Modifica di System logic (sezione)

==Systems Theory==
In the scientific field, systems theory, more properly general system theory (definition by Ludwig von Bertalanffy),<ref>{{Cita libro
|autore = von Bertalanffy L
|titolo = General System Theory: Foundations, Development, Applications
|url = https://archive.org/details/generalsystemthe0000bert
|anno = 1968
|opera = Arch Gen Psychiatry
|editore = George Braziller
|città = New York
|p = 295
|ISBN = 978-0807604533
|DOI = 10.1001/archpsyc.1969.01740200123021
}}</ref> is an often interdisciplinary field of study, straddling mathematics and natural sciences, which deals with the analysis of properties and the constitution of a system. It is essentially composed of the theory of dynamic systems (simple and complex) and of the theory of control: it is the basis of various disciplines such as automation, robotics and cybernetic physics, as well as the technical-scientific study of systems in general as much as in biology and medicine.

Systems theory is the interdisciplinary study of systems, that could be described as cohesive groups of interconnected and interdependent parts that can be natural or man-made. Each system is bounded by space and time, influenced by its environment, defined by its structure and expressed through its functioning. A system can be more than the sum of its parts if it expresses emerging synergies or behaviors.<ref>[https://pubmed.ncbi.nlm.nih.gov/?term=%22emergent+behaviour%22&filter=datesearch.y_10 Emergent Behaviour] on PubMed</ref>

Changing one part of a system might affect other parts or the whole system. It may be possible to predict these changes in behavior patterns. Some systems support other systems, keeping the others to prevent failure. The goals of systems theory are to model the dynamics, constraints, conditions of a system and to clarify the principles (such as purpose, measure, methods, tools) that can be identified and applied to other systems at any level of nesting and in a 'wide range of fields to achieve optimized equifinality.<ref>Wikipedia article for ''[[wikipedia:Equifinality|Equifinality]]''</ref>

To be practical and effective in the description of the concept 'System logic' we consider an approach to a part of the trigeminal motor system, since it is the cornerstone of this scientific work, in which the conceptual connection with the 'Theory of Systems'.

===Masticatory System Logic===

Regarding the analysis of the state of the masticatory system, the EMG technique has been widely used but there are still a number of concerns regarding the reliability of the measures based on the interferential EMG.<ref>{{cita libro 
 | autore = Reaz MB
 | autore2 = Hussain MS
 | autore3 = Mohd-Yasin F
 | titolo = Techniques of EMG signal analysis: detection, processing, classification and applications (Correction)
 | url = https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1455479/pdf/bpo_v8_p11_m115.pdf
 | volume = 
 | opera = Biol Proced Online
 | anno = 2006
 | editore = 
 | città = 
 | ISBN = 
 | DOI = 10.1251/bpo115
 | PMID = 16799694
 | PMCID = PMC1455479
 | oaf = <!-- qualsiasi valore -->
 | LCCN = 
 | OCLC = 
 }}</ref>

This is why most of the studies performed so far aimed at showing a possible correlation between EMG signals with Temporomandibular Disorders (TMD), Orofacial Pain (OP) or Malocclusion (IO), but they have not yielded convincing results.<ref>{{cita libro 
 | autore = Masci C
 | autore2 = Ciarrocchi I
 | autore3 = Spadaro A
 | autore4 = Necozione S
 | autore5 = Marci MC
 | autore6 = Monaco A
 | titolo = Does orthodontic treatment provide a real functional improvement? A case control study
 | url = https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3827987/pdf/1472-6831-13-57.pdf
 | volume = 
 | opera = BMC Oral Health
 | anno = 2013
 | editore = BioMed Central Ltd
 | città = 
 | ISBN = 
 | DOI = 10.1186/1472-6831-13-57
 | PMID = 24152806
 | PMCID = PMC3827987
 | oaf = CC-BY 2<!-- qualsiasi valore -->
 | LCCN = 
 | OCLC = 
 }}</ref> 

In an unknown percentage of OP patients visited by specialist dentists, some neurological diseases such as intracranial tumours, multiple sclerosis, etc. are the underlying symptoms cause of TMD or OP. 

These patients, who actually suffer from neurological symptoms superimposed on dental-facial ones, may undergo unnecessary dental interventions before the correct diagnosis is made, sometimes too late.<ref>{{cita libro 
 | autore = Moazzam AA
 | autore2 = Habibian M
 | titolo = Patients appearing to dental professionals with orofacial pain arising from intracranial tumors: a literature review
 | url = https://pubmed.ncbi.nlm.nih.gov/23036798/
 | volume = 
 | opera = Oral Surg Oral Med Oral Pathol Oral Radiol
 | anno = 2012
 | editore = 
 | città = 
 | ISBN = 
 | DOI = 10.1016/j.oooo.2012.06.017
 | PMID = 23036798
 | PMCID = 
 | oaf = <!-- qualsiasi valore -->
 | LCCN = 
 | OCLC = 
 }}</ref>
 
{{q2|When approaching the modeling of a diagnostic 'Index' it is essential to consider the 'Fundamental Unit' of the system to be studied mathematically.|... as said, the 'Observable' cannot be the occlusal element because it is hierarchically lower than the Trigeminal Nervous System.}}
 [[File:Bilateral Root-MEPs.jpg|thumb|center|500px|'''Figure 4:''' Virtual segmentation of the Trigeminal Nervous System and annotation of the motor Root level from which the trigeminal Motor Evoked Potentials (R-MEPs) are evoked |alt=]]

Cortical projections to the trigeminal motor neurons are generally believed to be bilateral and symmetrical and can be electrophysiologically analyzed by electrical or magnetic brain stimulation through the intact scalp.<ref>{{cita libro 
 | autore = Merton PA
 | autore2 = Morton HB
 | titolo = Stimulation of the cerebral cortex in the intact human subject 
 | url = https://www.nature.com/articles/285227a0.pdf
 | volume = 
 | opera = Nature
 | anno = 1980
 | editore = Springer Nature Limited
 | città = 
 | ISBN = 
 | DOI = 10.1038/285227a0
 | PMID = 7374773
 | PMCID = 
 | oaf = <!-- qualsiasi valore -->
 | LCCN = 
 | OCLC = 
 }}</ref>

In the ipsilateral masseter, the transcranial electrical stimulation (eTCS) is capable of evoking a large short-latency potential in relaxed and active muscles. The characteristics of ipsilateral Motor Evoked Potentials (MEPs) do not change under relaxed or active conditions. Mean onset latency is approximately 2 ms, peak latency of 3.9 ms and amplitude of 5.4 mV, and there is no latency variability in similar pacing conditions. These motor potentials, considered secondary to trigeminal motor root excitation, have been called Root-MEP (Root-MEP or simplified into R-MEPs) to differentiate them from M-waves and Cortex-MEPs.<ref>{{cita libro 
 | autore = Cruccu G
 | autore2 = Berardelli A
 | autore3 = Inghilleri M
 | autore4 = Manfredi M
 | titolo = Functional organization of the trigeminal motor system in man. A neurophysiological study
 | url = https://academic.oup.com/brain/article-abstract/112/5/1333/285684?redirectedFrom=fulltext&login=false
 | volume = 
 | opera = Brain
 | anno = 1989
 | editore = 
 | città = 
 | ISBN = 
 | DOI = 10.1093/brain/112.5.1333
 | PMID = 2804615
 | PMCID = 
 | oaf = <!-- qualsiasi valore -->
 | LCCN = 
 | OCLC = 
 }}</ref>

To make the understanding of 'Systems Theory' more suitable for the context of the masticatory system, we report some trigeminal electrophysiological procedures and implement them with the mathematical models of the theory.

==== Mathematical formalism in 'Systems Theory'====
The "systems theory" studies oriented systems, in which it becomes possible to classify the quantities of interest into two categories:

*quantities that vary over time independently from the others ('''inputs''')
*quantities whose evolution over time is to be studied, depending on the inputs, called '''outputs'''.

A real system can have multiple inputs and multiple outputs. In particular, we indicate with:

* <math>u(t)= (u_1(t),..., u_r(t))</math>the vector of the inputs at time <math>{t}</math>
*<math>y(t)= (y_1(t),..., u_m(t))</math>the vector of the output at time <math>{t}</math>

It is also generally defined as the state vector of the system in a generic instant <math>\tilde{t}</math> the information instantly <math>\tilde{t}</math> necessary to uniquely determine the output <math>y(t)</math> for each <math>t\geq{\displaystyle {\tilde {t}}}</math> once the entrance has been assigned <math>u(t), </math><math>t\geq{\displaystyle {\tilde {t}}}</math>.

We denote the state vector, whose components are defined as state variables, with the notation <math>x(t)= (x_1(t),..., x_n(t))</math> .

The inputs act on the state of the system and modify its characteristics at a given moment in time; these changes are recorded by the state variables. The values of the system outputs, usually the only measurable variables, in turn depend on the system state variables and the inputs.

The input, status and output quantities are functions of the time variable.

This takes values in an ordered subset <math>T \subseteq \R</math>, which can be continuous or discrete. In the following discussion we will consider a discrete subset of times:<math>T = \{t_0,..., t_s\}</math>

Therefore, given a set of times <math>T = \{t_0,..., t_s\}</math>, we can formally define a system as the pair of equations

<math>x(t_{k+1})=f\bigl(x(t_k), u(t_k), t_k\bigr)
</math>

<math>y(t_k)=g\bigl(x(t_k), u(t_k), t_k\bigr)
</math>

with <math>x(t_0)=x_0
</math>, where <math>f
</math> is called generating function e <math>g
</math> is called the output transformation.

In the field of biosignals, the (<math>g</math>) models are used to analyze EEG and vibration systems in vehicles, human hearing systems and vascular systems, and so on. While much is still unknown about the physiological mechanism or pattern of internal changes in the tested system, the output transfer or transformation function <math>g</math> in our context allows us to reconstruct a wave function by interpolating the points detected by the instrument which has its own particular sampling frequency. This <math>g</math> function, for our purposes, is a reconstruction of a wave function on which to search for latencies, amplitudes and integral areas and make the necessary conclusions,<ref>{{cita libro 
 | autore = Haebeom L
 | autore2 = Hyunho K
 | autore3 = Jungkuk K
 | autore4 = Hwan-Sup O
 | autore5 = Young-Jae P
 | autore6 = Young-Bae P
 | titolo = Feasibility study of transfer function model on electrocardiogram change caused by acupuncture
 | url = https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5299648/pdf/12906_2017_Article_1615.pdf
 | volume = 
 | opera = BMC Complement Altern Med
 | anno = 2017
 | editore = 
 | città = 
 | ISBN = 
 | DOI = 10.1186/s12906-017-1615-5
 | PMID = 28178964
 | PMCID = PMC5299648
 | oaf = yes<!-- qualsiasi valore -->
 | LCCN = 
 | OCLC = 
 }}</ref><ref>{{cita libro 
 | autore = Smith RJ
 | autore2 = Kamali G
 | autore3 = Hays M
 | autore4 = Coogan C
 | autore5 = Crone NE
 | autore6 = Kang JY
 | autore7 = Sarma SV
 | titolo = Transfer Function Models for the Localization of Seizure Onset Zone From Cortico-Cortical Evoked Potentials
 | url = https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7758451/pdf/fneur-11-579961.pdf
 | volume = 
 | opera = Front Neurol
 | anno = 2020
 | editore = Frontiers in Neurology
 | città = 
 | ISBN = 
 | DOI = 10.3389/fneur.2020.579961
 | PMID = 33362689
 | PMCID = PMC7758451
 | oaf = y<!-- qualsiasi valore -->
 | LCCN = 
 | OCLC = 
 }}</ref> and, obviously, by retesting the system in subsequent epochs, the integrity of the system itself can be compared. 

In the engineering field, various mathematical modeling of a system are possible, depending on whether or not they explicitly consider the state variables.
[[File:Finite Elements - electric field within the intracranial brain tissue - FEM.jpg|thumb|center|'''Figure 5:''' A. Positioning of the electrodes for the delivery of the electrical stimulus. B. Representation of the electric field within the brain structure. C. Localization of the induced electric field at the level of the trigeminal roots ]]

====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]]