Where
S = radial compressive stress in Pascal, Pa, (psi)The radial compressive force, Fc, can be determined from the mechanical engineering screw press equation as follows (11).
Some of the factors in the above equation are shown in Figure 1 and defined below. T = applied torque N-m (in.-lbs.) Substituting the constants into equation B provides a relationship between applied torque (T) and radial pressive force (Fc) that depends solely on thread coefficient of friction, u (mu).
The coefficient of friction u (mu) must be determined experimentally. The last variable to be determined in the calculations of radial compressive stress is the pin's area of contact as a function of applied torque and thread friction (reagent) As the halo pin is tightened, the skull is penetrated proportionately deeper (see Figure 2 ). Area of ContactThe relationship of halo pin tip contact to the diameter determined from the cranial bone hole diameter measurements using the following relationship (11).
Where A = diameter of halo pin tip contact m2 (in.) This relationship has been plotted so that the bone sample hole diameter measurement could be translated into areas of contact of the halo pin tip (see Figure 3 ). Pin contact area was determined from the cranial bone sample hole diameter, given the curve shown in Figure 3 . Diameter was measured three times to ensure reliability. The mean (+/- standard deviation) areas of the halo pin tip are shown in Table A . Apparatus and MaterialsAn apparatus employing a tensiometer5 was developed to allow the radial compression force of a halo pin to be measured as a function of applied torque (see Figure 4 ). Torque was applied to the halo pins with an analog type of torque wrench6. Because the apparatus used a 4:1 lever system between the tensiometer and the halo pin, the halo pin's radial compression force was four times the force indicated on the tensiometer. A standard 300 series stainless steel halo ring7 was sectioned, autoclaved and then mounted on the apparatus (see Figure 5a ). Autoclaved 300 series stainless steel halo pins8 containing slotted bases and concave radial tips were used. Testing was performed using uncoated threads and threads coated with the following reagents: 3 percent hydrogen peroxide solution, topical betadine solution, hibiclens cleansing solution and bacitracin-neomycin sulfate-polymycin B sulfate ointment. The human skull bone used for testing was obtained from autopsy. Six male frontal skulls (right and left) specimens were obtained from three different calvaria of 24, 50 and 74 years. These specimens were sectioned into samples of approximately 1.5 cm x 1.5 cm x .8 cm thick (see Figure 5b ). ProceduresThe effects of variations in thread friction were evaluated using uncoated halo pins and ring holes. Four different halo ring holes were tested with four different halo pins (16 combinations) at 0.23 (2), 0.45 (4), 0.68 (6), 0.9 (8), 1.0 (9) and 1.11 N-m (10 in.-lbs.) of torque. All halo pins and rings were autoclaved prior to and after application of each of the five conditions: four reagents and no reagent. Skull specimens were mounted between the metal bar and the halo pin tip (see Figure 5b ). Torque values of 0.23 (2), 0.45 (4), 0.68 (6), 0.9 (8), 1.0 (9) and 1.11 N-m (10 in.-lbs.) were applied, and radial compression forces were recorded for each reagent and uncoated thread. Bone samples were removed from the apparatus after each torque tightening, and the diameters of the resulting indentations were measured with the aid of a micro scale8 with .0254-cm (.01-in.) divisions and a lOX magnifying eye piece9. The area of contact of the tip of the halo pin (Ap) was related to this diameter. Radial compressive stress (Sc) was calculated from equation A since both radial compression force (Fc) and area of contact (Ap) were known. Data AnalysisThe data were screened prior to testing using univariate summaries. Means and standard deviations were calculated for radial compressive force and stress. The mean radial compression forces and stresses were compared by analyzing variances. The Scheffe' test was used for the multiple-paired comparisons. Statistical significance was determined at the .05 level. Simple regression was used to determine the linear relationship between radial compressive force and torque for the uncoated pins and pins coated with different reagents. Polynomial regression was used to determine the relationship between radial compressive stress and torque for each of the coating reagents and the uncoated condition. ResultsFriction Variation in Pins and HolesThe means (+/- standard deviation) radial compressive forces resulting from the applied torques for 16 combinations of four uncoated halo pins and four uncoated halo ring holes are shown in Figure 6 . No significant differences among the combinations were noted at any one of the applied torques. Therefore, the differences observed for the reagents tested were independent of slight variations in friction in any one of the four holes and/or four pins. Radial Compressive ForceFigure 7 shows the mean (+/- standard deviation) radial compressive forces resulting from the applied torques for different reagents tested. The ointment-coated and uncoated threads produced significantly higher radial compression forces at torque values above 0.45 N-m (4 in.lbs.). Moreover, ointment-coated threads produced significantly greater radial compressive forces than uncoated pins. The regression in Figure 7 shows two groups: low thread friction (uncoated threads and ointment-coated threads) and high-thread friction (hibiclens-, betadine- and hydrogen peroxide-coated pins). Radial Compressive StressThe mean radial compressive stress versus appplied torque for the u ncoated threads and reagent=coated threads are shown in Figure 8 . The radial compressive stresses were obtained by dividing the radial compressive force by the corresponding halo pin tip contact area, equation A. As was the case with radial copressive force, the calculated radial compressive stress restults could be sorted into two groups: higher friction (hydrogen peroxide, betadine, and hibiclens) and lower freiction (ointment and uncoated) (see Figure 8 ). Analysis of variances of the means of the radial copressive stresses indicates ointment-coated threads had substantially lower thread friction, resulting in significantly greater radial compressive stress than the other reagent-coated threads at all torque values tested except 0.45 N-m (4 in.-lbs.). Uncoated threads generated the next-highest radial compressive stresses. At 0.9 N-m (8 in.-lbs.) of applied torque, the mean stress due to ointment-coated and uncoated threads were 66.7 MPa (9,680 psi) and 63.9 MPa (9,270 psi), respectively, compared to approximately 51.7 MPa (7,500 psi) for the threads coated with the other three reagents. At intermediate torque values 0.45, 0.68 and 0.9 N-m (4, 6 and 8 in-lbs.), hydrogen peroxide-coated threads had significantly lower thread friction than betadine- or hibidens-coated threads but significantly higher thread than the lower-friction group (i.e., ointment-coated or uncoated threads). For the three coatings in the high-thread friction group (hydrogen peroxide, betadine and hibiclens), the thread friction and the resulting radial compressive stresses converged at the higher torque values 0.9, 1.0 and 1.11 N-m (8,9 and 10 in.-lbs). Coefficient of Friction The linear regression for the radial compressive force versus applied torque (see Figure 7 ) are of the form
Where y = radial compressive force, FcThe linear relationship for the radial compressive force as a function of applied torque for each of the regent coated and uncoated threads as shown in Figure 7 . Comparing these expressions with the general relationship, equation C, it is possible to calculate the corresponding coefficients of friction (see Table B ). The range of the low-friction group was .263 to .288, and the range for the high-friction group was .475 to .545. A twofold difference exists between the high- and low-friction groups. Ointment produced the lowest coefficient of friction and the hibiclens the highest. DiscussionThe antibiotic ointment- and hibiclens-coated pins produced the highest and lowest compressive stresses. These extremes of radial compressive stress indicate the impact of altered thread friction when coated with these two reagents. At the recommended halo pin-tightening torque of 0.9 N-m (8 in.-lbs.), the mean radial compressive stress was 66.7 MPa (9,680 psi) for ointment-coated threads and 47.5 MPa (6,900 psi) for hibiclens-coated threads, a 40 percent difference (6). The 66.7 MPa (9,680 psi) radial compressive stress at 0.9 N-m (8 in.-lbs.) for the ointment coated threads is precipitously close to the ultimate radial compression strength of cranial bone at 73.7 +/- 35.1 MPa (10,700 +/- 5,000 psi) reported by McElhaney (10) (see Figure 8 ). The data collected for antibiotic ointment may also be representative of the effect produced by hair grease, mousse and other oil-based hair products, thus cautioning clinicians not to excessively torque pins coated with oil based products. Also, for patients where traction is indicated, halo pins might loosen if coated with reagents that increase thread friction (i.e., hydrogen peroxide, betadine and hibiclens). At the recommended torque of 0.9 N-m (8 in.-lbs.), the mean radial compressive stress for these reagents was approximately 13.8 MPa (2,000 psi) lower than that of uncoated pins. Radial compressive force variations were relatively small for the low-friction reagents (2.3 to 7.85 N), com pared to that of the high-friction reagents (6.4 to 13 N) (see Table B ). Also interesting to note, the variation increased as torque was increased. This may indicate an inconsistency in "stickiness" of the high-friction-producing reagents, especially hydrogen peroxide. ConclusionAny reagent used to prepare the skin prior to pin insertion or to provide local pin-site care should be applied judiciously, avoiding the pin threads near the halo ring hole. This precaution minimizes the alteration of the coefficient of friction at this interface, profoundly effecting radial compressive stress. Finally, all clinical studies on halo pin care must consider the coefficient of friction and the effect of local pin-site care reagents. The radial compressive force exerted by a halo pin on the skull depends not only on the applied torque, but also on the coefficient of friction at the halo ring/halo pin thread interface. Stephen H. Liu, MD, is with the UCLA department of orthopedic surgery, 10833 Leconte Ave., Room 76-119, Los Angeles, CA 90024. Thomas R. Lunsford, MSE, CO, is director of the orthotic department at The Institute for Rehabilitation Research, 1333 Moursund, Houston, TX 77030. Robert L. Waters, MD, is with the Rancho Los Amigos Medical Center, 7601 Imperial Hwy., Downey, CA 90242.
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Home > JPO > 1993 Vol. 5, Num. 3 > pp. 67-72 |
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