ABSTRACT of the Doctoral Thesis
In medical treatment of pressure induced foot problems, orthopaedic shoes or insoles are prescribed to provide relief of plantar pressure at overloaded locations. A simulation tool to facilitate a favourable design of insoles, particularly for the diabetic foot, is presented in this work. In order to evaluate a given insole design, the time-dependent in-shoe pressure distribution during walking is simulated.
To this end, a combined experimental-numerical method is employed. The biomechanical model that is the basis of both experimental and numerical work, is a Winkler-like foundation model, describing the foot as a 2dimensional arrangement of non-linear springs. The implied simplifying assumptions are justified by anatomical and mechanical considerations and by verifications at two developement stages, and are substantiated by the special biomechanical features of the diabetic foot.
This approach divides the study into two major parts: the designing of a measurement system and the developement of a simulation algorithm. The measurement system, named Pedomech system, allows the acquisition of the input data necessary for the numerical simulation: The stiffness distribution and the geometry of the sole of the foot can be measured individually and in vivo. The particular setup, however, gives rise to a difficulty to obtain data for the arch region. A possible solution is suggested by enhancing the measurement system.
Applying the load history of walking to the model leads to a transient, non-linear, elasto-static problem, including a contact problem. By means of the Principle of Virtual Work and the Pure Newton-Raphson Method, a simulation algorithm is derived and implemented in a computer program. Program versions for barefoot and shoed walking are elaborated. When treating insoles that have high gradients of the thickness, it turns out to be necessary to consider also the kinematics of the ankle joint during the stance phase.
For barefoot walking, the simulation method is applied to a number of subjects, including one diabetic patient. Verifying these results against measurements yields a satisfactory agreement. It is observed, however, that a distinction has to be made concerning the considered load history. In slow walking the foot exhibits a different behaviour than in fast walking, which also agrees with anatomical findings. The simulation proves applicable for low walking speeds rather than for high ones.
From the point of view of practical applications, there are two different ways to employ the simulation method. In the standard case the user of the method prescribes the design of the insole; then, the simulation of the pressure distribution serves as an accompanying control of the design. Alternatively, the simulation may be performed iteratively in order to automatically find an ``optimized'' design. For this purpose, a functional adaptation algorithm is presented. Results from the simulation of in-shoe pressures as well as from the functional adaptation mechanism are given for one particular subject.
Additionally, the results from the Pedomech system can be used without a subsequent pressure simulation. First of all, the measured stiffness properties per se can interpreted for diagnostic purposes. As an example, the stiffness at the heel of the investigated diabetic foot is increased when compared to the healthy foot. Also, it is shown how the results from the Pedomech measurement system can be evaluated to express the overall behaviour of the foot in an approximate way through three global stiffness characteristics. This is believed to be useful in related disciplines such as gait analysis.