3.1 Physical Principles of Dual-Energy X-Ray Absorptiometry

Describe what the detector measures

Dual-energy X-ray absorptiometry (DXA) measures the transmission of two different X-ray spectra through the patient. Bone mineral and soft tissue change the transmitted signal differently as photon energy changes. The scanner uses those differences and its calibration to estimate bone mineral mass within the projected image.

For a narrow monoenergetic beam passing through a uniform material with negligible detected scatter, the Beer–Lambert model is

Here $I_0$ is the incident intensity, $I$ is the transmitted intensity, $\mu$ is the linear attenuation coefficient in cm⁻¹ and $x$ is path length in cm. The exponent is dimensionless. Writing the mass attenuation coefficient as $\mu/\rho$ in cm²/g and the areal mass as $M=\rho x$ in g/cm² gives $I=I_0e^{-(\mu/\rho)M}$. Attenuation includes photons absorbed and photons scattered out of the primary beam.

Photoelectric absorption removes the incident photon and ejects a bound electron. Its contribution is sensitive to elemental composition and increases at lower energies away from absorption edges. This helps distinguish mineral-rich bone from soft tissue. Compton scattering changes the direction and energy of a photon and transfers energy to an electron. Its contribution per unit mass relates to the number of electrons per gram and becomes relatively more important as energy rises in the diagnostic range. Coherent scattering can also contribute. Actual attenuation coefficients depend on photon energy and tissue composition. A single atomic-number power or fixed bone-to-soft-tissue contrast ratio cannot predict both spectra.

Solve a simplified two-basis measurement

Let $A_L=\ln(I_{0,L}/I_L)$ and $A_H=\ln(I_{0,H}/I_H)$ be the logarithmic attenuations at low and high energies. Let $b$ and $s$ stand for the bone and soft-tissue mass attenuation coefficients at each energy. In a two-basis model,

The unknowns $M_B$ and $M_S$ are the projected bone and soft-tissue mass per area. Multiply the second equation by $R_S=s_L/s_H$ and subtract to cancel the soft-tissue term.

The denominator must differ from zero. If both materials have the same low-to-high attenuation ratio, the measurements cannot separate the two contributions. As a worked example, use illustrative coefficients $b_L=0.80$, $b_H=0.35$, $s_L=0.25$, $s_H=0.20$ in cm²/g, with measured log attenuations of 1.14 and 0.68. Then $R_S=1.25$ and the estimated bone areal mass is $(1.14-1.25\times0.68)/(0.80-1.25\times0.35)=0.80$ g/cm². Substituting gives $M_S=2.0$ g/cm².

Commercial beams contain distributions of energies. Lower-energy photons are preferentially attenuated along the path, changing the transmitted spectrum. The ideal equations describe the separation principle. Commercial systems account for spectra and beam hardening with instrument-specific calibration. They also need assumptions about the soft tissue overlying bone. Two energy measurements cannot independently solve three unknown areal masses for mineral, fat and lean tissue in the same pixel. Estimated composition in nearby soft tissue helps model the overlying tissue. Nonuniform fat distribution and major body-composition change can bias measured BMD, with magnitude and direction depending on the site and setup.

Distinguish tube potential and photon energy

A tube potential in kilovolts describes electron acceleration and bounds the maximum bremsstrahlung photon energy in keV. For example, a 100 kV tube can produce photons up to about 100 keV. The beam includes a range of lower energies. Neither the tube voltage nor a filter's K edge alone specifies the average photon energy. Beam filtration changes the energy distribution and therefore its penetrating ability. A quality-control measurement such as half-value layer describes penetration by measuring the thickness of a specified material needed to halve air kerma under defined conditions. Compare the same beam and acquisition settings when using that measurement.

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