PhD Fekete - SZIE version - 2.2 - Szent István Egyetem

Materials and Methods
3.4. Experiments on human subjects
3.4.1. Introduction
In subsection 3.2, the new analytical-kinetical model of the non-standard squat has been fully
described, but as it was mentioned, seven important factors and variables (λ 1 (α), λ 3 (α), λ p , λ t , λ f ,
β(α) and γ(α)) are missing to solve the equations.
Among the above mentioned functions, only β(α) function has been investigated and published
earlier by several authors [Van Eijden et al., 1986, Yamaguchi and Zajac, 1989, Gill and
O’Connor, 1996, Victor et al., 2010], while the λ 1 (α), λ 3 (α) and γ(α) functions have not yet
appeared in other models or publications. Thus, by all means, they have to be determined
experimentally. Regarding the β(α) function, the authors were all in agreement.
The dimensionless constants raise another issue. The length of the patellar tendon (l p ) has
already been investigated in multiple works [Neyret et al., 2002, Lemon et al., 2007, Gellhorn et
al., 2012]. The patellar length is constant in case of healthy knee but shortening appears after
knee surgery in several cases starting from cruciate ligament reconstruction [Dandy and Desai,
1994, O’Brien et al., 1991] to knee arthroplasty [Tanaka et al., 2003, Weale et al., 1999]. The
mechanism of the patellar tendon shortening is currently unclear and it is considered
multifactorial [Noyes et al., 1991, Wojtys et al., 1997, Weale et al., 1999]. For this reason, the
elongation of the tendon is not studied in this thesis, but it is considered constant throughout the
investigations.
Although the patellar tendon length is known, and varies between 4.6 cm and 6.1 cm [Neyret et
al., 2002], no authors have compared this length to the tibial length as a dimensionless patellar
tendon length (Table 3.3). It is clearly possible to take a set of data from one author about the
patellar length and from another author about the length of the tibia, then creating the
dimensionless λ p constant for the mathematical model, but it is a question how adequate or valid
is using and mixing two different sets of data from different human subjects. Therefore, it is
more realistic if the same lengths are measured on each subject, and then the dimensionless
value of λ p is created.
The same problem stands for the two additional dimensionless parameters (λ t , λ f ). The height of
the tibial tuberosity (l t ), which is measured from the tibial axis (or from the averaged tibial
surface) has not been either compared to the tibial length, therefore this ratio can only be
created by using two different data set from different authors. The perpendicular distance
between the line of action of the quadriceps force and the femoral axis (l f ) has the same
problem.
Due to the absence of these data (the lack of dimensionless form), an experimental study is
required, where all these parameters can be measured on human subjects.
In order to place confidence in our measurements, the experimental results will be compared to
the averaged results of other authors from different literatures as follows: if author A published
results about l p and author B published results about l 10 , then from their results an averaged
λ pvalid can be created, which will be compared to the obtained experimental results.
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