Abstract：
:We compare the predictions of the differential equation form of a class of bone-density stress adaptation models with their associated discrete-time computational algorithms. Although our considerations apply to the class of adaptation models based on bulk or apparent bone-density remodeling, we focus attention on a particular model in this class, a model employed by Weinans et al. [Trans. Orthop. Res. Soc. 14, 310 (1989); Trans. First World Congress of Biomechanics, Vol. II, p. 75 (1990)]. We show that the discrete-time computational algorithm of that stress adaptation model has a well-known chaos mechanism for stress values of practical interest. Further, we obtain a condition on the discrete-time step that prevents the transition to chaos, and conditions that insure monotonic convergence. This chaos mechanism is only present in the discrete-time computational algorithm; we show that the corresponding differential equation form of the bone-density stress adaptation model is smooth, monotonic and nonchaotic.
journal_name
J Biomechjournal_title
Journal of biomechanicsauthors
Cowin SC,Arramon YP,Luo GM,Sadegh AMdoi
10.1016/s0021-9290(05)80007-7subject
Has Abstractpub_date
1993-09-01 00:00:00pages
1077-89issue
9eissn
0021-9290issn
1873-2380pii
S0021-9290(05)80007-7journal_volume
26pub_type
杂志文章abstract：:Among the most common causes of upper extremity fracture is a fall on the outstretched hand. Yet few data exist on the biomechanical factors which affect injury risk during this event. In this study, we measured impact forces during low-height (0-5 cm), forward falls onto the outstretched hand, and found that these ar...
journal_title：Journal of biomechanics
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doi：10.1016/0021-9290(95)00098-4
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pub_type： 杂志文章
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journal_title：Journal of biomechanics
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journal_title：Journal of biomechanics
pub_type： 杂志文章
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journal_title：Journal of biomechanics
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journal_title：Journal of biomechanics
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更新日期：1998-03-01 00:00:00
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journal_title：Journal of biomechanics
pub_type： 杂志文章
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pub_type： 杂志文章
doi：10.1016/s0021-9290(99)00112-8
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journal_title：Journal of biomechanics
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journal_title：Journal of biomechanics
pub_type： 杂志文章
doi：10.1016/0021-9290(93)90057-l
更新日期：1993-08-01 00:00:00
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journal_title：Journal of biomechanics
pub_type： 杂志文章
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更新日期：1991-01-01 00:00:00
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journal_title：Journal of biomechanics
pub_type： 杂志文章
doi：10.1016/j.jbiomech.2012.04.022
更新日期：2012-06-26 00:00:00
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journal_title：Journal of biomechanics
pub_type： 杂志文章
doi：10.1016/j.jbiomech.2016.09.035
更新日期：2016-11-07 00:00:00
abstract：:Bone is a dynamic tissue which, through the process of bone remodeling in the mature skeleton, renews itself during normal function and adapts to mechanical loads. It is, therefore, important to understand the effect of remodeling on the mechanical function of bone, as well as the effect of the inherent time lag in th...
journal_title：Journal of biomechanics
pub_type： 杂志文章
doi：10.1016/s0021-9290(00)00221-9
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journal_title：Journal of biomechanics
pub_type： 杂志文章
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journal_title：Journal of biomechanics
pub_type： 杂志文章
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journal_title：Journal of biomechanics
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更新日期：2013-01-04 00:00:00
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journal_title：Journal of biomechanics
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journal_title：Journal of biomechanics
pub_type： 杂志文章
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更新日期：1998-05-01 00:00:00
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journal_title：Journal of biomechanics
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journal_title：Journal of biomechanics
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更新日期：1996-01-01 00:00:00
