Normal Distribution of Humeral Neck-Shaft Angles
Bilateral humeri were obtained from the Cleveland Museum of Natural History (Hamann-Todd Human Osteological Collection, Cleveland, Ohio). All humeri from this collection were from the unclaimed dead in the City of Cleveland and Cuyahoga County, Ohio, during the years 1912 to 1938. The humeri selected were free from traumatic or degenerative changes, and the donors were within the age range of thirty to eighty years. A total of 2184 dry humeri from 1092 individuals were examined for this study. One hundred and twenty-six bones with incomplete information and evidence of obvious deformities such as arthritis and fracture malunion were excluded. Of the 2058 remaining humeri, 1752 (85%) were from men, 1300 (63.2%) were from people of European descent, 750 (36.4%) were from people of African descent, and eight (0.4%) were from people of Asian descent. The neck-shaft angle of each humerus was measured directly by one observer (J.J.) using a transparent mechanical goniometer. The angle formed by the intersection of the axis of the proximal part of the humeral shaft and a line drawn perpendicular to the anatomic neck was measured in the frontal plane. Multiple measurements were made of the same bones by the single observer (J.J.). These goniometric measurements were correlated with the measurements made with use of a three-dimensional computer surgical simulator by three additional observers, blinded to the original goniometric measurements, in a randomly selected sample of twenty humeri.
Study Population, Scanning, and Validation of the Computer Simulator
The 2058 humeri were placed into three groups on the basis of the neck-shaft angle. Thirty-six humeri were then chosen, with random selection from each group except as dictated by the need to obtain equal numbers of male and female specimens. The three groups were based on whether the neck-shaft angle was in varus (range, 120° to 129°; eleven humeri), standard (range, 130° to 139°; seventeen humeri), or in valgus (range, 140° to 149°; eight humeri). The groups were created on the basis of the assumption that a deviation of ±5° from the average neck-shaft angle was not clinically relevant and could not be accurately controlled with use of standard surgical tools and methods. The unequal sample sizes of the groups reflect the distribution of humeri within the total population. The average age at the time of the death of the donors of the thirty-six humeri selected for imaging was forty-four years (range, thirty to seventy-eight years). The male-to-female ratio was 20:16, and there was an equal number of right and left specimens. The average neck-shaft angle was 133.42° (range, 121.1° to 144.5°).
Two computed tomography scans were performed on each humerus. Twenty-gauge non-spring, malleable wire was carefully wrapped around the anatomic neck and held in place with tape. This was considered to be the most accurate method to determine the anatomic neck on the computed tomography scan. A metal marker (CT-SPOTS; Beekley, Bristol, Connecticut) was placed on each of the medial and lateral epicondylar prominences to define a transepicondylar axis. Determination of the orientation of the transepicondylar axis and the plane of the anatomic neck was considered to be the most accurate method with which to measure humeral head version on the computed tomography scan. A second computed tomography scan was also obtained for each humerus without these markers.
Twenty of the thirty-six unmarked scans were randomly selected for study in the computer simulator by four blinded independent observers to mark the anatomic neck. These measurements were then compared with measurements of the computed tomography scans of the wired specimens (the gold standard) to determine accuracy as well as interrater and intrarater reliability. This method was utilized to validate the ability of the computer simulator to accurately determine the plane of the anatomic neck and thus act as a surrogate for actual surgery for this anatomic parameter. The observers were blinded to the specimen's identity and any other measurements. Each observer was asked to choose and locate three markers on the anatomic neck according to the specified rules. Each observer measured the angles twice with an interval of at least three weeks between measurements. The same data were compared with the goniometric measurements made by one observer on these same twenty humeri and were used to validate the accuracy of the goniometric measurements made on the larger sample of 2058 humeri. All observers were orthopaedic surgeons specializing in shoulder surgery: two were full-time faculty shoulder surgeons, and two were shoulder and elbow fellows.
Scans were performed with a sixty-four-detector computed tomography scanner (SOMATOM Sensation 64; Siemens Medical Solutions USA, Malvern, Pennsylvania) with 1-mm axial increments and a B60 reconstruction kernel. These axial images were loaded into a custom-developed software program designed at the Cleveland Clinic specifically to simulate all of the surgical steps of total shoulder arthroplasty for both the humeral and the glenoid component under both normal and pathologic conditions. This software has been validated for accuracy and clinical utility for normal and pathologic scapulae16-19. This study is the first in which this software was used for assessment of the humeral component.
Anatomic Humeral Landmarks Selected by the Surgeon
Processing of the images for anatomic measurements and surgical simulations included operator identification of humeral landmarks and placement of computer markers to define several key landmarks (Fig. 1). The software demonstrated, on the screen, the three-dimensional structure of the humerus, which could be manipulated in any direction. Simultaneous with the three-dimensional view were three orthogonal two-dimensional views of any section of the humerus. The software calculated and displayed on the screen, in real time, all of the anatomic relationships defined below.
Distal Transepicondylar Axis ( "TEA" on Fig. 1)
Epicondylar markers could be placed either manually or automatically by a computer algorithm that selected the most lateral or most medial osseous prominence of the distal part of the humerus.
Central Intramedullary Axis of the Humeral Diaphysis ("HA" on Fig. 1)
The axis of the proximal part of the humeral shaft (from the metaphysis to the deltoid tuberosity) was defined through an automatic fitting algorithm written into the software. The straight portion of the proximal third of the shaft distal to the humeral head was interactively selected by the surgeon, and the algorithm determined the best-fitting line to a series of marrow space centroids of the intramedullary space detected in the selected region.
A Point on the Spherical and Central Portion of the Humeral Head ("a" on Fig. 1)
A point was placed on the surface of a region representing the central portion of the humeral head; then the software automatically displayed the best-fit sphere to the head with a best-fit radius of curvature and center of rotation ("COR" on Fig. 1). It also displayed the percentage of points that were within 1 mm of the best-fit sphere on the native humeral head that were within a 1.5 cm radius from the selected point. For the purpose of this study, normal humeral head anatomy was used and only the central part of the humeral head, where the head was spherical, was selected.
Apex of the Greater Tuberosity ("b" on Fig. 1)
The apex of the greater tuberosity was determined by placing a marker on the superiormost area of the greater tuberosity.
Anatomic Neck ("AN" on Fig. 1)
The anatomic neck was defined as the best-fit plane that was created by placing three markers on the border of the anatomic neck.
Anatomic Parameters Measured by the Software for Comparison Between the Native and Prosthetic Humeri
With use of the landmarks described above, the software automatically calculated and displayed all of the anatomic measurements listed below. Movement of any marker resulted in an immediate recalculation of all anatomic measurements as the marker was moved. In this way, the surgeon could determine the effect of any minor change in any osseous landmark on all anatomic parameters. With software designed for this specific study, the center line of the prosthetic humeral stem was placed over the center line of the humeral diaphysis as determined as described above. The stem was therefore fixed in a neutral position within the medullary canal and was in the same position for both the fixed and the adjustable-angle prosthetic designs. The height of the prosthesis could be adjusted by the operator, but its location was determined by the design of the prosthetic system to be 2 mm below the osteotomy surface such that the humeral head was in contact with the osteotomy surface. In this software, by design for this experiment, the stem was in the same location for all simulations and the only parameters selected and adjusted by the operator were the humeral osteotomy angle and location, head size, centered or eccentric head options, and location of the eccentric position of the head. All anatomic calculations and differences between the native anatomy and the prosthetic anatomy were calculated in three-dimensional space by the software (Fig. 1). The parameters measured in this study included:The humeral head center of rotation ("COR" in Fig. 1), defined as the center of the best-fit sphere to the native humeral head, and the distance between this point and the center of rotation of the implanted prosthetic head.The tuberosity-to-humeral head height ("i" in Fig. 1), defined as the distance between the most superior point on the greater tuberosity and the most superior point of the humeral head.The humeral head volume, defined as the volume (in cubic centimeters) of the resected humeral head and that replaced with the prosthetic head.The humeral head thickness ("h" in Fig. 1), defined as the longest distance between the head surface and the anatomic neck plane.The humeral head offset ("f" in Fig. 1), defined as the distance between the axis of the humeral shaft and the farthest medial point on the humeral head (the approximate insertion of the superior portion of the rotator cuff).The humeral head articular arc ("c" in Fig. 1), defined as the angle formed by the humeral head center of rotation, a line drawn from the most superior point of the anatomic neck plane, and a second line drawn from the most inferior point of the neck plane.The head surface match ("a" in Fig. 1), defined as the percentage of the surface of the replaced implant head that matches within 1 mm of the surface of the native humeral head.
The humeral head center of rotation ("COR" in Fig. 1), defined as the center of the best-fit sphere to the native humeral head, and the distance between this point and the center of rotation of the implanted prosthetic head.
The tuberosity-to-humeral head height ("i" in Fig. 1), defined as the distance between the most superior point on the greater tuberosity and the most superior point of the humeral head.
The humeral head volume, defined as the volume (in cubic centimeters) of the resected humeral head and that replaced with the prosthetic head.
The humeral head thickness ("h" in Fig. 1), defined as the longest distance between the head surface and the anatomic neck plane.
The humeral head offset ("f" in Fig. 1), defined as the distance between the axis of the humeral shaft and the farthest medial point on the humeral head (the approximate insertion of the superior portion of the rotator cuff).
The humeral head articular arc ("c" in Fig. 1), defined as the angle formed by the humeral head center of rotation, a line drawn from the most superior point of the anatomic neck plane, and a second line drawn from the most inferior point of the neck plane.
The head surface match ("a" in Fig. 1), defined as the percentage of the surface of the replaced implant head that matches within 1 mm of the surface of the native humeral head.
Surgical Simulations
The prosthetic system that we selected (Global AP; DePuy Orthopaedics, a Johnson and Johnson Company, Warsaw, Indiana) has an option for either an adjustable neck-shaft angle or a fixed neck-shaft angle taper intermediate component that connects the humeral head and the stem. There are no other differences in the component sizes or offsets, which allowed direct comparison between the fixed and adjustable neck-shaft angle prostheses within any humerus or with any variation in surgical technique. The adjustable-angle taper allows infinite variability of the neck-shaft angle or version in a range of ±15° from the location of the head with use of the fixed-angle device. The adjustable-angle taper allows adjustment of the humeral neck-shaft angle between 120° and 150°.
Simulation 1 was selected to define the difference between a fixed-angle prosthesis and an adjustable-angle prosthesis when the surgical procedure was uniform, the humeral head was cut along the anatomic neck, and the head size was the same for the two prosthetic designs. Simulation 2 was performed with the osteotomy at a fixed angle of 135° and the location of the osteotomy and the head size adjusted to optimize the center of rotation and the articular surface.
The surgical simulation software aligned the long axis of the prosthetic stem along the long axis of the medullary canal, and the operator could only move the stem caudad or cephalad along this defined axis. The best-fit implant stem was defined as the largest stem whose distal one-third matched the inner diameter of the corresponding medullary canal. A full inventory of DePuy Global AP head sizes (centered and eccentric) and standard-length stems was available for use in the software. The head implant was considered to be the best fit if its size was closest to that of the resected humeral head. If an eccentric taper was used, the prosthetic head was rotated by the surgeon to the best fit of the circumference of the osteotomy surface. For replication of humeral anatomy, three variables were considered to be primary: the center of rotation of the humeral head, the tuberosity-to-head height, and a best fit to the humeral surface area. When these three parameters were optimized, the data were collected and analyzed for each surgical simulation.
For simulation 1, a humeral head cut was made along the anatomic neck and either a prosthesis with an adjustable neck-shaft angle or one with a fixed neck-shaft angle was implanted; the head sizes, selected to be closest to the size of the removed anatomic humeral head, were the same for the two designs. An eccentric head was used if necessary. The humeral stem was adjusted up or down until there was contact between the prosthetic humeral head and the backside of the osteotomy surface. The neck-shaft angle of the adjustable prosthesis was adjusted within the range of 15° more or less than a 135° angle and was optimized to achieve full contact with the osteotomy surface. When a fixed-angle prosthesis is implanted in a humerus that has a high valgus or high varus neck-shaft angle, there is a substantial gap between the head and the osteotomy surface (Fig. 2).
For simulation 2, the humeral head was resected at the prescribed angle of 135°. In the group with a standard neck-shaft angle, this cut was very close to the anatomic neck-shaft angle. In the group with a varus neck-shaft angle, the fixed-angle prosthesis osteotomy was started at the superolateral point of the neck plane, thereby not violating the greater tuberosity (the rotator cuff insertion site). In the group with a valgus neck-shaft angle, the osteotomy was performed from the inferomedial point of the neck, thereby not violating the metaphyseal bone (Fig. 3). The head size and its location within the plane of the osteotomy (eccentric head position) were selected to best replicate the center of rotation, the head-to-tuberosity height, and the humeral articular surface match.
Statistical Analysis
Statistical analyses of the differences between the different types of prostheses and between humeri with different head-neck angles were performed with the Student t test or Mann-Whitney test and linear regression or Kruskal-Wallis analysis. Bias estimates and precision estimates were used to determine intraobserver and interobserver reliability and the accuracy of the measurements. Lin's concordance correlation coefficient was used to correlate the measurements made with the goniometer on the cadaver specimens and the computer simulator measurements of the neck-shaft angle on computed tomography scans of the same humeri by four independent observers.
Source of Funding
Funding for this study was provided by the Department of Orthopaedic Surgery at the Cleveland Clinic. No extramural source provided funds to the Department of Orthopaedic Surgery for this study.
Variation of Neck-Shaft Angles in the General Population (2058 Humeri)
The average neck-shaft angle was 134.7° (range, 115° to 148°), and 77.84% of the humeri had a neck-shaft angle of between 130° and 140°. Varus and valgus neck-shaft angles were found in 9.57% and 12.59% of the humeri, respectively (Fig. 4). The correlation between the neck-shaft angles measured with the goniometer and the angles measured with use of the computer simulator on the computed tomography scans of the wired specimens (the gold standard) was excellent (Lin's concordance, 0.9). The correlation between the computer-simulator measurements by the observers on the unmarked scans and the gold-standard measurements was excellent as well (Lin's concordance, 0.928).
Interrater and Intrarater Reliability, and Accuracy
The overall mean bias was 0.108° and the overall mean precision was 1.65° for measurement of the neck-shaft angle. For measurement of the retroversion angle, the mean bias and precision were -1.866° and 5.447°. Thus, on the average, the measurements of the neck-shaft angle and retroversion angle were within 1.65° and 5.447° of the true value. These data support the accuracy and reproducibility of this software.
Anatomic Parameters of the Study Population
Table I shows the anatomic parameters of the humeri selected for this study. There were significant differences between the valgus and varus neck-shaft-angle groups. The varus group had a significantly smaller radius of curvature, greater percentage of women, shorter tuberosity-to-head height distance, and greater retroversion.
Simulation 1: Comparison of Adjustable and Fixed-Angle Prostheses with Use of Anatomic Neck Cut
In the group with a standard humeral neck-shaft angle (130° to 139°) and the humeral head cut along its anatomic neck, the adjustable and fixed-angle prostheses produced very similar anatomic reconstructions of the humerus (Table II). There were small yet significant differences in the tuberosity-to-head height distance and the head thickness. However, in the humeri with an excessive varus or valgus neck-shaft angle, there was always an obvious gap between the head of the implanted fixed-angle prosthesis and the surface of the osteotomy. Large deviations from the normal center of rotation, humeral surface match, and tuberosity-to-humeral head height resulted when a prosthetic head of the same size as that of the variable-angle prosthesis was used (Fig. 2 and Table II). The adjustable neck-shaft angle device was best able to reconstruct the native anatomy of these humeri.
Simulation 2: Comparison of Adjustable and Fixed-Angle Prostheses with Use of a 135°-Angle Neck Cut
When the humerus was cut at a standard 135° angle, there was no significant difference between the adjustable and fixed-angle prostheses in the standard-neck group with regard to the center of rotation, humeral surface arc, or tuberosity-to-head height (Table III). In the groups with an excessive varus or valgus neck-shaft angle, however, the fixed-angle prosthesis required a humeral head with a decreased thickness, resulting in a decreased articular arc, when compared with the adjustable-angle prosthesis (Table III). When the head cut was adapted to the fixed-angle device, a portion of the normal humeral head remained. With the varus head cut the inferior part of the head remained, and with the valgus head cut the superior portion of the head remained. In the varus and valgus groups, the articular arcs differed between the adjustable and fixed-angle prostheses by an average of 14°. While this difference was significant, its clinical relevance is unknown.
Several anatomic studies, in which different methods of measurement were used, have shown variation in the angle between the humeral shaft and the anatomic head (the neck-shaft angle) as well as between the transepicondylar axis and the anatomic neck (humeral version)1-4. Neck-shaft angles have ranged from 122° to 145.5° (mean, 134.4° ± 3.8°) regardless of the method of measurement4. We measured this parameter in the largest number of normal humeri from white and black donors reported in the English-language literature, to our knowledge. This suggests that all variations and the distribution of neck-shaft angles were accurately defined in this particular population. The average neck-shaft angle was 135°, and the angle was within 5° of this average in 78% of the humeri. Thus, 22% of the humeri had an angle outside of this range, making them worthy of study to optimize prosthetic design or surgical technique to accommodate for differences in native anatomy.
In addition, we divided thirty-six humeri into three groups based on the neck-shaft angle: standard, varus, and valgus. The differences between these groups explain the wide range of anatomic parameters reported in this study as well as in previous reports1-4,20. Varus heads were seen more often in specimens from female donors and had a smaller radius of curvature than the valgus heads. Differences between valgus and varus heads also accounted for the large overall range in the distance between the apex of the humeral head and the apex of the greater tuberosity as well as for the wide range in the distance between the center line of the humeral shaft and the insertion site of the rotator cuff.
We found that the ability to measure the neck-shaft angle with use of a computer simulator was accurate within 2° and reproducible both within and between surgeons. Our data also validate the accuracy of the goniometric method of measurement of the neck-shaft angle.
The ability to vary the orientation of the humeral head with respect to the stem is embodied by prosthetic designs that (1) have modularity between the head and stem, (2) have a centered and eccentric taper between the head and stem, and (3) offer the capacity to vary the neck-shaft angle and version between the head and stem. These design features distinguish modern-day prostheses from the older monobloc prostheses. It is believed that these modern design features allow the prosthesis to be adapted to variations in normal anatomy with use of a more uniform surgical technique or to be adapted to deviations in anatomy as a result of pathologic conditions21. When there is less adaptability of the prosthetic system, the surgical procedure can be modified to improve the ability of the system to achieve an anatomic reconstruction.
Boileau and Walch14, Pearl et al.15, and Wirth et al.13 reported that prostheses that allow the head position to be varied in relation to the stem (i.e., third-generation prostheses) were better able to replicate the normal anatomy of the humerus than were conventional second-generation systems. The normal anatomy of the proximal part of the humerus was not perfectly replicated in any of those studies. However, in the present study, the mean center-of-rotation displacement was 1.67 ± 0.51 mm with the adjustable prosthesis as compared with 2.07 ± 1.00 mm in the study reported by Pearl et al.15. When the adjustable prosthesis was used in our study, the average decrease in the articular arc compared with that of the normal humerus was 5.6° ± 4.4° as compared with 13.7° ± 6.2° in the study by Wirth et al.13 and 12.01° ± 8.04° in the study by Pearl et al.15. When the fixed-angle prosthesis was used, even with a 135°-angle neck cut, the displacement of the center of rotation and the decrease in the articular arc compared with that of the normal humerus were only 1.61 ± 0.57 mm and 8.6° ± 5.8°, respectively, in our study, if the surgical technique was modified as we described. Prior studies10-15 were performed with use of both two-dimensional and three-dimensional methods but without simulation of some of the surgical implantation factors that we used in our study. We used precise three-dimensional methods and implanted both the adjustable-angle and the fixed-angle prosthetic stems in the same position within the canal while keeping all other prosthetic parameters the same.
Our study is limited by the fact that we studied only one implant design (Global AP). We determined that the adjustable-angle prosthesis is better than the fixed-angle prosthesis for replicating normal anatomy accurately, particularly when there is an excessive varus or valgus humeral neck-shaft angle and the head is cut along the native anatomic neck. Approximately 20% of normal individuals have an excessive valgus or varus neck-shaft angle. We found no significant advantage to using an adjustable prosthesis when the humeral neck-shaft angle is within 5° of 135°. Approximately 80% of the population has a neck-shaft angle in this range. Clinical experience suggests that the orientation of the humeral head to the shaft or of the humeral head to the tuberosities may be different when there are pathologic changes associated with arthritis and trauma and, in some cases, a prosthesis that is adaptable to the pathologic state may offer advantages.
It is clear that a fixed-angle prosthesis with an anatomically sized humeral head cannot be implanted properly when there is an excessive varus or valgus neck-shaft angle and the osteotomy is performed along the native anatomic neck. In this circumstance, there is a large mismatch between the prosthetic neck-shaft angle and the osteotomy surface and a resultant gap between the implant and the cut surface. This may cause a serious problem with overstuffing (stiffness) of the joint if an excessive valgus neck-shaft cut is used or with a prominent greater tuberosity in relation to the top of the prosthetic humeral head (rotator cuff problems) if an excessive varus neck osteotomy is used, unless the prosthetic humeral head is substantially undersized. On the other hand, we demonstrated that the fixed-angle prosthesis can replicate the normal anatomy of a humerus with an excessive varus or valgus neck-shaft angle as accurately as can the adjustable-angle prosthesis if the surgical procedure is modified to adjust the location of the humeral osteotomy and the prosthetic head is undersized. We verified, in a three-dimensional model, the useful principles initially described by others11,15 that help guide the surgical technique to optimize the anatomic result when a fixed-angle prosthesis is used. This is important because not all surgeons have an adjustable neck-shaft angle prosthesis available or they may choose not to use one.
Pearl et al.11,15 demonstrated that, when the head-shaft angle of the humerus is different from the head-stem angle of the fixed-angle prosthesis, the osteotomy line should be made so that it resects the largest amount of articular surface possible without cutting into the tuberosities or the metaphyseal bone. Thus, for implantation of the fixed-angle prosthesis, the osteotomy line should start from the superolateral margin of the articular cartilage if the native humerus has an excessive varus neck-shaft angle and from the inferomedial margin if it has an excessive valgus neck-shaft angle (Fig. 3). Use of a fixed-angle intramedullary cutting guide is recommended to ensure that this surgical principle is followed. When the osteotomy is done in this way, the center of rotation and the humeral head position (surface area) are replicated in the same manner as is achieved by cutting the head along the anatomic neck and using an adjustable device.
This change in surgical technique is not without compromise. Modification of the angle and location of the osteotomy from that of the anatomic neck reduces the thickness of the prosthetic humeral head as compared with that of the original humeral head. We found a significant difference in the articular arc and the head thickness between the variable and fixed-angle prostheses in the humeri with an excessive varus or valgus neck-shaft angle. The difference in the articular arc of the humeral head between the adjustable-angle prosthesis and the fixed-angle prosthesis in the group with a standard neck-shaft angle was 5°, which was not significant. The more varus or valgus the neck-shaft angle, the greater the portion of the head that is left behind, and the difference in the surface arcs between the adjustable and fixed-angle prostheses was 11° (range, 1.3° to 25°) in the group with a varus neck-shaft angle and 11° (range, 1° to 17°) in the group with a valgus angle. This difference in the prosthetic articular arcs was significant (p < 0.001), but its clinical relevance with regard to patients' functional or prosthetic kinematics, wear, or loosening is unknown. When the prosthetic humeral surface area does not replicate the normal head surface area (i.e., is undersized), then a portion of the humeral bone may extend beyond the periphery of the implant. When this occurs, the surgeon should take extra care to ensure that this bone is contoured to be within the same arc of curvature as the prosthetic head.
This study demonstrated, under ideal circumstances, the advantages of an adjustable-head prosthesis as compared with a fixed-head prosthetic device for a wide range of neck-shaft angles. It also demonstrates the surgical techniques required to adapt the anatomy and optimize the result when only a fixed neck-shaft angle device is available. Our findings probably underestimate the difficulty of reproducing these principles of surgical technique and prosthetic design in the operating room when there is substantial anatomic deformity and an inability to view the entire humerus (including its internal and external features) in three dimensions. In pathologic humeri, there is severe distortion of the anatomy, making it more difficult to define the normal neck-shaft angle or the location of the normal articular surface. 