Using fractal geometry to examine failed implants and prostheses.

OBJECTIVE: To develop a novel protocol that is precise and accurate for analyzing the fracture surfaces of ceramic specimens using fractal geometry and to demonstrate its use on both clinically retrieved specimens and standard test specimens.

METHODS: A MathCAD script was written to transfer data from atomic force microscope scans to the FRACTALS software of John Russ. This software provided six algorithms for analyzing surfaces, so an experiment was conducted to determine which algorithm provided the most precision in fractal dimensional increment (D*) values and to calibrate that algorithm on surfaces generated with known D* values. Physical specimens were then tested using the chosen algorithm. These included pure silica glass fractured in deionized water versus nominally identical specimens fractured in saliva. Light body polyvinysiloxane was used to make impressions of Y-TZP fracture surfaces, and replicas were casted using a low-viscosity, low-shrinkage epoxy. Clinically failed Y-TZP dental implants were also examined. In addition, the fracture toughness and D* values of four ceramic materials (silicon nitride, silica glass, Y-TZP, and lithium disilicate glass-ceramic) were tested using standard geometry flexure beam specimens (ISO 6872).

RESULTS: The Minkowksi Cover algorithm was the most precise algorithm, and it had a negative bias that was corrected. There was no difference in D* based on water vs. saliva environment (p>0.05), and D* values from the deionized water group had lower standard deviation. The mean D* value obtained from the epoxy replicas 2.247 (0.007) was the same as that obtained from the original Y-TZP specimens 2.245 (0.002) (p=0.43, paired t-test). All scanned areas of the dental implants were fractal in nature, and there was no difference in fractal dimension between the locations near the failure origin and those far from the origin (on the compression curl) (p=0.74, repeated measures ANOVA). There was little scatter in the data collected using the revised protocol on ISO 6872 specimens, and the regression models succeeded in passing through the origin while achieving a good fit to the data (R2 =0.99 and 0.95).

SIGNIFICANCE: The new protocol proved to be a powerful tool in analyzing fracture surfaces of dental ceramic materials.