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Sensitivity and Error Analysis in Conjunction with Tibial Intramedullary Guides in Total Knee Arthroplasty

Michael C. Durkin, MD
Luke Aram, BS
Farid Amirouche, PhD
Mark H. Gonzalez, MD

Several factors influence the long-term success of total knee arthroplasty. Many authors have shown proper component placement to be an important factor. ^1-4 Correct tibial and femoral component positioning creates a neutral mechanical axis, preventing malalignment from contributing to early failure of total knee arthroplasty. ⁵ Numerous alignment systems exist to determine the alignment of tibial and femoral bone cuts. Studies comparing intramedullary versus extramedullary alignment systems have shown higher percentages of femoral component positioning in the desired ranges with the use of intramedullary guides. ^6,7 However, for the tibial alignment, the debate continues as to which system is superior. Any component alignment mechanism must be correctly positioned to assure accurate femoral and tibial bone cuts. Using radiographic and mathematic analyses, past studies have investigated intramedullary alignment systems and quantified potential sources of error for the femoral component. ⁸ In the present study, the investigation of potential error in intramedullary alignment systems was continued with the tibial component.

The purpose of the current study was to analyze the potential error in intramedullary alignment systems used in total knee replacement. This analysis may aid in the design of intramedullary guides with increased accuracy. Understanding the variables that determine the accuracy of intramedullary alignment instruments is important. Their accuracy depends upon the intramedullary rod engaging the isthmus of the medullary canal to reestablish the anatomic axis. In this study, the rod length and diameter and the intramedullary diameter of the canal influenced the precision of placement. Another important variable examined was the location of the entry hole for the intramedullary guides. The additional potential alignment error produced by tibial guide malrotation was also analyzed.

The outcome of this investigation was based on the measurements of tibiae radiographs used to determine the tibial canal diameter and the appropriate position for the entry hole. These data were used for a mathematical analysis of potential error in alignment resulting from the use of intramedullary guides of varying lengths and diameters. It was expected that the tibial guide of greatest length and largest diameter, such as a 10-mm x 304.8-mm guide rod, would result in the least potential error in alignment. However, other factors indicated that the ideal intramedullary guide might not be the largest. Reasons that may account for this possibility include bowing in the tibiae, a smaller canal diameter, and the position of the entrance hole.

Materials and Methods

Twelve cadaveric tibiae were used for radiographic analysis. Radiographs were obtained in the anteroposterior and lateral planes. The entry point for the intramedullary guide was determined based on these radiographs, which were then scanned, digitized, and, with the aid of a computer program, used to map bone geometry based on pixel density. The pixel density was measured from 0 to 255, with a scale of 1 pixel per 1/150 of 1 inch ( Figure 1 ). The tibias were mapped every 10 pixels, ie, every 1/15 of 1 inch. The computer program then regenerated the tibia, and the regeneration was compared with the scanned image ( Figure 2 ). The digitized reconstruction was used to define to the proper dimensions and orientation of the medullary canal. A second computer program then located the center of the medullary canal of the tibia. By doing this at several levels, the ideal entry point for the tibia drill was located ( Figure 3 ). The location was defined as the point at the tibial articular surface that corresponded to a proximal continuation of the medullary canal. This ideal entry point was measured on all radiographs, and an average point location was derived ( Table 1 ).

Mathematic models were developed for the potential error of the proximal tibial bone cut. Each mathematic model was based on a three-dimensional cube, the sides of which represented the sagittal, coronal, and axial planes of the tibia ( Figure 4 ). A trigonometric analysis was done to derive equations, which corresponded to the possible deviations of the cutting guide in these three planes. This analysis was based on a goal of 90° to the anatomic axis of the tibia. Calculations were performed based on a right tibia, for which the average and sagittal widths were calculated and the canal widths were measured at 4 and 7 inches distal to the bone cuts. The maximum potential error, which was determined for rod-canal geometric mismatch based on correct and offset entry points, using rods 7 and 8 mm in diameter and 4 and 7 inches in length, was calculated in the anteroposterior plane corresponding to varus/valgus error. Next, the potential error of malrotating the 5°-posterior-slope cutting guide was calculated based on a mathematic model. The maximum alignment error was also assessed by a combination of rotation, offset entry point, and canal-rod geometry mismatch.

Results

The measured results from the digitized tibiae showed an average canal width of 0.673 inches (sd: 0.186) at 4 inches below the plateau; at 7 inches, the average width was 0.523 inches (sd: 0.088). These results, along with similar results for the lateral radiograph, were used both to extend the medullary canal to the tibial plateau and to define the location of the ideal entry point, as shown in Figure 3 . The ideal entry point was calculated as a ratio of the tibial plateau on the anteroposterior and lateral views. The medial offset distance was defined as the distance from the entry point to the medial edge of the tibia plateau, and the lateral offset distance was defined as the distance from the entry point to the lateral plateau. The averages of these distances were 1.047 and 1.058 inches, respectively, placing the ideal entry point in the approximate center of the plateau on the anteroposterior radiograph. Using the lateral radiograph, the anterior and posterior offset distances were similarly defined. The average anterior offset distance was 0.804 inches and the average posterior offset distance was 1.248 inches, placing the ideal entry point 0.39 tibial plateau lengths back from the anteriormost point on the tibial plateau. Figure 5 illustrates the possibility of clockwise and counterclockwise rotation of the tibial cutting guide. The equations below denote the potential error in guide placement derived from Figure 6 :

Figure 6 depicts the schematic diagram used to calculate the error induced through malrotation of a 5°-posterior-slope cutting guide. If the tibial cutting guide is in neutral varus/valgus alignment, but the guide is rotated externally 30°, the resultant cut will be in 1.9 degrees of varus with a posterior slope of 5° minus 2.857°, ie, 2.143°. These results are graphed in Figure 7 .

Figure 8 shows the schematic diagram used to calculate the potential error with guide rods using the ideal starting point. Rods of 4- and 7-inch lengths and 7- and 8-mm diameters were used. The average tibial canal widths were calculated 4 and 7 inches from the plateau; these widths were 17.1 and 13.3 mm, respectively. The potential error difference in using a 4-inch versus a 7-inch length rod was greater than the difference in using a 7-mm versus an 8-mm diameter rod. Changing a 4-inch length rod with a 7-mm diameter to an 8-mm diameter decreased the maximum error from 2.845° to 2.565°, whereas changing a 7-mm diameter rod with a 4-inch length to a 7-inch length improved the maximum error from 2.8565° to 1.014°. Table 2 displays the results of all four rod-length and diameter combinations.

The next scenario examined was that of maximum potential alignment error when the entry point was not ideal. A schematic representation of this error and the equations used to calculate it are shown in Figure 9 . The maximum errors shown in Figure 10 represent the total of two errors--the error of rod-tibia geometric mismatch and the additional error created by the offset of the entry point medially or laterally. The potential error created by placing the entry point 0.85-cm medial to the ideal point was 7.58° for the 4-inch rod and 3.74° of varus for the 7-inch rod.

Discussion

The proper orientation of prosthetic components is critical for the longevity of total knee arthroplasty.9 Postoperative alignment of the femur and tibia has been shown to directly affect the durability of implants.10 Ideal alignment occurs when a line from the center of the femoral head to the ankle passes through the center of the knee. Malalignment of the components has been shown to lead to early loosening. Bargren et al. ¹¹ showed that, when the knee is loaded unequally, liftoff occurs on the unloaded side and collapse occurs on the eccentrically loaded side. Furthermore, Aglietti and Buzzi ¹² found that a varus tilt of more than 2° of the tibial component correlated with the development of lucent lines around the implant.

The goal of any alignment system--intramedullary or extramedullary--is to produce accurate bony cuts. Both systems are based on the similarity between the mechanical and anatomic axes of the tibia. Bono et al. ¹³ showed that the anatomic axis approached the mechanical axis to within 1° on both the anteroposterior and lateral planes. For the production of accurate tibial cuts, many authors suggest that extramedullary alignment devices should be used, because the bony landmarks of the ankle make good reference points. ¹⁴ Although the exact center of the ankle mortise is still in estimation, the center of the ankle mortise usually lies 3 to 5 mm medial to the midpoint of the medial and lateral malleoli. However, excess soft tissue, bony abnormalities, or bulky surgical drapes may also obscure these references. As such, several authors recommend the use of intramedullary guides, stating that they are more accurate and reproducible than extramedullary guides, allowing more consistent and accurate bony cuts. ^15,16 Tibial bowing has been shown to interfere with the passage of intramedullary devices and can prevent the passage of guide rods inserted from the center of the tibial plateau. ¹⁷

Various authors have compared intramedullary and extramedullary guide systems. In a radiographic review of 29 knee arthroplasties, Rand and Bryan ¹⁸ found that 48% of the knees were substantially malaligned using an early extramedullary system that attempted to place the femur in 90° of valgus and the tibia in 3° of varus. After evaluating 148 total knee arthroplasties done with an alignment jig to reference the femoral head, Laskin ¹⁰ found alignment errors of greater than 4° in 24% of cases; he also reported alignment within 2° of normal in 86% of 124 knee arthroplasties done with intramedullary guides. Brys et al. ⁷ observed a higher percentage of satisfactory alignment using intramedullary guides, with 94% of tibial components inserted within 2° of perpendicular to the tibial mechanical axis, versus 85% for the extramedullary group. Denis et al. ¹⁹ compared postoperative tibial component alignment angles produced with intramedullary and extramedullary guides. Although satisfactory alignment was obtained with either system, a wider range of error was seen with the intramedullary group. However, the depth guide used was not reported, so the increase in range could have been due to incomplete seating of the guide rod.

The length of the intramedullary guide and the ability to seat it distally in the tibia are important factors in obtaining accurate alignment. Tibial bowing can interfere with the passage of the rod from the center of the tibial plateau, necessitating the use of a shorter guide or a starting hole that is off-center. In a radiographic review of 30 varus and 30 valgus knees, Simmons et al. ¹⁷ , showed that a 25-cm resection guide could be passed in 35 of the knees (58%) because of angular deformity. Of these 35 knees, a perpendicular tibial resection was obtained in 30 (86%). When the entry hole was moved from the center of the plateau, the 25-cm rod was passed in 98% of the entire group of 60 knees. However, this change in starting point will always produce cuts not perpendicular to the mechanical axis. A 12-mm displacement of the starting hole in 35-cm tibia produces 2° of extra angulation. The option of using a shorter, 17-cm guide rod was also explored in those tibiae in which the long rod would not pass through a central starting portal. This resulted in perpendicular tibial cuts in two of 25 knees (8%). Similarly, Bono et al. ¹³ used cadaver tibiae to quantify the angular error produced by incomplete insertion of the guide rod and insertion from off center starting portals. They were unable to fully seat the guide in 43% of tibiae from a central starting hole. The resulting malalignment correlated inversely with the depth of insertion. In the 57% of tibiae in which the rod was inserted more than 80% of the way, the accuracy of the alignment system increased to within 1° in both the anteroposterior and lateral planes.

Summary

Intramedullary alignment of the tibial component in total knee arthroplasty is an important technique that helps surgeons obtain tibial bony cuts perpendicular to the long axis of the tibia. Certainly, in tibiae without significant deformity, intramedullary alignment guides can produce accurate cuts. The results of maximum error calculation from the present study display the importance of both rod length and proper entry point. Additionally, the surgeon must entertain the concept of rotational alignment of the tibial cut. This concept, which is frequently overlooked, can add almost 2° of varus to the tibial component. To achieve long-term success in total knee arthroplasty, the surgeon must understand the factors that can introduce alignment error and strive to minimize them.

Acknowledgment

The authors thank the Department of Orthopaedics and the Department of Mechanical Engineering for their support.

MICHAEL C. DURKIN, MD, is a resident with the Department of Orthopaedic Surgery, University of Illinois at Chicago, Chicago, IL.

LUKE ARAM, BS, is a research assistant with the Department of Mechanical Engineering and Bioengineering, University of Illinois at Chicago, Chicago, IL.

FARID AMIROUCHE, PHD, is a professor of engineering with the Department of Mechanical Engineering and Bioengineering, University of Illinois at Chicago, Chicago, IL.

MARK H. GONZALEZ, MD, is a professor of clinical orthopedics with the Department of Orthopaedic Surgery, University of Illinois at Chicago, Chicago, IL. Farid M. L. Amirouche, Department of Mechanical Engineering and Bioengineering, Engineering Research Facility, 842 W. Taylor Street (M/C 251), Chicago, IL 60612. Phone: (312) 996-3601; Fax: (312) 413-0447; E-mail: Amirouch@uic.edu

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