Mathematical modeling of proximal femur geometry and bone mineral density
Mesut Taştan1, Özgür Çelik2, Gerhard-Wilhelm Weber3, Bülent Karasözen4, Feza Korkusuz5
04Department of Physical Education and Sports, 4Institute of Applied Mathematics and
Department of Physical Education and Sports, Institute of Applied Mathematics and Department of Mathematics, Ankara
1Department of Mathematics, University of Texas, Arlington, USA
2Middle East Technical University, Faculty of Education, Ankara
3Middle East Technical University, Institute of Applied Mathematics, Ankara
5Department of Physical Education and Sports, Institute of Applied Mathematics and Department of Mathematics, Ankara
Keywords: Bone density; densitometry, X-ray/methods; femur neck; hip fractures/physiopathology; models, theoretical; osteoporosis; risk factors.
Objectives: Bone mineral density measured by dual energy X-ray absorptiometry is a major determinant of proximal femoral fractures. In former studies, researchers considered the hip axis and femoral neck length as predictors of fracture risk and the width of the femoral neck was not considered. In this study, various functional relationships between density, length, and width were assessed using analytical models and numerical tests. Materials and methods: Fifty-eight healthy sedentary university students (age range 18 to 25 years) participated in the study. Bone mineral density was measured by dual energy X-ray absorptiometry in five rotation positions, namely external 30°, external 15°, neutral 0°, internal 15°, and internal 30°. The length and width of the femoral neck was measured in each position. Three mathematical models were developed and assessed. Least squares parameter estimation was used and errors of these models were assessed.
Results: Linear mathematical models demonstrated the importance of the neck width measurements in assessing fracture risk.
Conclusion: Our results suggest that femoral neck width is important and should be regarded as a risk factor when appropriate formula is used.