•
Computed Tomography
Quantification of Bone MineraUzation Using Computed Tomography1 Peter Ruegsegger, Ph.D., Urs Elsasser, M.Sc., Max Anllker, Ph.D, Hanspeter Gnehm, M.D., Hanspeter Kind, M.D., and Andrea Prader, M.D. Computed tomography was used to find a sensitive parameter for bone mineralization. A precision scanning instrument was constructed for determination of the mineral distribution in sections of the forearm. The quality of the reconstructed images allows separate quantification of compact and spongy bone even when gamma rays are used. Computer simulation and measurement of models and macerated human bones showed that under clinical conditions it is possible to quantify spongy bone density within an accuracy of ±2 % . INDEX TERMS: Bones, computed tomography, 4 [8] .1211 • Bones, mineralization (Densitometry, '4[8].1295) • Computed tomography, extremities
Radiology 121:93-97, October 1976
• RABECULAR
bone is claimed to show changes in
thereby maintaining the uncertainty of the measuring position at less than 5 J.L throughout the scanning range. To determine the geometric distribution of the local absorption coefficients in the plane of the scans, the shadowgraphs P(O, k) for each beam direction 0, given as a function of the scan interval k, are convolved with a weighting function g (k) as proposed earlier (10) to give
Tmineralization much faster than cortical bone. This has been inferred from the disproportional loss of bone mass in the metaphyseal region compared to the diaphyseal region of forearm bones after chronic corticosteroid administration (1). In addition, photon absorption measurements at the femoral neck (2) reveal much larger decreases in bone mineral content due to senile osteoporosis than that seen in the long bones (3, 4). Therefore, early detection of changes in bone mineralization calls for a method capable of resolving small alterations in the spongy bone, which in turn implies separate quantification of compact and trabecular bone. A first step in this direction was made by combining bone mineral measurements with estimates of the cross-sectional geometry (5). In this paper we offer a method of determining the mineral distribution in a bone section, based on measurements of the transmission of soft 'Y rays from an isotope source using a precision scanning instrument and a reconstruction technique already employed in the visualization of brain structures (6-8).
conv({), h')
=
L P({), h)' g(k' - k) k
The convolution is then projected back into the so-called reconstruction matrix. The weighting function utilized,
-2 n . N . (4k 2 g(k)
-
1)
k = 1,127 { N===48
=
1
+2
n -N
k === 0 { N===48
was first suggested by Shepp et al. (11). Whereas the total data acquisition time for one cross section is five minutes, the reconstruction calculated off-line with a PDP 11-40 requires somewhat less than two minutes. The result of the computation is a matrix of 128 X 128 local linear absorption coefficients which is then used for quantification of bone mineral distribution. By assigning different gray levels to the matrix elements (pixels) according to their magnitude, the mineral distribution is visualized. Validation of the method used in quantifying bone mineralization involved reconstruction from (a) computersimulated transmission data of mathematically described models, (b) transmission measurements of physical models and (c) transmission measurements of macerated bones. The mathematical and physical models were se-
METHOD
The instrumentation has been described previously (9). A highly collimated beam of 'Y rays from a 125 1 source traverses the object with constant velocity at the section to be analyzed. The photons transmitted through the object are detected with the aid of a sodium iodide crystal, counted during 128 equal time intervals, and stored on tape using a PDP 11-20 computer. After each linear scanning process, the 'Y beam is rotated by 3.75° until the procedure has been carried out 48 times. Linear scanning and rotation are effected by stepping motors which are computercontrolled to assure uniform time and space intervals,
1 From the Institute for Biomedical Engineering, University of Zurich, and the Swiss Federal Institute of Technology (P.R., U.E., M.A.) and the Department of Pediatrics, Kinderspital, University of Zurich (H.G., H.K., A.P.), Zurich, Switzerland. Accepted for publication in March 1976. This work was supported in part by grant 4.0600.72 from the Swiss National Science Foundation. sjh
93
October 1976
PETER RUEGSEGGER AND OTHERS
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Computed Tomography
Quantification of Bone MineraUzation Using Computed Tomography1 Peter Ruegsegger, Ph.D., Urs Elsasser, M.Sc., Max Anllker, Ph.D, Hanspeter Gnehm, M.D., Hanspeter Kind, M.D., and Andrea Prader, M.D. Computed tomography was used to find a sensitive parameter for bone mineralization. A precision scanning instrument was constructed for determination of the mineral distribution in sections of the forearm. The quality of the reconstructed images allows separate quantification of compact and spongy bone even when gamma rays are used. Computer simulation and measurement of models and macerated human bones showed that under clinical conditions it is possible to quantify spongy bone density within an accuracy of ±2 % . INDEX TERMS: Bones, computed tomography, 4 [8] .1211 • Bones, mineralization (Densitometry, '4[8].1295) • Computed tomography, extremities
Radiology 121:93-97, October 1976
• RABECULAR
bone is claimed to show changes in
thereby maintaining the uncertainty of the measuring position at less than 5 J.L throughout the scanning range. To determine the geometric distribution of the local absorption coefficients in the plane of the scans, the shadowgraphs P(O, k) for each beam direction 0, given as a function of the scan interval k, are convolved with a weighting function g (k) as proposed earlier (10) to give
Tmineralization much faster than cortical bone. This has been inferred from the disproportional loss of bone mass in the metaphyseal region compared to the diaphyseal region of forearm bones after chronic corticosteroid administration (1). In addition, photon absorption measurements at the femoral neck (2) reveal much larger decreases in bone mineral content due to senile osteoporosis than that seen in the long bones (3, 4). Therefore, early detection of changes in bone mineralization calls for a method capable of resolving small alterations in the spongy bone, which in turn implies separate quantification of compact and trabecular bone. A first step in this direction was made by combining bone mineral measurements with estimates of the cross-sectional geometry (5). In this paper we offer a method of determining the mineral distribution in a bone section, based on measurements of the transmission of soft 'Y rays from an isotope source using a precision scanning instrument and a reconstruction technique already employed in the visualization of brain structures (6-8).
conv({), h')
=
L P({), h)' g(k' - k) k
The convolution is then projected back into the so-called reconstruction matrix. The weighting function utilized,
-2 n . N . (4k 2 g(k)
-
1)
k = 1,127 { N===48
=
1
+2
n -N
k === 0 { N===48
was first suggested by Shepp et al. (11). Whereas the total data acquisition time for one cross section is five minutes, the reconstruction calculated off-line with a PDP 11-40 requires somewhat less than two minutes. The result of the computation is a matrix of 128 X 128 local linear absorption coefficients which is then used for quantification of bone mineral distribution. By assigning different gray levels to the matrix elements (pixels) according to their magnitude, the mineral distribution is visualized. Validation of the method used in quantifying bone mineralization involved reconstruction from (a) computersimulated transmission data of mathematically described models, (b) transmission measurements of physical models and (c) transmission measurements of macerated bones. The mathematical and physical models were se-
METHOD
The instrumentation has been described previously (9). A highly collimated beam of 'Y rays from a 125 1 source traverses the object with constant velocity at the section to be analyzed. The photons transmitted through the object are detected with the aid of a sodium iodide crystal, counted during 128 equal time intervals, and stored on tape using a PDP 11-20 computer. After each linear scanning process, the 'Y beam is rotated by 3.75° until the procedure has been carried out 48 times. Linear scanning and rotation are effected by stepping motors which are computercontrolled to assure uniform time and space intervals,
1 From the Institute for Biomedical Engineering, University of Zurich, and the Swiss Federal Institute of Technology (P.R., U.E., M.A.) and the Department of Pediatrics, Kinderspital, University of Zurich (H.G., H.K., A.P.), Zurich, Switzerland. Accepted for publication in March 1976. This work was supported in part by grant 4.0600.72 from the Swiss National Science Foundation. sjh
93
October 1976
PETER RUEGSEGGER AND OTHERS
94
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8
(3
i:i:
u.
~
o
7
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