Logique du système

Motor Evoked Potential of the ipsilateral Trigeminal Root

Ce chapitre ferme la boucle de la « Logique du langage médical » pour introduire un modèle de diagnostic dans le domaine des fonctions masticatoires qui combine la conceptualité de la logique des systèmes avec la mécanique quantique. Les modèles mathématiques statistiques d'une logique de système ne peuvent donc pas être subjectifs, ni approximatifs, encore moins vagues et non formels dans le contexte du modèle clinique. Pour obtenir ces caractéristiques, il est nécessaire de considérer les concepts de base de la « théorie des systèmes ».

La percée diagnostique irréfutable dans la plupart des disciplines médicales réside dans la bio-ingénierie, les progrès technologiques et plus particulièrement la théorie des systèmes. Il permet de vérifier l'état d'un système en comparant les variables de sortie générées par les variables d'entrée. Ce grand pas en avant réside dans l’introduction du concept de déclencheur. La bio-ingénierie dans le contexte électrophysiologique du trijumeau a permis l'utilisation d'une série de déclencheurs (stimulation électrique transcrânienne, stimulation magnétique transcrânienne, stimulation mécanique du district du trijumeau) qui nous permettent de tester le système avec une résolution beaucoup plus élevée que celle dans laquelle le système est testé. sans répondre à un déclencheur externe. Un autre élément clé est que le modèle de déclenchement est capable de fournir un instantané de l’état du système plusieurs années avant l’apparition d’un signe clinique pathologique évident.

Dans ce chapitre, nous expliquerons quelques étapes de base à suivre pour modéliser les méthodes de diagnostic selon la théorie des systèmes.

 

 

Avant-propos

Pourquoi en sommes-nous arrivés à la « logique système » ? Les étapes ne sont ni triviales, ni personnelles, et pour percevoir la valeur ajoutée de la « Logique Système » on ne peut s'empêcher de mentionner deux raisons essentielles qui ont jalonné ce chemin : celle des indices cliniques dentaires et de la logique du langage médical.

Index cliniques dentaires

Il existe des « indices » qui peuvent être considérés comme des éléments de la logique système en tant que données objectives, tels que « l'équation de Henderson-Hasselbalch » (pour l'analyse du pH sanguin) et d'autres « indices » développés dans le domaine médical dans des disciplines disparates.

Un test, une donnée de référence normative ou un « Indice » (ainsi qu'une « Constante ») sont des stratégies liées aux modèles mathématiques-statistiques qui génèrent des données. Ces données sont obligatoires pour l'exactitude du diagnostic, pour le diagnostic différentiel ainsi que pour les orientations thérapeutiques. Sur ces données de référence, au cours de l'histoire scientifique de la dentisterie, des implémentations et des modifications ont été générées, mais aussi des incertitudes et des croyances qui, sous forme d'axiomes ou d'écoles de pensée, ont fixé des lignes directrices qui ne sont pas toujours scientifiquement justifiables et parfois fausses.

Dans la littérature

Nous pouvons prendre en considération les données rapportées dans la littérature concernant les « Indices » étudiés sur des patients souffrant de 'Troubles temporo-mandibulaires' ou entrer plus spécifiquement dans les réhabilitations masticatoires et vérifier le thème « Indices cliniques » dans les disciplines orthodontiques.

Dans un article récent d'Andrea Scribante et collaborateurs, par exemple, les paragraphes suivants sont déduits :

1. L'introduction indique que l'évaluation des résultats du traitement orthodontique est traditionnellement réalisée en utilisant l'expérience et les opinions subjectives des cliniciens. Dans ce premier paragraphe, la limite du concept exprimé est comprise et le fait qu'un test diagnostique et/ou une ligne directrice thérapeutique ne doit jamais être scientifiquement évalué à l'aide de paramètres subjectifs.
2. Cependant, depuis les années 1990, des indices spécifiques ont été développés pour évaluer objectivement les résultats en matière de santé en analysant la qualité des traitements. Ces indices comparent les données avant et après traitement pour déterminer le résultat du traitement orthodontique et améliorer la qualité des traitements futurs. Ce deuxième paragraphe scientifiquement acceptable met en évidence le but des « Indices » et c'est la comparaison avant et après - mais qui a dit que le poste est en état de « normocclusion » et le pré en « malocclusion », l'alignement dentaire ?
3. L'indice le plus couramment utilisé pour évaluer le succès orthodontique est l'indice d'évaluation par les pairs (PAR), qui a été développé pour mesurer dans quelle mesure un patient s'écarte de l'occlusion et de l'alignement normaux. Cet indice a été utilisé pour évaluer les effets de la thérapie dans différentes circonstances: l'utilisation d'appareils fixes et mobiles, la comparaison des traitements orthodontiques entre cabinets privés et écoles d'orthodontie, l'évaluation de la stabilité occlusale après un traitement orthodontique, les traitements précoces et les résultats de la chirurgie orthognathique. Nous devons considérer que le PAR n'indiquerait pas le sain ou le malade, la normocclusion ou la malocclusion selon qu'il s'éloigne du seuil, mais face à une série de caractéristiques entrantes, il renverrait une réponse à large spectre (Index), valable pour traitements orthodontiques et orthognathiques. Cet état d'esprit est légitime mais les cliniciens doivent être prudents car les variables d'entrée (les « Constructeurs ») du modèle ou de l'entrée peuvent ne pas être liées au contexte de référence ou il peut y avoir d'autres variables cachées qui invalideraient le résultat lui-même. . Nous apprécierons plus fortement ces affirmations dans l’exposé des chapitres de Masticationpedia.

The fact is that the primum movens of the studio of Andrea Scribante and collaborators is concentrated in the following point:

«The most commonly used index to assess orthodontic success is Peer Assessment Rating Index (PAR), which was developed to measure how much a patient deviates from normal occlusion and alignment»
(Limitative .... the index can have an accuracy and truthfulness in dental alignment but not to validate a normocclusion, this latter assertion is much more complex to formulate and certainly cannot be reduced exclusively to an 'Occlusal observable'.)

Spyridon N. Papageorgiou in a very interesting study exposes a corageous statement that confirms what has just been exposed:

Noticeable long-term occlusal changes are observed in the post-debond, which mostly favor better settlement. The higher quality finish at the debond significantly influenced the possibilities for improvement. However, setting a cutoff score to denote treatment excellence has shown considerable instability over time.

Other authors state that relapse after orthodontic treatment can also occur in cases with good functional occlusion.

Further considerations

The etiology of recurrence is neither fully understood nor can it be fully predicted from a single factor, but includes factors such as the response of the traction and deconstructed periodontal fibers, physiological maturation of the human dentition which affects its width, length or perimeter, alterations of the craniofacial complex and parafunctions.

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. Most of the existing post-treatment stability studies evaluate short-term relapses of the anterior region by primarily measuring the irregularity of the incisors after extractive or non-extractive treatment and compare different retention patterns. These studies largely use the Peer Assessment Rating (PAR) index 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.

To the authors' knowledge at the time of publication of their study, only one study used the American Board of Orthodontics (ABO) detailed objective classification system for models and radiographs which measures the details of a well-finished and well-balanced occlusion.

«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?)

In Masticationpedia, we would like to launch interesting and constructive provocations to answer the question we just set out: 'How is an efficient chewing function and therefore a Normocclusion defined?'

Let's look at the two cases below, in figure 1 and in figure 2: which of the two clinical cases do you think is affected by malocclusion?

• 

  Figure 1: Patient with open bite and right posterior crossbite who according to classical orthodontic indices can only be considered in a state of 'Malocclusion'

• 

  Figure 2: Daughter of the patient in figure 1 who exhibits similar anatomical features such as the right posterior crossbite. There is no openbite in this case.

It seems irreverent for the canons of orthodox orthodoxy not to share the diagnosis of 'malocclusion', but we leave the reader in a little suspense. We intend to resume extensively in a few chapters, after deepening the topic of 'System Logic' and 'Systems Theory'. We only anticipate that the patient in figure 1 has already been proposed in the chapter 'Introduction', so we already know our clinical scientific opinion but if he gives us so much, also.....

«the daughter should also respond in the same way.»
(... be patient and you will see)

Medical language logic

Figura 3: The universe of classical and fuzzy logic.

In the previous chapters we highlighted the extreme difficulties we met in defining an exact, detailed and timely diagnosis in the right time; and this is not only due to the 'Complexity' of the living system, but also to a questionable and vague logic of medical language. If classical logic is too selective (true or false, and therefore 'there is no third answer' - principle of the excluded third), it is also true that probabilistic logic language, which trivially indicates the presence of a specific disease, breaks down in the 'significativity' parameter that acquires a certain value only in a 'specialist context'.

We perceived the need for a more elastic model called "fuzzy logic" that could translate the uncertainty inherent in some human language data into mathematical formalism, codifying the "elastic" concepts (such as almost high, fairly good, etc), in order to make them understandable and manageable by computers.

We have therefore frozen a much debated and approached concept in the chapter 'Introduction': not determining a clear separation between specialist know-how, but superimposing interdisciplinary knowledge, instead, through a 'Fuzzy' approach (see fuzzy logic language).

«But it is not so obvious to arrive at a more formal language in the medical field where events are complex and dynamic and, as we will see, they are not trivially deterministic. In order to better understand the 'System Logic', and at the same time introduce the concept of clinical 'Indices', it is necessary to start with the description of the 'Systems Theory'»

Systems Theory

In the scientific field, systems theory, more properly general system theory (definition by Ludwig von Bertalanffy), 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.

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.

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.

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.

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.

«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.)

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

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.

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.

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:

• $u(t)=(u_{1}(t),...,u_{r}(t))$the vector of the inputs at time ${t}$
• $y(t)=(y_{1}(t),...,u_{m}(t))$the vector of the output at time ${t}$

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

We denote the state vector, whose components are defined as state variables, with the notation $x(t)=(x_{1}(t),...,x_{n}(t))$ .

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 $T\subseteq \mathbb {R}$, which can be continuous or discrete. In the following discussion we will consider a discrete subset of times:$T=\{t_{0},...,t_{s}\}$

Therefore, given a set of times $T=\{t_{0},...,t_{s}\}$, we can formally define a system as the pair of equations

$x(t_{k+1})=f{\bigl (}x(t_{k}),u(t_{k}),t_{k}{\bigr )}$

$y(t_{k})=g{\bigl (}x(t_{k}),u(t_{k}),t_{k}{\bigr )}$

with $x(t_{0})=x_{0}$, where $f$ is called generating function e $g$ is called the output transformation.

In the field of biosignals, the ($g$) 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 $g$ 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 $g$ 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, 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.

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$T=\{t_{0},t_{1},t_{2}......t_{8}\}$.

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:

${\bigl (}u(t_{0}),u(t_{1}),u(t_{2}),u(t_{3}),u(t_{4}),u(t_{5}),u(t_{6}),u(t_{7}),u(t_{8}){\bigr )}={\bigl (}0,20,30,40,50,70,80,90,100{\bigr )}$mA.

Two state variables will correspond to each of these inputs: latency ${\bigr (}y_{1}(t){\bigl )}$ and amplitude ${\bigr (}y_{2}(t){\bigl )}$.

${\bigl (}y_{1}(t_{0}),y_{1}(t_{1}),y_{1}(t_{2}),y_{1}(t_{3}),y_{1}(t_{4}),y_{1}(t_{5}),y_{1}(t_{6}),y_{1}(t_{7}),y_{1}(t_{8}){\bigr )}={\bigl (}0,2.4,2.4,2.3,2.1,2,1.9,1.9,1.9{\bigr )}$ms

${\bigl (}y_{2}(t_{0}),y_{2}(t_{1}),y_{2}(t_{2}),y_{2}(t_{3}),y_{2}(t_{4}),y_{2}(t_{5}),y_{2}(t_{6}),y_{2}(t_{7}),y_{2}(t_{8}){\bigr )}={\bigl (}0,0.6,0.8,1.1,1.7,2.8,4.6,4.6,4.6{\bigr )}$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.

Figure 6:Ipsilateral trigeminal motor evoked potential

Conclusion

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..

It is plausible that the reader, or a colleague not accustomed to particular trigeminal electrophysiological procedures, may consider this type of bioengineering diagnostic models exaggerated, both for the difficulty in the execution (that can make the methodology seem dangerous - the Root-MEPs delivers an electric current of 100 V with an amperage of 100mA), and for the feeling he might have that the cost benefit is unjustified; so, he might prefer to continue with the now routine methodology in dentistry, such as performing a simple, fast and inexpensive interferential EMG (Figure 7A). We certainly accept the opinion of our hypothetical colleague, but we do not share it because, to save a human life, competence is always and critically required, together with dedication and both intellectual and economic investment.

The irrefutable step forward made in diagnostics in most medical disciplines, as already mentioned, lies precisely in bioengineering, technological progress; specifically, systems theory has allowed us to verify the system state by comparing output variables generated by variables incoming payments which are basically triggers of various types.

Figure 7 is a way of demonstrating this. Notably, like the interferential EMG test shows (Figure 7A), only a sort of interferential asymmetry typical of clinical situations of malocclusion can be observed, while through a trigger model (specifically, the bilateral transcranial electrical stimulation of the trigeminal roots) the system responds with a large amplitude asymmetry (Figure 7B) and even with an absence of the jaw jerk response (evoked with a mechanical trigger by striking the chin with a neurological piezoelectric hammer). (Figure 7C) The diagnostic conclusion of this patient was of skull base menygoma.

For the experts, of course, a glance is enough to understand whether the trigeminal motor system evoked through electrical transcranial stimulation of the motor roots is in a physiological or pathological state; but, as we will see in the next chapters, the biological reality is so complex and paradoxically indeterministic, that a bioengineering model paired with an adequate statistical mathematician will allow us to approach more accurately the real physiopathological state of the system, reduce the uncertainty of the measurement and consequently the differential diagnostic error but above all make early diagnosis.

In any case, if this patient had undergone the described diagnostic model, he would not have died, because the growth of the tumor mass of a meningioma is extraencephalic, and slow, and would have shown an electrophysiologically documentable destructuring many years before the vertiginous symptomatology.(see: 3° Clinical case: Meningioma ​)

Bibliography & references

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particularly focusing on the field of the neurophysiology of the masticatory system
 

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