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The Journal of Bone and Joint Surgery 81:660-71 (1999)
© 1999 The Journal of Bone and Joint Surgery, Inc.

Geometric Analysis of Commonly Used Prosthetic Systems for Proximal Humeral Replacement*

MICHAEL L. PEARL, M.D.{dagger} and SAM KURUTZ, B.S.{dagger}, LOS ANGELES, CALIFORNIA

Investigation performed at Southern California Permanente Medical Group, Los Angeles


   Abstract
Top
 Abstract
Introduction
 Materials and Methods
 Results
 Discussion
 References
 
Background: The anatomy of the proximal part of the humerus is extremely variable. The extent to which existing prosthetic systems and operative technique allow replication of this variability has not been established. Methods: Four commonly used press-fit prosthetic systems for shoulder arthroplasty were compared with respect to their ability to match the superior-inferior and medial-lateral dimensions of the articular surface in twenty-one cadaveric humeri. The comparisons were accomplished with a computer optimization algorithm that searched a database of prosthetic geometry and selected the best match to the original anatomy. The algorithm assumed an osteotomy of the humeral head at an angle equivalent to the stem-head angle of the prosthesis, without violation of the greater tuberosity or the metaphyseal bone. The best match was defined as the prosthetic combination (stem and head) that least displaced the center of rotation and the articular surface, with both factors weighted equally. Results: None of the prosthetic systems that were evaluated allowed identical replication of the articular surface. Rather, they displaced the center of rotation a mean of 14.7 millimeters (range, 3.3 to 31.4 millimeters) from its original position. To reach this minimized displacement, the prosthetic combinations that were selected by the algorithm also resulted in a mean diminution of the arc of the articular surface (a smaller head size) of 26 degrees (range, 11 to 41 degrees). In every instance, the selected prosthesis imposed a superior and lateral shift of the center of rotation that in effect shifted a smaller prosthetic humeral head up the slope of the humeral osteotomy. Conclusions: Press-fit prosthetic systems for shoulder arthroplasty that are commonly used necessitate marked alterations of the original anatomy. To the extent that a shoulder arthroplasty is an attempt to reproduce the normal anatomy, these findings have profound implications for operative technique and future prosthetic design. Clinical Relevance: We believe that the superior position of the prosthetic head predicted by the present study plays a role in late complications of shoulder arthroplasty, such as rotator cuff tendinopathy, superior humeral migration, and loosening of the glenoid component.


   Introduction
Top
 Abstract
 Introduction
Materials and Methods
 Results
 Discussion
 References
 
The anatomy of the proximal aspect of the humerus is extremely variable6,16,19,25,26. Although the articular surface of the proximal part of the humerus consistently spans an arc of approximately 150 to 160 degrees17,26, it differs markedly between individuals with respect to its diameter and its relationship to the adjoining humeral shaft. The radius of curvature ranges from approximately twenty to thirty millimeters6,16,19,26. The inclination angle between the base of the articular surface and the shaft ranges from 30 to 55 degrees6,16,19,26. Retroversion spans a variable range of nearly 50 degrees, whether it is referenced to some axis at the elbow or to the forearm6,16,25. In addition, the center of rotation is variably offset from the canal in both the medial and the posterior direction2,16,19,26. The extent to which existing prosthetic systems and operative technique allow replication of this variability has not been established.

For clinical conditions in which the anatomical derangement involves primarily the articular surfaces of the glenohumeral joint (osteonecrosis and osteoarthritis), a prosthetic arthroplasty that most nearly restores the original geometry of the articular surfaces should allow for the most physiological motion. An anatomical reconstruction would maintain the excursion of the joint, preserve the original position of the center of rotation, and place appropriate tension on the overlying soft tissues. Anatomical and biomechanical studies have shown that small changes in the anatomy may have important biomechanical consequences2,15. Increasing the thickness of the humeral head by only five millimeters markedly diminishes the range of motion and results in obligate translation of the humeral head on the glenoid15. Decreasing the thickness of the humeral head by a similar amount theoretically diminishes excursion of the glenohumeral joint by 24 degrees from an already limited arc of 63 degrees in the coronal plane17.

The goal of the present study was to provide an analytical framework from which to compare prosthetic geometry with normal anatomy and all its variability. Toward this end, four commonly used press-fit prosthetic systems were compared with respect to their ability to match the coronal plane anatomy of twenty-one humeri from human cadavera. In an arthroplasty with a press-fit component, the prosthesis theoretically follows the reamed canal. Anatomical measurements made in reference to the reamed canal then can serve as a reference from which to compare the original anatomy with that of the intended prosthetic reconstruction.


   Materials and Methods
Top
 Abstract
 Introduction
 Materials and Methods
Results
 Discussion
 References
 

Prosthetic Systems
The four press-fit prosthetic systems that were analyzed included the Bio-Modular total shoulder system (Biomet, Warsaw, Indiana), the Global total shoulder arthroplasty system (DePuy, Warsaw, Indiana), the Select shoulder system (Intermedics Orthopedics, Austin, Texas), and the Kirschner II-C shoulder system (Biomet).The analysis was based on information solicited from the respective manufacturers in the calendar year of 1996. Since the inception of this project, new prosthetic designs have emerged and additional head sizes have been added to existing designs. To date, however, there have been no fundamental design changes in the press-fit systems examined in the present study that challenge the pertinence of this analysis.

The sizes of the head and stem that are available within each prosthetic system are readily determined from commercially available material and templates. The stem-head angle, which is equivalent to the head-shaft angle, was 35, 45, 45, and 50 degrees for the Bio-Modular, Global, Select, and Kirschner II-C prostheses, respectively. Additional geometric specifications that were necessary for this analysis were obtained from the manufacturers. (The measurements from the manufacturers, which are available by request, typically are given to a tenth or hundredth of a millimeter. The information is also available, with less precision, from the prosthetic templates. Commercially available templates usually are magnified by a specified amount, and the lines may be several tenths of a millimeter thick.) These data included the medial offset of all stem-head combinations and pertinent dimensions of the collar and locking taper (Table I). Only the standard head sizes that were available at the time of this analysis were studied.


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  		TABLE I SELECTED DIMENSIONS OF THE FOUR PROSTHETIC SYSTEMS THAT MATCHED SPECIMENS

 
Prosthetic geometry differs from normal humeral anatomy in that the articular surface sits on a stem rather than being connected to the adjacent tuberosities (Fig. 1). In the modular systems in the present study, the stem and head are separated by a collar and a space between the collar and the head created by the locking taper. The combined thickness of the collar and the space between the collar and the head was designated as the gap. Furthermore, the margins of the prosthetic heads are beveled; thus, a discrete edge was not present. (The gap created by the collar of the prosthesis and the space between the collar and the prosthetic head ranged from 3.5 to 5.0 millimeters. The beveled edge typically constituted about 2.0 millimeters of the height of the head, with the radius of curvature varying among the prosthetic systems.) The biomechanical consequences of these differences were not considered in the present study except to the extent that they affected the determination of the arc of the surface. We defined the arc of the articular surface as the angle formed by lines drawn from the center of rotation to intersection points extrapolated from the articular surface and the base of the head, as if there were no beveled edge.



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  		Fig. 1 Schematic representation showing the geometry of the prosthesis. Note that the stem-head angle is formed by the center line of the prosthetic stem and the base of the collar. CR = center of rotation, RC = radius of curvature, HH = height of head, OS = offset of humeral head, SA = arc of articular surface, AP = articulation point, and SHA = stem-head angle.

 

Cadaveric Specimens
The dimensions in the coronal plane of twenty-one normal shoulders from cadavera were known from a previous radiographic study26. The length of the humeral bone was a mean (and standard deviation) of 33.3 ± 2.1 centimeters (range, thirty to thirty-eight centimeters); the size of the canal, a mean of 12 ± 1.7 millimeters (range, ten to fourteen millimeters); the head-shaft angle, a mean of 40.7 ± 4.7 degrees (range, 32 to 51 degrees); the radius of curvature, a mean of 25.3 ± 2.3 millimeters (range, twenty-two to thirty millimeters); the height of the head, a mean of 18.5 ± 2.0 millimeters (range, fifteen to twenty-two millimeters); the humeral head offset, a mean of 9.7 ± 1.7 millimeters (range, six to twelve millimeters); and the head-to-tuberosity height, a mean of 8.7 ± 1.2 millimeters (range, six to ten millimeters). The mean age of the individuals at the time of death was seventy-two years (range, fifty-nine to eighty-three years). Eleven of the cadavera were male and ten were female. In contrast to the prosthetic systems in the present study, the coronal plane of the proximal aspect of the humerus is not apparent from its symmetry and needs definition. It was defined by an anteroposterior radiograph made after rotating the humerus through its retroversion angle about its reamed canal (the orthopaedic axis) (Fig. 2). Geometrically, this plane, which passes through the center of rotation, bisects the articular surface and is parallel to the orthopaedic axis26.



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  		Fig. 2 Anteroposterior radiograph of the proximal aspect of a humerus from a cadaveric specimen, showing the center of rotation (black dot), the base of the articular surface (white broken line), and the center line of the reamed canal (vertical black line). RC = radius of curvature, HH = height of head, OS = offset of humeral head, SA = arc of articular surface, HT = head-to-tuberosity height, and HSA = head-shaft angle.

 

Computer Analysis
The analyses were performed with use of a computer optimization algorithm developed with use of a software program (Mathematica; Wolfram Research, Champaign, Illinois). This program searched a database of stem-head combinations in a given prosthetic system to identify the prosthetic geometry that best fit the anatomy of each specimen. The best fit between a prosthesis and a cadaveric specimen was defined as the one that least displaced the original center of rotation and the articular surface. The locations of the center of rotation for the cadaveric specimens and for the prostheses were known, and the difference between their relative positions was identified accordingly. Displacement of the articular surface was described by localizing the central point of the articulating surface, which was designated the articulation point (Fig. 1).

Each prosthetic system was analyzed separately to determine its ability to match the position of the center of rotation and the articulation point in the coronal plane of each specimen, with use of two constraints. First, the center line of the prosthetic stem was aligned with the center line of the reamed cadaveric humeral canal, as determined by the position of the reamer on the radiographic image. The size of the stem that was most nearly equal to, but not greater than, the size of the canal was chosen. Second, the osteotomy line in the humeral head was placed at an angle equivalent to the stem-head angle of the prosthesis. This osteotomy line would follow the anatomical neck if it was equivalent to the stem-head angle of the prosthesis, but this was not usually the case.

When the head-shaft angle of the specimen was different from the stem-head angle of the prosthesis, the osteotomy line was placed so that it resected the most articular surface possible without cutting into the tuberosities or the metaphyseal bone. Thus, the osteotomy line was not permitted to course below the anatomical neck (Fig. 3). These boundaries ensured that the osteotomy line represented a resection that would not damage the insertion of the rotator cuff and would leave the full complement of metaphyseal bone for fixation of the press-fit prosthesis. For specimens with a head-shaft angle that was less than the prosthetic stem-head angle, the osteotomy line began at the superolateral articular margin and exited through the inferior aspect of the humeral articular surface. For specimens with a head-shaft angle that was greater than the prosthetic stem-head angle, the osteotomy line began at the inferomedial articular margin and exited through the superior aspect of the humeral articular surface.



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  		Fig. 3 Illustration showing the placement of the osteotomy (broken line) at 45 degrees on specimens with head-shaft angles of 45 degrees (A), 32 degrees (B), and 51 degrees (C).

 
With use of these constraints, the computer optimization algorithm identified the prosthetic stem-head combination for each specimen that resulted in the minimum displacement of the center of rotation and the articulation point. The displacement values for both parameters were weighted equally; neither was considered to be more important than the other. Accordingly, the choice of prosthesis was optimum if the sum of these displacements was minimized.

The optimum prosthetic stem-head combination chosen for each specimen then was assessed to determine the magnitude of the resulting displacement of the center of rotation and the articulation point. The effect on the arc of the articular surface was analyzed. The change in the head-to-tuberosity height was calculated as the vertical difference between the most superior point of the proposed prosthetic articular surface and the most superior point of the anatomical articular surface.

In certain clinical circumstances, such as a hemiarthroplasty in a patient who has an intact anatomical glenoid, it seems desirable to match the anatomical radius of curvature as well. The same calculations, therefore, were repeated, with an additional requirement that the algorithm minimize the differences between the prosthetic and anatomical radii of curvature as well as the displacement values for the center of rotation and the articulation point. Again, all values were weighted equally, making the optimum prosthetic choice for this algorithm one that minimized the sum of the differences in the radius of curvature, the displacement of the center of rotation, and the displacement of the articulation point.

The distribution of continuous variables was tested for normality with use of the test of Shapiro and Wilk30. Spearman correlation coefficients were calculated to examine the relationships between the structure of the specimen (humeral length, radius of curvature, head-shaft angle, and offset of the humeral head) and the displacement of the center of rotation, the displacement of the articulation point, increases in head-to-tuberosity height, and changes in the arc of the articular surface. All analyses were two-tailed and were conducted with SAS software (version 6.12 for Windows; SAS Institute, Cary, North Carolina). The type-I error was set at the level of 0.05.


   Results
Top
 Abstract
 Introduction
 Materials and Methods
 Results
Discussion
 References
 
For all systems evaluated, the selected prosthesis resulted in a displacement of the center of rotation and the articulation point that differed from the original anatomy by a mean of 14.7 millimeters (range, 3.3 to 31.4 millimeters) and 16.0 millimeters (range, 4.1 to 26.7 millimeters), respectively (Table II). The displacements were consistently in the same direction—that is, superior in the vertical direction and lateral (toward the center line of the canal) in the horizontal direction. Accordingly, the head-to-tuberosity height increased a mean of 11.3 millimeters (range, 3.2 to 26.6 millimeters). In order to minimize these displacements, the algorithm selected smaller heads that resulted in a mean diminution in the arc of the articular surface of approximately 26 degrees (range, 11 to 41 degrees).


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  		TABLE II DATA ON THE PROSTHETIC SYSTEMS SELECTED WITH THE ALGORITHM TO MINIMIZE DISPLACEMENT OF THE CENTER OF ROTATION AND THE ARTICULATION POINT*

 
The minimum displacement of the articular surface occurred when a specimen with a head-shaft angle of 43 degrees was matched to the Global shoulder prosthesis, with a stem-head angle of 45 degrees (Fig. 4). The displacement of the center of rotation was 3.3 millimeters (2.5 millimeters laterally and 2.2 millimeters superiorly). The displacement of the articulation point was 4.2 millimeters (2.3 millimeters laterally and 3.4 millimeters superiorly). The head-to-tuberosity height increased 3.2 millimeters. The displacements were small, but the selection of a smaller-sized head reduced the arc of the articular surface by 30 degrees, from 150 to 120 degrees.



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  		Fig. 4 Plot of the articular surfaces for the prosthesis (shaded) and specimen (clear) combination with the least displacement of the articular surface. The displacement of the center of rotation (CR) was 3.3 millimeters, and the displacement of the articulation point (AP) was 4.2 millimeters. The specimen had a head-shaft angle of 43 degrees, the radius of curvature was 23.0 millimeters, the height of the head was 17.0 millimeters, and the humeral head offset was 8.1 millimeters. The Global shoulder prosthesis that was selected had corresponding measurements of 45 degrees, 24.0 millimeters, 12.0 millimeters, and 5.6 millimeters. The head-to-tuberosity height necessarily increased 3.2 millimeters. The arc of the articular surface decreased by 30 degrees, from 150 to 120 degrees.

 
When this same specimen was matched to the prosthetic systems with stem-head angles that were different from 45 degrees (35 degrees for the Bio-Modular prosthesis and 50 degrees for the Kirschner II-C prosthesis), the center of rotation and the articulation point were displaced further (Figs. 5-A and 5-B). For the Bio-Modular prosthesis, the displacement of the center of rotation was 20.2 millimeters and the displacement of the articulation point was 16.9 millimeters. For the Kirschner II-C prosthesis, the displacement of the center of rotation was 9.3 millimeters and the displacement of the articulation point was 12.4 millimeters. These displacements resulted in part because of the different inclination angles of the prosthetic systems and the anatomical specimens and also because of their different offsets.



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  		Figs. 5-A and 5-B: Plots of articular surfaces showing the best match of the Bio-Modular and Kirschner II-C prostheses to the same specimen shown in Fig. 4. Fig. 5-A: The Bio-Modular prosthesis that was selected had a stem-head angle of 35 degrees, the radius of curvature was 22.0 millimeters, the height of the head was 13.0 millimeters, and the humeral head offset was 0.5 millimeter. The center of rotation (CR) and the articulation point (AP) were displaced 20.2 and 16.9 millimeters, respectively. The head-to-tuberosity height increased 17.7 millimeters. The arc of the articular surface decreased by 18 degrees, from 150 to 132 degrees.

 


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  		Fig. 5-B The Kirschner II-C prosthesis that was selected had a stem-head angle of 50 degrees and a radius of curvature of 25.4 millimeters. The height of the head was 13.5 millimeters, and the humeral head offset was 1.1 millimeters. The center of rotation and the articulation point were displaced 9.3 and 12.4 millimeters, respectively. The head-to-tuberosity height increased 8.6 millimeters. The arc of the articular surface decreased by 26 degrees, from 150 to 124 degrees.

 
The maximum displacement of the center of rotation (31.4 millimeters) occurred when a specimen with a head-shaft angle of 50 degrees and a humeral head offset of 8.1 millimeters was matched to the Bio-Modular prosthesis with a stem-head angle of 35 degrees (Fig. 6). The humeral head offset of the chosen prosthesis was 0.5 millimeter. The displacement of the center of rotation was primarily in the superior direction (29.6 millimeters) and, to a lesser extent, in the lateral direction (10.4 millimeters). The displacement of the articulation point (24.6 millimeters) was less than that of the center of rotation but also was notable. The head-to-tuberosity height increased by a similar amount (26.6 millimeters). The arc of the articular surface was reduced by 16 degrees, from 148 to 132 degrees.



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  		Fig. 6 Plot of articular surfaces for the prosthesis (shaded) and specimen (clear) combination with maximum displacement of the center of rotation (CR) (31.4 millimeters). This specimen had a head-shaft angle of 50 degrees, the radius of curvature was 25.0 millimeters, the height of the head was 18.0 millimeters, and the humeral head offset was 8.1 millimeters. The Bio-Modular prosthesis that was selected had corresponding measurements of 35 degrees, 22.0 millimeters, 13.0 millimeters, and 0.5 millimeter. The head-to-tuberosity height increased 26.6 millimeters. The arc of the articular surface decreased by 16 degrees, from 148 to 132 degrees.

 
The greatest diminution of the arc of the articular surface (41 degrees) occurred when the Global shoulder prosthesis was matched to the anatomical specimen with the largest head-shaft angle (51 degrees) (Fig. 7). The displacements of the center of rotation and the articulation point were 6.7 millimeters and 4.1 millimeters, respectively. The head-to-tuberosity height increased 4.3 millimeters.



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  		Fig. 7 Plot of articular surfaces for the prosthesis (shaded) and specimen (clear) combination with greatest diminution in the arc of the articular surface (41 degrees), from 161 to 120 degrees. This specimen had a head-shaft angle of 51 degrees, the radius of curvature was 24.0 millimeters, the height of the head was 20.0 millimeters, and the humeral head offset was 10.7 millimeters. The Global shoulder prosthesis that was selected had corresponding measurements of 45 degrees, 24.0 millimeters, 12.0 millimeters, and 5.6 millimeters. The head-to-tuberosity height increased 4.3 millimeters. The displacements of the center of rotation (CR) and the articulation point (AP) were 6.7 millimeters and 4.1 millimeters, respectively.

 
Some of the original anatomical dimensions consistently correlated with the displacement of the prosthetic articular surface for all prosthetic systems. The length of the humerus correlated with increasing displacement of the center of rotation, with the strongest correlation for the Kirschner II-C prosthesis (r = 0.58, p = 0.006) and the weakest correlation for the Global shoulder prosthesis (r = 0.53, p = 0.014). The radius of curvature of each specimen correlated with the magnitude of displacement of the center of rotation and the articulation point, with the strongest correlation for the Bio-Modular prosthesis (r = 0.76, p = 0.0001) and the weakest correlation for the Select shoulder prosthesis (r = 0.59, p = 0.005). The medial offset of the specimen showed a very strong correlation with the magnitude of displacement of the center of rotation for all systems, with the strongest correlation for the Bio-Modular prosthesis (r = 0.86, p = 0.0001) and the weakest correlation for the Kirschner II-C prosthesis (r = 0.67, p = 0.0009). Thus, a longer humerus with a larger head had more displacement.

The head-shaft angle of the anatomical specimen correlated inversely with superior displacement of the prosthetic head for all systems except the Bio-Modular prosthesis, which showed a positive correlation. This positive correlation was seen for the superior displacement of the center of rotation, the articulation point, and the head-to-tuberosity height (Table III). It is of note that the mean head-shaft angle in the anatomical study was approximately 41 degrees, which is greater than the stem-head angle of the Bio-Modular prosthesis but less than that of the others. A larger anatomical head-shaft angle, therefore, usually resulted in a better match and less superior transposition of the prosthetic head for the prosthetic systems other than the Bio-Modular system.


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  		TABLE III CORRELATION OF THE HEAD-SHAFT ANGLE OF THE CADAVERIC SPECIMENS WITH THE SUPERIOR DISPLACEMENT OF THE CENTER OF ROTATION, ARTICULATION POINT, AND HEAD-TO-TUBEROSITY HEIGHT

 
Optimizing for the radius of curvature, in addition to the center of rotation and the articulation point, did not appreciably alter the parameters studied (Table IV). The prosthetic choices were, for the most part, indistinguishable from those of the original algorithm. Exceptions to this were related to the number of head sizes with the same radius of curvature that were available in a given prosthetic system. For the Select and Kirschner II-C prostheses, the prosthetic selections were identical with use of both algorithms. Different selections were made for two specimens with the Bio-Modular prosthesis and six specimens with the Global prosthesis. In these cases, the positions of the center of rotation and the articulation point differed by less than two millimeters from those of the prosthetic selection when the radius of curvature was not included in the optimization algorithm.


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  		TABLE IV DATA ON THE PROSTHETIC SYSTEMS SELECTED WITH THE ALGORITHM TO MINIMIZE RADIUS OF CURVATURE IN ADDITION TO DISPLACEMENT OF THE CENTER OF ROTATION AND THE ARTICULATION POINT*

 


   Discussion
Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
References
 
Total shoulder arthroplasty has been shown to be a reliable intervention to improve the comfort and function of patients who have degenerative disease of the glenohumeral joint1,4,10,20,22. It could be argued that the success of the procedure questions the need for this kind of analysis. However, persistent problems such as loosening of the glenoid component, superior humeral migration, and tendinopathy of the rotator cuff have been well documented4,10,18,29,33, and we believe that it is likely that the superior position of the prosthetic head predicted by this study plays a role.

A prosthetic head in a superior position, rotating about a superiorly located center of rotation, would inevitably result in eccentric forces on the glenoid that could undermine glenoid fixation and increase the chances of polyethylene wear13,15. The supraspinatus tendon must course over the elevated prosthetic head precisely where that tendon is most vulnerable. Not surprisingly, late tendinopathy, even in what were otherwise successful shoulder arthroplasties, also has been reported5,10,22,33. Taken together, these factors provide a compelling explanation for reports of superior humeral migration on the glenoid4,9,10,31,33.

The inability of the prosthetic systems in the present study to replicate the normal anatomical variability results from both a limited inventory of implant sizes and certain geometric features of the prosthetic systems themselves. Similar concerns with respect to arthroplasty of the hip and knee have been discussed extensively in the literature11,23,24,27. Those studies showed not only that matching normal anatomy is difficult but also that altering the anatomy by prosthetic reconstruction has biomechanical consequences.

The single geometric feature intrinsic to the prosthetic systems in the present study that causes the most problems is the gap created by the collar of the prosthesis and the locking taper, which mandates a reduction in the arc of the articular surface for any given size of head. This feature has been discussed in other studies20,26. With this type of prosthetic construct, use of a head that is similar in size to the original anatomy makes it very difficult to avoid overstuffing the joint20. As a result, increased tension in the overlying soft tissues reduces the glenohumeral range of motion and causes obligate translation of the humeral head on the glenoid earlier in this curtailed range15.

Use of a smaller size of prosthetic head also may lead to several undesirable consequences. The contact between the prosthetic head and the glenoid articular surface may decrease earlier in the range of motion. The glenoid may not be able to capture a humeral head with which it is only partially in contact, leading to instability. Contact pressures may increase for a given joint-reaction force, possibly accelerating wear of the glenoid. If these pressures are at the periphery of the glenoid, eccentric loading may promote loosening of the glenoid component.

Friedman observed a reversal of the normal two-to-one ratio of glenohumeral-to-scapulothoracic motion in a radiographic analysis of elevation of the shoulder after this procedure12,14. Specific information on the geometric features of these shoulder replacements, other than the use of nonconstrained prostheses, was not given. Nonetheless, it merits attention that, even in the hands of an experienced shoulder surgeon, shoulder arthroplasty with use of the prosthetic designs available in the 1980s resulted in glenohumeral motion that was essentially one-fourth of normal12,14. Boileau et al. made similar observations in cineradiographic studies6, further supporting the contention that shoulder arthroplasty does not consistently restore normal motion.

Consideration should be given to whether surgeons adhere to the constraints used in the algorithm in the present study. Intraoperative maneuvers may have been devised in order to implant these systems in a nearly anatomical manner. This possibility certainly applies somewhat to the Neer prosthesis when it is implanted with cement. The relatively tapered metaphyseal area and cylindrical stem of that prosthesis allow the surgeon some opportunity to shift and tilt the prosthesis in the canal, which effectively adjusts the offset and the head-shaft angle. Similar techniques that may apply to the press-fit prosthetic systems in the present study are best evaluated by considering the assumptions made by each constraint imposed by the algorithm.

We imposed a humeral osteotomy line at the stem-head angle of the prosthesis that exactly reproduced the retroversion of the original humerus. This osteotomy line did not violate the greater tuberosity or the metaphysis, considered as the boundaries of the anatomical articular surface. This represented the greatest problem for the Bio-Modular prosthesis, which has a stem-head angle (35 degrees) that was less than the mean anatomical head-shaft angle of the specimens (41 degrees), resulting in the largest displacement values in the present study. Experienced surgeons may seat the prosthesis more effectively than the osteotomy line that was imposed by the computer program allowed, but as a consequence they must cut below the humeral anatomical neck into metaphyseal bone. This technique may not represent a problem when shoulder arthroplasty is performed with this system, but it is nonetheless useful to know that cutting below the humeral neck is a necessary part of the operative technique. Accordingly, failure to osteotomize into the metaphyseal area or, even more of a problem, an osteotomy that undercuts the humeral head above this level will certainly result in a nonanatomical reconstruction that displaces the articular surface as already described.

For the other prosthetic systems, which had stem-head angles of 45 and 50 degrees, the proposed osteotomy line most often presented the opposite problem, leaving unresected humeral head inferiorly. In this circumstance, we were probably justified in using an algorithm that did not allow the osteotomy line simply to be lowered because the insertion of the rotator cuff is vulnerable below this level. If anything, the opposite may be true. Surgeons may elect to leave some articular surface superiorly in order to protect the rotator cuff. Another possible solution, however, is to angle the osteotomy inferiorly along the anatomical neck. To the extent allowed by the metaphyseal bone or the inner diameter of the canal, the surgeon may then tilt the prosthesis into varus alignment8.

This last possibility highlights another constraint imposed by the algorithm—namely, that the prosthetic stem must be aligned with the reamed canal. If this condition was met clinically, then the operative adjustments already described would not be possible. If this condition was not met clinically, then yet another opportunity exists for intraoperative maneuvering that would allow the surgeon to manipulate the offset by sliding the prosthetic head back down the slope of the osteotomy. In our opinion, it is not uncommon to see postoperative radiographs that show a prosthetic stem that is not perfectly centered in the canal.

We designed the algorithm to select prosthetic heads that minimized the displacement of the center of rotation and the articulation point, but we could have configured the algorithm to select for other parameters. Consider the computer's choice that resulted in the greatest diminution of the arc of the articular surface (Fig. 7). On the basis of an intraoperative assessment of glenohumeral motion and laxity, or simply to avoid the use of this choice of humeral head because it has a diminutive surface arc, a surgeon could have chosen to use a larger-sized head. In this example, the prosthetic system offered two larger head sizes with the same radius of curvature (Figs. 8-A and 8-B). With each successive head size, the center of rotation and the articulation point are displaced further, but the arc of the articular surface increases and even exceeds that of the original anatomy with the largest head. The relative clinical importance of these variables is not yet entirely clear. Therefore, the surgeon must assess these factors intraoperatively.



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  		Figs. 8-A and 8-B: Plots of articular surfaces for the Global shoulder prosthesis and the same specimen as shown in Fig. 7, with use of larger head sizes. Fig. 8-A: A prosthesis with a medium-sized head. The height of the head was 17.0 millimeters, and the offset was 9.2 millimeters. The displacements of the center of rotation (CR) and articulation point (AP) were 9.0 and 7.0 millimeters, respectively. The arc of the articular surface decreased by only 15 degrees, from 161 to 146 degrees.

 


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  		Fig. 8-B A prosthesis with a large-sized head. The height of the head was 22.0 millimeters, and the humeral head offset was 12.9 millimeters. The displacements of the center of rotation (CR) and articulation point (AP) were 12.1 and 10.9 millimeters, respectively. The articular surface arc actually increased 10 degrees, from 161 to 171 degrees.

 
The computer algorithm that minimized the differences in the radius of curvature in addition to the displacement of the center of rotation and the articulation point did not appreciably alter the selection of the prosthesis from that of the original algorithm. When different head sizes were selected, the changes were either negligible or for the better. For example, with use of the Global shoulder prosthesis in one specimen, the choice of prosthesis improved the position of the center of rotation by only 0.7 millimeter as compared with the choice made by also minimizing the difference in the radius of curvature (Figs. 9-A and 9-B). In this particular case, the displacement of the articulation point was unchanged and the arc of the articular surface and the head-to-tuberosity height actually improved. When a hemiarthroplasty is performed, therefore, it seems reasonable to incorporate the goal of matching the radius of curvature into the intended prosthetic reconstruction. This approach may apply to total shoulder arthroplasty as well, depending on the prosthetic system. In some systems, such as the Global shoulder prosthesis, the sizing of the humeral head is based on the glenoid component.



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  		Figs. 9-A and 9-B: Plots of articular surfaces for the Global shoulder prosthesis and specimen, with use of both algorithms. One algorithm (Fig. 9-A) selected for minimum differences in the center of rotation (CR) and the articulation point (AP), and the other (Fig. 9-B) selected for the minimum difference in the radius of curvature in addition to those of the center of rotation and the articulation point. The specimen had a head-shaft angle of 35 degrees, and the radius of curvature was 22.0 millimeters. The height of the head was 15.0 millimeters, and the humeral head offset was 8.2 millimeters. Fig. 9-A: Plot of the Global shoulder prosthesis with a head-shaft angle of 45 degrees. The radius of curvature was 28.0 millimeters; the height of the head, 12.0 millimeters; and the humeral head offset, 2.7 millimeters. The center of rotation (CR) and the articulation point (AP) were displaced 7.3 and 12.5 millimeters, respectively. The head-to-tuberosity height increased 10.2 millimeters. The arc of the articular surface decreased by 33 degrees, from 143 to 110 degrees.

 


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  		Fig. 9-B Plot of the Global shoulder prosthesis with a head-shaft angle of 45 degrees. The radius of curvature was 24.0 millimeters; the height of the head, 12.0 millimeters; and the humeral head offset, 5.6 millimeters. The center of rotation (CR) and the articulation point (AP) were displaced 8.0 and 12.5 millimeters, respectively. The head-to-tuberosity height increased 9.6 millimeters. The arc of the articular surface decreased by 23 degrees, from 143 to 120 degrees.

 
In order for a prosthetic system to replicate normal anatomy, it must be able to do so in three dimensions. It should be emphasized that, in the present study, two dimensions were analyzed and anatomical and prosthetic geometry were considered in the coronal plane only. The articular surface of the proximal part of the humerus is not typically coaxial with the humeral shaft3,6 and may be offset posteriorly by as much as 10.0 millimeters28,32. The prosthetic systems that we analyzed did not allow for anterior or posterior offset. To the extent that the anatomical articular surface is offset from the canal in this dimension, the prosthetic reconstruction will differ from the original anatomy accordingly.

The findings of the present study may be useful in the planning and execution of shoulder arthroplasty. A preoperative radiograph that profiles the coronal plane of the humerus may be compared with templates specifically as a way to avoid a superior position of the prosthetic head. For patients who have excessively small or tapered metaphyseal regions, it may be prudent to undersize the prosthesis. The surgeon should be cognizant of the stem-head angle of the prosthetic system and should be prepared to assess how the necessary osteotomy of the humeral head may relate to the differing anatomy of each patient. As a general rule, with these prosthetic systems, we support resecting as much of the humeral head as possible without damaging the rotator cuff or compromising metaphyseal bone stock.


   Footnotes
 
*One or more of the authors has received or will receive benefits for personal or professional use from a commercial party related directly or indirectly to the subject of this article. Funds were received in total or partial support of the research or clinical study presented in this article. The funding source was the Kaiser Permanente Regional Research Committee.

{dagger}Southern California Permanente Medical Group, Los Angeles Medical Center, 4747 Sunset Boulevard, Los Angeles, California 90027. E-mail address for Dr. Pearl: michael.l.pearl@kp.org. E-mail address for Mr. Kurutz: samukuru@pacificnet.net.


   References
Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 References
 

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