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Trabecular bone strength at the human os calcanei
EVALUATION OF FRACTURE DYNAMICS STABILISATION BY STEREORADIOGRAMMETRY V.Nikolic, T.Fiedler, V.Rabic, D.Sajko, B.Hranilovid the University of Zagreb, 41000 Zagreb, Department of Anatomy “D.Perovid” Salata 11, Yugoslavia Teaching Hospital for Traurnatology Zagreb
Department of Photogrammetry, Faculty of Geodesia,University of Zagreb. Bone fragment or internal fixation alenthesis (screws) relative motion in different periods of bone fracture healing was evaluated by the method of analytical stereoradiogranunetry (AsR) on 20 injured patients. The ASR method, based on X-rays stereomeasuring in a mathematical model, enables accurate and objective determination of spatial co-ordinates of a discrete number of points, which are defined not only in space but also in time. For reconstruction of the 3-D model a two-dimensional image coordinate is determined by the arbitrary orthogonal coordinate system. The referent coordinate system is in the form of a spatial grid made of perspex with lead markers of 0.8 mm in diametar. The markers in the patient were either infixed into the fracture fragments during internal fixation surgery or they were parts of alenthesis (points of the screws). Control of mobility in two time periods can demonstrate the changes in mobility within the time interval, especially within all 3-axis coordinates. Two controls enable only linear graphical presentation of the changes, while at least 3 controls
are
necessary
to
show
nonlinear
changes
in
fracture
stability.
TRABECULAR BONE STRENGTH AT THE IIUHAN OS CALCANEI. Niels Christian Jensen, tars Madsen and Frank Linde
Biomcchanics Laboratory, Orthopaedic Hospital, University of Aarhus, Denmark. Theobjectofthis study wastodescribe the bone strength pattern and the relation between bone strength parameters at the human OS calcanei, a bone which is exposed to complex loading conditions. Nineteen human OS calcanei were used for the penetration test (mean age 75 years, range 50 to 87 A pointed needle, with a 90 degree cone, a 2.5 mm projected diameter years). was forced into the cancellous bone. A depthforce curve was obtained. Strength data are reported as: average penetration strcnqth = force avcraqed over the 1 mm intervals/projected area of the measurinq profile. Twenty specimens were used for the compression test (mean age 73 years, ranqe 42 to 93 years). Cuts was done to produce the bone slices where from bone cylinders (diameter 7.3 mm) could be obtained. Straincontrolled non-destructive compression test was done. Afterwards they tested until failure. Mean penetration strength at facirs cuboidea at level one was 40 MPa,at faciestalaris posterior 65 MPa and at tuber calcanei it was 20 MPa the corresponding values of the compression test was for ultimate strength 8.9 MPa, 7.4 MPa and 3.2 MPa. There was a statistically significant reduction in bone strength with depthat facies cuboidca and at facies talaris posterior but not at the tuber calcanei. The strength ratio between these measurements indicates that a major part of the load is placed on the facies talaris posterior of the subtalar joint.
C&JOINT DATA SMOOTHING USING SPLINES Les 5. Jennings and Graeme A. Wood Departments of Mathematics and Human Movement Studies The University of Western Australia, Nedlands, W.A. 6009, AUSTRALIA A spline procedure for the simultaneous smoothing of multivariate time series data is presented which can provide a coherent and logically consistent basis for the derivation of kinematic information from 'noisy' position-time data. It is shown how 3-dimensional coordinate data for two adjacent joints in a bio-kinematic link system can be smoothed in the one operation. Furthermore, the smoothing can be constrained such that a known distance is required between adjacent points, even though each may have independently specified accuracy. The mathematical basis of this approach is outlined, and graphical illustration is given of its superiority over conventional univariate smoothing. The multivariate approach has been programed in FORTRAN-77 and uses special matrix techniques to invert the 7n + 2 order matrix in Newton's method, thereby providing a computational speed approximately the same as would be required for six univariate smoothing operations.
Department of Photogrammetry, Faculty of Geodesia,University of Zagreb. Bone fragment or internal fixation alenthesis (screws) relative motion in different periods of bone fracture healing was evaluated by the method of analytical stereoradiogranunetry (AsR) on 20 injured patients. The ASR method, based on X-rays stereomeasuring in a mathematical model, enables accurate and objective determination of spatial co-ordinates of a discrete number of points, which are defined not only in space but also in time. For reconstruction of the 3-D model a two-dimensional image coordinate is determined by the arbitrary orthogonal coordinate system. The referent coordinate system is in the form of a spatial grid made of perspex with lead markers of 0.8 mm in diametar. The markers in the patient were either infixed into the fracture fragments during internal fixation surgery or they were parts of alenthesis (points of the screws). Control of mobility in two time periods can demonstrate the changes in mobility within the time interval, especially within all 3-axis coordinates. Two controls enable only linear graphical presentation of the changes, while at least 3 controls
are
necessary
to
show
nonlinear
changes
in
fracture
stability.
TRABECULAR BONE STRENGTH AT THE IIUHAN OS CALCANEI. Niels Christian Jensen, tars Madsen and Frank Linde
Biomcchanics Laboratory, Orthopaedic Hospital, University of Aarhus, Denmark. Theobjectofthis study wastodescribe the bone strength pattern and the relation between bone strength parameters at the human OS calcanei, a bone which is exposed to complex loading conditions. Nineteen human OS calcanei were used for the penetration test (mean age 75 years, range 50 to 87 A pointed needle, with a 90 degree cone, a 2.5 mm projected diameter years). was forced into the cancellous bone. A depthforce curve was obtained. Strength data are reported as: average penetration strcnqth = force avcraqed over the 1 mm intervals/projected area of the measurinq profile. Twenty specimens were used for the compression test (mean age 73 years, ranqe 42 to 93 years). Cuts was done to produce the bone slices where from bone cylinders (diameter 7.3 mm) could be obtained. Straincontrolled non-destructive compression test was done. Afterwards they tested until failure. Mean penetration strength at facirs cuboidea at level one was 40 MPa,at faciestalaris posterior 65 MPa and at tuber calcanei it was 20 MPa the corresponding values of the compression test was for ultimate strength 8.9 MPa, 7.4 MPa and 3.2 MPa. There was a statistically significant reduction in bone strength with depthat facies cuboidca and at facies talaris posterior but not at the tuber calcanei. The strength ratio between these measurements indicates that a major part of the load is placed on the facies talaris posterior of the subtalar joint.
C&JOINT DATA SMOOTHING USING SPLINES Les 5. Jennings and Graeme A. Wood Departments of Mathematics and Human Movement Studies The University of Western Australia, Nedlands, W.A. 6009, AUSTRALIA A spline procedure for the simultaneous smoothing of multivariate time series data is presented which can provide a coherent and logically consistent basis for the derivation of kinematic information from 'noisy' position-time data. It is shown how 3-dimensional coordinate data for two adjacent joints in a bio-kinematic link system can be smoothed in the one operation. Furthermore, the smoothing can be constrained such that a known distance is required between adjacent points, even though each may have independently specified accuracy. The mathematical basis of this approach is outlined, and graphical illustration is given of its superiority over conventional univariate smoothing. The multivariate approach has been programed in FORTRAN-77 and uses special matrix techniques to invert the 7n + 2 order matrix in Newton's method, thereby providing a computational speed approximately the same as would be required for six univariate smoothing operations.