Modifica di System logic (sezione)

====Mathematical formalism of the Trigeminal System Logic====
We consider the Trigeminal Motor System as a black box with inputs (figure 5) and outputs (figure 6), and we try to adapt to it the above described theory.

Figure 6 shows the neuromotor responses to the electrical transcranial stimulation of the trigeminal root of the right hemilate. We wanted to set up the test following the mathematical model of 'systems theory' to better understand the difference between the information obtained from a now almost inflated test such as the interferential EMG, and a more complex test such as a motor and/or somatosensory evoked potential; the evoked potential has the prerogative of a system response to an external input called 'trigger', which in this context is of an electrical type.

We divided the test by delivering a series of progressively greater electrical stimuli in the ordered times corresponding to<math>T=\{t_0, t_1,t_2......t_{8}\}</math>.

In our context, we will have one input, i.e. the electrical stimulation amperage and two outputs, i.e. latency and amplitude.

We will therefore have:

<math>\bigl(u(t_0), u(t_1), u(t_2), u(t_3), u(t_4), u(t_5), u(t_6), u(t_7), u(t_8)\bigr)=\bigl(0,20,30,40,50,70,80,90,100\bigr)</math>mA.

Two state variables will correspond to each of these inputs: latency <math>\bigr( y_1(t) \bigl)</math> and amplitude <math>\bigr( y_2(t) \bigl)</math>.

<math>\bigl(y_1(t_0), y_1(t_1), y_1(t_2), y_1(t_3), y_1(t_4), y_1(t_5), y_1(t_6), y_1(t_7), y_1(t_8)\bigr)=\bigl(0,2.4,2.4,2.3,2.1,2,1.9,1.9,1.9\bigr)</math>ms

<math>\bigl(y_2(t_0), y_2(t_1), y_2(t_2), y_2(t_3), y_2(t_4), y_2(t_5), y_2(t_6), y_2(t_7), y_2(t_8)\bigr)=\bigl(0,0.6,0.8,1.1,1.7,2.8,4.6,4.6,4.6\bigr)</math>mV

All these variables generate a plotting of multiple mediated traces as in figure 6, in which some important considerations can be made, such as the decrease in latency and the increase in amplitude as the amperage increases.
 

[[File:Potenziale Evocato della Radice Trigeminale.jpg|thumb|'''Figure 6:'''Ipsilateral trigeminal motor evoked potential|alt=|378px|right]]