PhD Fekete - SZIE version - 2.2 - Szent István Egyetem

Literature review
2.2. Analytical-mechanical models of squat
2.2.1. Introduction
Mathematical models mean comprehensive tools to expand the possibilities of analysing
complicated structures in any field of science.
The investigation of the musculoskeletal system, like those of any system, usually requires the
development of a model. A model is used to answer some questions about the behaviour of a
system. It may be constructed as a physical apparatus, or alternatively it may be theoretical or
computational.
The ability to devise the best model to answer a specific question is one of the hallmarks of
excellence in scientific investigation. Neither should the model be so complex that the inputs
cannot be measured, nor should it be so simple that the predictions are too obvious. Creating a
model that balances these two aspects requires knowledge of modelling tools, and how they
may be applied [Csizmadia and Nádori, 2003].
Naturally, it also requires judgment and experience. In order to give a hint about the modelling,
five simple but concrete statements can be summarized [Csizmadia and Nádori, 2003], which
will be applied in our further investigations:
1. None of the investigations – theoretical or experimental – should be overemphasised.
Only the proper combination of the two leads to solution.
2. The observed phenomenon can be divided into parts. Useful information can be
gained by only investigating the individual parts and not the complete system.
3. The laws of nature are constant in space, valid in every field, can be summarized in
mathematical formulas, independent respectively of the observer or the state of the
phenomenon. These laws are parts of the nature, not made-up mathematical
formulations.
4. The model is defined by the aim of the investigation as well. The aim of the model –
in the view of the related laws of nature – is to determine the behaviour of the
investigated phenomenon. The knowledge, related to the phenomenon, can only be
expanded by the model results.
5. Through the new models, new information can be gained regarding the phenomenon
in interest, but the obtained results must be always compared to experiments. This is
the adequate way to conclude whether the model is correct or not.
Although, it is not mentioned as an individual statement, another relevant comment has to be
added to the modelling issues. Since a model only follows some major similarity with the
observed phenomenon, eventually it will not be able to describe it entirely. There is always a
range where the model gives a good approximation related to the phenomenon but beyond that,
due to the lack of perfect description, the obtained results are not in agreement with reality.
This is the applicability range of the model. In any case, if a theoretical model is used, this
range has to be appointed.
It is well known, that patellofemoral problems are common causes of failure after total knee
replacement (TKR). Patellar resurfacing implants have often shown loosening or wear of their
polyethylene surfaces [Garcia et al., 2009, Sharkey et al., 2002]. Besides that large increases in
anterior patellar strain have been reported after total knee replacements, suggesting, that joint
replacements may have adverse effects on the mechanics of the extensor mechanism of the knee
joint [McLain et al., 1986, Reuben et al., 1991].
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