Vertical Root Fracture in Non-Endodontically and Endodontically Treated Teeth: Current Understanding and Future Challenge

A vertical root fracture (VRF) is a complex complication that usually leads to tooth extraction. The aim of this article is to review the prevalence, demography, distribution, diagnostic methods, etiology and predisposing factors, clinical features, radiographic characteristics and treatment strategies of VRFs in non-endodontically treated teeth (VRFNETT) and endodontically treated teeth (VRFETT). Search terms for each subject related to VRFNETT and VRFETT were entered into MEDLINE, PubMed and Google Scholar. Systematic reviews, retrospective cohort studies, demographic research, clinical studies, case reports and case series were reviewed. Most of the VRFs were found in patients older than 40 years old. Older populations were discovered in the non-endodontically treated VRF group when compared to the endodontically treated VRF group. Male patients were found at a greater prevalence than females in the non-endodontically treated VRF group. The initial occurrence of a VRF may accompany radiolucent lines within the root canal, unusual space between the canal wall and intracanal material, a widening of the PDL space along the periradicular surfaces, angular bony destruction, step-like bone defects, V-shaped diffuse bone defects, or root resorptions corresponding to the fracture line before the clear separation of the fractured fragment. The indicative clinical and radiographic signs of VRF included a coronally positioned sinus tract, deep-narrow periodontal defects, the displacement of a fractured fragment, periradicular radiolucent halos and the widening of the root canal space. Interestingly, VRFNETT are more often observed in the Chinese population. Some patients with multiple VRFs were observed, suggesting possible predisposing factors in genetics and tooth development. The management of a VRF usually involves a multidisciplinary approach. The common distribution and features of VRFNETT and VRFETT were elucidated to facilitate recognition and diagnosis. Besides extraction, variable therapeutic schemes, such as the repair of the VRF, root amputation and others reported in earlier literature, are available. A long-term prognosis study of the various therapeutic strategies is needed.


Introduction
A vertical root fracture (VRF) is defined as a longitudinally oriented fracture of the root [1]. Clinical detection of this phenomenon is challenging, not only for general practitioners, but also for endodontic specialists. A VRF usually occurs in endodontically treated teeth, but it has occasionally also been reported in non-endodontically treated teeth [2,3].
Males showing VRFNETT were found to be more common than female patients [2,19,20]. This may be because males often exhibit stronger masticatory forces and chew harder food than females [4], thus leading to a higher possibility of VRFNETT.

Age
Most VRFs occurred in patients aged between 30 and 69 years old [3,4,14,19]. A demographic analysis illustrated that 86.79% of the patients were older than 40, which was a significant factor [6]. Older patients have more chances of receiving extensive restorations leading to a weakening of the tooth structure [21].
VRFNETT usually occur in older populations when compared to the endodontically treated group [2,3,19,20]. The average ages were 69 years old in the non-endodontically treated group and 56 in the endodontically treated group [22], suggesting that endodontic treatment is a predisposing factor for a VRF. The teeth of the older people may sustain higher occlusal forces and more prolonged stress over time, which may lead to VRFs even without endodontic treatment [2,22]. Another possible explanation is that endodontic treatment procedures weaken the tooth structure and cause a VRF even in younger patients [4,22].

Tooth and Root Distribution of VRF
Based on demographic research, maxillary premolars and mandibular molars were found to be the most frequently fractured teeth in cases of VRFETT [6,[23][24][25].
In both VRFETT and VRFNETT, roots with a cross-section of a smaller mesiodistal diameter and with a deep oval or flattened shape ( Figure 1) are more susceptible to VRFs [4,27]. VRFs were, thus, mainly detected in the maxillary premolars and mesial roots of mandibular molars [28]. [2,19,20]. This may be because males often exhibit stronger masticatory fo harder food than females [4], thus leading to a higher possibility of VRFNE

Age
Most VRFs occurred in patients aged between 30 and 69 years old [3 mographic analysis illustrated that 86.79% of the patients were older than a significant factor [6]. Older patients have more chances of receiving ext tions leading to a weakening of the tooth structure [21].
VRFNETT usually occur in older populations when compared to the treated group [2,3,19,20]. The average ages were 69 years old in the nontreated group and 56 in the endodontically treated group [22], suggesting t treatment is a predisposing factor for a VRF. The teeth of the older peop higher occlusal forces and more prolonged stress over time, which may lea without endodontic treatment [2,22]. Another possible explanation is th treatment procedures weaken the tooth structure and cause a VRF even tients [4,22].

Tooth and Root Distribution of VRF
Based on demographic research, maxillary premolars and mandibula found to be the most frequently fractured teeth in cases of VRFETT [6, VRFNETT were often found in maxillary and mandibular first molars population [2][3][4]19,20,26]. Severely attrited first molars without or with m tions were a common feature [2,20].
In both VRFETT and VRFNETT, roots with a cross-section of a smal diameter and with a deep oval or flattened shape ( Figure 1) are more susce [4,27]. VRFs were, thus, mainly detected in the maxillary premolars and mandibular molars [28].

Diagnostic Methods
Diagnosis should combine the patient's subjective complaints and objective evaluations, rather than a single pathognomonic result [6]. The early diagnosis of a VRF is important to avoid unnecessary nonsurgical retreatment, continued soft tissue swelling, bone loss, or apical surgery [29], leading to difficulty in subsequent implant surgery. The possible diagnostic signs and methods are listed for clinical verification.

Coronally Positioned Sinus Tract
When a sinus tract is found in a VRF tooth, it is usually located in the coronal rather than apical area [28]. This type of sinus tract was found in 35-42% of VRFs [14,30]. Multiple sinus tracts are also a common feature [31,32].

Biting Pain and Bite Test
In order to reproduce the discomfort of the patient while chewing and thus reconfirm their chief complaint, a bite test was suggested [33]. Tools such as rubber wheels or a Tooth Slooth ® Fracture Detector (Professional Results Inc., Laguna Niguel, CA, USA) can be applied [33]. Endodontically treated teeth with a good quality root canal filling that exhibited specific biting pain is regarded as highly suspicious [34].

Deep Periodontal Probing Depth
A deep periodontal pocket is a common sign, reported in 64-93% of VRFs [22,35]. Unlike periodontal diseases, here, a deep probing depth has been found corresponding to the root fracture line. A deep narrow periodontal defect suggests underlying bony destruction caused by a VRF [28,33]. In the early stages of a VRF, some cases did not show deep probing, but the fractured line could be detected using periapical radiographs ( Figure  2A1,A2,B1,B2). Diagnosis should combine the patient's subjective complaints and objective evaluations, rather than a single pathognomonic result [6]. The early diagnosis of a VRF is important to avoid unnecessary nonsurgical retreatment, continued soft tissue swelling, bone loss, or apical surgery [29], leading to difficulty in subsequent implant surgery. The possible diagnostic signs and methods are listed for clinical verification.

Coronally Positioned Sinus Tract
When a sinus tract is found in a VRF tooth, it is usually located in the coronal rather than apical area [28]. This type of sinus tract was found in 35-42% of VRFs [14,30]. Multiple sinus tracts are also a common feature [31,32].

Biting Pain and Bite Test
In order to reproduce the discomfort of the patient while chewing and thus reconfirm their chief complaint, a bite test was suggested [33]. Tools such as rubber wheels or a Tooth Slooth ® Fracture Detector (Professional Results Inc., Laguna Niguel, CA, USA) can be applied [33]. Endodontically treated teeth with a good quality root canal filling that exhibited specific biting pain is regarded as highly suspicious [34].

Deep Periodontal Probing Depth
A deep periodontal pocket is a common sign, reported in 64-93% of VRFs [22,35]. Unlike periodontal diseases, here, a deep probing depth has been found corresponding to the root fracture line. A deep narrow periodontal defect suggests underlying bony destruction caused by a VRF [28,33]. In the early stages of a VRF, some cases did not show deep probing, but the fractured line could be detected using periapical radiographs (Figure 2A1, A2, B1, B2).

Pulp Vitality Test
VRFNETT may show vital or necrotic pulpal responses [22]. The nerve tissue may necrotize when the fracture lines progressively extend into the pulp. A VRF is highly suspected in nonvital teeth with an intact structure or minimal restorations, when no other evident etiology can be identified [33].

Magnification
A microscope may assist in identifying the fracture line during nonsurgical or surgical endodontic/periodontal treatments. Magnification and direct light sources are helpful [36].

Radiographic Assessment
Although radiographic images do not always reveal a clear vertical fracture line, X-rays are still necessary. Employing different X-ray angles may reveal the fracture line ( Figure 2C1,C2). If the fractured root fragment is displaced from the original tooth structure, then a definite diagnosis of root fracture can be made [36].
Superimposition and distortion are the most common problems encountered with two-dimensional radiographs. Cone beam-computed tomography (CBCT) images could assist in the verification of VRFs [37][38][39]. However, radiopaque intracanal materials may result in artifacts or obscure the fracture line, thus limiting its diagnostic value [36,40]. An in vivo study analyzed the accuracy of high-resolution CBCT used for detecting VRFs and concluded that the tool was non-diagnostic. Intracanal metal posts and multirooted teeth limited the diagnostic outcome [40]. Thus, CBCT is more useful in the diagnosis of non-endodontically treated VRFs [41] ( Figure 2D1-D3), otherwise materials must be removed before performing the CBCT. There is still no consensus on the accuracy of CBCT in detecting endodontically treated VRFs. The voxel size also plays an important role in the observation of fracture lines. In a study assessing VRFETT via micro-computed tomography, a 9-micrometer voxel size was recommended for accurately observing a VRF [29]. The smallest currently used voxel size for CBCT is not comparable to that used for micro-computed tomography [40]. Thus, limitations remain when detecting VRFs via CBCT.

Exploratory Surgery
Surgical intervention is suggested when a VRF is highly suspected but cannot be confirmed through other examinations [36]. During surgery, a sharp explorer or methylene blue staining may be used to detect a possible VRF. Changing the position of the light and employing different reflections is sometimes useful when trying to observe the fracture line [32]. Many studies have concluded that direct visualization of the VRF via exploratory surgery is the gold standard [4, 13,31,33,36,42]. If the clinical and radiographic examination results are inconclusive, exploratory surgery is an option ( Figure 2E1,E2). The diagnostic procedures are illustrated as a flowchart in Figure 3.

Excessive Tooth Structure Removal or Over-Preparation during Root Canal Instrumentation
Excessive tooth structure removal could result in the weakening of the tooth and increase the occurrence of VRFs [28,33]. Dentinal defects, such as craze lines or incomplete fractures, may be generated during these procedures [43,44]. These cracks may initiate and lead to further root fractures. The root thickness following dentin removal is intrinsic to withstanding masticatory forces and should be always considered [25].

Excessive Force during Root Canal Obturation
Excessive pressure during lateral or vertical compaction may result in a VRF [13,25,[45][46][47]. The wedging forces may initiate stresses and strains, and further lead to root fracture [48][49][50][51]. However, other studies have demonstrated that the prevalence of VRFs caused by lateral condensation force is relatively low [48,52]. The maximum stress and strain produced during root canal obturation were investigated, and the results were significantly lower than those observed with condensation force, which could cause root fractures. Thus, condensation forces may not be the direct cause of root fracture. A weaker radicular structure tends to generate initial cracks, which could lead to root fracture even after the application of normal force [46].  Excessive tooth structure removal could result in the weakening of the tooth and increase the occurrence of VRFs [28,33]. Dentinal defects, such as craze lines or incomplete fractures, may be generated during these procedures [43,44]. These cracks may initiate and lead to further root fractures. The root thickness following dentin removal is intrinsic to withstanding masticatory forces and should be always considered [25].
However, other studies have demonstrated that the prevalence of VRFs caused by lateral condensation force is relatively low [48,52]. The maximum stress and strain produced during root canal obturation were investigated, and the results were significantly lower than those observed with condensation force, which could cause root fractures. Thus, condensation forces may not be the direct cause of root fracture. A weaker radicular structure tends to generate initial cracks, which could lead to root fracture even after the application of normal force [46].

Excessive Post Space Preparation
Post space preparation may weaken the radicular structure and further result in VRFs [13,47,[53][54][55]. Post space design should minimize the removal of the intact radicular dentin structure. Posts should be placed into the canal with minimal force [28]. Any intracanal wedging effects generated during treatment procedures should be avoided, because these may exceed the elasticity of dentin [25]. Fiber posts possess a similar modulus of elasticity to dentin. Studies have suggested that fiber posts could reduce root fractures and increase the survival rate of endodontically treated premolars [56,57].

Loss of Remaining or Internal Tooth Structure
Preservation of the remaining and internal tooth structure should be emphasized when restoring endodontically treated teeth [58,59]. Endodontically treated teeth are more susceptible to VRFs because they are usually associated with tooth or root structural loss.

Specific Anatomies of the Susceptible Roots
Roots with a narrow mesiodistal width, such as upper premolars and mandibular molars, are more susceptible to VRFs [4,54,60-62]. A VRF usually initiates from the area of the canal wall with the greatest curvature as a result of asymmetrical stress distribution [63]. Irregularities in the inner canal surface may increase localized stress [63]. Canal shape, root shape and dentin thickness have been investigated to confirm which affects the tensile stress distribution the most. Among the three factors, canal shape was determined to be the most important. The conclusion of the research was that an ovoid root and ovoid canal, combined with reduced proximal dentin thickness, would increase the occurrence of VRFs [27].

Age-Related Microstructural Changes
Increases in brittleness and reductions in fracture resistance are expected with aging [64]. Thus, the teeth of older patients may be more susceptible to root fractures than those of younger patients [65]. Another study suggested that fractures are significantly associated with sclerotic dentine formation, which increases with aging. Sclerotic dentin displays lower toughness and reduced flexibility in older people. Thus, age-related microstructural changes may also be an underlying cause of VRFs in endodontically treated teeth [66]. However, some clinical patients showed multiple VRFs in different teeth during sequential follow-up periods ( Figure 4A1-A8), suggesting the presence of genetic and developmental factors that may make the intrinsic dentin structures more susceptible to VRFs.

Implant-Related VRFs
An implant-protective occlusion, which minimizes the occlusal loading on the implant, may make the adjacent natural teeth vulnerable to greater occlusal forces [67][68][69]. Endodontically treated teeth have been reported to exhibit lower fracture resistance than vital teeth [70]. Therefore, the possibility of implant-related VRFs in endodontically treated adjacent teeth has been suggested [71].

Repetitive Heavy and Stressful Chewing Habits
Non-endodontically treated VRF teeth are usually related to occlusal factors. The Chinese population presents some unique chewing habits. For example, the chewing of betel quid, bones in meat, or food that is not easily sheared are risk factors that may predispose teeth to VRFs in non-endodontically treated teeth [2][3][4]19,22,72]. Chewing betel quid (a product of the areca nut, with coarse fibers) is more popular in males in Taiwan [73]. This oral habit is reported to contribute to VRFs in Chinese populations [3,74].

Implant-Related VRFs
An implant-protective occlusion, which minimizes the occlusal loading on the implant, may make the adjacent natural teeth vulnerable to greater occlusal forces [67][68][69]. Endodontically treated teeth have been reported to exhibit lower fracture resistance than vital teeth [70]. Therefore, the possibility of implant-related VRFs in endodontically treated adjacent teeth has been suggested [71].

Repetitive Heavy and Stressful Chewing Habits
Non-endodontically treated VRF teeth are usually related to occlusal factors. The Chinese population presents some unique chewing habits. For example, the chewing of betel quid, bones in meat, or food that is not easily sheared are risk factors that may predispose teeth to VRFs in non-endodontically treated teeth [2][3][4]19,22,72]. Chewing betel quid (a product of the areca nut, with coarse fibers) is more popular in males in Taiwan [73]. This oral habit is reported to contribute to VRFs in Chinese populations [3,74].

Clinical Features
The clinical features of VRFs are extremely variable. The symptoms and signs may be different depending on the extent of the fracture line, the time after fracture, the architecture of the surrounding apparatus and the inflammatory stage [32].

Pain
A history of discomfort or pain when biting is a common finding, and is accompanied by localized chronic inflammation. Dull pain or a mild degree of discomfort may arise, but severe pain is relatively rare [13,32].

Soft Tissue Swelling and Sinus Tract
The sinus tract of a VRF tooth may be coronally located closer to the gingival margin than the apical area. Sinus tracts may be situated some distance from the fractured tooth. Thus, the insertion of a gutta-percha point into the sinus tract to trace the offending tooth assists in diagnosis [32]. If the gutta-percha cone appears parallel to the periodontal ligament (PDL), a VRF is highly suspected. This unique tracing pattern provides an important diagnostic difference between a VRF and other endodontic or periodontal pathologies [33].

Deep Periodontal Probing Depth
A deep, narrow, isolated periodontal pocket close to the fracture site was discovered in 64-93% of VRF cases [13,14,25,30]. A periodontal pocket is generally formed as bony destruction is exacerbated during the progression of a VRF [25]. However, in its early stage, no osseous defect or deep probing depth may be evident.

Attrited Occlusal Surface
Most of the non-endodontically treated VRF teeth showed moderate to severe attritions in relatively intact crowns with minimal restorations [4,19]. The attrited occlusal surface may indicate excessive, repetitive and heavy masticatory stress, which may further lead to root fractures in these patients [4,19].

Other Clinical Symptoms and Signs
Pain in response to percussion, palpation and mastication may be reported by these patients [6,13,36]. The common clinical symptoms and signs of VRFs elucidated in previous studies are shown in Table 1. Radiographic examination is essential to the diagnosis of a VRF. Radiographic changes in the surrounding apparatus can sometimes be the only clue of a root fracture. An immediate radiographic diagnosis can be made if separated root fragments [13,76] or a hair-like radiolucency, interpreted as a crack in the dentin, are recognized [72].
Possible radiographic changes in VRFs include the following: displacement of a fractured fragment, a radiolucent line within the root canal, an unusual space between the canal wall and intracanal material, a widening PDL space, a periradicular radiolucent halo, angular bony destruction, a step-like bone defect, a V-shaped diffuse bone defect, root resorption that corresponds to the fracture line, widening of the root canal space, endodontic failure after healing has occurred, or no evident radiographic finding.

Displacement of Fractured Fragment
When the root fragments are separated, a root fracture is visible on the radiographic image ( Figure 5A) [25]. The proliferation of granulation tissue would cause the movement of the fragment away from the original tooth structure and is a definitive indicator of a root fracture [32].
Radiographic examination is essential to the diagnosis of a VRF. Radiographic changes in the surrounding apparatus can sometimes be the only clue of a root fracture. An immediate radiographic diagnosis can be made if separated root fragments [13,76] or a hair-like radiolucency, interpreted as a crack in the dentin, are recognized [72].
Possible radiographic changes in VRFs include the following: displacement of a fractured fragment, a radiolucent line within the root canal, an unusual space between the canal wall and intracanal material, a widening PDL space, a periradicular radiolucent halo, angular bony destruction, a step-like bone defect, a V-shaped diffuse bone defect, root resorption that corresponds to the fracture line, widening of the root canal space, endodontic failure after healing has occurred, or no evident radiographic finding.

Displacement of Fractured Fragment
When the root fragments are separated, a root fracture is visible on the radiographic image ( Figure 5A) [25]. The proliferation of granulation tissue would cause the movement of the fragment away from the original tooth structure and is a definitive indicator of a root fracture [32].

Radiolucent Line within the Root Canal
A root fracture may be displayed as an unusual and wide radiolucent line in the root canal space or the root filling material ( Figure 5B). In endodontically treated teeth, the fracture line can sometimes be observed more clearly in the radiograph after the removal of the root canal filling material.

Unusual Space between the Canal Wall and Intracanal Material
The mild displacement of VRF fragments could create a radiolucent space adjacent to the root filling material in a well-obturated canal ( Figure 5C). Posts are usually tightly cemented to the canal wall. If a suspicious radiolucent space is present between the post and the root canal space, a VRF may have occurred [32].

Widening PDL Space
An enlargement of the PDL around the root apex or even the whole root surface may indicate that the tooth is vertically fractured ( Figure 5D) [1,4,13,32]. This radiographic description is quite different from that of typical endodontic lesions, which are limited to the apical area and do not include the destruction of the lamina dura along the periradicular surfaces.

Periradicular Radiolucent Halo
Radiolucent halos represent periradicular rarefaction, which can be observed on the lateral or even opposite side of the root surface ( Figure 5E) [14,31,76,77]. Halo radiolucency is recognized as one of the most common radiographic characteristics of a VRF [1,25,28,31,78]. In addition, J-shaped lesions around the root have also been identified as a radiographic feature of a VRF [11,36].

Angular Bony Destruction
Angular periodontal defects may extend from the marginal bone to the fracture line in a VRF. This depends on the extent of the fracture and the inflammation [25]. Osseous defects break down faster in areas of thin buccal bone plate, such as around the maxillary premolars and the mesial roots of the mandibular molars [28,30,33].

Step-Like Bone Defect
Step-like bone destruction may develop if the vertical fracture line extends obliquely through the root or does not appear in the apical portion [31,32,79]. Shifting 15 degrees in the mesial or distal direction may assist in the observation of the defect. However, step-like bony destruction is not a definite indication of a VRF. Besides a VRF, canal perforations and endodontic lesions are also possible. Thus, the exact diagnosis of a VRF needs to be confirmed with other diagnostic methods [32].

V-Shaped Diffuse Bone Defect
V-shaped bone destruction may derive from the discrepancy between buccal and lingual bony destruction. This kind of destruction is wide at the crestal bone and narrows toward the root apex [31]. If diffuse bone loss occurs in a single root or tooth, a VRF is highly suspected [32].
9.9. Root Resorption Correspond to the Fracture Line ( Figure 5F1,F2) Root resorption forming a V-shaped notch at the root apex has been reported as a feature of a VRF. The root canal filling material may disintegrate when there are irregular resorptive defects in the root [80]. The root canal usually becomes subtle as it extends to the apical region. Sudden changes in the radiodensity of the root canal, or the unusual widening of the canal space, may indicate a VRF, especially in non-endodontically treated teeth [22,26].

Endodontic Failure after Healing has Occurred
If an endodontically treated tooth deteriorates rapidly after many years without symptoms, or if rarefaction reoccurs without other specific problems, a VRF should be considered [32].

No Evident Radiographic Finding
About 13-14% of the VRFs show no detectable periapical or lateral radiolucency on the radiograph [25,30]. This may be because the bony destruction had not penetrated into the cortex yet, and the results were based on two-dimensional radiographs.

years
The tooth functioned normally without periodontal defect and radiographic pathosis.

Extraoral and intentional replantation
Biocompatible glass-ionomer bone cement in conjunction with an expanded polytetrafluoroethylene (Gore-Tex) membrane.

year
The tooth functioned normally without periodontal pocket and exhibited good healing outcome. Selden, 1996 [93] 6 VRFETT Intraoral Apply silver glass-ionomer cement to bond the fracture fragment and perform guided tissue regeneration.

to 1months
Five cases failed within 2 to 11 months. The other one was asymptomatic but failed at 1 year due to exacerbation of the fracture line.
Floratos and Kratchman, 2012 [105] 4 VRFETT Intraoral The fracture line was removed by resecting the root fragment. Retrograde preparation and retrograde filling were performed with MTA. An absorbable collagen membrane was covered over the bone defect.

to 24 months
The teeth were asymptomatic. Periapical healing with periodontal ligament re-formation was noted.

Extraoral and intentional replantation
Prepare the fracture gap with a small diamond bur and fill with Biodentine. Then, replant the tooth with fixation.

months
The tooth was asymptomatic, and the periodontal pocket returned to normal.
Some studies also provided clinical suggestions for preventing VRFs. The clinicians should use the dental instruments as conservative as possible in order to avoid root fracture [46,92]. Minimizing the forces applied during endodontic or prosthetic procedures was significant in reducing the possibility of VRF [27]. Minimal or conservative root canal enlargement and flare preparation had been suggested [59]. Intracoronal and intraradicular restorations should be placed passively with caution [13]. For patients with the habit of bruxism or clenching, night guards were able to provide some protection to minimize the risk of VRF [33].

Conclusions
VRFs in non-endodontically and endodontically treated teeth share some common factors, such as age-related microstructural changes, the specific anatomies of the susceptible roots, biting pain, deep periodontal pockets and periodontal or periradicular radiolucency. The attrition of the occlusal surface is a common feature in VRFs of non-endodontically treated teeth. The possible etiologies are related to iatrogenic problems or masticatory and occlusal factors. Radiographic assessment, CBCT imaging and visual inspection during exploratory surgery are used for diagnosis.
The value of this article is its provision of an overview of the current knowledge of VRFs in endodontically and non-endodontically treated teeth concomitantly. It provides an opportunity to improve the identification and treatment principles of VRFs. Further investigations regarding the mechanism of VRFs from basic and clinical aspects should be conducted. In addition to this, the long-term prognosis of various therapeutic schemes should be assessed to avoid inappropriate treatment and frustrated results.