evaluation by finite element analysis of dentinal …

Romanian Reports in Physics 72, 608 (2020)

EVALUATION BY FINITE ELEMENT ANALYSIS OF DENTINAL STRESS AND STRAIN DURING ENDODONTIC INSTRUMENTATION

OF STRAIGHT ROOT CANALS

O.E. AMZA1, D. NIŢOI2, B. DIMITRIU1, I. SUCIU1, M. CHIRILĂ1 1 “Carol Davila” University of Medicine and Pharmacy Bucharest,

37 Dionisie Lupu, 020021 Bucharest, Romania 2 “Politehnica” University of Bucharest, 313 Splaiul Independentei,

060042, Bucharest, Romania E-mail: [email protected]

Received July 23, 2020

Abstract. Stress and strain always occur in the root canal dentin during endodontic instrumentation. Subsequently dentinal microcracks formation and propagation may be observed, with the potential of generating vertical root fractures. This study aims to a theoretical determination of the stress state by modeling these processes of dentinal stress development during straight root canals shaping using finite element analysis and ANSYS software.

Key words: endodontic instrumentation, dentinal stress and strain, finite element

analysis.

1. INTRODUCTION

The evolution of endodontic instrumentation aimed at achieving a more effective and safe root canal shaping during the chemo-mechanical treatment stage. The approach to the fulfillment of this purpose was enabled by the introduction, development and diversification of different rotary nickel-titanium file systems. Characterized by superelasticity and used under well-defined values of torque and speed, as well as different types of rotary movement (constant, reciprocal), these instruments facilitate a successful approach to often difficult clinical situations, namely unfavorable root canal morphology: narrow, sharply curved or multiple curved canals, etc.

Regardless of the successive emergence of new generations of instruments, with a permanent improvement of the elements concerning the type of rotary motion, the metallurgical characteristics of the nickel-titanium alloy used and the file design, stresses and strains inevitably occur in the root canal dentin. These lead to the formation of microcracks, which can evolve, under the action of occlusal forces, towards cracks and even root fractures [1].

Dentinal cracks occur when the value of the tensile stress exerted on dentin by the endodontic instrument exceeds the value of the dentin tensile strength [2].

Article no. 608 O.E. Amza et al. 2

These dentinal microcracks are initiated at the level of stress concentration areas, due to elements specifically related to the endodontic instruments used: active or inactive tip, helical angle, taper, cross section geometry, pitch, flute, rake and cutting angles. There are multiple factors involved in stress concentration in dentinal walls, thus increasing the risks of dentinal cracks occurrence: endodontic instruments with an active tip and an “aggressive” cutting profile – which tend to have a screw-in effect in root canal dentin, a larger taper, a file design that leads to accumulation of debris, additional stress induced by the removal of root canal filling materials during endodontic retreatment, type of occlusion, occlusal load, etc.

Rotary systems based on the use of a single instrument operated by reciprocal rotational movements have a higher taper and despite the cyclic clearance of the instrument at the walls of the root canal, can also cause dentinal microcracks.

Parameters of the instrument rotation movement are also involved: the increase of speed and torque are directly proportional to the number of dentinal microcracks [3].

Dentin has a composite hierarchical structure. The effects of stress exerted on root canal walls are influenced by the intrinsic characteristics of the dentin, which in turn depend on certain factors, mainly represented by the tooth beeing vital or nonvital at the time of endodontic instrumentation, the existence of possible previous root canal treatments and age. Regarding this, the following may be taken into account: dentin dehydration, progressively installed following pulp pathology and dental pulp removal [4, 5]; alteration of the mechanical properties of dentin, due to the action of endodontic irrigants [6], root canal medication and root canal filling materials [7]; obliteration of the dentinal tubules with age, resulting in decreased effectiveness of the mechanisms for maintaining dentin resistance [8, 9,10,11]: non-obliterated dentinal tubules of young dentin allow deviation and branching of microcracks, thus preventing their convergence and accumulation with the formation of cracks and subsequent dentinal fractures [12].

The causative factors of root-originating microcracks, also known as dentinal defects [13], are relatively uncertain, but stress build-up occuring during shaping of the root canals – even though controversial – is among the most cited [14, 15, 16]. Already since 2010 it has been shown that dentin’s tensile strength is 106 MPa, while rotary files generate 311–368 MPa of stress on the radicular dentin, thus leading to the formation of micro-cracks [17].

The postendodontic development of microcracks, respectively dentinal cracks, are further amplified by the occlusal forces transmitted through the coronal or corono-radicular restorations, especially as change in bite forces after root canal treatment has been advocated [18].

The effect of propagation and accumulation of cracks in the root dentin over time, due to the combined effects of ductile fracture of intertubular dentin and brittle cracking of peritubular dentin on the crack initiation and propagation [19] can lead to a dreaded complication, namely the vertical root fracture, which in most cases requires extraction of the tooth.

3 Evaluation by finite element analysis of dentinal stress Article no. 608

Several different methodologies have been used in an attempt to reproduce in vitro the visualization of dentinal defects after endodontic procedures such as thermography, scanning electronic microscopy, finite elements, root sectioning, micro-CT scan, LED transillumination [13], without presenting the dentinal stress and strain developed during root canal shaping and involved in microcrack formation.

The impossibility of displaying by clinical or imagistic methods the stresses that cause microcracks and later dentinal cracks as a precursor to a possible vertical root fracture [13] requires a different approach, allowing the highlighting and localization of stresses due to the interaction between endodontic instruments and dentin root canal walls.

From this perspective, this paper aims to identify, analyze and determine the states of stress and strain occurring in the root canal dentin walls during endodontic instrumentation.

2. ANALYSIS OF THE DENTINAL STRESS AND STRAIN OCCURING DURING ENDODONTIC INSTRUMENTATION

Both mathematical modelling and finite element analysis were performed during the conduct of this study. Modeling involved creating the model of a tooth with a straight root canal mimicking a real single rooted tooth. The simulation consisted in assigning certain working conditions for the studied tooth model.

The lateral forces that are created by different instrumenting systems largely depend on their geometrical design and are increasing directly proportional with the root canal curvature [21]. In this case of straight root canals, in order to perform a comparative study, three states of stress were established, taking into account the possible forces applied by the clinician on the root canal walls when using the endodontic instruments, thus taking into account the cases: F1 = 1.0 N; F2 = 2.0 N; F3 = 4.0 N.

The magnitude of the forces applied to the dentinal walls was considered to be constant, whether it was the coronal third, the middle third or the apical third of the root canal. By acting with these forces exerted by the endodontic instruments onto the dentin, corresponding stresses will appear, which oppose these forces and respectively the removal of a dentin layer during root canal shaping, according to the principle of action and reaction. Taking into account the magnitude of the dentinal stress is important because when this exceeds the dentin fracture toughness, respectively its modulus of elasticity, microcracks and eventually cracks will occur. Highly mineralized peritubular dentin has a Young's modulus of 40–42 GPa, whereas weakly mineralized intertubular dentin has a Young's modulus of 17 GPa [20].

Simulation and study of the functional conditions of the tooth is the most important step in performing finite element analysis.

In this purpose a comparative analysis of the average embedding height in the alveolar bone structure was performed for such a single rooted tooth with a straight root canal. The graphical representation of this embedding is shown in Fig. 1.


Fig. 1 –Single rooted tooth embedded in bone structure (Color online). The diagram of the state of dentinal stress and strain that appear at the

endodontic instrumentation of the straight root canal is presented in Fig. 2, where a is shear stress, i is tensile stress and co is compression stress.

Fig. 2 – Dentinal stress and strain developing during the straight root canal instrumentation.


The analysis of the types of root canals and the different endodontic shaping techniques showed that the maximum dentinal stress occurs in the apical third area of the root canal [21, 22].

Beeing the narrowest space of the root canal, with the smallest cross section, the friction between the dentinal walls and the endodontic instrument is here the largest compared with the rest of the root canal. Therefore, in the apical third the volume of the cavity to be processed is smaller, has a relatively conical shape and predisposes to the appearance of a stress concentrator.

It should also be noted that the movement of the instrument in the axial direction of the root canal builds alternating tensile and compressive stress σi – σco. When the endodontic instrument moves towards the apical third, it produces compressive stresses and a compression of the material, while when moving in the opposite direction, it produces tensile stresses with the tendency to remove dentin from the root canal walls. At each contact point Mi and Ni between the endodontic instrument and the canal walls will appear tensile and compression stresses.

Their values are variable on the three axes because the endodontic instrument has both an axial and a rotary motion around its axis τf.

Fig. 3 – Force of 1N applied on the dentinal walls in the apical third of the root canal (Color online). Figure 3 shows the forces operating in the apical third of the root canal if the

endodontic instrument is acting with a force F1 = 1.0 N. As a result, in the apical third the material tends to move mostly in the

direction of the force (OY axis) with displacement UY. Figure 4 shows the displacements and the strains on the OY axis, respectively,

in case of exerting a force F1 = 1.0 N to an endodontic instrument used in the apical third of the root canal.


Fig. 4 – Displacements and respectively strains on the OY axis, in case of application of force F1 = 1.0 N; UY = 0.016 mm (Color online).

As a result of the application of this force F1 = 1.0 N and the appearance in

the apical third of the root canal of the system of forces shown in Fig. 3, a state of stress appears in the tooth structure, characterized by the presence of shear stresses, namely Von Mises axial stresses (Fig. 5).

Fig. 5 –Study of stresses: F1 = 1.0 N exerted on the endodontic instrument; Von Mises τmax = 12 · 109 N/m2 (Color online).

Figure 6 shows stresses occurring in the dentinal structure along the OY axis,

along which the debridement forces act during root canal shaping. As can be seen, in the dentinal structure there is the possibility of a state of compression stresses,


while in other areas the stresses are of a tensile nature and have a maximum value Τimax = 1.3 · 1010 N/m2. This value implies an elastic behavior of dentin but is closer to the value of the modulus of elasticity, which can lead to the removal of dentinal tissue and the widening of the root canal.

Fig. 6 – Study of stresses: F1 = 1.0 N exerted on the endodontic instrument on OY axis Von Mises τmax = 1.3·1010 N/m2 (Color online).

If the same system of forces acts in the apical third of the root canal but their

value is F2 = 2.0 N (Fig. 7) in the area of the apical third strain much larger than in the first case appear: UY = 0.031 mm (Fig. 8).

Fig. 7 – System of forces in the apical third of the root canal in the case of force F2 = 2.0 N exerted on the endodontic instrument (Color online).


Fig. 8 – State of stress in the apical third of the root canal in the case of force F2 = 2.0 N exerted on the endodontic instrument; UY = 0.031 mm (Color online).

Dentinal compression stresses have a lower value than tensile stresses:

σco = 2 · 109 N/m2 is smaller than σi max = 13 · 109 N/m2. The value is higher than the similar stress in the first case of loading, but is in the area of stresses that involve an elastic behavior of dentin. However, this value is closer to the value of the Young modulus of dentin, which also implies the possibility of deformation of the root canal, respectively of widening it during endodontic instrumentation (Fig. 9).

Fig. 9 – State of stress along OY direction in the case of force F2 = 2.0 N exerted on the endodontic instrument (Color online).


The third case of consists in the application of a system of four forces in the apical third of the root canal – there are 4 nodes resulting from finite element discretization – with the value of F3 = 4.0 N. Figure 10 shows the displacements in the studied area that reach a value in the OY direction of UY = 0.06 mm, a value significantly higher than in previous cases.

Fig. 10 – Displacements on the OY axis in the third case, with F3 = 4.0 N (Color online).

Figure 11 shows the corresponding stresses on the OY axis, when the system of forces acts towards the root canal wall.

Fig. 11 – Stress on the OY axis, when the system of forces acts towards the root canal wall with F3 = 4.0 N – stress introduced by the endodontic instrument (Color online).


Figure 12 displays the stress developed into the dentinal walls of the root canal during its shaping and remained as residual stress in the root dentin after the endodontic instrumentation is completed.

Fig. 12 – Stress on the OY axis, when the system of forces acts towards the root canal wall with F3 = 4.0 N – residual stress in the root canal dentin after endodontic instrumentation (Color online).

The forces exerted onto the root canal walls induce at this level shear stresses

with a maximum value of τf max = 51 · 109 N/m2 (Fig. 13), much higher than dentin elasticity modulus. Tensile stress has maximum values of σimax = 16 · 109 N/m2, close to the tensile strength of dentin.

Fig. 13 – Stress on the OX axis, F3 = 4.0 N; τf max = 51·109 N/m2 (Color online). This involves an elasto-plastic behavior of dentin, which means that it will

permanently deform during endodontic instrumentation without returning to its original


shape. In this case, during the action of this system of forces a state of tensile stresses will build-up into dentin, with a maximum value σimax = 0.5 · 1010 N/m2 (Fig. 14), close to the fracture toughness of dentin.

Fig. 14 – Von Mises at force F3 = 4.0 N; τf max = 42 · 109 N/m2 (Color online). The Von Mises stress was studied according to Fig. 14, where the maximum

value is shown to be that of the shear stress τf max = 42 · 109 N/m2, higher than the elasticity modulus of dentin. This value confirms the elasto-plastic deformation of dentin during the endodontic instrumentation of the root canal by removing an amount of dentin until the corresponding shaping of the apical third is obtained.

3. CONCLUSIONS

Being an important tool widely used to investigate complex systems, the finite element method applied in this research by using the Ansys software brings clarifications and answers in a field of research in which experimental methods cannot give conclusive results. The peculiarity of the access to the endodontic system and its unique environment do not allow the use of tensiometric probes or other experimental methods that can give real time information about the stress and strain of the root canal dentinal walls developed during endodontic instrumentation. In this situation numerical solutions are able to reveal the endodontic instrumentation effects and provide a suggestive image of the dentinal behaviour to a very realistic level.

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