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A more recent study indicated that both vertebral stiffness and vertebral strength is almost completely attributable to spongy bone, and the cortical shell plays only a very small role in the weight-bearing capacity [16]. Further biomechanical studies suggested a power–law relationship between apparent bone density ρ and elastic modulus E and maximum compressive stress σmax in the form of (9.1),

	E = ρ A =	Vb	A	σmax = ρ B =	Vb	B
			;			(9.1)
					Vt
		Vt

where Vb is the apparent bone volume, Vt is the total volume, and A and B are experimentally-determined constants [17]. Although a case can be made that microstructural deterioration is reflected in a loss of bone density [18], the deterioration of trabeculae is not isotropic. Rather, deterioration of vertical trabeculae occurs more rapidly than that of horizontal trabeculae [9]. Non-isotropic deterioration may in part explain differences in failure load at the same bone density [19]. Consequently, analysis of bone microstructure remains under active investigation [20].

The focus of recent research has been three-pronged. On the treatment side, scientists are striving to understand the cellular mechanisms that determine the balance between bone-resorbing cells (osteoclasts) and bone-forming cells (osteoblasts), with the long-term goal to influence this balance in favor of bone formation. On the diagnostic side, researchers are striving to obtain information about the bone microarchitecture, because the combined measurement of bone density and microstructural parameters promise to improve the prediction of the fracture load and therefore the individual fracture risk. Finally, basic research efforts are aimed at understanding the complex biomechanical behavior of bone. In all three cases, imaging methods play a central role.

9.2 Bone Imaging Modalities

The clinical modalities for imaging bone include X-ray imaging and the related dual energy X-ray absorptiometry (DEXA), computed tomography, magnetic resonance imaging, and ultrasound imaging.

9.2.1 X-Ray Projection Imaging

X-ray imaging provides excellent bone-tissue contrast, with a spatial resolution of about 30–40 μm. Dual-Energy X-ray Absorptiometry (DEXA) reduces the influence of soft tissue, such as muscle or marrow, which surrounds the bone. Since X-ray attenuation coefficients are energy-dependent, the X-ray intensity is measured at two different energies along the same path to eliminate the contribution of the soft

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tissue. Like conventional X-ray imaging, DEXA is a projection imaging method. It is typically applied to the thoracic or lumbar spine, the femoral neck, or the calcaneus.

The accuracy of the DEXA method is limited because the X-ray beam is polychromatic and because the soft tissue may be composed of muscle and adipose tissue, with varying absorption coefficients between individuals. It is possible to obtain the soft tissue composition from the DEXA image [21] to correct for the error. DEXA is best known for the measurement of bone density. Typical DEXA scanners feature a spatial resolution in the millimeter range, which is not sufficient to image structural details.

9.2.2 Computed Tomography

Computed tomography (CT) is an X-ray based technique that provides crosssectional images of the X-ray absorption coefficient. Unlike projection imaging methods, computed tomography provides bone density as a true volumetric value that can be calibrated in mg/cm3. Accuracy and reproducibility of bone density measurements can be further increased by introducing a calibration phantom into the image. With a phantom that provides representative image values of bone IB and of soft tissue IS, bone density D, calibrated in milligrams of hydroxyapatite per milliliter of bone volume, can be computed from the average image value < I > in the bone region and the known specific density of bone, ρB, through (9.2):

D =	< I > −IS	ρB	(9.2)
	IB − IS

The computed tomography method that provides calibrated bone density values is often referred to as quantitative CT. It is further possible to use a dual-energy principle similar to DEXA to eliminate artifacts caused by soft tissue and bone marrow [22]. Dual-energy quantitative CT is often regarded as the gold-standard for the noninvasive measurement of bone density.

Whereas a low spatial resolution, dominantly in the form of a wide slice thickness, is used for bone density measurement, CT can be used to image the bone microarchitecture when a high resolution is selected. Slice thicknesses of 1 mm with in-plane pixel sizes of 0.2 × 0.2 mm are possible with many clinical CT scanners. Micro-CT scanners are available that feature isotropic voxel sizes in the micron range, but these devices can hold only small samples, and are therefore reserved for biopsies or for in vivo imaging of, for example, the wrist (Fig. 9.1). The interior of the radius and ulna show a clear texture that can be related to the trabecular microarchitecture.

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Fig. 9.1 Cross-sectional Micro-CT image of a human forearm. The voxel size is 70 μm, small enough to make the trabecular structure visible. Note the presence of reconstruction artifacts (the pseudo-texture that is particularly prominent in the air region surrounding the arm) and beamhardening artifacts (straight lines extending from bone edges). Note also the low tissue-tissue contrast that makes tissue structures (blood vessels, muscle, tendons) indiscernible. The scale bar represents 10 mm

9.2.3 Magnetic Resonance Imaging

Magnetic resonance imaging (MRI) is presently not clinically used for imaging bone because of the low water content of bone, which leads to a very weak resonance signal. Figure 9.2 shows a T1-weighted high-resolution spin-echo image of the wrist, acquired with a conventional clinical 1.5T scanner. Inside the ulna and radius areas, texture becomes apparent that is related to the trabecular architecture, analogous to Fig. 9.1. In-plane resolution is approximately 120 μm, with pixels almost twice as large as in Fig. 9.1. The long T1 relaxation of bone marrow makes spongy bone appear bright in this image, although compact bone itself appears dark. Although MRI is not currently a method of choice for bone densitometry, there is a rising popularity of MRI methods in research to examine bone microstructure and its changes in osteoporosis.

9.2.4 Ultrasound Imaging

Ultrasound is widely used for bone densitometry. Sound waves travel much faster in bone than in soft tissue, with the speed of sound being approximately 4,080 m/s in compact bone and 1,600 m/s in muscle tissue [23]. A broadband ultrasound signal is attenuated in tissue in a frequency-dependent manner. Broadband ultrasound attenuation is commonly measured in transverse transmission mode by computing