Techniques for deriving tissue structure from multiple projection dual-energy x-ray absorptiometry

A method for deriving bone properties from images generated by a dual-energy x-ray absorptiometry apparatus having an x-ray source in fixed relation to an x-ray receiver, the source and the receiver moveably mounted to measure attenuation through a subject at a plurality of projection angles, the method comprising:

• receiving first image data comprising pixels indicating bone mineral density projected at a first angle of the plurality of projection angles;
• receiving second image data comprising pixels indicating bone mineral density projected at a different second angle of the plurality of projection angles;
• and
• based on the first image data and the second image data, computing a magnification factor relating distances associated with pixels in the first image data and the second image data to corresponding distances at a bone in the subject.

A method for deriving bone properties from images generated by a dual-energy x-ray absorptiometry apparatus having an x-ray source in fixed relation to an x-ray receiver, both the source and the receiver moveably mounted to measure attenuation through a subject at a plurality of projection angles, the method comprising:

• receiving first image data comprising pixels indicating attenuation of a first photon energy projected at a first angle of the plurality of projection angles;
• receiving second image data comprising pixels indicating attenuation of a second photon energy projected at the first angle;
• receiving third image data comprising pixels indicating attenuation of the first photon energy projected at a different second angle of the plurality of projection angles;
• receiving fourth image data comprising pixels indicating attenuation of the second photon energy projected at the second angle;
• and
• based on the first image data, the second image data, the third image data and the fourth image data, computing a value indicating a bone mineral density for a particular pixel in the first image data.

A method for deriving bone properties from images generated by a dual-energy x-ray absorptiometry apparatus having an x-ray source in fixed relation to an x-ray receiver, the source and the receiver moveably mounted to measure attenuation through a subject at a plurality of projection angles, the method comprising:

• receiving image data comprising pixels indicating bone mineral density projected at a first angle of the plurality of projection angles;
• determining a long axis for a bone in the image data;
• selecting a first set of pixels in the image data substantially along a line segment crossing the bone and perpendicular to the long axis;
• and
• based on the first set of pixels, computing cross sectional moment of inertia.

A method for deriving bone properties from images generated by a dual-energy x-ray absorptiometry apparatus having an x-ray source in fixed relation to an x-ray receiver, the source and the receiver moveably mounted to measure attenuation through a subject at a plurality of projection angles, the method comprising:

• receiving first image data comprising pixels indicating bone mineral density projected at a first angle of the plurality of projection angles;
• receiving second image data comprising pixels indicating bone mineral density projected at a different second angle of the plurality of projection angles;
• receiving third image data comprising pixels indicating bone mineral density projected at a third angle of the plurality of projection angles, the third angle different from the first angle and the second angle;
• and
• based on the first image data, the second image data and the third image data, computing principal moments of inertia for a bone in the subject.

A method for deriving bone properties from images generated by a dual-energy x-ray absorptiometry apparatus having an x-ray source in fixed relation to an x-ray receiver, the source and the receiver moveably mounted to measure attenuation through a subject at a plurality of projection angles, the method comprising:

• receiving first data indicating a plurality of principal moments of inertia for a bone in the subject based on a plurality of images taken at the plurality of projection angles;
• determining a stress on the bone associated with a particular scenario;
• determining a probability of the particular scenario;
• determining a risk of injury based on the probability of the particular scenario, the stress associated with the particular scenario, and the plurality of moments of inertia;
• and
• reporting the risk of injury for presentation to a human operator.

A computer-readable medium carrying one or more sequences of instructions for deriving bone properties from dual-energy x-ray absorptiometry images, wherein execution of the one or more sequences of instructions by one or more processors causes the one or more processors to perform the steps of:

• receiving first image data comprising pixels indicating attenuation through a plurality of known thicknesses of a first two calibration materials at a first photon energy;
• receiving second image data comprising pixels indicating attenuation through the plurality of known thicknesses of the first two calibration materials at a second photon energy;
• determining first conic surface function relating attenuation data from first image data to the plurality of known thicknesses;
• determining second conic surface function relating attenuation data from second image data to the plurality of known thicknesses;
• inverting the first conic surface function and the second conic surface function to determine a pair of thickness functions, each thickness function relating thickness of one calibration material to attenuations from the first image data and the second image data;
• and
• applying the pair of thickness functions with attenuations from image data comprising pixels indicating attenuation through tissue of a subject.

A computer-readable medium carrying one or more sequences of instructions for deriving bone properties from images generated by a dual-energy x-ray absorptiometry apparatus having an x-ray source in fixed relation to an x-ray receiver, the source and the receiver moveably mounted to measure attenuation through a subject at a plurality of projection angles, wherein execution of the one or more sequences of instructions by one or more processors causes the one or more processors to perform the steps of:

• receiving first image data comprising pixels indicating bone mineral density projected at a first angle of the plurality of projection angles;
• receiving second image data comprising pixels indicating bone mineral density projected at a different second angle of the plurality of projection angles;
• and
• based on the first image data and the second image data, computing a magnification factor relating distances associated with pixels in the first image data and the second image data to corresponding distances at a bone in the subject.

A computer-readable medium carrying one or more sequences of instructions for deriving bone properties from images generated by a dual-energy x-ray absorptiometry apparatus having an x-ray source in fixed relation to an x-ray receiver, the source and the receiver moveably mounted to measure attenuation through a subject at a plurality of projection angles, wherein execution of the one or more sequences of instructions by one or more processors causes the one or more processors to perform the steps of:

• receiving first image data comprising pixels indicating attenuation of a first photon energy projected at a first angle of the plurality of projection angles;
• receiving second image data comprising pixels indicating attenuation of a second photon energy projected at the first angle;
• receiving third image data comprising pixels indicating attenuation of the first photon energy projected at a different second angle of the plurality of projection angles;
• receiving fourth image data comprising pixels indicating attenuation of the second photon energy projected at the second angle;
• and
• based on the first image data, the second image data, the third image data and the fourth image data, computing a value indicating a bone mineral density for a particular pixel in the first image data.

A computer-readable medium carrying one or more sequences of instructions for deriving bone properties from images generated by a dual-energy x-ray absorptiometry apparatus having an x-ray source in fixed relation to an x-ray receiver, the source and the receiver moveably mounted to measure attenuation through a subject at a plurality of projection angles, wherein execution of the one or more sequences of instructions by one or more processors causes the one or more processors to perform the steps of:

• receiving image data comprising pixels indicating bone mineral density projected at a first angle of the plurality of projection angles;
• determining a long axis for a bone in the image data;
• selecting a first set of pixels in the image data substantially along a line segment crossing the bone and perpendicular to the long axis;
• and
• based on the first set of pixels, computing cross sectional moment of inertia.

A computer-readable medium carrying one or more sequences of instructions for deriving bone properties from images generated by a dual-energy x-ray absorptiometry apparatus having an x-ray source in fixed relation to an x-ray receiver, the source and the receiver moveably mounted to measure attenuation through a subject at a plurality of projection angles, wherein execution of the one or more sequences of instructions by one or more processors causes the one or more processors to perform the steps of:

• receiving first image data comprising pixels indicating bone mineral density projected at a first angle of the plurality of projection angles;
• receiving second image data comprising pixels indicating bone mineral density projected at a different second angle of the plurality of projection angles;
• receiving third image data comprising pixels indicating bone mineral density projected at a third angle of the plurality of projection angles, the third angle different from the first angle and the second angle;
• and
• based on the first image data, the second image data and the third image data, computing principal moments of inertia for a bone in the subject.

A computer-readable medium carrying one or more sequences of instructions for deriving bone properties from images generated by a dual-energy x-ray absorptiometry apparatus having an x-ray source in fixed relation to an x-ray receiver, the source and the receiver moveably mounted to measure attenuation through a subject at a plurality of projection angles, wherein execution of the one or more sequences of instructions by one or more processors causes the one or more processors to perform the steps of:

• receiving first data indicating a plurality of principal moments of inertia for a bone in the subject based on a plurality of images taken at the plurality of projection angles;
• determining a stress on the bone associated with a particular scenario;
• determining a probability of the particular scenario;
• determining a risk of injury based on the probability of the particular scenario, the stress associated with the particular scenario, and the plurality of moments of inertia;
• and
• reporting the risk of injury for presentation to a human operator.