Métodos de representación del modelo 3D facial

The following conclusions can be drawn from the work presented in this thesis.

A knee that has prosthetic articulations will be of stable anterior/posterior

equilibrium if its total anterior/posterior stiffness is positive. The factors that

determine the anterior/posterior stability of the knee are the configuration

variables, input load-parameters, and ‘constants’ of the system constituted by

the knee and its inputs.

The configuration variables that determine the anterior/posterior stability of

knees that have prosthetic articulations are the flexion/extension angle, the

sagittal femoro-tibial (or femoro-meniscal) contact angle, and the

anterior/posterior displacement of the meniscal bearings (or plastic tibial-insert)

relative to the tibia.

The input load-parameters that determine the anterior/posterior stability of a

knee that has prosthetic articulations can be stated as the anterior/posterior

force, the inferior/superior force, and the flexion/extension moment that act on

the femur relative to the tibia (or on the tibia relative to the femur).

The system ‘constants’ that determine the anterior/posterior stability of a knee

that has prosthetic articulations can be classified as articular system ‘constants’

and ligament-based system ‘constants’.

The articular system ‘constants’ that can determine the anterior/posterior

stability of a knee that has prosthetic articulations are the femoro-tibial (or

femoro-meniscal) conformity ‘constant’, the femoro-tibial inferior/superior

spacing, and three geometrical constants that describe the tangential blending

of two circular arcs, to create the sagittal profile of the femoral articular

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The ligament-based ‘constants’ that determine the stability of the knee are the

coordinates of the centre of insertion of each ligament fibre into the tibia,

relative to a tibia-based coordinate frame; and the coordinates of the centre of

insertion of each ligament fibre into the femur, relative to a femur-based

coordinate frame.

The manner in which each of these factors determine the anterior/posterior

stability of knees that have prosthetic articulations have been established by

means on analytical models.

1. The stability of a knee that has prosthetic articulations can worsen as the

flexion angle reaches the 15 to 25 deg. range of flexion, and as the flexion

angle exceeds about 60 deg.

2. Anterior/posterior displacement of the femur away from an initial equilibrium

position enhances the anterior/posterior stability of the knee.

3. Increasing the sagittal conformity of the femorotibial (or femoro-meniscal)

articular surfaces improves the degree of stability of the knee. Increasing

the inferior/superior spacing of the femoral and tibial transverse axes of the

knee by just 2mm, can enhance the stability of the knee.

4. The membership and physical attributes of the set of functional ligaments

that exist within the knee and the activity of each of the ligaments, can

influence the stability of the knee. The stability characteristics of the knee

can be worsened by a 1 mm increase in the unstretched-length of a knee

ligament, and it can also be worsened by a decrease in the stiffness

coefficient or stiffness index of the ligament.

5. An increase in the magnitude of the anterior/posterior force can have a

6. A compressive (superior/inferior) femorotibial force can have a stabilizing

effect on the knee. A distractive (inferior/superior) femorotibial force can

have a destabilizing effect on the knee.

7. Deactivation of knee ligaments is a major cause of anterior/posterior

instability of the knee.

Other conclusions of this work are described below.

8. The stability of anterior/posterior equilibrium of the knee can be

investigated by applying the static criterion, catastrophe theory, or the

multiple parameter theory, to the nonlinear equilibrium equations of the

system constituted by the knee and its inputs.

9. There is a need to rethink the traditional misuse of femorotibial equilibrium

as a sufficient condition for knee stability. The existence of a system under

equilibrium does not necessarily imply the stability of its equilibrium; the

equilibrium state can be stable, unstable or critical.

10.The regions of the configuration/parameter space at which a given knee will

be of negative or zero-valued anterior/posterior stiffness may lie outside the

region of the configuration/parameter space that is utilized during activities

of daily living. Under this situation the knee will be functionally stable.

11. A force versus deflection curve of the knee involves a highly localized

region of the knee's configuration/parameter space. Such a curve cannot

provide adequate information on the equilibrium of the knee outside the

localized region.

12. It is illogical to refer to a particular knee as 'stable' or 'unstable' without due

reference to specific values of the configuration variables and input load-

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13. Given an experimentally-obtained anterior/posterior force versus deflection

curve of a knee that has prosthetic articulations, a model-based technique

now exists for predicting the limiting values of the input loads, at which

anterior/posterior instability of the knee will occur. This method can be

incorporated into clinical knee function assessment schemes.

14. If the sagittal profile of the femoral component of a condylar prosthesis can

be represented by two or three tangentially-blended arcs, a change in the

degree of conformity and stiffness versus deflection characteristics of the

knee can occur as the anterior/posterior femorotibial displacement is varied

at constant flexion. This phenomenon should be taken into consideration,

in the interpretation of the results of knee-laxity tests.