Glenoid diameter is an inaccurate method for percent glenoid bone loss quantification: analysis and techniques for improved accuracy

PURPOSE

To compare diameter-based glenoid bone loss quantification with a true geometric calculation for the area of a circular segment.

METHODS

By use of Maxima 12.01.0 mathematics modeling software (Macysma, Boston, MA), the diameter-based glenoid bone loss equation (% Bone loss = [Defect width (w)/Inferior glenoid circle diameter (D)] × 100%) was compared with a true geometric calculation for the area of a circular segment of the glenoid (Wolfram Research, Champaign, IL) rearranged in terms of w and D: Percent bone loss = (100/2π) (2 × arccos [1 - 2 (w/D)] - sin {2 × arccos [1 - 2 (w/D)]}). Percent error was calculated by taking the difference between the diameter equation and the true geometric calculation at varying true glenoid defect widths (w) (0% to 50% of diameter).

RESULTS

The commonly used diameter equation overestimated true glenoid bone loss at all values of w except at 0% and 50% of the diameter. The mean overestimation error was 3.9% ± 1.9% (range, 0.0% to 5.8%), with the maximum error occurring when w was 20% of the diameter: At this value, w/D × 100% (diameter equation) predicts 20% bone loss when true bone loss is actually 14.2%.

CONCLUSIONS

Diameter-based glenoid bone loss quantification overestimates true glenoid bone loss, with the maximum error occurring when theorized bone loss is 20%. To address situations for which a diameter-based bone loss quantification method must be performed or to improve the accuracy of surface-area calculations in previous diameter-based bone loss estimations, a corrective factor can be applied. Clinicians quantifying glenoid loss to make treatment decisions should be aware of the measurement methods used in the biomechanical studies on which they are basing their surgical decisions.

CLINICAL RELEVANCE

Diameter-based glenoid bone loss quantification overestimates true glenoid bone loss, with the maximum error occurring when theorized bone loss is 20%, a commonly used threshold for bone grafting.

Predictive force model for haptic feedback in bone sawing

Bone sawing simulators with force feedback represent a cost effective means of training orthopedic surgeons in various surgical procedures, such as total knee arthroplasty. To develop a machine with accurate haptic feedback, giving a sensation of both cutting force and rate of material removal, algorithms are required to forecast bone sawing forces based on user input. Presently, studies on forces generated while machining bone are not representative of the high cutting speeds and low depths of cut common to the bone sawing process. The objective of this research was to quantify sawing forces in cortical bone as a function of blade speed and depth of cut. A fixture was developed to simulate linear bone sawing over a range of speeds comparable to surgical reciprocating and oscillating (sagittal) bone saws. A single saw blade tooth was isolated and used to create a slotted cut in bovine cortical bone. Over a range in linear sawing speed from 1700 to 7000 mm/s, a t-test (α=0.05) revealed there was no statistically significant effect of blade speed on either cutting or thrust force. However, an increase in depth of cut from 2 to 10 μm resulted in a 30% increase in thrust force, while cutting force remained constant. The increase in thrust force with depth of cut was relatively linear, R(2)=0.80. Using a two factor, two level design of experiments approach, regression equations were developed to relate sawing forces to changes in blade speed and depth of cut. These equations can be used to predict forces in a haptic feedback model.

Sagittal Bone Saw With Orbital Blade Motion for Improved Cutting Efficiency

Sagittal bone saws are used by orthopedic surgeons for resection of bone; for example in total joint arthroplasty of the hip and knee. In order to prevent damage to surrounding tissue, sagittal saw blades typically oscillate through a small angle, resulting in reduced cutting rates due to short stroke lengths. To improve bone cutting efficiency, sagittal saws oscillate at high speeds, but this creates frictional heating that can harm bone cells. The focus of this research was to design a new sagittal sawing device for improved cutting efficiency. It was hypothesized that the addition of an impulsive thrust force during the cutting stroke would increase cutting rates in cortical bone. A cam-driven device was developed and tested in bovine cortical bone. The impulsive thrust force was achieved by creating a component of blade motion perpendicular to the cutting direction, i.e., orbital blade motion. At the start of each cutting stroke, the mechanism drove the saw blade into the surface of the bone, increasing the thrust force with the intention of increasing the depth of cut per tooth. As each cutting stroke was completed, the blade was retracted from the surface for the purpose of clearing bone chips. The design parameters investigated were cutting stroke length, thrust stroke length, and blade oscillation frequency. A three-factor, two-level design of experiments approach was used to simultaneously test for the effect of design parameters and their interactions on volumetric cutting rate (n = 32). The addition of orbital blade motion to the sagittal saw improved bone cutting rates over traditional oscillatory motion, especially at lower cutting stroke lengths and higher oscillation frequencies (p < 0.05). However, the magnitude of orbital blade motion based on thrust stroke length was limited by a threshold value of approximately 0.10 mm that when exceeded caused the sagittal saw to rebound from the surface of the bone causing erratic cutting conditions. The factor with the greatest positive effect on cutting rate was oscillation frequency. Cutting rates in cortical bone can be improved with the proposed orbital action sagittal saw.

Rounded Cutting Edge Model for the Prediction of Bone Sawing Forces

A new analytical model to predict bone sawing forces is presented. Development of the model was based on the concept of a single tooth sawing at a depth of cut less than the cutting edge radius. A variable friction model was incorporated as well as elastic Hertzian contact stress to determine a lower bound for the integration limits. A new high speed linear apparatus was developed to simulate cutting edge speeds encountered with sagittal and reciprocating bone saws. Orthogonal cutting experiments in bovine cortical bone were conducted for comparison to the model. A design of the experiment’s approach was utilized with linear cutting speeds between 2600 and 6200 mm/s for depths of cut between 2.5 and 10 μm. Resultant forces from the design of experiments were in the range of 8 to 11 N, with higher forces at greater depths of cut. Model predictions for resultant force magnitude were generally within one standard deviation of the measured force. However, the model consistently predicted a thrust to cutting force ratio that was greater than measured. Consequently, resultant force angles predicted by the model were generally 20 deg higher than calculated from experimental thrust and cutting force measurements.