Development of a compact MRI system for trabecular bone volume fraction measurements



A compact MRI system for measuring trabecular bone volume fraction (TBVF) of the calcaneus was developed with the use of a 0.21 T permanent magnet and portable MRI console. The entire system weighed < 600 kg and was installed in a 2 m × 2 m space. Two cross-sectional spin-echo images of a heel acquired with external reference phantoms (total measurement time = 5 min) were used to quantify the TBVF of the calcaneus. The linearity and reproducibility of the measurements were evaluated by means of proton density-adjusted phantoms. Comparative measurements with quantitative ultrasound (QUS) in groups of healthy female volunteers showed a relatively high positive correlation (R2 = 0.4539, 0.2693) between TBVF and the speed of sound (SOS). These results demonstrate the potential of this new system for measuring bone density. Magn Reson Med 52:440–444, 2004. © 2004 Wiley-Liss, Inc.

Bone mineral density (BMD) measurements are indispensable for the diagnosis and follow-up of osteoporosis. Dual-energy X-ray absorptiometry (DXA) is the current gold-standard method to measure BMD. However, because DXA emits ionizing radiation, it cannot be used repeatedly—especially in young people. Another disadvantage of DXA is that it measures only area density, and cannot provide information about the volume density of bone. Quantitative ultrasound (QUS) has recently become a widely used screening method for osteoporosis because it is relatively inexpensive and does not emit ionizing radiation. However, QUS is essentially a transmission measurement made through a bulk tissue (mainly the heel), and its physical interpretation at the microscopic level is not clear. Thus, for quantitative evaluation of bone status, more precise and noninvasive methods must be developed. MRI is a promising tool for measuring bone density that meets these requirements. At present, three different MRI approaches have been reported (1–7), as described below.

The first such approach, called MR micro-imaging, can spatially resolve trabecular bone from bone marrow using a small voxel (∼100 μm cube) (1–3). This approach is informative and very useful if the MR microscopic images can be acquired in a short period of time. The second approach is based on measuring the relaxation rate Rmath image of transverse nuclear magnetization, which originates from differences in magnetic susceptibility between trabecular bone and bone marrow (4–6). Rmath image yields information on trabecular structure in addition to bone density, because it depends on the direction of the static magnetic field relative to the bone. The third approach is based on quantification of bone marrow proton density in a voxel, which is the reverse quantity of trabecular bone volume fraction (TBVF) in the voxel (7).

To our knowledge, all of the above MRI in vivo bone measurements have been performed with whole-body MRI systems. However, since whole-body MRI is not cost-effective, it would be desirable to have a compact or dedicated MRI system for routine bone measurements in hospitals and laboratories. In this study, we developed a compact MRI system designed for heel imaging, and evaluated it in proton density phantoms and healthy female volunteers (8, 9).


Compact MRI System for Heel Imaging

Figure 1a shows an overview of our MRI system. The system consists of a permanent magnet, gradient coil assembly, RF probe, and portable MRI console (10). The entire system was installed within a 2 m × 2 m space. The specifications of the magnet were as follows: field strength = 0.21 T, gap = 16 cm, homogeneity = 50 ppm over 12 cm dsv, and weight = ∼500 kg. The RF coil was a seven-turn solenoid with an oval cross-section (14 cm × 8 cm) encased in an RF shield box with an oval aperture (21 cm × 8.4 cm), as shown in Fig. 1b. A polystyrene foam pad cut to fit the shape of the heel was inserted into the bore of the RF coil. Four cylindrical oil phantoms were buried in the pad and used as the proton density external reference.

Figure 1.

a: Overview of the compact MRI system for heel imaging. b: RF probe for heel imaging. Aperture size = 21 cm × 8.4 cm (oval), coil cross section = 14 cm × 8 cm (oval), and coil length = 8 cm.

Method for Measuring TBVF


A method was previously presented (7) for quantifying proton density within a trabecular bone. However, in the present work we describe our own approach for measuring the proton density of the calcaneus, because the implementation of this method depends on the configuration and/or specifications of the hardware used.

The image intensity I(x,y) acquired with a spin-echo sequence can be expressed according to Eq. [1], with the exception of the J modulation effect of lipids:

equation image(1)

where k is a constant that is determined by the receiver gain; f(x,y) represents the spatial variation of the image intensity for a uniform sample, which is determined by the inhomogeneity of the static magnetic field, magnetic field gradients, RF magnetic field, and coil sensitivity; ρ(x,y) is mobile proton density; p(x,y) is a factor that reflects the status of the longitudinal magnetization, which is unity for perfect 90° and 180° excitation over the cross-sectional plane; TR* is a time close to the repetition time (TR) and TR when TE = 0; T1(x,y) and T2(x,y) are the T1 and T2 distributions in the cross-sectional plane; and TE is the spin-echo time.

For sequences with a long TR, in which the term exp(–TR*/T1(x,y) can be neglected, and spin-echo decay exp(–TR*/T2(x,y) is corrected by two spin-echo images acquired with two different TEs, the relaxation time-corrected image intensity I0(x,y) is expressed as

equation image(2)

To quantify proton density at the calcaneus, we imaged both a heel and a proton-density standard phantom containing the same plant oil as the external reference phantoms, using two spin-echo sequences with different TEs.

When Ic and Ie are defined as corrected image intensities integrated over the ROIs located in the calcaneus and the external reference phantom, and Ip and Imath image are defined as the corrected image intensities in the proton density standard phantom measured instead of a heel, and the external reference phantom measured with the proton density standard phantom, these can be expressed according to Eqs. [3][6]:

equation image(3)
equation image(4)
equation image(5)
equation image(6)

where k and k′ are constants when the heel and proton density standard phantom, respectively, are measured; fc is f(x,y) averaged over the ROI in the calcaneus, fe is f(x,y) averaged over the ROI in the external reference phantom, and ρc and ρo are proton densities of the calcaneus and plant oil averaged over the ROIs. Equation [3] uses the following approximation:

equation image(7)

where A is the area of the ROI in the calcaneus, because variation of f(x,y) is small around the center of the magnet.

From Eqs. [3][6], the proton density at the calcaneus relative to that of the plant oil can be expressed as

equation image(8)

If we assume that the proton density of the plant oil is the same as that of bone marrow in the calcaneus (11, 12), we can use Eq. [8] to determine the bone marrow volume fraction in the calcaneus. Thus, TBVF can be calculated according to

equation image(9)

Because of the J-modulation effect of the lipid protons of the bone marrow, the spin-echo image intensity is not exactly as described by Eq. [1]. However, because the J-modulation period is nearly constant (∼100 ms) for most lipids in the calcaneus (8), the T2 decay can be approximately corrected by using two spin-echo images with the TEs of the shortest one (e.g., 12 ms) and longer one (e.g., about 100 ms) when most of the J-modulated nuclear spins are nearly refocused.

Imaging Protocol for Proton Density Measurements

The image acquisition protocol consisted of two scans: a reference scan and an object scan. The reference scan was performed with the use of a cylindrical proton density standard phantom (diameter = 82 mm, thickness = 50 mm) containing the same plant oil as the external reference. The imaging sequences consisted of conventional single-slice 2D spin-echo sequences (TR = 1200 ms, TE = 12 ms and 96 ms, slice thickness = 10.5 mm or 15 mm, image matrix = 128 × 128, pixel size = 1 mm × 1 mm). The object scan was performed with the same 2D spin-echo sequences. Since NEX = 1, the total measurement time for one object was about 5 min.

System Evaluation Using Phantoms


We made proton density phantoms by mixing oleic acid and carbon tetrachloride in volume ratios. Because no volume contraction was observed through mixing, these phantoms were used as relative proton density standards. Oleic acid was used because the calcaneal bone marrow is composed almost entirely of lipids (11). We measured the phantoms using the protocol described above; however, to avoid a saturation effect, we determined the TR for each phantom individually.


We measured the 70% volume proton density phantom successively in 10-min intervals using the above protocol to evaluate the reproducibility of the measurements. The scans were repeated 24 times in 4 hr.

Human Volunteer Studies

To evaluate our new method of measurement, we studied three groups of healthy female volunteers (designated as groups A–C). Groups A and B were recruited from our university. Group A consisted of 22 female students (18–23 years old; mean = 19.8 years), and group B consisted of 47 women (24–58 years old; mean = 40 years). Group C consisted of 108 healthy women (12–81 years old; mean = 30.2 years) who voluntarily applied to participate during open-laboratory days.

After the volunteers gave informed consent, MRI and QUS measurements were performed on the right calcaneus. QUS measurements were not performed on group C subjects. In group A, we performed eight successive MRI measurements twice a week over 4 weeks to evaluate the reproducibility of the measurements.

Spin-echo 2D images of the heel (slice thickness = 10.5 mm) were measured by means of the above protocol. The TBVF was computed from the proton density in the 3.5-ml orthogonal region in the calcaneus. The QUS measurements were performed with a commercially available instrument (Achilles 1000+; Lunar Corp., Madison, WI).


Figure 2a–c show 2D cross sections selected from a 3D image data set of a heel acquired with a 3D gradient-echo sequence (TR = 100 ms, TE = 10 ms, FA = 90°, NEX = 1, matrix = 1283, 1-mm3 voxel). The anatomical structure of the calcaneus is clearly visualized. Figure 2d shows a 2D cross section of the same heel acquired with a 2D spin-echo sequence (TR = 1200 ms, TE = 12 ms, NEX = 1, matrix = 1282, 1-mm2 pixel). The square regions of interest (ROIs) displayed over the figure are those used for the proton density measurements (as described in the previous section).

Figure 2.

2D MR images of a heel. a-c: Cross sections selected from a 3D-image data set acquired with a 3D gradient-echo sequence (TR/TE/FA = 100 ms/10 ms/90°). Image matrix = 128 × 128 × 128, FOV = 12.8 cm cube, voxel = 1 mm cube, and data acquisition time = 28 min. a: Sagittal and vertical cross section. b: Vertical cross section perpendicular to the sagittal section. c: Horizontal cross section. The deformed phantom shape is due to nonuniformity of the field gradients. d: Sagittal cross section acquired with a 2D spin-echo sequence (TR/TE = 1200 ms/12 ms). Slice thickness = 15 mm, image matrix = 128 × 128, FOV = 12.8 cm square, pixel = 1 mm square, data acquisition time = 2 min 34 s.

Figure 3a shows measured proton densities of the phantoms plotted against the volume fraction of the oleic acid. The linearity was very high (R2 = 0.9992). Figure 3b shows proton densities of the 70% volume proton density phantom that was successively measured at 10-min intervals. The coefficient of variance (CV; defined as the variance divided by the mean) for these measurements was 0.53%.

Figure 3.

a: Measured proton density plotted against oleic acid volume proportion. b: Repeatedly measured phantom proton density at 10-min intervals.

Figure 4 shows the TBVF plotted against the speed of sound (SOS) measured by the QUS for groups A and B. The R2 values were 0.4539 and 0.2693 for groups A and B, respectively. Figure 4a shows TBVF values averaged over the eight measurements. The relatively high correlations between the TBVF and SOS suggest that a considerable part of the SOS is determined by the TBVF.

Figure 4.

TBVF plotted against the SOS measured with QUS: (a) 22 female students (18–23 years old; mean = 19.8 years), (b) 47 women (24–58 years old; mean = 40 years).

Figure 5 shows the correlation between two series of calcaneal proton density measurements performed across approximately 10 days in group A. This result shows good long-term reproducibility. However, the CV values for each subject computed over the eight serial measurements varied from 2.2% to 5.3%.

Figure 5.

Correlation between two series of proton density measurements performed approximately 10 days apart.

Figure 6 shows TBVF plotted against age for group C. A 15-mm slice thickness was used for these measurements. The results demonstrate a gradual decrease of TVBF with age, in agreement with previous results obtained with other bone density measurement modalities.

Figure 6.

TBVF plotted against age for 108 women (12–81 years old; mean = 30.2 years).


In phantom experiments and human volunteer studies, the current method showed good linearity and reproducibility. Our data were also highly correlated with those obtained with the use of an established method (QUS). However, we believe that further improvements are needed before this new method can be used in routine clinical practice.

First, the long-term reproducibility of the measurements must be established. As stated above, the long-term reproducibility of the calcaneal proton density for each subject varied from 2.2% to 5.3%. These values are sufficient for osteoporosis screening, because the method can easily detect bone density that is one standard deviation (SD), or more than several percentage points, lower than average bone density. However, the long-term reproducibility of our system is not yet adequate for follow-up studies on drug effectiveness in patients with osteoporosis, because such studies require a more accurate detection of bone density. At present, other established modalities, such as DXA and QUS, cannot be successfully applied for this purpose either. To achieve better reproducibility, we must develop more stable hardware (e.g., RF electronics, a gradient power supply, and a permanent magnet) and methods.

Second, we must determine the absolute experimental accuracy of the bone density measurements. We defined the proton density of the plant oil as unity, and calculated the volume fraction of bone marrow at the calcaneus. However, at present, the difference between the proton densities of the bone marrow and the plant oil is not clear. Therefore, further work using a human bone model or sample is needed to determine that relation.

The third needed improvement is to find a best ROI in the calcaneus. Recent studies (13, 14) have reported bone density heterogeneity in the calcaneus. In the present experimental configuration, the ROI in the calcaneus was fixed and confined by the RF magnetic distribution. We are now planning to improve the RF field homogeneity in order to use a wider area for the measurements.

Finally, we would like to comment on the relation between TBVF measured by MRI and SOS measured by QUS. As shown in Fig. 4, we observed relatively high positive correlations between TBVF and SOS. However, we believe there are several points to consider when evaluating these results. First, although TBVF and SOS are closely related, they represent different physical quantities of bone status. Second, in the QUS measurements, we were unable to precisely determine the measurement locations in the calcaneus because the ultrasonic transducer had a wide circular aperture (1 inch), and QUS was a transmission measurement. In contrast, the location was precisely determined in 3D in the calcaneus for MRI. Because QUS is a widely accepted and established method of bone measurement, the high correlation between QUS and MRI suggests, but does not guarantee, the usefulness of the present MRI system, because the QUS method can characterize only one aspect of bone status.


We have developed a compact MRI system for measuring bone density of the calcaneus. We confirmed the validity of the method by phantom experiments and human volunteer studies. The reproducibility of the measurements was sufficient for screening, but not for follow-up, of osteoporosis. Although further improvements are needed to achieve a better CV value, the method has potential because of its flexibility.


This study was performed as a part of the Ground-Based Research Program for Space Utilization promoted by the Japan Space Forum.