Volume-based non-continuum modeling of bone functional adaptation.
BACKGROUND
Bone adapts to mechanical strain by rearranging the trabecular geometry and bone density. The common finite element methods used to simulate this adaptation have inconsistencies regarding material properties at each node and are computationally demanding. Here, a volume-based, non-continuum formulation is proposed as an alternative. Adaptive processes corresponding to various external mechanical loading conditions are simulated for the femur.


RESULTS
Bone adaptations were modeled for one-legged stance, abduction and adduction. One-legged stance generally results in higher bone densities than the other two loading cases. The femoral head and neck are the regions where densities change most drastically under different loading conditions while the distal area always contains the lowest densities regardless of the loading conditions. In the proposed formulation, the inconsistency of material densities or strain energy densities, which is a common problem to finite element based approaches, is eliminated. The computational task is alleviated through introduction of the quasi-binary connectivity matrix and linearization operations in the Jacobian matrix and is therefore computationally less demanding.


CONCLUSIONS
The results demonstrated the viability of the proposed formulation to study bone functional adaptation under mechanical loading.
Wang
Zhengyuan
Z
Medical and Clinical Informatics Group, Bioinformatics Institute, #07-01 Matrix, 30 Biopolis Street, 138671 Singapore. wzhengyuan@gmail.com
Mondry
Adrian
A
D000222:Adaptation, Physiological; D001842:Bone and Bones / Q000166:cytology / Q000502:physiology*; D003198:Computer Simulation; D050723:Fractures, Bone / Q000473:pathology; D008954:Models, Biological; D009929:Organ Size; D013314:Stress, Mechanical; D016474:Weight-Bearing
Am J Anat. 1989 Oct;186(2):186-216
2683714
Anat Rec. 1990 Apr;226(4):414-22
2184696
J Orthop Res. 1990 Sep;8(5):651-61
2388105
J Orthop Res. 1990 Sep;8(5):662-70
2388106
J Biomed Eng. 1990 Sep;12(5):389-97
2214726
J Biomed Eng. 1992 Nov;14(6):483-9
1434570
J Biomech. 1992 Dec;25(12):1425-41
1491020
Bone Miner. 1993 Feb;20(2):167-78
8453332
J Biomech. 1994 Nov;27(11):1389-94
7798290
J Biomech. 1995 Jan;28(1):69-81
7852443
J Biomech. 1995 Apr;28(4):449-59
7738054
J Orthop Res. 1995 Jul;13(4):503-12
7674066
Calcif Tissue Int. 1995 Nov;57(5):344-58
8564797
Bone. 1996 Aug;19(2):143-9
8853858
J Biomech. 1997 Feb;30(2):147-53
9001935
J Biomech. 1997 Jun;30(6):555-63
9165388
J Orthop Res. 1997 Jul;15(4):593-600
9379270
J Biomech. 1987;20(11-12):1095-109
3323201
J Biomech. 2000 Nov;33(11):1349-57
10940393
J Orthop Res. 2001 Sep;19(5):919-26
11562142
J Biomech Eng. 2001 Dec;123(6):613-22
11783733
Clin Biomech (Bristol, Avon). 2002 Feb;17(2):81-8
11832257
J Biomech. 2002 Jul;35(7):951-60
12052397
J Biomech. 2002 Aug;35(8):1101-14
12126669
J Biomech Eng. 2002 Oct;124(5):512-20
12405593
J Biomech. 2002 Dec;35(12):1541-51
12445607
J Biomech. 1987;20(11-12):1135-50
3429459
J Biomech. 1989;22(3):231-44
2722894