Clinically-Compatible MRI Strategies for Discriminating Bound and Pore Water in Cortical Bone

A Model for the NMR Lineshape of Water in Cortical Bone

In order to explain the widely different T₂s but apparently similar T₂*s arising from bound and pore water, consider a simple, qualitative model of the observed free induction decay (FID) rate as a sum of reversible and irreversible transverse relaxation rates. That is $R_2^{\ast }=R_2+R_2^{\prime }$, where $R_2^{\ast }=1/T_2^{\ast }$ is the observed transverse relaxation rate in the FID, R₂ = 1/T₂ is the time-irreversible rate as observed in a Carr-Purcell-Meiboom-Gill (CPMG) measurement, and $R_2^{\prime }$ is the time-reversible rate. With this model, consider bound water to exhibit $R_2\gg R_2^{\prime }$ (such that $R_2^{\ast }\cong R_2$), a condition of so-called homogenous line-broadening. This arises from dipolar interactions of motionally-restricted bound water spins throughout the bone matrix space, as well as from magnetization transfer with dipolar broadened collagen/semisolids observed in (9,13). Conversely, consider the pore water signal to result from the sum of numerous isolated free water pools, each with relatively low R₂ values but collectively with off-resonant frequencies described by a broad distribution. Such would be the case for the polydisperse pore size distribution observed in bone (e.g. Haversian canals, lacunae, and cannaliculi (15,26)), wherein pores contain motionally-averaged mobile water surrounded by a bone matrix of different magnetic susceptibility (27) that perturbs the local Larmor frequency. Thus, the pore water FID is primarily governed by $R_2^{\prime }$ (such that $R_2^{\ast }\cong R_2^{\prime }$), a condition of so-called inhomogenous line-broadening. In this sense, cortical bone pore water bears similarity to water within porous media (14). Figure 1 demonstrates NMR frequency-domain representations of this bound/pore water model, and indicates that to effectively manipulate the bulk pore water magnetization a broadband RF pulse is needed to nutate the full distribution of individual off-resonant pore magnetizations within the bulk pore water lineshape.

T₂ Selective Adiabatic RF pulses

From the model above and previous wideline NMR studies (13,28), it is readily apparent that any RF pulse designed to perturb the entire pore water magnetization must possess a relatively large bandwidth (≈ 3500 Hz at 4.7T, estimated ≈ 2000 Hz at 3.0T). A conventional amplitude modulated RF pulse with this bandwidth would be short in duration and similarly responsive for T₂s of both bound and pore water. However, an adiabatic pulse has an additional degree of freedom in design by way of its frequency modulation and can invert spins across a wide bandwidth using a relatively long, frequency-swept RF waveform. Although relaxation during an adiabatic pulse is complicated due to the spectral density contribution at γB₁(t) (29), we approximate such relaxation with the Bloch equations and invariant T₁ and T₂ relaxation time constants. Figure 2 shows the effect of a 5 ms duration, 5 kHz bandwidth hyperbolic secant (sech) adiabatic full passage (AFP) pulse (24) applied to equilibrium magnetization, as determined by numerical solution of the Bloch equations. This figure demonstrates the T₂-selectivity of such RF pulses, in accord with previous work (22,25), and their suitability for differentially rotating bound water (T₂ < 1 ms) and pore water (T₂ > 1 ms) magnetizations. The inversion efficiency of a given RF pulse is described by a scalar multiplier (−1≤α≤1) representing the change in longitudinal magnetization caused by each AFP pulse.

Pulse Sequences

Human cortical bone preparation

The Musculoskeletal Tissue Foundation (Edison, NJ), a non-profit tissue allograft bank, and the Vanderbilt Donor Program (Nashville, TN) supplied human femurs from 14 cadaveric donors (8 male, 6 female, 22–98 years old, mean ± standard deviation (SD) = 70 ± 25 years) under instruction to not provide tissue from donors who had tested positive for a blood borne pathogens. Cortical bone specimens for either NMR or mechanical testing were extracted under irrigation from adjacent sites in the medial mid-shaft of each donor’s right femur and were machined to ≈ 10×2×4 mm or 40×2×4 mm dimensions, respectively, providing uniform cortical bone, free of endosteal and periosteal surfaces. Note that volume of the NMR samples, determined by digital caliper measurement, was on the order one or a few voxels in a typical lower leg quantitative uTE bone image (6). Specimens were stored in phosphate-buffered saline at −80 °C between processing and measurements, and specimens were thawed at 4 °C approximately 18 hours prior to measurements. Immediately prior to NMR measurements, thawed specimens were removed from PBS and blotted dry to remove pooled surface water.

Mechanical Testing

Standard three-point bend mechanical testing was performed at room temperature to determine several mechanical properties relevant to fracture risk in bone: flexural modulus, yield stress, peak stress, fracture stress, and toughness to failure. A material testing system (Dynamight 8841; Instron, Canton, OH) recorded the force-displacement data from a 100 Newton load cell and the linear variable differential transformer at 50 Hz. Hydrated bone was loaded to failure at 5 mm/min on a 35 mm support span. Various mechanical properties were determined from force-displacement data following the standard methods described previously (18).

NMR

NMR measurements were performed at 200 MHz and ≈ 20°C using a 4.7T horizontal bore magnet with a DirectDrive console (Varian/Agilent, Santa Clara, CA). An in-house loop-gap style RF coil with Teflon structural support was used (similar to the coil described in (33)), which provided 90°/180° RF pulses of ≈ 5 μs/10 μs duration and contributed negligible background ¹H signal (<1% of net cortical bone signal). In all NMR measurements, bone specimens were placed with osteonal direction orthogonal to B₀ to maintain consistent magic angle effects. In all measurements of the CuTE, DAFP, and AIR sequences, a microsphere containing 21.2 μL of deionized H₂O (T₂ ≈ 2.5 s) was placed adjacent to bone specimens as a reference marker for signal size quantitation. Also, to ensure there were no significant time-dependent changes of the bone T₂ characteristics during NMR measurements, equilibrium CPMG measurements were collected before and after each series of measurements.

Using experimental parameters described elsewhere (13), transverse relaxation was measured at equilibrium with a CPMG pulse sequence (100 μs echo spacing), and longitudinal relaxation was characterized with inversion-recovery-prepared CPMG (IR-CPMG). To observe the effects of a single AFP pulse on bound and pore water signals in cortical bone (α^bw and α^pw), the CPMG measurements were repeated with and without a preparatory sech pulse (AFP-CPMG) of varying duration and bandwidth (combinations of 5,10,15 ms and 1,2,3.5,5 kHz were utilized). During a 5 ms delay between the sech pulse and the excitation RF of the CPMG acquisition, a spoiler gradient (2 ms, 10 G/cm) removed any net transverse magnetization.

CuTE and DAFP and AIR sequences were driven to steady state by replacing their uTE imaging modules (Fig 3) with a non-imaging acquisition: hard RF excitation (10 μs, 20°) followed by an FID acquisition and a subsequent spoiler gradient (5 ms, 10 G/cm). FID and CPMG acquisitions were collected at steady state. The DAFP and AIR sequences used sech pulses of 10 ms duration and 3.5 kHz BW. (These pulses used ≈ 24 μT peak B₁, which is near the maximum available on typical human MRI systems but can be reduced by using higher order hyperbolic secant, HSn, pulses (34)). Both AIR and DAFP used TR = 300 ms; CuTE used TR = 35 ms. AIR measurements were repeated with 11 TI values spanning 70–110 ms to empirically determine a single optimal TI for nulling pore water across all specimens (minimal signal in T₂ spectral pore water domain).

The BEuTE method was evaluated by analyzing non-imaging FIDs collected from equilibrium magnetization (pulse-acquire measurement: TR = 5 s, 90° flip, acquisition of a 10 ms window at 2.5 MHz bandwidth, 64 averages, 8 μs receiver dead time prior to acquisition). These equilibrium FIDs provide an idealized test bed for evaluating the BEuTE method, as they are free of imaging artifacts and unwanted coherence pathways potentially present in the steady state imaging version of BEuTE. Bound and pore water T₁-weighting, which is not present in the equilibrium FIDs but would be in BEuTE imaging, is not required to evaluate the soundness of the BEuTE method.

Data Analysis

All data processing was performed using MATLAB (The Mathworks, Natick, MA). The freely-available MERA_Toolbox (Multi-Exponential Relaxation Analysis, http://vuiis.vanderbilt.edu/~doesmd/MERA/MERA_Toolbox.html) provided a regularized non-negative least-square (NNLS) approach to estimate multi-exponential T₂ spectra from CPMG data and T₁-T₂ spectra from IR-CPMG data as described in (13). Because AFP-CPMG measurements contained decaying signals of both positive and negative amplitude, direct NNLS analysis was not possible. Instead, the complex AFP-CPMG signals were first summed with the complex equilibrium-CPMG signals, and the resulting summed signal, comprised solely of non-negative amplitude decaying exponentials, was fitted with a T₂ spectrum. This T₂ spectrum was then subtracted on a peak-by-peak basis from the equilibrium T₂ spectrum to construct an estimated AFP-CPMG T₂ spectrum.

Population averaged bound/pore R₁s were computed from each specimen’s T₁-T₂ spectra by computing the mean R₁ in the appropriate T₂ domains (for bound and pore water) and the resulting R₁s were averaged across all specimens. A population average for net water ${\text{R}}_1(R_1^{nw})$ was similarly computed from mean R₁s across both bound and pore water T₂ domains. Population averaged AFP efficiency parameters, α^bw and α^pw were estimated by dividing bound or pore water T₂ spectral intensities from the AFP-CPMG measurements by those from the equilibrium CPMG measurements and then averaging across specimens.

Steady state longitudinal magnetizations of CuTE, DAFP, and AIR pulse sequences were discriminated on a T₂ basis via NNLS fitting of CPMG data collected in the final TR periods. CuTE CPMG data satisfied the NNLS constraint, so fitting directly gave T₂ spectra. However DAFP and AIR CPMGs potentially contained both positive and negative decays, so T₂ spectra were calculated in the same manner as those from AFP-CPMG data (described above).

FIDs from the CuTE, DAFP, and AIR sequences were quantified similarly to previous in vivo studies that employ reference signals (6,7), although transverse relaxation decay during TE periods was not considered (assumed TE ≪ T₂* in all sequences). FID magnitudes at TE = 50 μs, which consisted of both short-T₂* bone water and long-T₂* marker water, were stripped of long-T₂* marker water contributions by subtracting magnitudes at TE = 3 ms, and the resulting signal was defined as S_CuTE, S_DAFP, or S_AIR. (When imaging, the reference signal would be spatially resolved from cortical bone and so the long-TE signal subtraction would only be used to suppress contaminating soft tissue signals.) S_CuTE and $R_1^{nw}$ were then used with a mono-exponential form of Eq [1] (i.e. the standard spoiled gradient echo signal equation) to estimate the net water proton density, $S_0^{nw}$, while S_DAFP, S_AIR and the appropriate population-averaged a priori parameter estimates were used with Eq [2] or [3] to estimate $S_0^{bw}$ or $S_0^{pw}$. To convert $S_0^{nw},S_0^{bw}$, and $S_0^{pw}$ into units of absolute proton concentration, these estimates were multiplied by $V_{\text{ref}}{\rho }_{\text{ref}}/V_{\text{bone}}{S}_0^{\text{ref}}$, where V_ref and V_bone are the water reference and bone volumes, respectively, ρ_H2O = 111.1 mol ¹H/L_H2O was the assumed proton concentration of the reference, and $S_0^{\text{ref}}$ is the total signal arising from the water marker (obtained by integrating the equilibrium CPMG T₂ spectrum over T₂s > 1000 ms, where the entire marker signal is clearly discriminated from bone water). Resulting proton concentration estimates from the CuTE, DAFP, and AIR signals were pairwise linearly regressed to the aforementioned bone mechanical properties, as well as to reference-standard measures of net, pore, and bound water, respectively. These reference-standard measures were calculated from equilibrium CPMG-derived T₂ spectra by integrating over the appropriate T₂ domains, as previously demonstrated in (13,18).

Equilibrium FIDs, chosen as surrogates to BEuTE signals (see rationale above), were fit with bi-exponential decays via least-squares fitting to Eq [1], assuming e^−R₁TR ≈ 0 (i.e. TR ≫ T₁). FIDs were fit across a time domain of 50 μs to 4.5 ms (similar to that shown in the aforementioned bone bi-exponential imaging study (31)) to isolate bound and pore water decays while avoiding signal from a large matrix-related T₂ ≈ 10 μs component. Resulting short and long-T₂* signal fractions were compared to the fractions of bound and pore water (relative to total water) determined from reference-standard equilibrium CPMG T₂ spectra. While this gave a straightforward evaluation of BEuTE’s ability to discriminate bound and pore water, short and long-T₂* signal sizes were also converted to units of proton concentration (via the aforementioned $V_{\text{ref}}{\rho }_{\text{ref}}/V_{\text{bone}}{S}_0^{\text{ref}}$ factor), which were pairwise linearly regressed to bone mechanical properties for the purpose of comparing the diagnostic utility of BEuTE to that of CuTE, DAFP, and AIR. Since the water reference was not present during equilibrium FID measurements (to avoid confounding off-resonance effects), this quantitation step used water reference signals acquired in separate experiments, which introduced another source of experimental variance but was expected to be negligible (on the order of 5% of the water reference’s signal size (13)).

A Model for Cortical Bone Bound and Pore Water Transverse Relaxation

The model of inhomogenously-broadened and spatially-sequestered pore water is supported by observations of both its long T₂ (≫ 1 ms) and short T₂* (≈ 1 ms), as well as the poor inversion performance of narrow-band AFPs (Fig 4). Thus, the broad pore water NMR spectral line is interpreted as a superposition of chemically-shifted narrow lines that do not exchange significant magnetization with each other on the timescale of MRI measurements. This condition likely arises from expected magnetic susceptibility effects (27), a micro-anatomical pore size distribution (previously linked to the pore water T₂ distribution (15)), and the lack of rapid mixing across spatially-disparate pores. Importantly, at high fields this dictates that pore water is inhomogenously broadened to such an extent that some is likely to exhibit a T₂* similar to that of bound water. As such, the strongly multi-exponential nature of the cortical bone T₂ spectrum—with separable bound and pore water domains spanning several decades in T₂—is not preserved in the T₂* domain, and it will be challenging to quantitatively discriminate bound from pore water using spectroscopic imaging (30,31) or multiple gradient echo schemes adapted to uTE MRI. Additionally, straightforward chemical shift-based discrimination is impractical, given the similarly-broad and spectrally-overlapping bound and pore water lineshapes at high fields—lineshape differences between the two were not readily apparent in a previous study (13). An alternative scheme for pore/bound water discrimination is warranted for clinical and high field cortical bone MRI, and the concept of T₂-filtering bound from pore water with adiabatic pulses is explored herein.

Current Bone MRI Methods: Non-selective Imaging

Most cortical bone MRI to date has utilized broad-band excitation pulses and strategies for soft tissue suppression (6–8,32), but imaging results have not been well characterized with regards to bound vs. pore water contributions. BEuTE and CuTE were duplicated herein and did not exhibit significant bound/pore water discrimination. BEuTE’s poor discrimination (Fig 5B) arises from a mixture of confounding factors, such as i) similar bound/pore water T₂*s that give rise to artifactual fitted signal fractions and ii) off-resonance effects from fat and other species that contribute non-monotonic characteristics to the FIDs and disrupt exponential fitting. Although short and long-T₂* fractions from high field imaging were attributed to bound and free water recently (31), the present findings suggest that such long-T₂* fractions do not capture all of the pore water contributions. We anticipate this will become even more problematic as bone imaging moves to higher fields (e.g. the 7T imaging shown in (36)), and further in vivo studies on this point are merited.

Since the CuTE signal includes both bound and pore water contributions, quantitation was performed with the net water T₁ (weighted average of bound and pore water), similar to the approaches taken by (3,6–8). Despite the observed ≈ 2-fold difference between bound and pore water T₁s, the CuTE signal agreed well with the net water content, showing a strong linear correlation and minimal bias (Fig 6D). Thus, this method is useful for net cortical bone water measurements, which supports the findings of other investigators (7).

AFP Pulses for Bound Water Selection

AFP-CPMG data (Fig. 4) showed that AFP pulses with bandwidths ≥ 2 kHz created a condition of strongly saturated bound water (α^bw≈ 0.1) and well-inverted pore water (α^pw≈−0.8), which generates useful contrast between the two pools. For a variety of AFP pulse parameters and bandwidths ≥ 2 kHz, bone water behavior over a broad range of T₂s followed Bloch equation simulations (Fig. 2) but was not saturated/inverted as strongly as simulations predicted. This discrepancy may arise from unaccounted relaxation effects (e.g. T_1ρ) or from magnetization transfer (37) with a semisolid spin pool (T₂ ≈ 10 μs) that would remain largely unaffected by the AFP pulses herein. However, evaluating such mechanisms is beyond the scope of this study. All AFP pulses with 1 kHz bandwidth still saturated bound water but failed to coherently invert the pore water, which is consistent with the model of homogeneously-broadened bound water and heterogeneously-broadened pore water. Thus, it appears that ≈ 2kHz is the minimum AFP bandwidth (at 4.7T) for effective manipulation of the pore water pool at high fields, and a 3.5 kHz bandwidth was used in the following.

DAFP for Pore Water-Selective Imaging

Incorporating a broadband DAFP pulse into steady-state imaging was found to strongly saturate bound water and result in a signal dominated by pore water (Fig 6B). The assumption that the observed DAFP signal arises entirely from pore water may contribute to overestimation of pore water content (Fig 6E), which is largely a consequence of signal contamination from incompletely saturated bound water and shorter-lived T₂s (≈ 50 μs) from collagen. However, there is still a strong correlation (r² = 0.7) between the DAFP signal and CPMG measures of pore water, even though sample-specific relaxation and AFP efficiency parameters were not included (i.e. population averages were used to scale the signal into proton concentration units). Thus, the DAFP signal is a useful measure of pore water. Unlike the AIR sequence, no prior information (e.g. R₁ estimates) is needed when planning the DAFP sequence timings. However, because of specific absorption rate constraints, the power deposition of DAFP pulses may lengthen the TR of the sequence relative to CuTE. For example, the DAFP sequence can be executed on our 3T clinical scanner with TR ≈ 80 ms, which can be further reduced by using higher-order hyperbolic secant (HSn) pulses (34).

AIR for Bound Water-Selective Imaging

The AIR approach has been successfully shown for general soft tissue suppression in cortical bone MRI (8,32), but its bound/pore water specificity has not been evaluated. Herein, it is shown that signal from an optimized AIR sequence (TR/TI = 300/90 ms) is dominated by bound water contributions and is largely insensitive to pore water (Fig 6C). Sources of bias in the signal quantitation include transverse relaxation during the TE period and magnetization transfer with a semisolids pool during the TI period. However, there was negligible bias, even without sample-specific relaxation or AFP efficiency correction, as seen by a strong correlation to reference-standard bound water measures (r² = 0.91, Fig 6F). Thus, the AIR signal provides a useful measure of bound water.

The high degree of AIR’s bound water selectivity is advantageous, but it requires an estimate of pore water T₁ for optimal IR-nulling. Herein, a single empirically-determined 90 ms TI gave satisfactory pore water nulling across specimens, so a patient-specific estimate of pore water T₁ is not necessary for clinical bound water quantitation. However, since the pore water signal contains a distribution of T₁s, non-nulled pores with T₁s shorter and longer than the mean would be placed in anti-phase during bound water signal acquisition. To maintain this state and minimize pore water contamination, the imaging module in AIR should favor minimal echo and acquisition times.

Correlations to Mechanical Properties

Strong pairwise linear correlations (r² ≈ 0.3–0.7) between various mechanical properties and the AIR and DAPF signals (Fig 7) provide a proof of concept that these strategies hold diagnostic relevance for predicting fracture risk. Importantly, donor-specific measures of bound/pore/net water T₁, T₂, and AFP pulse effects are not needed for mechanical property prediction (population averages were used herein) but may further strengthen correlations if available. The BEuTE fitted signal fractions, which were poor discriminators of bound/pore water, as well as the CuTE signal, which contains a mixture of both bound and pore water, were not found to have statistically significant correlations to any mechanical property, in agreement with our previous findings (18). In that study, with a three-fold-larger bone specimen population, both bound and pore water had similar mechanical correlation strengths. Herein, DAFP pore water showed considerably stronger mechanical correlations than AIR bound water, but the high correlation between the AIR-signal and equilibrium CPMG-derived bound water measures implies that stronger AIR/mechanical property correlations could emerge in a larger population. Additionally, there is likely to be an optimal imaging TE, since TE < 50 μs will introduce matrix-related signals (T₂* ≈ 10 μs, (11,13,17)) that confound pore water estimation, and TE > 50 μs enhances bound/pore water T₂* weighting that may vary across bones in a manner not correlated with mechanical properties.

Finally, we note the possibility of combining any two of the CuTE/AIR/DAFP measurements to determine all three of $S_0^{\mathit{net}},S_0^{bw}$, and $S_0^{pw}$. This follows the premise that $S_0^{\mathit{net}}=S_0^{bw}+S_0^{pw}$, where $S_0^{\mathit{net}}$ is determined from CuTE and $S_0^{bw}$ and $S_0^{pw}$ are determined from AIR and DAFP, respectively. For example, the AIR sequence’s maximum temporal signal-to-noise ratio efficiency, ( $\propto S_{\mathit{AIR}}/\sqrt{TR}$), occurs at TR≈ 500 ms and θ≈ 90° for practical AFP and tissue characteristics (α^bw = 0.1, α^pw = −0.85, $R_1^{bw}=2.9\text{Hz},R_1^{pw}=1.9\text{Hz}$). Such a long TR may be acceptable for 2D imaging, but 3D imaging may require impractically long scan times unless MP-RAGE (38) or similar acquisition schemes are employed to collect several lines of k-space during each TR. However, bound water information can be synthesized from two separate CuTE and DAFP scans in perhaps less time. Alternately, adding a small flip-angle imaging excitation to the AIR sequence immediately following the AFP pulse would provide a measure of pore water (bound water is relatively saturated at this point), and subsequent imaging after the TI period would give the bound water information demonstrated above, providing a complete measure of discriminated bone water in a single sequence. Thus, CuTE/DAFP/AIR sequences serve as building blocks for generating bound, pore, and/or net bone water maps.

Additionally, as an alternative to DAFP, we note that a spin echo measurement with a minimal (≈10 ms) echo time can, in principle, be used to selectively image the long-T₂ pore water (39) while allowing sufficient time for complete bound water T₂ decay, but the broad bandwidths needed to refocus the pore water spins will test the limits of clinical MRI (e.g. peak |B₁| and specific absorption rate safeguards).