The double Fourier decomposition of the sinogram is obtained by first taking the Fourier transform of each parallel -ray projection and then calculating the coefficients of a Fourier series with respect to angle for each frequency component of the transformed projections.

No abstract

The stability of union following the conservative treatment of tibial shaft fractures has been examined in 157 patients by a non-invasive method. With this technique it is possible to ascertain when the fragments are united and whether the strength of union is sufficient for full weight-bearing without protection. The mean time required for union was 14.0 +/- 9.2 weeks, with a range of 4 to 48 weeks. In 31 cases union was judged to be delayed; in 22 of these, intended operations were avoided because repeated stability determinations indicated progressive union. Of nine fracture variables examined, the only ones which significantly affected the time required to achieve union were the age and the weight of the patient. Irrelevant factors were the type and level of the fracture, the energy of trauma, soft-tissue injury and the presence of multiple injuries.

(1977) Knee instability and tibial osteotomy aclinicalstudy, Acta Orthopaedica Scandinavica, 48:1, 95-98,

The stability of the union in tibial shaft fractures was followed by repeated non-invasive radiographic measurement of a deflection induced in the area of the fracture. By means of a Shift Comparator the difference in the angle between the two fragments before and during application of the deflecting force can be measured. The relative measure of the strength of the union is furnished by a quantity, the deflection ratio, which is based on the quotient of the induced deflection by the magnitude of the applied bending moment. When this ratio falls below a certain value the union is considered to be stable enough for full weight bearing during walking. A plot of the deflection ratio against time, with logarithmic scales on both axes had a negative slope and was more or less linear. This graph can serve as an aid in detecting the course of union, in deciding when the cast should be removed, and in detecting any irregularity in the process of union. In the management of 207 fractures of the tibial shaft 508 such deflection measurements were performed.