that in water. This applies for cortical and trabecular bone from cow and pig femurs and for rat vertebrae and demineralized bone, all in various conditions (fresh, dried, defatted and saturated, dried further).
4. Conclusions The separation of the solid-like and liquid-like components, the quasi-continuous distribution analysis by UPEN, the evolution of the distributions with the drying process, the results on demineralized samples, and the known structural differences between cortical and trabecular bone allow us to conclude that: - In water-saturated trabecular bone samples, where UPEN identifies two T1 peaks, the longer peak is due to water in intertrabecular spaces and shows surface effects. - The shorter T1 peak (at about 70 ms) associated with the 300-500 s T2 peak, present also in cortical bone, is due to water inside the solid material of the bone whether trabecular or cortical. - The shorter T1 peak (at about 70 ms) for water has the same T1 as the solid-like signal from the collagen. - Some kind of exchange appears between solid- and liquid-like 1H, with an exchange time for collagen of the order of 300 s, and it is independent, or nearly so, of the kind or condition of the samples. - Several kinds of porosities can be quantified, including the trabecular porosity, and we do not know any other method to estimate ⌽trabec in a non-destructive way.
Acknowledgments The instrumentation and the data processing were funded by MURST (5% Multimedialita`) and by University of Bologna (Funds for selected research topics). The authors wish to thank Mara Camaiti for cleaning and demineralizing the bone samples; C. Garavaglia, F. Peddis, B. Ravaglia, and C. Vescogni for technical assistance.
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