General characteristics of the model

The first think we notice with the result of the identification process is :

1. For the same subject the coefficient of the A polynom are very similar for the normals volumens. That means that the dynamical comportment and the frequency response of this systems are quite close.
2. On a other hand the coefficients of the B polynom could be drasticly different. This affect particularly the static gain of the function and by the way the amplitude of the response. But this result was already known by the physician [2]. The increasing of the amplitud of the response is presented as a logarithm function of the volumen of the balloon [3]. The result we have dont give us really this kind of progression, but maybe we are working on a to small set of subjects.
3. The muscular system act as a low-pass filter who completly cut all the frequencies bigger than 0.5Hz. In fact the gain is clearly decreasing after 0.01Hz and less than 0dB after 0.1Hz as shown on the frequencie responses (figure 5) of the model shown in figure (4).

  
Figure 5: Bode plot of the Model

This conclusions seems to be available for the all the subject of the same class (e.g. the healthy one). For example the gap in term of frequencies responses between healthy subject is very short and the gain decreasing take place in any case for the same game of frequencies (less than a decade centered on 0.01Hz). Another interesting conclusion we can give just looking on the frequencies responses of the different linear models is the following. The upper bound frequencie of the filter is decreasing with the volumen of the balloon. We can see this purpose on the next figure (6). We wont discuss the consequence of this effect in the next section.

  
Figure 6: Bode plot of 3 models for the same subject

Currently the model we obtain as (in transfer function form) this kind of values

 

Where the sampling interval is 0.2 second.

We will try now to look on a continuous linear model in order to find a mechanical device usable for our prothesis project. To establish all the frequencies responses curves, we work first with Matri . But all the graphs of this paper are made with lab the freeware of the META2 group from INRIA.