Method and apparatus for measuring long bone density of small-animals

An apparatus for measuring long bone density of small animals, comprising:

• a phosphor screen or plate of a type that transduces incident ionizing radiation to emitted light;
• a source of X-radiation having an energy level in the range of 10 to 16 Kev;
• a stage for supporting a small animal between the screen or plate and the source;
• a digital camera for capturing light emitted by the phosphor screen or plate from a small animal positioned on the stage and producing a digital X-ray image of a long bone of the animal;
• and
• a computer for receiving the digital X-ray image, the computer comprising:
• means for transforming the digital X-ray image into an X-ray density image;
• means for defining a region of interest of the long bone in the X-ray density image;
• means for scanning at least one row of pixels within the region of interest of the X-ray density image;
• and
• means for conducting a nonlinear least squares analysis of data obtained from the scanning step using a virtual, cylindrical model for the long bone within the region of interest and adjusting values of parameters of the model so as to minimize the chi square of a residual between the data and the model.

A method for measuring long bone density of small animals, comprising steps of:

• providing a phosphor screen or plate of a type that transduces incident ionizing radiation to emitted light;
• positioning a small animal before the phosphor screen or plate;
• exposing the animal to X-radiation having an energy level in the range of 10 to 16 Kev;
• capturing light emitted by the phosphor screen or plate using a digital camera and preparing a digital X-ray image of a long bone of the animal;
• transforming the X-ray image into an X-ray density image;
• defining a region of interest of the long bone in the X-ray density image;
• scanning at least one row of pixels within the region of interest of the X-ray density image;
• and
• conducting a nonlinear least squares analysis of data obtained from the scanning step using a virtual, cylindrical model for the long bone within the region of interest, wherein the cylindrical model is according to the following relationship:
• CASE 1:
• if (abs(x−xin)<Rin), then
• D=2dbone(√{square root over (Rout2−(xout−x)2)}−√{square root over (Rin2−(xin−x)2)})+2dmarrow√{square root over (Rin2−(xin−x)2)}+bx+a
• CASE 2:
• else if (abs(x−xout)<Rout), then
• D=2dbone√{square root over (Rout2−(xout−x)2)}+bx+a
• CASE 3:
• else,
• D=bx+a,
• Wherein
• D=measured X-ray density
• dbone=excess column density of the bone above background column density;
• dmarrow=excess column density of the marrow above background column density;
• Rout=outer radius of the bone
• RoutRin=inner radius of the bone;
• xout=x coordinate of the center of the outer radius of the bone;
• xin=x coordinate of the center of the outer radius of the bone;
• b=slope of linear background density;
• and
• a=intercept of linear background density.

An apparatus for measuring long bone density of small animals, comprising:

• a phosphor screen or plate of a type that transduces incident ionizing radiation to emitted light;
• a source of X-radiation having an energy level in the range of 10 to 16 Kev;
• a stage for supporting a small animal between the screen or plate and the source;
• a digital camera for capturing light emitted by the phosphor screen or plate from a small animal positioned on the stage and producing a digital X-ray image of a long bone of the animal;
• means for transforming the digital X-ray image into an X-ray density image;
• means for defining a region of interest of the long bone in the X-ray density image;
• means for scanning at least one row of pixels within the region of interest of the X-ray density image;
• and
• means for conducting a nonlinear least squares analysis of data obtained from the scanning step using a virtual, cylindrical model for the long bone within the region of interest, wherein the cylindrical model is according to the following relationship:
• CASE 1:
• if (abs(x−xin)<Rin), then
• D=2dbone(√{square root over (Rout2−(xout−x)2)}−√{square root over (Rin2−(xin−x)2)})+2dmarrow√{square root over (Rin2−(xin−x)2)}+bx+a;
• CASE 2:
• else if (abs(x−xout)<Rout), then
• D=2dbone√{square root over (Rout2−(xout−x)2)}+bx+a
• CASE 3:
• else,
• wherein:
• D=bx+a;
• where
• D=measured X-ray density
• dbone=excess column density of the bone above background column density;
• dmarrow=excess column density of the marrow above background column density;
• Rout=outer radius of the bone;
• Rin=inner radius of the bone;
• xout=x coordinate of the center of the outer radius of the bone;
• xin=x coordinate of the center of the outer radius of the bone;
• b=slope of linear background density;
• and
• a=intercept of linear background density.