Cortical bone porosity measured with micro computed tomography (μCT) correlates significantly with collagen protons fraction from ultrashort echo time magnetization transfer (UTE-MT) MRI modeling

Abstract

Intracortical bone porosity is a key microstructural parameter that determines bone mechanical properties. While clinical magnetic resonance imaging (MRI) visualizes the cortical bone with a signal void, ultrashort echo time (UTE) MRI can acquire high signal from cortical bone thus enabling quantitative assessments. Magnetization transfer (MT) imaging combined with UTE-MRI can indirectly assess protons in the bone collagenous matrix, which is inversely related to porosity. This study aimed to examine UTE-MT MRI techniques to evaluate intracortical bone porosity. Eighteen human cortical bone specimens from the tibial and fibular midshafts were scanned using UTE-MT sequences on a clinical 3T MRI scanner and on a high-resolution micro-computed tomography (μCT) scanner. A series of MT pulse saturation powers (500°, 1000°, 1500°) and frequency offsets (2, 5, 10, 20, 50 kHz) were used to measure the macromolecular fraction (MMF) and macromolecular T2 (T2_MM) using a two-pool MT model. The measurements were performed on 136 different regions of interests (ROIs). ROIs were selected at three cortical bone layers (from endosteum to periosteum) and four anatomical sites (anterior, mid-Medial, mid-Lateral, and posterior) to provide wide range of porosity. MMF showed moderate to strong correlations with intracortical bone porosity (R=−0.67 to −0.73, P<0.01) and bone mineral density (BMD) (R=+0.46 to +0.70, P<0.01). Comparing the average MMF between cortical bone layers revealed a significant increase from endosteum towards periosteum. Such a pattern was in agreement with porosity reduction and BMD increase towards periosteum. These results suggest that the two-pool UTE-MT technique can potentially serve as a novel and accurate tool to assess intracortical bone porosity.

Graphical Abstract

1. Introduction

Cortical bone plays a main role in load bearing and comprises around 80% of human bone mass ^1,2. Intracortical bone porosity is an influential property for bone biomechanics and its fracture risk prediction ^3,4. Haversian canals (10–200 µm), lacunae (1–10 µm), and canaliculi (0.1–1 µm) ^5,6 are the three classes of pores existing in cortical bone, and average intracortical bone porosity may reach up to 20% ^1,2,7. Bone porosity varies with age and various bone diseases such as osteoporosis ⁸.

Cortical bone assessment has been widely performed using x-ray based techniques such as computed tomography (CT) ^1,7,9–15. Magnetic resonance imaging (MRI) based assessment of cortical bone has received great attention to avoid potential harms associated with x-ray based techniques. However, clinical MRI is not able to detect considerable signal of cortical bone because of its very short apparent transverse relaxation time (T2*) ^1,2,16,17.

Ultrashort echo time (UTE) MRI can image cortical bone ^{1,2,7,9–14,18–24} and other tissues with low transverse relaxation times ^1,25,26. With UTE-MRI, signal can be acquired after radiofrequency (RF) excitation, as quickly as allowed by the RF hardware (tens of microseconds), before major decay in transverse magnetization. In addition to morphological imaging, UTE-MRI allows for quantitative assessment of cortical bone.

At least three hydrogen proton pools with different T2* values are present in bone: 1) collagen backbone protons, 2) bound water, and 3) pore water and lipid ^2,7,27,28. The associated T2* values for the aforementioned proton pools, on a 3T MR scanner, are <50 µs, 300–400 µs, and >1 ms, respectively ^1,2,7. The T2* of collagen backbone protons are extremely short and are challenging to be imaged directly with current MRI scanners²⁹.

Magnetization transfer (MT) imaging combined with UTE-MRI has been recently introduced as a technique to indirectly measure protons in collagenous matrix relative to water protons ^{19,23,30–32}. With MT techniques, a high-power saturation RF pulse (such as Fermi type pulse) is used with a defined frequency offset from the water protons’ resonance frequency to saturate mainly protons in collagenous matrix. The saturated magnetization transfers from the collagenous matrix to water protons that can be detected by UTE-MRI. The magnitude of the transferred saturation to water protons correlates with the quantity of collagen protons relative to water protons in the tissue. Complexity of UTE-MT measurements may range from a simple MT ratio ^30,32 to macromolecular fraction (MMF) and T2 (T2_MM) obtained from a two-pool UTE-MT model ^19,23,31,33.

UTE-MT estimation of collagen protons relative to water protons is assumed to be correlated with cortical bone porosity and the mechanical properties of the bone. MT ratio derived from 2D UTE-MT imaging has been shown to be significantly correlated with µCT based cortical bone porosity ³⁰. Higher MT ratios indicate more transferred saturation to the water pool, implying less water and porosity in bone. However, describing collagen content would be challenging based on MT ratios, because the ratios significantly vary for different RF pulse powers and frequency offsets.

In a two-pool UTE-MT model, fraction of collagen protons (i.e., MMF) can be obtained using a set of RF pulse powers and frequency offsets ^19,31,33. MMF is assumed to represent the bone matrix volume, whereas the water pool fraction indicates the total water existing in the bone which may correlate with bone porosity. Thus, the two-pool UTE-MT technique has the potential to diagnose certain bone diseases associated with porosity variation such as osteoporosis. More importantly, for diseases affecting bone collagenous matrix and bone minerals differently, such as osteomalacia ³⁴, the two-pool UTE-MT technique can provide complementary information to bone mineral density (BMD) measurements. Recently, the two-pool UTE-MT technique has been utilized to detect ex vivo fibular bone stress injury induced cyclic loading where the bone collagenous matrix is affected despite an unchanged BMD ²³. MMF demonstrated a significant reduction after the induced partial bone stress injury ²³. Nevertheless, the relationship between UTE-MT measures and intracortical bone porosity needs to be determined prior to investigating the clinical performance of UTE-MT methods.

The purpose of this study was to investigate the relationship between the two-pool UTE-MT measures and intracortical bone porosity as measured using high-resolution micro-computed tomography (µCT). This study helps to highlight the potential applications of UTE-MT methods for assessing intracortical porosity in the human skeleton.

2. Materials and methods

2.1. Sample preparation

Eighteen cortical bone specimens were harvested from fresh-frozen human tibial (n=9, 63±19 years old, 5 women and 4 men) and fibular (n=9, 52±18 years old, 3 women and 6 men) midshafts, provided by a nonprofit whole-body donation company (United Tissue Network, Phoenix, AZ). Bone specimens were cut to 25 mm in length using a Delta ShopMaster layer saw (Delta Machinery, Tennessee, USA).

2.2. UTE-MR imaging

All bone specimens were immersed in phosphate-buffered saline (PBS) for 2 hours at room temperature before the MRI scans. Specimens were placed in a plastic container filled with perfluoropolyether (Fomblin, Ausimont, Thorofare, NJ) to minimize dehydration and susceptibility artifacts. The UTE-MRI scans were performed on a 3T clinical scanner (MR750, GE Healthcare Technologies, Milwaukee, WI) using an eight-channel knee coil for both RF transmission and signal reception. The UTE-MRI scans involved the following two quantitative protocols: A) an actual flip angle - variable TR (AFI-VTR) based 3D UTE-Cones sequence (AFI: TE = 0.032 ms, TRs = 20 and 100, flip angle (FA) = 45˚; VTR: TE = 0.032 ms, TRs = 20, 30, 50, and 100 ms, FA = 45˚, rectangular RF pulse with a duration of 150 µs) for T1 measurement, which is a prerequisite for accurate MT modeling³⁵, and B) a 3D UTE-Cones-MT sequence (Fermi saturation pulse power = 500°, 1000°, and 1500°, frequency offset = 2, 5, 10, 20, and 50 kHz, FA = 7˚, 9 spokes were acquired after each MT preparation; rectangular RF excitation pulse with a duration of 26 µs) for two-pool MT modelling. Details of the 3D UTE-Cones sequence are given in previous studies ^36–38. Field of view (FOV), matrix dimension, nominal in-plane pixel size, and slice thickness were 140×140 mm², 256×256, 0.54×0.54 mm², and 2 mm for tibial specimens, respectively. Fibular specimens are much smaller than tibial specimens, therefore, to improve the resolution for fibular specimens, FOV, matrix dimension, pixel size, and slice thickness were 100×100 mm², 256×256, 0.39×0.39 mm², and 4 mm, respectively. FOVs were selected in the range of used FOVs for in vivo studies. This helps future translational study of cortical bone in human subjects. Also such larger FOVs enabled scanning every few samples together in one container.

2.3. Micro-computed tomography

All eighteen bone specimens were scanned using a Skyscan 1076 (Kontich, Belgium) µCT scanner at 8.78 µm isotropic voxel size. For measuring BMD in addition to bone porosity, specimens were scanned in the presence of two hydroxyapatite phantoms (0.25 and 0.5 gr/cm³). Other scanning parameters were as follows: a 0.05 mm aluminum plus 0.038 mm copper filter, 100 kV, 100 mA, 0.4˚ rotation step, and 5 frame-averaging. µCT scan time was 6 hours.

2.4. Data analysis and statistics

UTE-MT results in one slice at the middle of the specimens were compared with the µCT-based measures in the corresponding number of slices (222 and 444 slices for tibial and fibular specimens, respectively). The comparison between MRI and µCT results was performed within 12 and 4 ROIs for tibial and fibular specimens, respectively. Finally, Pearson’s correlations were calculated between UTE-MT results and µCT-based measures (cortical bone porosity and bone mineral density). Moreover, UTE-MT and microstructural results were compared between different layers of the cortical bone from the endosteum towards the periosteum. Specifically, average values associated with each cortical bone layer were compared with those of other layers using the two-tailed paired student’s t-test. P-values below 0.05 (α=0.05) were considered significant. Multiple comparison correction based on Holm approach, was applied after ordering the calculated p values ascendingly. All statistical analyses were performed using Microsoft Excel (Version 2013, Microsoft Corporation, WA, USA).

ROIs were selected by a medical imaging expert at different cortical bone layers and anatomical sites on the UTE images. This approach for ROI selection provided an adequate range of porosity in bone to examine the presented techniques. Figure 1a shows schematically the selected twelve ROIs in a representative tibia sample at three cortical bone layers (from endosteum to periosteum) and four anatomical sites (anterior, mid-Medial, mid-Lateral, and posterior). Likewise, Figure 1b shows schematically the selected four ROIs in a representative fibula sample at two cortical bone layers and two anatomical sites (medial and lateral).

Figure 1:

Schematics of selected region of interests (ROIs) in UTE-MRI images. (a) Selected twelve ROIs depicted on the UTE-MRI image of a representative tibial bone specimen (Male, 73 years old). (b) Selected four ROIs depicted on the UTE-MRI image of a representative fibular bone specimen (Male, 54 years old).

2.4.1. UTE-MT modeling

The acquired data with the set of MT saturation pulse powers (500°, 1000°, and 1500°) and frequency offsets (2, 5, 10, 20, and 50 kHz) were fitted by a modified rectangular pulse approximation (mRP) approach which was previously described ^19,31,33 . In the two-pool model, cortical bone is assumed to have two different proton pools. The first pool is macromolecular proton pool which has a very broad spectrum or extremely short T2 (~10 us). The second pool is water proton pool which includes both bound and pore water protons. Protons of the two pools in this model are continuously exchanging their magnetizations. If the macromolecular proton magnetization is partially saturated, the acquired water signal intensity decreases due to the magnetization transfer. A two-pool MT model can be built based on the Bloch equation such that the signal in UTE-MT is given as a function of MMF and following MRI properties of the two pools. Considered MRI properties in this model are 1) fully relaxed magnetization of the macromolecular pool (M_0m) and water pool (M_0W), 2) the longitudinal rate constants of macromolecular pool (R_1m) and water pool (R1w), 3) the proton exchange rate constant between the two pools (k), and 4) the loss rate of longitudinal magnetization of the macromolecular pool ^19,31,33. A Gaussian line shape was used to model the macromolecular proton spectrum. The loss of the longitudinal magnetization of the macromolecular pool was also fitted by a Gaussian line shape function ³¹. As a prerequisite for UTE-MT modeling, T1 was measured using a recently developed 3D UTE AFI-VTR method on acquired UTE images with variable TRs for B₁ error correction³⁵.

The UTE-MT analysis was performed offline on the acquired DICOM images using an in-house code written in MATLAB (version 2016, Mathworks, Natick, MA, USA). A Levenberg-Marquardt algorithm was employed for the non-linear least-squares fitting in both UTE-MT modeling and T1 fitting within the earlier selected ROIs (Fig.1).

2.4.2. Bone porosity and mineral density measurements

A single gray level threshold was used for µCT image segmentation to distinguish between bone and pores. The gray level threshold was selected for each set of µCT data using the peaks of gray level histograms and visual inspection of the raw images. Thresholding resulted in a stack of binary images. A porosity pixel map was generated for each bone specimen by superimposing the corresponding number of binary images (222 and 444 slices for tibial and fibular specimens, respectively). Bone mineral density (BMD) was calculated for each voxel by comparing its gray level with the average gray level of the scanned hydroxyapatite phantom with known density (0.25 and 0.5 gr/cm³). BMD pixel map was then generated by averaging the BMD values in the corresponding number of images. Afterwards, the average bone porosity and BMD were calculated within each ROI. Affine image registration was used to propagate the ROIs used for MRI analysis to the µCT data.

3. Results

Figures 2a and 2b show the axial UTE-MRI and μCT images of a representative tibial bone specimen (Male, 73 years old), respectively. Likewise, Figures 2c and 2d, show the axial UTE-MRI and μCT images of a representative fibula bone specimen (Male, 54 years old), respectively. A 20% water phantom is placed in the center of the tibial specimen shown in Figure 2a for calibration purposes and to evaluate bone water content to be followed in future steps. The samples in UTE-MRI images (Fig 2a,c) were cropped for presentation purposes to avoid showing other specimens in the field of view.

Figure 2:

(a) UTE-MRI and (b) μCT images of a representative tibial bone specimen in the axial plane (Male, 73 years old). (c) UTE-MRI and (d) μCT images of a representative fibular bone specimen in the axial plane (Male, 54 years old). A 20% water phantom is shown in the center of the tibial specimen (Fig.2a) for calibration purposes and to evaluate bone water content to be followed in future steps.

Figure 3a illustrates a zoomed μCT image of a representative tibial bone specimen focused on the anterior tibia. Porosity and BMD are measured for two selected ROIs in middle and outer layer of the cortex. Two-pool MT modeling analysis of the selected ROIs are shown in Figure 3b and 3c, repressively, using the three MT saturation pulse powers (500°, 1000° and 1500°) and five off-resonance frequencies (2, 5, 10, 20, and 50 kHz).

Figure 3:

(a) μCT image of a representative tibial specimen (Male, 73 years old) focused on anterior tibia with two selected ROIs in middle and outer layers. Measured porosity (Po) in middle layer (ROI-1.2) is higher than that of outer layer (ROI-1.3). The two-pool MT modeling analyses in (b) ROI-1.2 and (c) ROI-1.3 using three pulse saturation powers (500˚ in blue, 1000˚ in green and 1500° in red) and five frequency offsets (5, 10, 20, 50 kHz). MMF, and T2_MM refer to macromolecular fraction and macromolecular T2, respectively.

Pearson’s correlation coefficients between UTE-MRI markers (T1, MMF, and T2_MM) and μCT measures (bone porosity and BMD) are presented in Table 1. MMF showed moderate to strong correlations with bone porosity (R=−0.67 to −0.73, P-values <0.01) and BMD (R=+0.46 to +0.70, P-values <0.01) as measured with µCT for all bone specimens regardless of the tibia or fibula harvest location⁴⁰. The numbers of data points for correlation calculation were the numbers of analyzed ROIs and were equal to 108 and 36 for tibial and fibular specimens, respectively. T2_MM did not demonstrate significant correlations with bone porosity or BMD (P-values >0.05). T1 showed a moderate and consistent correlation with µCT-based bone porosity for both tibial (R=+0.56) and fibular (R=+0.60) bone specimens. However, only a poor correlation was found between T1 and BMD (R=−0.16 to −0.47, P-values <0.01, Table 1).

Table 1:

Pearson’s correlations between UTE-MT modeling results and μCT-based bone porosity and mineral density measures.

			Two-pool MT modelling
		T1 (ms)	MMF (%)	T2MM (μs)
Porosity (%)	Tibia	0.56	−0.73	0.10
	Fibula	0.60	−0.67	0.49
	All	0.53	−0.70	0.26
BMD (gr/cm3)	Tibia	−0.36	0.70	−0.04
	Fibula	−0.47	0.61	−0.54
	All	−0.16	0.46	−0.29

Figures 4a and 4b demonstrate the scatter plot and the linear regressions of MMF on bone porosity and BMD as measured with µCT, respectively, for all tibial bone specimens. Likewise, Figures 4c and 4d show the regressions of MMF for all fibular specimens. The linear regressions of MMF on bone porosity and BMD, when considering all bone specimens, are shown in Figures 4e and 4f, respectively.

Figure 4:

Significant (p<0.01) correlation between MMF measure and microstructural properties of cortical bone specimens. Scattered plot and linear regressions of MMF on bone porosity considering (a) only tibial, (c) only fibular, and (e) all bone specimens. Scattered plot and linear regressions of MMF measure and bone mineral density considering (b) only tibial, (d) only fibular, and (f) all bone specimens.

Figures 5a-c show MMF (from UTE-MT modeling), bone porosity, and BMD (as measured with µCT) pixel maps for a representative tibial specimen (Male, 73 years old), respectively. Similarly, Figures 5d-f present pixel maps for a representative fibular bone specimen (Male, 54 years old). Regions of higher MMF in tibial and fibular samples (Fig.5a and 5d) corresponded to the regions of lower porosity in the porosity maps (Fig.5b and 5e). To avoid the pixelation effect in the presented maps, MMF, porosity and BMD maps were smoothed using a Gaussian filter in 3×3, 5×5, and 5×5 sub-windows, respectively.

Figure 5:

(a) Macromolecular fraction (MMF), (b) bone porosity, and (c) bone mineral density (BMD) maps of a representative tibial bone specimen (Male, 73 years old). (d) Macromolecular fraction (MMF), (e) bone porosity, and (f) BMD maps of a representative fibular bone specimen (Male, 54 years old).

Table 2 presents the variations of microstructural properties and UTE-MT biomarkers between different selected layers in cortical bone. µCT based porosity showed a significant reduction from the inner layer towards the outer layer of the cortex for both tibial and fibular bone specimens (P<0.01). In contrast, BMD, MMF and T1 showed significant increases from the inner layer towards the outer layer (P<0.01). T2_MM demonstrated no significant variation between selected cortical bone layers (Fig.1). Applying multiple comparison correction based on Holm approach resulted in 0.025 threshold for p values to be considered as significant.

Table 2:

Variation (mean±SD) of bone microstructure and UTE-MT measures between selected cortex layers in tibia and fibula

		μCT- based microstructure			Two-pool MT modelling
		Porosity (%)	BMD (gr/cm3)	T1 (ms)	MMF (%)	T2 (μs)
Tibias	Inner layer	25±14	0.94±0.13	238±24	46±16	15.0±0.4
	Middle layer	11±8	1.07±0.08	227±15	57±11	15.0±0.3
	Outer layer	6±5	1.12±0.08	209±14	65±9	14.9±0.3
	P-value (In vs. Mid)	<0.01	<0.01	<0.01	<0.01	0.22
	P-value (Mid vs. Out)	0.01	<0.01	0.02	<0.01	0.35
Fibulas	Inner layer	19±18	1.21±0.25	250±22	46±12	15±0.7
	Outer layer	6±5	1.35±0.1	227±23	56±13	15±0.5
	P-value (in vs. out)	<0.01	0.01	<0.01	<0.01	0.39

4. Discussion

This study focused on recently developed UTE-MT based measures of collagenous matrix for ex vivo assessment of intracortical bone porosity. UTE-MT modeling techniques can provide an estimation of the collagen content in cortical bone ^19,31,33,39. It is assumed that such estimation of the collagenous matrix content correlates with bone viscoelastic properties such as mechanical toughness. It is hypothesized that the bone porosity and bone volume density (or mineral density) are correlated with the collagen content in bone.

Previous UTE-based assessments of the bone microstructure have been reported via focusing only on water hydrogen pools. The pore water pool has been estimated for its potential correlation with porosity through the following three approaches. First, T2* decay analysis using a bi-component exponential model to distinguish and evaluate the pore and bound water fractions in bone ^2,41. Using this technique, pore water fractions presented good correlations with µCT-based porosity in bone ⁴¹. Second, the signal ratio between the UTE image and an image with longer TE (i.e., 2 ms), so-called porosity index, was used by Rajapakse et el. ¹⁰ to estimate pore water fraction ¹⁰. Porosity index also demonstrated good correlation with µCT-based porosity ¹⁰. Third, UTE imaging after bound water saturation was used to estimate the pore water content through comparing the signal in bone with the signal of an external water reference (i.e., 10% H₂O plus 90% D₂O) ²⁰. Estimated pore water content showed good correlation with µCT-based porosity¹⁴.

This study was the first investigation to draw correlations between the bone microstructural parameters and macromolecular fraction, obtained from a two-pool UTE-MT model. UTE-MT modelling focuses on evaluation of the collagenous matrix of the bone for its potential applications in predicting viscoelastic properties. Chang et al. ³⁰ have shown earlier that the MT ratio from 2D radially acquired MT images correlates significantly with bone porosity. Although, MT ratio and UTE-MT modeling share similar principles, describing collagen content would be challenging based on MT ratios since the ratios significantly vary for different RF pulse powers and frequency offsets.

To validate the correlations between the UTE-MT measures and bone microstructural properties, μCT was used for bone porosity and BMD measurements. From the two-pool UTE-MT modeling, MMF presented strong negative correlation with bone porosity and moderate positive correlation with BMD for ROIs in tibial specimens (Table 1, Fig.5). Similarly, the MMF correlation coefficients in fibular specimens with bone porosity and BMD were moderate to high. Such consistently moderate to high correlations indicated that the MMF enables accurate detection of bone microstructural variations regardless of the type of the long bone. T2_MM did not demonstrate consistently good correlations with either bone porosity or BMD (Table 1). T1 values presented consistently moderate correlations with bone porosity, however its correlations with BMD were poor (Table 1).

The variations of UTE-MT biomarkers and microstructural properties between different selected cortical layers were also investigated through this study (Fig.1). MMF showed a significant increase from inner towards the outer layers of the cortex for both tibial and fibular bone specimens (P<0.01). MMF variations between bone layers agreed with the porosity variation pattern measured by μCT. Porosity significantly decreased towards the outer layer of the cortex for both tibial and fibular bone specimens (P<0.01). BMD and T1 showed significant increases from inner layer towards the outer layer (P<0.01). Such results were in agreement with the multiple previous studies that have shown lower intracortical porosity and pore size at the periosteal side compared with the endosteal side using a variety of methods including high-resolution microscopy, histology, and high-resolution quantitative CT ^42–45.

The results of this study suggested that MMF from UTE-MT modeling is a useful and promising surrogate for assessing human intracortical porosity and BMD particularly for specimens from donors with no known bone disease. This MRI-based technique is a non-invasive, x- ray free, and importantly translatable technique to in vivo studies. Focusing on the collagen matrix of the bone instead of the mineral density would be valuable for evaluating the bone viscoelastic properties. Moreover, certain bone diseases may demonstrate variations in the collagenous matrix prior to changes in bone minerals.

This study was performed on ex vivo bone specimens where the bone marrow and surrounding muscles were removed. A well-designed in vivo study should be performed to examine similar correlations between UTE-MT measurements and bone porosity and BMD. Penetration of bone marrow fat into large pores of the cortex would be challenging for two-pool UTE-MT modeling. Considering three-pool UTE-MT modeling will be a promising path in future studies. Additionally, different fat suppression techniques followed by two-pool MT modeling would be an alternative for future in vivo studies. Optimizing fat suppression to minimize the contamination on water proton signal would be a crucial prerequisite in this path. Furthermore, the correlation of UTE-MT measures with biomechanics of cortical bone is full of interest and remains to be investigated.

5. Conclusion

Two-pool UTE-MT modelling was investigated for its capability to assess intracortical bone porosity in an ex vivo study performed on human tibial and fibular midshafts. MMF obtained from MT modeling, as a quantification for collagenous matrix content, showed strong correlations with bone porosity and BMD. The correlations were consistently high for both tibial and fibular bone specimens, insensitive to the type of long bone. MMF showed a significant increase from endosteum towards periosteum in the cortex for both tibial and fibular specimens. The MMF variation between the cortical bone layers was in agreement with porosity reduction and BMD increase towards periosteum. This study highlighted UTE-MT MRI techniques as useful methods to assess intracortical bone porosity, which may be used in future clinical studies.

Abbreviations:

MR

magnetic resonance

MRI

magnetic resonance imaging

3D

three-dimensional

3D UTE

three-dimensional ultrashort echo time imaging

RF

radio frequency

FOV

field of view

MT

magnetization transfer

MTR

magnetization transfer ratio

ROI

region of interest

TE

echo time

TR

repetition time

μCT

micro computed tomography

CT

computed tomography

MM

macromolecules

MMF

macromolecules fraction

T2_MM

macromolecular T2

M₀

fully relaxed magnetization

R1

longitudinal rate constant

R1obs

apparent longitudinal relaxation rate

k

proton exchange rate constant

FA

flip angle

AFI-VTR

actual flip angle - variable TR

VTR

variable TR

PO

porosity

BMD

bone mineral density

PBS

phosphate buffered saline