Systemlogik

Dieses Kapitel schließt den Kreis der 'Logik der medizinischen Sprache', um ein diagnostisches Modell im Bereich der Kau- und Schluckfunktionen einzuführen, das die Konzeptualität der Systemlogik mit der Quantenmechanik kombiniert. Die statistisch-mathematischen Modelle einer Systemlogik können daher weder subjektiv noch approximativ sein, geschweige denn vage und informell im Kontext des klinischen Modells. Um diese Eigenschaften zu erlangen, ist es notwendig, die Grundkonzepte der 'Systemtheorie' zu berücksichtigen.

Der unbestreitbare diagnostische Durchbruch in den meisten medizinischen Disziplinen liegt in der Bioingenieurwissenschaft, den technologischen Fortschritten und speziell in der Systemtheorie. Diese ermöglicht es, den Zustand eines Systems zu überprüfen, indem die Ausgangsvariablen mit den Eingangsvariablen verglichen werden. Dieser enorme Fortschritt liegt in der Einführung des Triggerkonzepts. Die Bioingenieurwissenschaft im trigeminalen elektrophysiologischen Kontext hat die Verwendung einer Reihe von Triggern ermöglicht (transkranielle elektrische Stimulation, transkranielle magnetische Stimulation, mechanische Stimulation des trigeminalen Gebiets), die es uns ermöglichen, das System mit einer viel höheren Auflösung zu testen als ohne das Reagieren auf einen externen Trigger. Ein weiteres Schlüsselelement ist, dass das Triggermodell viele Jahre vor dem Auftreten eines offensichtlichen pathologischen klinischen Zeichens einen Momentaufnahme des Systemzustands liefern kann.

In diesem Kapitel werden einige grundlegende Schritte erläutert, die bei der Modellierung diagnostischer Methoden nach den Grundsätzen der Systemtheorie zu beachten sind.

 

 

Vorwort

Warum sind wir zur 'Systemlogik' gelangt? Die Schritte sind weder trivial noch persönlich, und um den Mehrwert der 'Systemlogik' wahrzunehmen, müssen wir zwangsläufig zwei wesentliche Gründe erwähnen, die diesen Weg geprägt haben: den der zahnärztlichen klinischen Indizes und den der Logik der medizinischen Sprache.

Zahnärztliche klinische Indizes

Es gibt "Indizes", die als Elemente der Systemlogik betrachtet werden können, da sie objektive Daten liefern, wie z.B. die "Henderson-Hasselbalch-Gleichung" (für die Blut-pH-Analyse) und andere "Indizes", die in verschiedenen medizinischen Disziplinen entwickelt wurden.

Ein Test, ein normatives Referenzdatum oder ein "Index" (sowie eine "Konstante") sind Strategien, die mit mathematisch-statistischen Modellen verbunden sind und Daten generieren. Diese Daten sind für die Genauigkeit der Diagnose, für die differenzielle Diagnose sowie für die therapeutischen Leitlinien unerlässlich. Auf diesen Referenzdaten basieren in der wissenschaftlichen Zahnmedizingeschichte Implementierungen und Modifikationen, aber auch Unsicherheiten und Überzeugungen, die in Form von Axiomen oder Denkschulen Richtlinien festgelegt haben, die nicht immer wissenschaftlich gerechtfertigt und manchmal sogar unrichtig sind.

In der Literatur

Wir können die in der Literatur gemeldeten Daten in Bezug auf die untersuchten "Indizes" bei Patienten mit "Temporomandibulären Störungen" berücksichtigen oder genauer gesagt die Themen der klinischen Indizes in orthodontischen Disziplinen überprüfen.

In einem kürzlich erschienenen Artikel von Andrea Scribante und Kollegen werden beispielsweise die folgenden Absätze abgeleitet:

1. Die Einleitung besagt, dass die Bewertung der Ergebnisse der kieferorthopädischen Behandlung traditionell auf der Erfahrung und den subjektiven Meinungen der Kliniker beruht. In diesem ersten Absatz wird das Limit des ausgedrückten Konzepts verstanden, nämlich dass ein diagnostischer Test und/oder eine therapeutische Leitlinie niemals wissenschaftlich anhand subjektiver Parameter bewertet werden sollten.
2. Jedoch wurden seit den 1990er Jahren spezifische Indizes entwickelt, um die Gesundheitsergebnisse objektiv zu bewerten, indem die Qualität der Behandlung analysiert wird. Diese Indizes vergleichen Vor- und Nachbehandlungsdaten, um das Ergebnis der kieferorthopädischen Therapie zu bestimmen und die Qualität zukünftiger Behandlungen zu verbessern. Dieser zweite wissenschaftlich akzeptable Absatz hebt den Zweck der "Indizes" hervor, nämlich den Vorher-Nachher-Vergleich. Es ist jedoch wichtig zu berücksichtigen, wer festlegt, dass der Zustand nach der Behandlung als "Normokklusion" betrachtet wird, während der Zustand vor der Behandlung als "Malokklusion" im Sinne der Zahnstellung kategorisiert wird?
3. Der am häufigsten verwendete Index zur Bewertung des Erfolgs von kieferorthopädischen Maßnahmen ist der Peer Assessment Rating Index (PAR), der entwickelt wurde, um zu messen, wie weit sich ein Patient von einer normalen Okklusion und Ausrichtung entfernt. Dieser Index wurde verwendet, um die Auswirkungen der Therapie in verschiedenen Situationen zu bewerten: die Verwendung von festen und mobilen Geräten, den Vergleich der kieferorthopädischen Behandlung zwischen privaten Praxen und kieferorthopädischen Schulen, die Bewertung der okklusalen Stabilität nach kieferorthopädischer Behandlung, frühzeitige Behandlungen und Ergebnisse kieferorthopädischer Chirurgie. Wir müssen berücksichtigen, dass der PAR je nach Abweichung von einem festgelegten Standard nicht den gesunden oder kranken Zustand, die Normokklusion oder Malokklusion anzeigt, sondern angesichts einer Reihe von eingehenden Merkmalen eine breite Spektrumantwort (Index) liefert, die für kieferorthopädische Behandlungen und Kieferorthopädische Operationen gültig ist. Diese Denkweise ist legitim, aber die Kliniker müssen vorsichtig sein, da die Eingangsvariablen (die 'Konstruktoren') des Modells oder Inputs möglicherweise nicht mit dem Referenzkontext zusammenhängen oder es möglicherweise andere versteckte Variablen gibt, die das Ergebnis ungültig machen würden. Diese Aussagen werden wir in der Darstellung der Kapitel von Masticationpedia noch stärker zu schätzen wissen.

Der Hauptpunkt der Studie von Andrea Scribante und seinen Mitarbeitern konzentriert sich darauf:

«Der am häufigsten verwendete Index zur Bewertung des Erfolgs der Kieferorthopädie ist der Peer Assessment Rating Index (PAR), der entwickelt wurde, um zu messen, wie stark sich ein Patient von einer normalen Okklusion und Ausrichtun»
(Einschränkend ... der Index kann eine Genauigkeit und Wahrhaftigkeit in Bezug auf die Zahnstellung haben, aber nicht zur Validierung einer Normokklusion, diese letztere Aussage ist viel komplexer zu formulieren und kann sicherlich nicht ausschließlich auf eine 'okklusale Beobachtung' reduziert werden.)

Spyridon N. Papageorgiou stellt in einer sehr interessanten Studie eine mutige Aussage auf, die das bestätigt, was gerade dargelegt wurde:

Deutliche langfristige okklusale Veränderungen werden nach der Entfernung der Zahnspange beobachtet, die größtenteils eine bessere Abrechnung begünstigen. Die höhere Qualität des Abschlusses bei der Entfernung der Zahnspange beeinflusste signifikant die Möglichkeiten für Verbesserungen. Die Festlegung eines Grenzwertes zur Kennzeichnung von Behandlungsexzellenz hat sich jedoch im Laufe der Zeit als erheblich instabil erwiesen.

Andere Autoren geben an, dass Rückfälle nach kieferorthopädischer Behandlung auch in Fällen mit guter funktioneller Okklusion auftreten können.

Weitere Überlegungen

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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