Comparison with previous work and contributions to knowledge

Comparison with previous work

The findings of this thesis on the anterior/posterior equilibrium and stability of the

knee were compared to previous findings in sections 5.1 and 5.2 of Chapter 5. The

nonlinear quasi-static equilibrium equations that were used to develop models on

the anterior/posterior stability of the knee, in this thesis, were found to be

consistent with previous research findings. Also, the stability results of this thesis

were found to be consistent with real-life observations on the stability of knees that

have prosthetic articulations.

Contributions to knowiedge

The major set-backs of the three previous attempts at determining knee stability

analytically that were reviewed in section 1.3 of Chapter 1, have now been

overcome. In this thesis stability has been dealt with directly, not a knee stability-

related parameter of the type defined by W alker (1982). Also, in this thesis,

articulations, ligaments, and the combined influence of muscle forces and external

forces were modelled; in contrast to the work of Delp et al. (1995) which involves

articulations and a dislocation safety factor only. Although the work of Delp et al.

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structures (Tuma 1969), it has been shown to be of highly limited scope due to

reasons stated in section 1,3 of Chapter 1.

Furthermore, by means of the approach employed in subsection 5.2.2 of Chapter

5, numerical data can now be provided for rating the relative stability of a given

knee. Given the empirically-obtained force versus curve of a knee, the lowest

value of anterior/posterior stiffness Kap can be measured and this can be denoted

as K a p .io w e s t- Next, the knee can be considered to be subjected to a distractive

inferior/superior femorotibial load F in f./s u p . and an anterior/posterior drawer force

Fap. Then, with the aid of validated mathematical models, the limiting values of

loads F in f ./s u p . and Fap that will just allow anterior/posterior buckling of the

particular knee to occur, can be calculated; and these can be denoted as

F in f./s u p .b u ck iin g and F a p .b u c k lin g respectively. In this manner, the relative stability of

a given knee can be rated in terms of the magnitudes of Kap.iow est» f"inf./su p.b ucklin g

and Fap .buckllng-

In addition to the areas identified above, contributions to the knowledge of the

stability and instability of the knee have also been made in the following areas.

The shortcomings of previous orthopaedic notion of knee stability that were

pointed out in section 1.3 of Chapter 1 have been avoided in this work, by

employing well tested scientific methods on the stability of systems.

Concerning clinical knee testing techniques, a link has now been established

between excessive anterior/posterior laxity of the knee and the occurrence of

anterior/posterior instability of the knee during activities of daily living. This link

has been established by means of the anterior/posterior equilibrium equations,

anterior/posterior stiffness equations, and associated graphical results of Chapters

The analytical stability models of this thesis can be used to system atically

establish how designers of prosthetic components, surgeons, physiotherapists and

the mode of usage of the knee, can contribute to the prevention of

anterior/posterior instability of the knee. This can be done by studying the detailed

form of the equation that describes the anterior/posterior stiffness of the knee

(equation 3.30a, 3.31a and 3.32a).

Concerning research-based empirical knee stability studies, the link between the

anterior/posterior stiffness, force versus deflection characteristics and stability of

knees that have prosthetic articulations; has now been established by means of

empirically validated analytical equations (sections 5.1 and 5.2 of Chapter 5).

Also, it has now been shown that the overall stiffness of the system constituted by

the knee and its inputs can be positive, negative or zero; not just positive as

commonly presented in previous work. In addition, by means of knee stability

models it is now possible to show how knee stability is simultaneously affected by

several factors such as; gravitational forces, elastic stiffness, and load-dependent

stiffness. It is also possible to show how these factors are in turn determined by

the system 'constants', configuration variables and input load-parameters of the

knee. In this thesis, the knee was positioned and loaded in a manner that can be

representative of what happens during a vast number of critical activities of daily

living such as standing, seating, walking, squatting, stooping, and stair-climbing;

unlike the 'seated patient' approach adopted in most previous stability-related

studies.

The limitations of empirical knee stability studies that were identified in section 1.3

of Chapter 1 have now been bypassed by the combined use of analytical and

empirical techniques.

Lastly in this work, by means of analytically explicit models and a unified set of

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knees that have prosthetic articulations and other aspects of the mechanical

behaviour of such knees; namely the kinematic constraint, elastic potential energy,

quasi-static force (and torque) versus deflection curves, and stiffness.