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# Metrics for prosthetic cervical margin integrity assessment after dental CAD/CAM milling: a critical analysis from engineering viewpoint

Lebon Nicolas, Laurent Tapie

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Lebon Nicolas, Laurent Tapie. Metrics for prosthetic cervical margin integrity assessment after dental CAD/CAM milling: a critical analysis from engineering viewpoint. Odontology, 2025, 10.1007/s10266-025-01066-9. hal-04946721

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# Metrics for prosthetic cervical margin integrity assessment after dental CAD/CAM milling: a critical analysis from engineering viewpoint

Nicolas Lebon<sup>1,2</sup> · Laurent Tapie<sup>3</sup>

Received: 28 October 2024 / Accepted: 28 January 2025

© The Author(s), under exclusive licence to The Society of The Nippon Dental University 2025

## Abstract

Dental prostheses have significantly evolved due to advances in Computer Aided Design and Manufacturing (CAD/CAM) technology. CAD/CAM systems provide a variety of biomaterials like ceramics, Polymer-Infiltrated Ceramic Network (PICN), and composites, which are preferred for their mechanical and aesthetic properties. However, ceramics, despite their popularity, are brittle and prone to chipping during the machining process, impacting the prosthesis's clinical functions, aesthetics, biological integrity, and mechanical performance. Chipping, especially at thin cervical margin, can cause visible defects, poor sealing, and bacterial growth, reducing prosthesis lifespan. Milling factors influence cervical margin integrity. Chipping assessment involves understanding biomaterial mechanical and machinability characteristics regarding dimensional characterization of milled prosthesis shape. Thus, different type of metrics, based on biomaterial properties or dimensional measurement can be used to assess chipping phenomenon for milled dental ceramics. These metrics are both, based on experimental studies found in literature, and proposed by this paper authors to fill the existing lacks. The brittleness index, based on the ratio between hardness and fracture toughness, predicts susceptibility to chipping after milling. Unidirectional dimensional metrics like the Chipping Factor and weighted Chipping Factor characterize the chipping ratio of the cervical margin. Advanced 2D and 3D metrics, including chip projected area, total weighted chip projected area, and Surface Aspect Ratio, offer more detailed assessments. 3D analysis involves comparing scanned files with CAD models to compute chipped volumes. The aim of this paper is to propose a critical analysis from an engineering viewpoint on metrics used to assess cervical margin integrity for milled dental prosthesis.

**Keywords** Dental milling · CAD/CAM · Cervical integrity · Margin chipping · Indicators · Prosthesis

## Introduction

Dentistry is constantly evolving, thanks to the technological advances in prosthetic restoration design and CAM devices and biomaterials [1, 2]. CAD/CAM ceramics are

increasingly used in restorative dentistry and remain preferred materials for practitioners with a significant market share (42% in 2017) [3, 4]. Indeed, recent technical ceramics have received special attention due to their excellent properties, such as good fracture resistance, high wear resistance, chemical stability, biocompatibility, and aesthetics. Although, their brittleness remains a real weak point for milling shaping process.

The combination of brittleness and prosthesis local thickness is one common concern for CAD/CAM ceramics materials milling, which can cause damage. A typical machining-induced surface damage is so-called chipping, which is characterized by a significant volume of material loss. The detached piece of material from the edge of the component is called a chip (or a flake) [5]. It mainly occurs at the cervical margin where the thickness is thin (Fig. 1) and more particularly on ceramic materials, which

<figure><img src="image_3.png" /></figure>

<footnote>Nicolas Lebon
nicolas.lebon@devinci.fr</footnote>

<footnote>Laurent Tapie
laurent.tapie@univ-paris13.fr</footnote>

<footnote n="1">1. De Vinci Higher Education, De Vinci Research Center, Paris, France</footnote>

<footnote n="2">2. Université Paris Cité and Sorbonne Paris Nord, Inserm, Santé Orale, F-92120 Montrouge, France</footnote>

<footnote n="3">3. Université Sorbonne Paris Nord and Université Paris Cité, Inserm, Santé Orale, F-92120 Montrouge, France</footnote>
<figure><img src="image_4.png" /><figcaption>**Fig. 2** Chipping comparison according to the biomaterial (ceramic) used [6]. (Nota: for these millings, a wall thickness of 0, 2 mm was adopted by Dentsply, which does not follow minimum thickness manufacturers recommendations (to avoid chipping))</figcaption></figure>

are more brittle (Fig. 2). The process of producing a chip (or flake) from the edge of a component is called edge chipping (or edge flaking) [5]. Figure 3 illustrates the three-way correlation between the machining process, the cervical margin integrity, and its clinical impact. Correlation A corresponds to the link between clinical impact and chipping. Unfortunately, chipping compromises the prosthesis expected clinical functions, such as aesthetic, biological (cavities, dental plaque growth, cervical seal), and mechanical (retention, lifetime) functions. From an aesthetic point of view, a chip within a millimeter may be visible to the naked eye, revealing the yellowish color of the dentin in the case of a juxta- or supra-gingival margin. From a clinical point of view, chipping of the cervical margin causes poor sealing of the tooth-prosthetic joint. It also favors the development of cavities and bacteria which increases the risk of periodontal inflammation and the growth of dental plaque [9, 10]. More discontinuous the cervical margin is, the greater the risk of recurrence of cavities is. Moreover, this risk increases with the size of the chips, as it is a source of stagnation and is conducive to the development of bacteria that cause cavities and accumulation of dental plaque [11]. In addition, these

chips are a source of crack initiation in the prosthesis, which further reduces the life of the restorations, and are unsightly. Furthermore, damages can limit the minimum thickness of the material that can be achieved with the machining process and affect the accuracy of the final part with respect to the original designed dimensions. All of this is detrimental to the lifespan of the entire prosthetic restoration. Correlation B corresponds to the link between manufacturing parameters (set during machining) and cervical margin integrity. The milling feedrate, the cutting speed, the machining strategy used, the tool diamond grit size, and the wall thickness are some factors influencing chipping at the cervical margin [12–17].

The FDI Science Committee emphasizes, concerning the quality of dental restorations, that the cervical margin integrity is an important determinant of quality [18]. An increase in the lifespan of dental prostheses would be a clinical benefit for the patient and financial benefit to the society, which covers part of the cost. Since today around 50% of the European population has a dental prosthesis (fixed or removable) [19, 20]. Therefore, the impact of the milling parameters on the cervical margin damages remains an important drawback to maintain the

<figure><img src="image_5.png" /></figure>
<figure><img src="image_6.png" /><figcaption>**Fig. 3** Process—cervical margin integrity—clinical impacts triptych</figcaption></figure>

restoration longevity and quality. Towards this goal, cervical margin integrity assessment is a necessary step that consists of characterizing and quantifying the chipping phenomenon when milling.

Different type of metrics, based on biomaterial properties or dimensional measurements can be used to assess chipping phenomenon for milled dental ceramics. These metrics are both, based on experimental studies available in literature, and extended indicators formalized in this paper. Some of the extended indicators are linked to the clinical functions. The main objective of this paper is to propose a critical analysis, including the possible relationships with the clinical expectations, from an engineering viewpoint on current metrics used and proposed to characterize the chipping phenomenon on cervical margin for milled dental prosthesis.

<table><caption>**Table 1** Classification summary of chipping metrics associated indicators</caption><thead><tr><th>Dimension</th><th>Indicator</th><th>Local/Global</th><th>Clinically linked</th></tr></thead><tbody><tr><td rowspan="2">Biomaterial mechanical characterization</td><td>BI: Brittleness Index</td><td>Global</td><td></td></tr><tr><td>CF: Chipping Factor</td><td>Global</td><td></td></tr><tr><td rowspan="10">Dimensional characterization</td><td>CFw: weighted Chipping Factor</td><td>Global</td><td>Yes</td></tr><tr><td>Si: chip projected area</td><td>Local</td><td></td></tr><tr><td>S: total chipped projected area</td><td>Global</td><td></td></tr><tr><td>Sw: total weighted chipped projected area</td><td>Global</td><td>Yes</td></tr><tr><td>SARI: Surface Aspect Ratio</td><td>Local</td><td></td></tr><tr><td>Vi: individual chipped Volume</td><td>Local</td><td></td></tr><tr><td>V: global chipped Volume</td><td>Global</td><td></td></tr><tr><td>Wv: global weighted chipped Volume</td><td>Global</td><td>Yes</td></tr></tbody></table>

## Metrics classification for margin chipping assessment

First, an indicator linked to mechanical characteristics, the Brittleness Index (BI), is detailed. Then, 9 indicators
all based on dimensional characterizations, ranging from 1-dimension to 3-dimensions, are explained. All these 10 indicators are summarized Table 1.

## Biomaterial mechanical characteristics

Removal of biomaterial by milling involves deformations, micro-fractures, and finally chipping. These 3 phenomena are the consequences of a bad response to machinability. A method to determining machinability has been suggested by using mechanical characteristics of a biomaterial as parameters for estimating its machinability. One useful approach for the quantification of the brittleness of biomaterials consisting of a simple index of brittleness (BI) that can be derived from the hardness (H) and fracture toughness (Kic) of the biomaterial (Eq. 1) [21, 22]:

$$BI = \frac{H}{K_{Ic}} \qquad (1)$$

The brittleness index seems to be the right indicator of the level of machinability rather than hardness or toughness taken separately, since biomaterials with higher BI are more susceptible to chipping [23]. A biomaterial with a high BI would not represent the best choice as it would compromise its cervical integrity. Based on experimental evaluations, the authors agree to claim that to have good biomaterial machinability, its brittleness index must be less than 4.3√μm [22–24]. Figure 4 shows the BI for the 3 main biomaterial families used in restorative dentistry. It appears that, even if manufacturers produce biomaterials with a BI below this limit, ceramics are

still the closest to this machinability limit and indeed more impacted by chipping.

Nevertheless, the brittleness index being an intrinsic indicator of biomaterials, it does not consider the complete tool-material couple and the associated milling strategy. The machinability cannot be completely and precisely quantified by this index only.

## Unidirectional indicators

Two global unidirectional indicators to assess chipping are detailed. The Chipping Factor (CF) comes from literature and the weighted Chipping Factor (CFw) is an extend indicator including the clinical functions link, proposed by the authors.

### Chipping factor

To determine the cervical integrity, an estimation of the degree of cervical chipping was performed by calculating the 1-dimension Chipping Factor (CF) implemented by Tsitrou and Giannetopoulos [24, 25]. The following equation is used to calculate CF (Eq. 2):

$$CF = \left[ \frac{L}{P} \right] \times 100. \qquad (2)$$

With L the sum of the individual curvilinear chip length (Li) of each chip i (Eq. 3):

$$L = \sum_{i=1}^{n} Li, \qquad (3)$$

<figure><img src="image_7.png" /><figcaption>Fig. 4 Biomaterials brittleness index (BI)</figcaption></figure>
where *n* is the number of chips to be evaluated on the cervical margin and *P* is the cervical perimeter of the restoration multiplied by 100 to give the percentage of chipping. Figure 5 illustrates the experimental assessment of this 1-dimension chipping factor. ISO 18675:2022 standard propose a test part including merlon walls (solid upright section of a battlement between two embrasures) to evaluate

chipping according to the wall thickness, the biomaterial, and the milling parameters (Figs. 6, 7a) [27]. According to the FDI recommendations, each merlon wall width is average 25% of the total perimeter [11]. This specimen replicates the thin cervical margin of a dental prosthesis. According to the ISO standard, the wall is considered to be fractured as more than one third of its top edge is broken (Fig. 7b, c).

<figure><img src="image_8.png" /><figcaption>**Fig. 6** Representative samples of failed merlon wall fractures at 0.5 mm and successful merlon specimens at 0.6 mm. (The yellow ones are fully crystallized glass-ceramic (Straumann, Bâle, Switzerland) and the purple ones are lithium disilicate. (Ivoclar, Schaan, Liechtenstein) [26])</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 7** ISO 18675 merlon geometries [27]. **a** 3D view. **b** Intact free-standing walls (= merlons). **c** Fractured free-standing walls (= merlons)</figcaption></figure>
Thus, if CF < 33%, the cervical margin is considered to be suitable for use. From a clinical point of view, it seems to be a too high threshold regarding the expected clinical functions. It is difficult to accept a prosthesis with 1/3 of chipping on less than 1/4 of the marginal limit, deliberately bonded in a patient's mouth.

Jeong et al. milled merlons specimen and showed that CF is impacted by the wall thickness and the biomaterial milled, even if the authors did not include ceramic biomaterials in their study [28].

Hany et al. showed that CF increases when the feedrate is higher. The authors also indicated that the milled ceramic biomaterial influence the CF. With the same milling parameters, lithium disilicate (Ivoclar, Schaan, Liechtenstein) ceramic have the highest CF compared to those obtained on PICN (Vita, Bad Säckingen, Germany) or leucite-reinforced glass-ceramic (Ivoclar, Schaan, Liechtenstein) materials [29].

Furthermore, some authors have shown that there was a strong relationship between the Chipping Factor (CF) and the Brittleness Index (BI) [24]. This relationship highlights the impact of the milled material's mechanical characteristics on chipping. As a result, BI can be used as a predictor of CF, as chipping increases with material brittleness.

### Weighted chipping factor

The CF indicator can be generalized by weighting each curvilinear length (Li). The weighted chipping factor (CFw) is given by Eq. 4:

$$CFw = \left[ \frac{\sum_{i=1}^{n} \alpha_i Li}{P} \right] \times 100 \quad \text{with} \quad \sum_{i=1}^{n} \alpha_i = 1. \qquad (4)$$

The weighting system, more detailed in Sect. “Weighting system”, makes it possible to give importance to each chip depending on its location on the cervical margin and its impact on the clinical functions.

<figure><img src="image_10.png" /><figcaption>**Fig. 8** 2-dimensional chipping indicators. a 3D view of the simplified CAD crown. b Si projected area of the chip i. c Li length of the chip i. d Di depth of the chip i</figcaption></figure>

If all the weighting coefficients are equal ($\alpha = \frac{1}{n} = \alpha1 = \alpha2 = \dots \alpha n$), then $CFw = CF$.

### 2-dimensions indicators

Four 2-dimensions indicators to assess chipping (Fig. 8) are proposed.

#### Chip projected area

This 2D indicator, corresponds to the individual projected area (Si) of each chip i (Figs. 8b, 9a). The individual projected areas of each chip (Si) can be summed to obtain a global area indicator (S) (Eq. 5), corresponding to the total chipped projected area:

$$S = \sum_{i=1}^{n} Si. \qquad (5)$$

With n the number of chips to be evaluated on the cervical margin.

#### Total weighted chip projected area

The chip projected area indicator can be generalized by weighting each projected area (Si). The total weighted chipped projected area indicator (Sw) is given by Eq. 6:

$$Sw = \sum_{i=1}^{n} \alpha_i Si \quad \text{with} \quad \sum_{i=1}^{n} \alpha_i = 1. \qquad (6)$$

The weighting system, more detailed §3.1, makes it possible to give importance to each chip depending on its location on the cervical margin and its impact on the clinical functions.

If all the weighting coefficients are equal ($\alpha = \frac{1}{n} = \alpha1 = \alpha2 = \dots \alpha n$), then $Sw = S$.

<figure><img src="image_11.png" /></figure>
<figure><img src="image_12.png" /><figcaption>**Fig. 9** Chip indicator projected on a plane in ZEISS inspect optical 3D software implementation. **a** Projected surface (Si) of the chip i. **b** Chip curvilinear length (Li) of the chip i. **c** Chip depth (Di) of the chip i</figcaption></figure>

## Surface aspect ratio

The adoption of dimensionless indicators to characterize the surface is widely used in engineering sciences. The surface aspect ratio (SARi) of a chip i can be defined according to Eq. 7:

$$SARi = \frac{Li}{Di}, \qquad (7)$$

where Li is the chip curvilinear length (Figs. 8c, 9b) and Di the Chip depth (Figs. 8d, 9c).

If SARi > 1 then Li is higher than Di, so the chip fits a flattened rectangular box.

If SARi = 1 then Li equals Di, so the chip fits a squared box.

If SARi < 1 then Li is smaller than Di, so the chip is non flattened.

<figure><img src="image_13.png" /><figcaption>**Fig. 10** Chipping highlighted with a 3D CAD-CAM software (Catia V5), using a best-fit comparison. Chips are shown in brown color</figcaption></figure>

## 3-dimension indicators

The definition of 3-D indicators involves quantifying the volume of the chips. Figure 10 highlights the volume difference
<figure><img src="image_14.png" /><figcaption>**Fig. 11** Chipping highlighted using best-fit alignment and Hausdorff distance</figcaption></figure>

between a real chipped prosthesis scanned file and its CAD model file, using a best fit comparison. Nevertheless, it is only a qualitative comparison, and no indicator is computed.

To go further, the Hausdorff distance algorithm can be used to compute distances between two STereoLitography (STL) files after a best fit superposition (Fig. 11) [30]. A colormap can be established to headlight the height, the depth, and the width of each chip. This solution is quite easy to implement, but still does not give the volume of the chip.

STL models are surfaces (skins) and not filled volumes. As a result, they are hollow. The chipped volume assessment is not trivial, due to the nature of the STL mesh models itself. A simple Boolean operation (subtraction, addition, union, etc....) between the two STL models cannot be used. First, each hollow STL model (Fig. 12a) must be filled to obtain a volume instead of a skin (Fig. 12b). Then due to a very high number of facets making up the STL models from IOS, local cutting of the file isolating

a single chip is mandatory (Fig. 12c). Finally, a Boolean operation between the two volumes can be done (Fig. 12d), leading to the volume of the chip (Vi).

## Global chipped volume

The sum of the individual volume of each chip (Vi) can be calculated to obtain a global relative volume indicator (V) (Eq. 8):

$$V = \frac{\sum_{i=1}^{n} V_i}{V_p} \times 100. \qquad (8)$$

With n the number of chips to be evaluated on the cervical margin, and Vp the volume of the theoretical/CAD prosthesis. This indicator is in the same line as the chipping factor introduced by Tsitrou et al. [24, 25], but it deals with the volume instead of the perimeter.

<figure><img src="image_15.png" /><figcaption>**Fig. 12** Illustrations of the steps leading from a hollow skin to the chip volume. **a** Hollow STL, highlighted by a sectional view. **b** Filled STL, highlighted by a sectional view. **c** Region of interest cut. **d** Boolean operation done</figcaption></figure>
## Global weighed chipped volume

The weighted sum of the individual volume of each chip (Vi) can also be calculated to obtain a global weighted chipped volume indicator (Vw) (Eq. 9):

$$Vw = \left[ \frac{\sum_{i=1}^{n} \alpha_i V_i}{V_p} \right] \times 100 \text{ with } \sum_{i=1}^{n} \alpha_i = 1. \quad (9)$$

The weighting system, more detailed §3.1, makes it possible to give importance to each chip depending on its location on the cervical margin and its impact on the clinical functions.

If all the weighting coefficients are equal ($\alpha = \frac{1}{n} = \alpha1 = \alpha2 = \dots \alpha n$), then $Vw = V$.

## Metrics use and ease of implementation

Unfortunately, some difficulties associate to the implementation of chipping metrics exists, and some precautions must be taken.

### Weighting system

Three indicators, proposed in this article, are weighted. A particular attention must be paid to the choice of each coefficient. Weighting is a multi-physics concept which can be established according to the clinical implications involved in mechanical, aesthetic, and biological aspects.

From a mechanical point of view, chip-induced damage to fixed dental prostheses is influenced by the distribution of mechanical stresses. Some areas of the prosthetic margin are more prone to fracture initiated by chipping due to the loads generated during chewing. Occlusal marginal ridges are often subjected to high shear loads, especially when they are used as the main point of contact with antagonistic teeth. Cracks or chips on these ridges can rapidly extend to the cervical edges, compromising the entire prosthesis. The angles between occlusal surfaces and proximal surfaces (mesial and distal) are particularly vulnerable. These areas are subject to increase stress concentrations during lateral mastication. The lingual cervical margin is crucial as it supports the reverse masticatory loads. To prevent mechanical failure initiated by chipping in these areas, a high weight should be applied to the chips.

From an aesthetic point of view, the position of the chips is a key factor to the aesthetics of the smile. Poorly location can lead to problems such as discoloration, gingival recession, the creation of dark spaces, and a breakdown in aesthetic harmony. Chips in visible areas can expose the metal substructure of the prosthesis, creating an unsightly demarcation. In anterior areas, they can break the continuity with

the natural tooth, compromising the aesthetics of the smile. In addition, chips can lead to the formation of unsightly “black triangles” between the prosthesis and the tooth. Chips can also trap pigments and bacteria, causing local discoloration. All these poorly positioned chips can make the prosthesis misaligned with adjacent teeth. To avoid the attention of third parties these chips can be higher weighted.

From a biological point of view, the position of chips on the cervical margin can have significant consequences for oral health, particularly in terms of soft tissue and periodontal health. A chip in the mesial or distal area (areas close to the contact with the adjacent teeth), or near the contact with adjacent teeth, is harder to clean with a toothbrush, increasing the risk of bacterial buildup and gingival inflammation, or secondary caries along the cervical margin. Poorly positioned and/or too pronounced scales can exert pressure or friction on soft tissue, leading to ulceration or gingival recession. More importance (higher weight) will be applied to these chips.

### 1-dimension indicators

The unidirectional CF and CFw metrics are derived from manual measurements on images taken by the mean of a microscope. Measurement uncertainties related to manual measurement and the image levelling (to be such that the measurement is not impacted by a tilt image) will affect the result. Moreover, chipping factors are global criteria, i.e. CF/CFw only gives a value for the entire chipped perimeter. As such, it is not possible to establish possible relationships between machining parameters, intrinsic chip geometry and chip location on the cervical margin. Finally, these indicators do not consider the depth of the chip, nor its thickness, but only its length, whereas a chip can have a small depth and a significant length, and vice versa, impacting the clinical functions. To quantify the risk of secondary caries, which is higher if cervical edge is more discontinuous, the CF and CFw indicators seem to be the most suitable [11]. Nevertheless, 2D or 3D chipping indicators related to the chipped surface or volume would be more relevant and more representative of chipping than 1D-indicators.

### 2-dimension indicators

These indicators, linked to the chips surface are able to give further information about chipping. According to dentists in our laboratory [31], the projected surface of the chip (Si) seems to be a good indicator of several clinical functions affected by chipping. Indeed, it might have a strong possible relationship with optical properties, a medium possible relationship with cervical sealing, mechanical retention, restoration lifetime and dental plaque growth (Table 2). The Si indicator can be obtained using optical microscopy allowing
<table><caption>**Table 2** 2D indicators according to clinical functions</caption><thead><tr><th>Functions</th><th colspan="2">Mechanical</th><th colspan="2">Biological</th><th>Aesthetic</th></tr></thead><tbody><tr><td>2D indicators</td><td>Mechanical retention</td><td>Lifetime</td><td>Dental plaque growth</td><td>Cervical sealing</td><td>Optical properties</td></tr><tr><td>Si : Chip projected area</td><td>medium possible relationship</td><td>medium possible relationship</td><td>medium possible relationship</td><td>strong possible relationship</td><td>strong possible relationship</td></tr><tr><td>SARi : Surface Aspect Ratio</td><td>Li : Chip curvilinear length</td><td>Low possible relationship</td><td>medium possible relationship</td><td>medium possible relationship</td><td>strong possible relationship</td></tr><tr><td></td><td>Di : Chip depth</td><td>Low possible relationship</td><td>strong possible relationship</td><td>strong possible relationship</td><td>medium possible relationship</td></tr></tbody></table>

the acquisition of a photo, followed by a post-processing software such as ImageJ, as shown Fig. 8b. It can also be obtained through 3D scanning. The mesh model obtained is then processed in a 3D metrology software such as Zeiss inspect optical 3D (Fig. 9). In this method, the contour of the chip is projected onto a plane thus allowing its projected surface (Si) to be obtained (Fig. 9a).

The chip curvilinear length (Li), the numerator of the SARi indicator, is important to quantifying the chipping phenomenon. According to dentists in our laboratory [31], Li seems to be a good indicator of several clinical functions affected by chipping. Indeed, it might have a strong possible relationship with cervical sealing, a medium possible relationship with dental plaque growth, restoration lifetime and optical properties. A low possible relationship is observed with the mechanical retention (Table 1).

The chip depth (Di), the denominator of the SARi indicator, is also important to quantifying the chipping phenomenon. According to dentists in our laboratory [31], Di seems to be a good indicator of several clinical functions affected by chipping. Indeed, it might have a strong possible relationship with cervical sealing and restoration lifetime, a medium possible relationship with optical properties and dental plaque growth. A low possible relationship is observed with the mechanical retention (Table 1).

Globally, greater the SARi is, more the scale extends along the marginal margin, resulting in a less clinical (plaque retention) and mechanical impacts (crack initiation). Smaller the SARi is, deeper the scale is, resulting greater impacts on plaque retention, or on crack initiation, hence fatigue fracture.

Nevertheless, these metrics need a projection plane. To ensure relevance, the projection plane must be well chosen according to the clinical expectations. Evaluations of Si and SARi metrics on a simplified pyramidal milled crown have been conducted (Fig. 8a) [32]. This simplified pyramidal crown offers the advantage of being fitted with four flat faces, facilitating the acquisition of a projection plane (Fig. 8b). However, implementing this recommendation can be challenging in the case of a complex prosthetic shape. As the practitioner define, at the CAD step, an insertion axis

for each prosthesis, a perpendicular plane to this insertion axis can be used. Another way is to use a plan including the insertion axis. In the case of using a virtual projection plane (as an example, in Zeiss inspect optical 3D software), the plane can be computed to maximize the projected surface.

## 3-dimension indicators

Assessments of the chipped volume on an onlay had been undertaken (Fig. 12). The main problems encountered are the conversion of a hollow STL volume into a full volume and the Boolean subtraction operation, linked to the limitation of CAD software in connection with the limitation of the number of triangles to process.

To quantify the risk of biological complications, the V and Vw indicators seem to be suitable. Indeed, the higher the value of these indicators is, the greater the potential for bacterial accumulation is. Moreover, the increase in chipped volume reduces the intrados contact surface, resulting in a potential loss of retention of the prosthesis [33].

## Conclusion

While CAD/CAM technology has significantly advanced the field of dental prosthetics, ongoing research and refinement of material chipping assessment methods are crucial. The biomaterial mechanical characteristics knowledge can guide us as to whether chipping may occur. This qualitative approach is often insufficient and requires more in-depth quantitative investigations carried out by a unidirectional measurement up to a volume measurement, ranging from the simplest to the most complex to implement. Improved quantification techniques, detailed in this article, enhance the dimensional characterizations process, leading to higher quality prostheses that better meet the clinical needs of patients and practitioners.

While brittleness index provides an initial indication of machinability, it does not encompass the full scope of the tool-material interaction during the milling process. Unidirectional and two-dimensional indicators offer more detailed insights but still have limitations in terms of manual measurement accuracy and representation of actual chip geometry. The most comprehensive approach involves three-dimensional assessment, which quantifies the chipped volume using advanced imaging and computational techniques. Despite its complexity and the challenges associated with 3D mesh model manipulation, this method provides a more accurate representation of the damage, enabling better possible relationship with clinical outcomes.

Both global and localized assessments are proposed. Local indicators are not available in 1D, while global indicators are available for material machinability index and all
dimensional indicators. A weighted indicator is available
from 1 to 3D indicator, enabling the link with the clinical
functions. A comprehensive set of indicators is essential to
accurately characterize chipping phenomena, considering its
clinical implications.

**Acknowledgements** The authors want to thank ELMANNIOUI Hamza for his contribution to this paper.

**Data availability** The data sets used and analyzed during the cur-
rent study are available from the corresponding author on reasonable
request.

Declarations

**Conflict of interest** The authors declare that they have no known com-
peting financial interests or personal relationships that could have ap-
peared to influence the work reported in this paper.

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