A fuzzy logic model of fracture healing

Ament, Christoph; Hofer, Eberhard P.

doi:10.1016/s0021-9290(00)00049-x

Cited by 89 publications

(68 citation statements)

References 12 publications

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“…More recently, these theories were implemented in computer models and tested extensively. [27][28][29] Further progress is significantly hindered by the lack of reliable experimental data, which allow a one-to-one comparison between experimental outcome and simulation result, ideally at different time points during healing. Averaged tissuetype patterns, as presented in this work, will help to sharpen our understanding of which parts in the healing process are more biologically or mechanically controlled.…”

Section: Discussionmentioning

confidence: 99%

Temporal tissue patterns in bone healing of sheep

Vetter

Epari

Seidel

et al. 2010

Journal Orthopaedic Research

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Secondary fracture healing in long bones leads to the successive formation of intricate patterns of tissues in the newly formed callus. The main aim of this work was to quantitatively describe the topology of these tissue patterns at different stages of the healing process and to generate averaged images of tissue distribution. This averaging procedure was based on stained histological sections (2, 3, 6, and 9 weeks post-operatively) of 64 sheep with a 3 mm tibial mid-shaft osteotomy, stabilized either with a rigid or a semi-rigid external fixator. Before averaging, histological images were sorted for topology according to six identified tissue patterns. The averaged images were obtained for both fixation types and the lateral and medial side separately. For each case, the result of the averaging procedure was a collection of six images characterizing quantitatively the progression of the healing process. In addition, quantified descriptions of the newly formed cartilage and the bone area fractions (BA/TA) of the bony callus are presented. For all cases, a linear increase in the BA/TA of the bony callus was observed. The slope was greatest in the case of the most rigid stabilization and lowest in the case of the least stiff. This topological description of the progression of bone healing will allow quantitative validation (or falsification) of current mechano-biological theories. © 2010 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J. Orthop. Res. 28: 1440Res. 28: -1447Res. 28: , 2010 Keywords: bone healing; tissue pattern; osteotomy; animal model; averaged image Secondary fracture healing of long bones proceeds via the formation of a callus. 1-3 The task of the callus is to stabilize the fracture fragments resulting in a reduction of the strains in the fracture area, allowing the bone ends to be united. Usually the process of secondary fracture healing is subdivided into three main phases: the inflammatory phase, the reparative phase, and the remodeling phase. 4 These phases, however, are not well separated in time, and significant overlap can occur between them. During the inflammatory phase, vascular damage leads to hematoma formation. The reparative phase includes revascularization and the formation of fibrous tissue and cartilage, and new bone is formed at the periosteal side of the cortex by intramembranous ossification. [4][5][6] Soft callus bridging occurs via cartilage, which is later transformed into bone by endochondral ossification. During the remodeling phase, lamellar bone replaces woven bone, the callus is resorbed, and finally the original shape of the bone is restored. [7][8][9][10] To understand the progression of the healing process, and in particular the influence of the mechanical environment, a number of animal experiments have been performed. In these experiments, either "static" fixators with different degrees of stability [11][12][13][14] or "dynamic" fixators, which induce micro-movement to stimulate callus formation, 15,16 were used. These experiments d...

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Section: Discussionmentioning

confidence: 99%

Temporal tissue patterns in bone healing of sheep

Vetter

Epari

Seidel

et al. 2010

Journal Orthopaedic Research

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“…Callus growth was incorporated in the model controlled by the proliferation of granulation tissue and realistic healing patterns were obtained. Another approach was followed by Ament & Hofer (2000) who implemented a set of fuzzy logic rules guiding the tissue differentiation using strain energy density as mechanical stimulus. Table 1 summarizes the most important mathematical models of tissue differentiation, mentioning their most important characteristics.…”

Section: Bone Regeneration (A ) Biology Of Bone Regenerationmentioning

confidence: 99%

In silicobiology of bone modelling and remodelling: regeneration

Geris

Sloten

Oosterwyck

2009

Phil. Trans. R. Soc. A.

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Bone regeneration is the process whereby bone is able to (scarlessly) repair itself from trauma, such as fractures or implant placement. Despite extensive experimental research, many of the mechanisms involved still remain to be elucidated. Over the last decade, many mathematical models have been established to investigate the regeneration process in silico. The first models considered only the influence of the mechanical environment as a regulator of the healing process. These models were followed by the development of bioregulatory models where mechanics was neglected and regeneration was regulated only by biological stimuli such as growth factors. The most recent mathematical models couple the influences of both biological and mechanical stimuli. Examples are given to illustrate the added value of mathematical regeneration research, specifically in the in silico design of treatment strategies for non-unions. Drawbacks of the current continuum-type models, together with possible solutions in extending the models towards other time and length scales are discussed. Finally, the demands for dedicated and more quantitative experimental research are presented.

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“…Gardner et al (2000) investigated the healing process in long bone fractures and in oblique fractures. Ament and Hofer (2000) went one step further by simulating the kinetics of the healing process using linear elastic FE simulation in combination with their fuzzy logic model. Lacroix and Prendergast (2002a) and Lacroix et al (2002) assumed a poroelastic nature of the callus and simulated dispersal of the mesenchymal cell as a diffusion process.…”

Section: Introductionmentioning

confidence: 99%

Simulation of fracture healing incorporating mechanoregulation of tissue differentiation and dispersal/proliferation of cells

Andreykiv

Keulen

Prendergast

2007

Biomech Model Mechanobiol

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Modelling the course of healing of a long bone subjected to loading has been the subject of several investigations. These have succeeded in predicting the differentiation of tissues in the callus in response to a static mechanical load and the diffusion of biological factors. In this paper an approach is presented which includes both mechanoregulation of tissue differentiation and the diffusion and proliferation of cell populations (mesenchymal stem cells, fibroblasts, chondrocytes, and osteoblasts). This is achieved in a three-dimensional poroelastic finite element model which, being poroelastic, can model the effect of the frequency of dynamic loading. Given the number of parameters involved in the simulation, a parameter variation study is reported, and final parameters are selected based on comparison with an in vivo experiment. The model predicts that asymmetric loading creates an asymmetric distribution of tissues in the callus, but only for high bending moments. Furthermore the frequency of loading is predicted to have an effect. In conclusion, a numerical algorithm is presented incorporating both mechanoregulation and evolution of cell populations, and it proves capable of predicting realistic difference in bone healing in a 3D fracture callus.

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A fuzzy logic model of fracture healing

Cited by 89 publications

References 12 publications

Temporal tissue patterns in bone healing of sheep

Temporal tissue patterns in bone healing of sheep

In silicobiology of bone modelling and remodelling: regeneration

Simulation of fracture healing incorporating mechanoregulation of tissue differentiation and dispersal/proliferation of cells

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