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[[File:Potenziale Evocato della Radice Trigeminale.jpg|Motor Evoked Potential of the ipsilateral Trigeminal Root |alt=|thumb|250px|left]]
 
This chapter closes the loop of the 'Logic of medical language' to introduce a diagnostic model in the field of masticatory functions that combines the conceptuality of system logic with quantum mechanics. The statistical mathematical models of a system logic, therefore, cannot be subjective, nor approximate, much less vague and non-formal in the context of the clinical model. To obtain these characteristics it is necessary to consider the basic concepts of 'Systems Theory'.
 
The irrefutable diagnostic breakthrough in most medical disciplines lies in bioengineering, technological advances and specifically systems theory. It allows to verify the state of a system by comparing output variables generated by input variables. This huge step forward lies in the introduction of the trigger concept. Bioengineering in the trigeminal electrophysiological context has allowed the use of a series of triggers (transcranial electrical stimulation, transcranial magnetic stimulation, mechanical stimulation of the trigeminal district) that let us test the system with a much higher resolution than that in which the system is tested without responding to an external trigger. Another key element is that the trigger model is able to provide a snapshot of the system state many years before an obvious pathological clinical sign occurs.
 
In this chapter we will explain some basic steps to take in modeling diagnostic methods following systems theory.


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| autore7 = Irene Minciacchi
| autore7 = Irene Minciacchi
}}
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'''Abstract:''' The transition to "System Logic" in medical science, particularly within the dental field, is guided by two fundamental elements: dental clinical indices and the logic of medical language. Clinical indices, such as the Henderson-Hasselbalch equation, offer objective reference points critical for accurate diagnoses, yet their validity is often debated. While indices provide measurable data, subjective interpretations have historically influenced clinical outcomes. In orthodontics, indices like the Peer Assessment Rating (PAR) have been adopted to assess treatment success, but concerns arise over their ability to fully capture the complexity of dental occlusion and function.
 
The logic of medical language also faces scrutiny for its limitations in addressing the dynamic, complex nature of living systems. Classical logic and probabilistic models, while useful, often fall short when dealing with the uncertainties inherent in medical diagnoses. This has led to the introduction of "fuzzy logic" as a more flexible approach that can handle gradations of truth and uncertainty in clinical decision-making.


Furthermore, this work delves into Systems Theory as a framework for understanding biological and clinical phenomena. The masticatory system is examined through this lens, using electrophysiological tests such as Root-MEPs (Motor Evoked Potentials) to demonstrate the practical application of systems logic. By integrating bioengineering models with clinical practice, this approach aims to enhance diagnostic accuracy, reduce errors, and allow for early detection of pathologies, thereby improving patient outcomes.
==Foreword==
==Foreword==


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A test, a normative reference datum or an 'Index' (as well as a 'Constant') are strategies related to mathematical-statistical models that generate data. These data are mandatory for the accuracy of the diagnosis, for the differential diagnosis as well as for the therapeutic guidelines. On these reference data, in the times of scientific dental history, implementations and modifications have been generated but also uncertainties and beliefs that in the form of axioms or schools of thought have set guidelines that are not always scientifically justifiable, and sometimes untrue.
A test, a normative reference datum or an 'Index' (as well as a 'Constant') are strategies related to mathematical-statistical models that generate data. These data are mandatory for the accuracy of the diagnosis, for the differential diagnosis as well as for the therapeutic guidelines. On these reference data, in the times of scientific dental history, implementations and modifications have been generated but also uncertainties and beliefs that in the form of axioms or schools of thought have set guidelines that are not always scientifically justifiable, and sometimes untrue.


===In literature===
=== In literature===
We can take into consideration the data reported in the literature regarding the 'Indices' studied on patients suffering from 'Temporomandibular Disorders'<ref>Results in [https://pubmed.ncbi.nlm.nih.gov PubMed] for "[https://pubmed.ncbi.nlm.nih.gov/?term=%22temporomandibular+disorders+index%22&filter=datesearch.y_1 Temporomandibular disorders Index]"</ref> or enter more specifically about masticatory rehabilitations and verify the 'Clinical Indices' topic in orthodontic disciplines.<ref>Results in [https://pubmed.ncbi.nlm.nih.gov PubMed] for "[https://pubmed.ncbi.nlm.nih.gov/?term=%22orthodontics%20index%22&filter=simsearch2.ffrft&filter=datesearch.y_1 Orthodontics Indexes]"</ref>  
We can take into consideration the data reported in the literature regarding the 'Indices' studied on patients suffering from 'Temporomandibular Disorders'<ref>Results in [https://pubmed.ncbi.nlm.nih.gov PubMed] for "[https://pubmed.ncbi.nlm.nih.gov/?term=%22temporomandibular+disorders+index%22&filter=datesearch.y_1 Temporomandibular disorders Index]"</ref> or enter more specifically about masticatory rehabilitations and verify the 'Clinical Indices' topic in orthodontic disciplines.<ref>Results in [https://pubmed.ncbi.nlm.nih.gov PubMed] for "[https://pubmed.ncbi.nlm.nih.gov/?term=%22orthodontics%20index%22&filter=simsearch2.ffrft&filter=datesearch.y_1 Orthodontics Indexes]"</ref>  


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  | LCCN =  
  | LCCN =  
  | OCLC =  
  | OCLC =  
  }} - see also: {{cita libro
  }} - ''[https://grortho.gr/associations-between-pretreatment-age-and-treatment-time-with-orthodontic-treatment-outcome-a-comparison-by-means-of-two-orthodontic-indices/?lang=en see also]''</ref> and to improve the quality of future treatments.<ref>{{cita libro  
| autore = Onyeaso CO
| autore2 = Begole EA
| titolo = Associations between pretreatment age and treatment time with orthodontic treatment outcome: A comparison by means of two orthodontic indices
| url = https://grortho.gr/associations-between-pretreatment-age-and-treatment-time-with-orthodontic-treatment-outcome-a-comparison-by-means-of-two-orthodontic-indices/?lang=en
| volume =
| opera = Hellenic Orthodontic Review
| anno = 2008
| editore = Greek Orthodontic Society
| città = Athens
| ISBN =
| DOI =
| PMID =
| PMCID =
| oaf = yes<!-- qualsiasi valore -->
| LCCN =
| OCLC =
}}</ref> and to improve the quality of future treatments.<ref>{{cita libro  
  | autore = Hickman JH
  | autore = Hickman JH
  | titolo = Directional edgewise orthodontic approach. 5
  | titolo = Directional edgewise orthodontic approach. 5
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  | url = https://www.researchgate.net/publication/6389456_PAR_Index_in_the_Evaluation_of_the_Stability_of_the_Orthodontic_Treatment_Results_A_Review/fulltext/5adbdc64a6fdcc29358a3491/PAR-Index-in-the-Evaluation-of-the-Stability-of-the-Orthodontic-Treatment-Results-A-Review.pdf?origin=publication_detail
  | url = https://www.researchgate.net/publication/6389456_PAR_Index_in_the_Evaluation_of_the_Stability_of_the_Orthodontic_Treatment_Results_A_Review/fulltext/5adbdc64a6fdcc29358a3491/PAR-Index-in-the-Evaluation-of-the-Stability-of-the-Orthodontic-Treatment-Results-A-Review.pdf?origin=publication_detail
  | volume =  
  | volume =  
  | opera = Acta Medica (Hradec Kralove)
  | opera = Acta Medica (Hradec Králové)
  | anno = 2006
  | anno = 2006
  | editore =  
  | editore =  
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Spyridon N. Papageorgiou<ref>{{cita libro  
Spyridon N. Papageorgiou<ref>{{cita libro  
  | autore = Spyridon N. Papageorgiou
  | autore = Angst C
  | autore2 = Theodore Eliades
  | autore2 = Eliades T
  | autore3 = Christine Angst
  | autore3 = Papageorgiou SN
  | titolo = Stability of occlusal outcome during long-term retention: the time-dependent variation of the American Board of Orthodontics index
  | titolo = Stability of occlusal outcome during long-term retention: the time-dependent variation of the American Board of Orthodontics index
  | url = https://www.zora.uzh.ch/id/eprint/194364/1/p01_ok.pdf
  | url = https://www.zora.uzh.ch/id/eprint/194364/1/p01_ok.pdf
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Retention of treatment results is therefore considered to be one of the most difficult problems in orthodontics, and relapses, especially of the mandibular incisors, could also be observed with the use of retention devices after debonding.<ref>{{cita libro  
Retention of treatment results is therefore considered to be one of the most difficult problems in orthodontics, and relapses, especially of the mandibular incisors, could also be observed with the use of retention devices after debonding.<ref>{{cita libro  
  | autore = Jeanett Steinnes
  | autore = Steinnes J 
  | autore2 = Gunn Johnsen
  | autore2 = Johnsen G
  | autore3 = Heidi Kerosuo
  | autore3 = Kerosuo H
| autore4 =
| autore5 =
| autore6 =
| autore7 =
  | titolo = Stability of orthodontic treatment outcome in relation to retention status: An 8-year follow-up
  | titolo = Stability of orthodontic treatment outcome in relation to retention status: An 8-year follow-up
  | url = https://pubmed.ncbi.nlm.nih.gov/28554448/
  | url = https://pubmed.ncbi.nlm.nih.gov/28554448/
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  | LCCN =  
  | LCCN =  
  | OCLC =  
  | OCLC =  
  }}</ref> which is not a trigeminal electrophysiological analysis approach in considering 'Normocclusion' much less the details of a well balanced occlusion (such as contacts, inclinations and alignment of each tooth) or changes in retention only in the short term.<ref>Hoybjerg, A.J., Currier, G.F., Kadioglu, O. [https://pubmed.ncbi.nlm.nih.gov/23810041/ Evaluation of 3 retention protocols using the American Board of Orthodontics cast and radiograph evaluation.] American Journal of Orthodontics and Dentofacial Orthopedics, 2013, 144, 16-22.</ref>   
  }}</ref> which is not a trigeminal electrophysiological analysis approach in considering 'Normocclusion' much less the details of a well balanced occlusion (such as contacts, inclinations and alignment of each tooth) or changes in retention only in the short term.<ref>{{cita libro
| autore = Hoybjerg AJ
| autore2 = Currier GF
| autore3 = Kadioglu O
| titolo = Evaluation of 3 retention protocols using the American Board of Orthodontics cast and radiograph evaluation
  | url = https://pubmed.ncbi.nlm.nih.gov/23810041/
| volume =
| opera = Am J Orthod Dentofacial Orthop
| anno = 2013
| editore =
| città =
| ISBN =
| DOI = 10.1016/j.ajodo.2013.02.022
| PMID = 23810041
| PMCID =
| oaf = <!-- qualsiasi valore -->
| LCCN =
| OCLC =
}}</ref>   


To the authors' knowledge at the time of publication of their study, only one study<ref>Nett, B.C., Huang, G.J.[https://pubmed.ncbi.nlm.nih.gov/15821689/ Long-term posttreatment changes measured by the American Board of Orthodontics objective grading system]. American Journal of Orthodontics and Dentofacial Orthopedics, 2005, 127, 444-50.</ref> used the American Board of Orthodontics (ABO)<ref>Casko, J.S., Vaden, J.L., Kokich, V.G., Damone, J., James, R.D., Cangialosi, T.J., Riolo, M.L., Owens, S.E. Jr and Bills, E.D. [https://pubmed.ncbi.nlm.nih.gov/9810056/ Objective grading system for dental casts and panoramic radiographs. American Board of Orthodontics.] American Journal of Orthodontics and Dentofacial Orthopedics, 1998, 114, 589–599.</ref> detailed objective classification system for models and radiographs which measures the details of a well-finished and well-balanced occlusion.       
To the authors' knowledge at the time of publication of their study, only one study<ref>{{cita libro
| autore = Nett BC
| autore2 = Huang GJ
| titolo = Long-term posttreatment changes measured by the American Board of Orthodontics objective grading system
| url = https://pubmed.ncbi.nlm.nih.gov/15821689
| volume =
| opera = Am J Orthod Dentofacial Orthop
| anno = 2005
| editore = Elsevier Inc
| città =
| ISBN =
| DOI = 10.1016/j.ajodo.2004.03.029
  | PMID = 15821689
| PMCID =
| oaf = <!-- qualsiasi valore -->
| LCCN =
| OCLC =
}}</ref> used the American Board of Orthodontics (ABO)<ref>{{cita libro
| autore = Casko JS
| autore2 = Vaden JL
| autore3 = Kokich VG
| autore4 = Damone J
| autore5 = James RD
| autore6 = Cangialosi TJ
| autore7 = Riolo ML
| author8 = Owens SE Jr
| author9 = Bills ED
| titolo = Objective grading system for dental casts and panoramic radiographs
| url = https://pubmed.ncbi.nlm.nih.gov/9810056
| volume =
| opera = Am J Orthod Dentofacial Orthop
| anno = 1998
| editore =
| città =
| ISBN =
| DOI = 10.1016/s0889-5406(98)70179-9
| PMID = 9810056
| PMCID =
| oaf = <!-- qualsiasi valore -->
| LCCN =
| OCLC =
}}</ref> detailed objective classification system for models and radiographs which measures the details of a well-finished and well-balanced occlusion.       


{{q2|The aforementioned study is not only interesting but also stimulating, from a scientific point of view, as it states that relapses could occur even in the presence of adequate functional occlusion. |Constructive criticism, however, is inherent in the statement itself: how is an efficient masticatory function and, therefore, a 'Normocclusion' defined? }}
{{q2|The aforementioned study is not only interesting but also stimulating, from a scientific point of view, as it states that relapses could occur even in the presence of adequate functional occlusion. |Constructive criticism, however, is inherent in the statement itself: how is an efficient masticatory function and, therefore, a 'Normocclusion' defined? }}
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{{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.}}
{{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=]]
  [[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  
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  
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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.
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'====
==== 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:
The "systems theory" studies oriented systems, in which it becomes possible to classify the quantities of interest into two categories:


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A real system can have multiple inputs and multiple outputs. In particular, we indicate with:
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>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>
*<math>y(t)= (y_1(t),..., u_m(t))</math>the vector of the output at time <math>{t}</math>


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In the engineering field, various mathematical modeling of a system are possible, depending on whether or not they explicitly consider the state variables.
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 ]]
[[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====
====Mathematical formalism of the Trigeminal System Logic====
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[[File:Potenziale Evocato della Radice Trigeminale.jpg|thumb|'''Figure 6:'''Ipsilateral trigeminal motor evoked potential|alt=|378px|right]]
[[File:Potenziale Evocato della Radice Trigeminale.jpg|thumb|'''Figure 6:'''Ipsilateral trigeminal motor evoked potential|alt=|378px|right]]


==Conclusion==
== Conclusion==


[[File:FIGU01.jpg|alt=|left|thumb|'''Figura 7:''' The figure shows three ways of analyzing the system. In A the interferential EMG trace, in B the bilateral Root-MEPs and in C the jaw jerk..|200px]]  
[[File:FIGU01.jpg|alt=|left|thumb|'''Figura 7:''' The figure shows three ways of analyzing the system. In A the interferential EMG trace, in B the bilateral Root-MEPs and in C the jaw jerk..|200px]]  
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