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. Author manuscript; available in PMC: 2023 Nov 1.
Published in final edited form as: J Endod. 2022 Sep 12;48(11):1414–1420.e1. doi: 10.1016/j.joen.2022.08.011

Minimal Detectable Width of Tooth Fractures Using Magnetic Resonance Imaging and Method to Measure

Beth R Groenke *, Djaudat Idiyatullin , Laurence Gaalaas †, Ashley Petersen #, Hooi Pin Chew ±, Alan Law **, Brian Barsness ¶¶, Mathew Royal **, Ronald Ordinola-Zapata ‡, Alex Fok ǁ, Wondwosen Aregawi ǁ, Donald R Nixdorf *,§
PMCID: PMC9704057  NIHMSID: NIHMS1835607  PMID: 36100083

Abstract

INTRODUCTION:

Vertical root fracture (VRF) in root canal treated (RCT) teeth is a common cause of pain, bone resorption, and tooth loss. VRF is also difficult to diagnose and measure. Magnetic Resonance Imaging (MRI) has the potential to identify VRF due to beneficial partial volume averaging, without using ionizing radiation. This investigation aims to describe the narrowest VRFs detectable based on MRI, using micro-computed tomography (microCT) as the reference standard and proposes a method utilizing profile integrals to measure the widths of small VRFs.

METHODS:

VRFs were induced in 62 RCT tooth root samples. All samples were imaged in a phantom using MRI and reference imaging was obtained using microCT. The stacks of 3D axial MRI images were assessed by three board-certified endodontists. Evaluators determined the most coronal slice within the stack that was discernible as the extent of the VRF. This slice was measured on correlated microCT sections to determine the minimum VRF width (μm) detectable using a profile integral-based method to measure small fractures and negate the effects of the point spread function.

RESULTS:

Using profile integrals to measure VRF width was repeatable and resulted in estimates that were on average 1 μm smaller than known reference widths. Adjusted median VRF width detected using MRI was 45 μm (first quartile: 26 μm, third quartile: 64 μm).

CONCLUSION:

Using profile integrals is a valid way to estimate small VRF width. MRI approach demonstrated ability to repeatedly detect VRF as small as 26μm.

INTRODUCTION

Vertical root fractures (VRF) are discontinuities in tooth roots parallel to the long axis (1). Prevalence estimates vary widely between 1.4–13.4%, likely based on difficulty of diagnosis and on study methodology (2–8). If VRFs are undiagnosed, the probability for complications increases (2, 4–9).

The most accepted imaging method to diagnose VRF is cone-beam computed tomography (CBCT) (9–11); however, CBCT has several shortcomings: endodontic materials create artifacts (12–15), CBCT relies on identifying bone loss adjacent to the VRF (16–19), and it exposes patients to ionizing radiation (20).

Magnetic resonance imaging (MRI) is a promising method for detecting VRF for several reasons (21, 22): endodontic materials do not generate artifact (21), improved signal contrast (22), and no ionizing radiation (23). Finally, because of beneficial partial volume averaging, MRI has previously detected VRF as small as 20μm (22). Partial volume averaging occurs when signal from a small, sub-voxel sized object is strong enough to change the overall signal of the voxel (24). Although this effect can obscure structural boundaries, it allows for detection of anatomical structures smaller than voxel size, especially if there is a large signal discrepancy between two adjacent tissues, such as that between dentin and fluid, as in the case of VRF.

There are no methods known to the authors addressing precise measurement of small VRFs with potential for in vivo use. Previous methods have used: calipers, which only measures macroscopically (25), line measurement tools that rely on the human eye to distinguish VRF boundaries and can be inconsistent, especially at the micron level (26, 27), or optical coherence tomography which measures with high resolution, but capabilities are limited to segments visible to its light source, thus preventing in vivo VRF detection in sealed teeth (16, 18, 28, 29).

Prior studies exploring VRF detection in obturated RCT teeth found VRFs to measure between 50–770μm using CBCT (16, 18, 28) and 13–194μm using digital subtraction radiography (DSR) (26). The minimum detectable VRF width using MRI is unknown. The aim of this study was to develop and validate a robust method for quantification of VRFs and to determine the smallest VRF width detectable using MRI, based on the opinion of 3 board-certified endodontists, while using microcomputed tomography (microCT) as reference standard._We hypothesized MRI would have VRF detection capability at the limit of 10–20μm in extracted endodontically treated teeth, using micro-computed tomography (microCT) as a reference standard. We also propose a new method to measure small anatomical details, such as VRF, that have great importance in endodontics and are currently not accurately measured. Incorporating such a measurement within viewing software has potential to translate into more accurate assessments in clinical practice and is pertinent to all submillimeter imaging methods used like CBCT, optical coherence tomography and MRI.

MATERIALS AND METHODS

Materials and Sample Preparation

University of Minnesota’s Institutional Review Board exempted this research from oversight. Permanent human teeth extracted for non-study related purposes were collected, stored in 10% buffered formalin, and maintained hydrated either via complete submersion or regularly dripping water on the samples throughout the study to prevent desiccation and fracture propagation. Exclusion criteria were third molars and teeth with prior RCT or obvious anatomical abnormalities. Teeth were decoronated at the cementoenamel junction, and 2 mm of apices resected.

RCT was performed on each root using the recommended clinical protocol for WaveOne Gold (Dentsply Sirona), irrigation with 6% NaOCl (Chlorox®), and a 17% EDTA (Vista Dental Products) rinse. Canals were obturated using Pulp Canal Sealer (Kerr) and GuttaCore (Dentsply Sirona).

We induced VRFs using an 858 MTS Mini Bionix II (MTS Systems Corporation, Eden Prairie, MN) by advancing a 0.25mm tapered probe in the apical foramina 0.5mm, pausing 5–10s, then repeating until a VRF was induced. Audible and visual (transillumination) cues were used to monitor fracture initiation. When detected, the process was stopped.

Generated fractures varied from very small to completely cleaved. If cleaved samples could be reapproximated, VRFs were reduced and secured by tightly wrapping with wet Kimwipes® in vials.

Imaging of Samples

Reference imaging was obtained using microCT (XT H 225; Nikon Metrology, Brighton, MI). Imaging parameters were: 80kV, 95μA, 708ms with 720 projections and field of view minimized to include only the tooth root to achieve the smallest voxel size for imaging of each sample.

MRI imaging was obtained using a 4.0-Tesla (T) whole-body MRI scanner (90cm bore, Oxford, UK) with an Agilent DirectDrive console (Palo Alto, CA) and a custom intraoral coil (28). The pulse sequence used was Multiband Sweep Imaging with Fourier Transformation (MB-SWIFT) (29) with: scan time=5m39s, field-of-view (FOV)=120×120×120mm3, flip angle=12.0°, repetition time=4ms, bandwidth=128kHz, pulse length=4μs, delay after pulse=3.7μs, voxel size=0.25mm isotropic by using 64000-number of views. MRI images were acquired using an agar-filled, purpose-built phantom to hold the samples and intraoral coil in a clinically-oriented position.

Image Preparation

MicroCT image resolution was optimized per specimen based on size; therefore, the number of image slices varied. To match the number of slices in the corresponding MRI sample, microCT axial stacks were scaled in ImageJ™ (software version 1.52t, NIH, USA), with bilinear interpolation using VRF geometry and root morphology as guides for alignment.

Rater Data Collection

Raters were board certified endodontists, and familiar with three-dimensional imaging. At three training and calibration sessions, raters were provided axial image stacks with standardized criteria for VRF identification (Appendix 1). Raters determined if a discontinuity (i.e. VRF) was present. When a fracture was reported, the rater recorded the most coronal slice, which is typically the smallest portion of the fracture, where the VRF was discernible for measurement.

Measurement of VRF Width

Images were rotated so the VRF aligned longitudinally with the y-axis, then we used a rectangle to select a representative area of the VRF to analyze. We ensured the selected area of width (m) encompassed the entire VRF profile (f) by checking the profile of the selected area. We recorded the integral (mean intensity) of the selected area. Three additional means were obtained using the same selection box: immediately right (R) and left (L) of the VRF, to obtain integrals of variations in nearby dentin signal, and one of the background noise (b) (Figure 1).

Figure 1:

Figure 1:

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MicroCT visual representation of integral areas overlaying a VRF on a sample. Area “A” indicates the filled canal, and the VRF extends vertically above the annotated boxes. m=width of box used to calculate all integrals, w=VRF width, f=VRF width profile, L=left integral box, R=right integral box, b=background integral box

We then calculated fracture width using Equation 1. In summary, by maintaining a consistent rectangular area for all measurements, and after correcting for background noise, a ratio of the overall contribution of signal from dentin plus VRF to dentin alone was determined to estimate VRF width.

VRFw=[1−((∫f−∫b)(((∫R+∫L)2)−∫b))]⋅m (1)

Equation 1: Method to calculate VRF width where m=width of box used to calculate all integrals, w=VRF width, f=VRF width profile, L=left integral box, R=right integral box, b=background integral box.

The proposed profile integral method was validated using a convenience sample of 9 images from the data set. We generated rectangles of monochromatic dentin color and set the rectangles apart with known spacing intervals based on pixel size to simulate VRF. Exact size varied slightly based on resolution, but collectively were ~10μm, ~20μm, ~30μm, and ~50μm apart. Each sample was measured with 2 different sized integral measurement boxes (0.2×0.1mm2 and 0.2×0.4mm2) at each interval.

We measured VRF width using the scaled microCT stacks in ImageJ™ at the slice number provided by the endodontists based on analyzing MRI images. For fractures extending the entire diameter of the specimen, 2 independent representative areas were measured; one on each side of the canal, and averaged. For fractures extending from the canal through half of the sample, one representative area was analyzed.

To evaluate error introduced by scaling, full and scaled axial microCT image stacks for the same specimen were evaluated independently by a radiologist and an orofacial pain specialist, both board-certified and familiar with the technology. For both stacks, evaluators determined the most coronal slice with the smallest detectable VRF, or in instances of oblique fractures, determined the most representative slice comparable to the most coronal slice of the scaled stack. In instances of disagreement, evaluators established consensus on one slice. We measured microCT VRF widths at the consensus slices for both the full and scaled stacks and recorded the absolute value of the difference between these values and measures of spread, as well as the correlation coefficient. This measurement allowed us to estimate scaling distortion between the full and scaled microCT image stacks (Figure 2).

Figure 2:

Figure 2:

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Visual depiction of potential sources of measurement discrepancies and methods in place to estimate these variations. 1) accounts for distortion from full to scaled microCT stacks, 2) accounts for image positioning and potential registration errors between scaled microCT and MRI stacks.

To account for variation in sample positioning during image acquisition and for registration errors, additional VRF measurements were obtained one slice above and one slice below the identified VRF slice. We calculated the absolute value of change in VRF width measured from the additional slices for a subset of 22 samples. We selected a range of 3 slices, approximately 0.5mm total, since many small VRF were only evident in a total of 2–3 slices of the sample. This measurement allowed us to estimate inaccuracies from sample position (Figure 2).

Statistical Analysis

To estimate the measurement error itself and the impact of both VRF width and the integral method measurement box size on said measurement error, linear mixed effect models were used with random intercepts to account for correlation of measurements from the same scan.

To summarize detectable VRF widths, descriptive statistics (median, interquartile range [IQR], minimum and maximum values) were used due to the skewed data distribution. To err on the side of providing more conservative measurements and to account for errors introduced during scaling and stack alignment, we calculated total error by combining the absolute error between the full and scaled microCT stacks and the average absolute change in VRF width. Analyses were performed using R version 3.6.1 (R Foundation for Statistical Computing, Vienna, Austria).

RESULTS

Samples Processed

We induced VRF in 72 samples. Three samples had catastrophic failure and were discarded, six did not have a VRF detectable on microCT and one had recognizable anatomy and was used only for training. Therefore, final sample size was 62 VRFs. Of these, raters correctly identified VRF in 34 samples and specified a slice to measure.

Profile Integral Measurement Method Validation

On average, measured VRF widths using the 0.2×0.1mm2 box were 4.0% shorter than known widths based on pixel size (95% CI: 2.5–5.5%) corresponding to measured widths that were, on average, 1.0μm shorter (95% CI: 0.6–1.4μm) than the actual widths. Using the 0.2×0.4mm2 box resulted in 4.2% shorter measured widths than the actual widths (95% CI: 3.1–5.3%), or measured widths 1.0μm shorter (95% CI: 0.7–1.3μm) than the actual widths. The box size did not significantly impact the relative (p=0.65) or absolute (p=0.79) error. The relative error was fairly constant regardless of VRF width with 0.3% more error (95% CI: 0.03% less error to 0.7% more error) for each additional 10μm of VRF width for the 0.2×0.1mm2 box (Figure 3A). Wider VRF had higher absolute error with 0.31μm more error (95% CI: 0.17–0.45μm) for each additional 10μm of VRF width for the 0.2×0.1mm2 box (Figure 3B). Results were very similar for the 0.2×0.4mm2 box and robust to excluding the outlier with overmeasurements for both box sizes. Re-inspection of the outlier revealed artifact in the background.

Figure 3:

Figure 3:

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Association between the actual known VRF widths and the (A) absolute relative error (measured width / actual width) (left) and (B) relative absolute error (measured width - actual width) (right) in VRF width measurements using a 0.2 × 0.1 mm2 and 0.2 × 0.4 mm2 boxes. Lines connect measurements from the same scan.

Imaging Analysis and MRI/microCT Correlations

MicroCT image stacks contained an average of 1,356 slices/sample (range: 839–1,818 slices). MRI image stacks averaged 58 slices/sample (range: 41–80 slices). Using bilinear interpolation, we scaled full axial microCT image stacks to individually correlate with the same number of slices in corresponding MRI image stacks. MicroCT resolution of samples averaged 8.3μm (range 7.3–9.6μm).

Two primary types of VRF based on orientation were identified in the study during the scaling process: primarily non-oblique (n=53) and primarily oblique (n=9) VRF. Of note, 6 of the 9 oblique VRFs were samples that were complete VRF, meaning VRFs that resulted in 2 pieces that were reapproximated. The oblique VRFs exhibited more distortion after scaling (mean width change ± SD: 4.1 ± 19 μm smaller for scaled stack) than those in the non-oblique group (mean width change ± SD: 0.6 ± 3 μm larger for scaled stack); however, this was not statistically significant; therefore, we pooled all data (p = 0.48).

Measurement error introduced by scaling the pooled full microCT axial image stacks resulted in scaled microCT stack widths that were 0.6μm smaller on average compared to the full microCT stack widths (minimum: −33μm, IQR: −2μm to 1.75μm, maximum: 36μm) This scaling difference was not statistically significant (p=0.71).

To account for variation in positioning of samples between imaging modalities and discrepancies introduced from aligning scaled microCT and MRI image stacks, we also summarized the average absolute change in width over 3 consecutive scaled microCT slices, using the average rater identified slice as the middle reference point. Median change in VRF width between 3 slices was 2.5μm (minimum change: 0.5μm, IQR: 2.0μm to 3.4μm, maximum: 34μm). While VRFs typically propagate in a “V” pattern, narrowing toward the coronal aspect, that course is not always purely linear, leading to a transient, counter-intuitive widening of the VRF as it is measured coronally.

To provide conservative estimates, we calculated total measurement error by combining the absolute error between full and scaled microCT image stacks, the absolute average change in width over 3 consecutive microCT slices, and the measurement error using the integral method. Median total error was 6μm (minimum: 2.5μm, IQR: 4.0μm to 15.3μm, maximum: 42.5μm).

VRF Width Detection

Of the 62 samples, consensus raters correctly identified 34 as having VRF. VRF widths measured from the scaled microCT stack correlated with the last MRI slice in which raters could visualize VRF had a raw median value of 39μm (minimum: 3μm, IQR: 20μm to 58μm, maximum: 93μm) (Figure 4). Adjusting for the calculated median total measurement error of 6μm, the smallest detectable VRF widths consistently fell within 26μm-64μm and were as small as 9μm. Figure 5 shows examples of various fracture sizes detected by MRI with the corresponding microCT slice.

Figure 4:

Figure 4:

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VRF distribution of identified VRF width by rater consensus (μm) using violin plot of raw data.

Figure 5:

Figure 5:

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Examples of identified VRF sizes. Width includes +6μm estimate for measurement error to provide most conservative measurement.

DISCUSSION

The most direct way to measure VRF width is to measure the width of the VRF’s rectangular gray scale profile oriented orthogonally, however; this method has two shortfalls. First, is measurement inconsistency due to judgement or algorithms determining a threshold corresponding to the VRF wall. Second, is direct measurement is highly inaccurate if the VRF width is comparable to or less than the width of the point spread function (PSF). The PSF is a property of how an imaging system itself responds to one point object being imaged. The image interpreted by end-users is a convolution of the PSF and the actual image from the object. Thus, the blurring radius due to the PSF is a limiting factor for direct measurements for structures smaller than the PSF. Because this study’s VRF widths are smaller than the PSF, the VRFs’ profiles do not have expected rectangular shapes, but are convolved with the PSF, similar to low-pass filtering. The width obtained by direct measurements in this case will overestimate VRF width. However, a profile integral (orthogonal to VRF) of the area underneath a VRF profile is less susceptible to human error and is not affected by low-pass filtering. Based on this property, a new method using profile integrals to measure VRF width was developed.

MRIs reviewed were specifically collected using a protocol for human study (i.e., large FOV, in vivo scan time, etc.), had minimal image processing, and no smoothing. Therefore, images appeared more granular than those conventionally reviewed in dental settings (Figure 4). VRFs often only extended a few slices into the sample, and there were not adjacent structures to guide raters as with in vivo studies (e.g., surrounding bone loss), Despite this, evaluators detected 55% of the VRF samples and demonstrated ability to detect VRF on MRIs with adjusted median width of 45μm and IQR 26μm-64μm. The smallest VRF width detected by raters was at the calculated theoretical limit of detection for MRI of 10–20μm (22).

We found 5 studies that previously reported specific VRF widths: 4 pertained to CBCT (15, 17, 25, 30) and 1 to DSR (26). None had the same aim as our study. One study used microCT as a reference standard, though reported VRF data on length only; therefore, findings cannot be compared (11). Of the studies that reported VRF width, one study used electronic calipers to set widths to be <200μm, ≥200μm, or ≥400μm (25). Three studies used OCT to measure along the tooth’s surface. One study reported VRF widths ranging from 60–770μm (17). Another categorized simulated VRF as either complete or incomplete, and reported incomplete VRF widths ranging from 50–110μm (15). A subsequent study used OCT to measure the widest portion of identified VRF and reported widths ranging from 30–110μm (30). The final study used a microscope’s calibrated line measuring feature and found fracture sizes ranging from 13–194μm (26). Despite differing aims, these studies inform the detectable VRF widths using CBCT and DSR. This study confirms MRI has similar capabilities to detect small VRF.

A limitation of our study is that teeth needed to be imaged in a separate container for microCT and MRI, resulting in positioning discrepancies between the reference images and test modality. Additionally, stack alignment between scaled microCT and MRI stacks was performed using visual inspection based on VRF geometry and tooth anatomy. Accordingly, some misalignment between samples occurred. Efforts were made and reported to quantify this error. However, to increase the precision of future studies, it is recommended a calibration marker be incorporated with samples to facilitate alignment.

This study used an agar-filled phantom to simulate the effect of soft tissues. Further iterations should consider incorporating a phantom to also mimic boney structures.

Using profile integrals with the proposed formula to measure small VRFs is a valid way to estimate small VRF widths and has the potential to be used in vivo. Raters demonstrated the ability to detect VRFs with median widths of 45μm, with interquartile range of 26–64μm. This suggests that MRI is a potential methodology that can be further developed for the purpose of in vivo VRF detection.

ACKNOWLEDGEMENTS

The authors deny any conflicts of interest.

Thanks to Estephan Moana-Filho, Bonita VanHeel and Dr. Young Heo for assistance.

FUNDING

Supported by American Academy of Orofacial Pain; National Institutes of Health [P41-EB027061, S10-RR023730]; and by the National Center for Advancing Translational Sciences of the National Institutes of Health [UL1-TR002494]. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. Materials donated by: Dentsply Sirona and Kerr.

APPENDIX

Criteria for CBCT/MRI Crack/Fracture Presentation

A separation of the adjacent root segments on multiple contiguous image slices without the continuation of the bright or dark signal line into the adjacent tissue (or water as was present in this ex vivo study design). This signal line must be observed within the confines of tooth structure, delineated by:

  1. External tooth surface: bounded by enamel, the external surface of dentin, or cemental tissue depending on the level of axial slice.

  2. Internal tooth surface: external extent of the pulpal cavity

For purposes of this study, the physical discontinuity must have the following criteria to be given a designation of a crack/fracture.

  1. Signal line(s) must extend from the external boundary of the tooth toward the pulpal cavity (or vice versa)* on contiguous image slices.^

  2. The overall contour of the external tooth surface and pulpal cavity must be maintained.** The signal line(s) must be visible near the apex of the tooth.#

Explanation of stated criteria:

  1. *These cracks are thought to be clinically significant.

  2. ^The criteria of multiple image slices allow for detection of an angled crack.

  3. **To prevent gross root discontinuities from mistakenly being classified as a crack.

  4. #To prevent other defects or craze lines from being misclassified as a VRF.

Furthermore, it is important to differentiate cracks/fractures from other commonly encountered pathologic changes in tooth morphology that may be observed, and to rule out artifact and possible false positive identification. The following entities should be differentiated from cracks/fractures:

  • Multiple streak artifacts from root fillings that traverse the root and adjacent tissue.

  • Aberrations in dental anatomy or morphology which may include
    • Accessory, lateral, or secondary pulp canal(s)
    • Canal ramifications
  • Physiologic or pathologic processes which may include
    • Root Resorption (Inflammatory, Replacement, Surface, Cervical, External, Internal)
    • Caries

Footnotes

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