TRABECULAR
ARCHITECTURE
OF THE HUMAN
PATELLA”
P. RAUXt. P. R. TOWNSEW:. R. MEGEL:. R. M. ROSE: and E. L. RADIN~\
Abstract--The internal architecture of the human patella was studied bk quantitative stereologul anal!sis ofmicroradiographs made from sagittal and horizontal sections. The predominant structural (trabecular) element was found to be oriented sheets of hard tissue connected laterall? b> rods of the ume material. The sheets change orientation in a correlated and systematic manner which appears to be in response to the biomechanicdl demands made on the patella. The predommnnt variable in the determination of densit! (and. presumably. other physical properties)was the intertrabecuiar spacing rather than trabecular thickness. It was found that the sheet-and-rod model could be used to calculate all of the structural parameters in a consistent manner.
INTRODUCTlOK This work is the first phase of an investigation of the structure and function of human patella. To follow are
measurements of the mechanical properties, the relation of the properties to the structure, and the application to the known biomechanics of the patella. The key to the problem is the cancellous bone which lies between the articular surface and the anterior cortex. This region constitutes most of the patella, and must meet all of the mechanical demands placed upon it. To characterize the internal architecture. we have used serial sections in three planes and quantitative stereological techniques. The present literature on internal architecture is rather sparse: the only publication. to the best of our knowledge. consists of sagittal. coronal and horizontal radiographs of sawed sections made by Hall ( 1966). Since the techniques used by Hall (cutting sections with a band saw and radiography of defatted material) are relatively unsophisticated and should not be’ expected to have the geometrical retention or resolution necessary to quantitative microscopic studies. further discussion of internal architecture will be postponed to the final sections of this paper.
* RZL.CIW~20 Mu>, 1974. t Department of Anatomy. Faculte Necker-Enfants Malades. Parls. France. : Department of Metallurgy and Materials Science. Massachusetts Institute of Technology, Cambridge. Massachusetts 02139. U.S.A. $ Department of Orthopaedic Surgery. Harvard Medical School. Boston. Massachusetts 02115. U.S.A.
ESPERIMEYTAL PROCEDI’RE I, Material
ard prrparatiorl
Ten grossly normal knee caps were obtained at autopsy from cadavers whose age range was 4C76 yr old with a mean of 59. There were 6 males. 4 females. 5 right and 5 left sides. In each case the cause of death was known to have no effect on skeletal joints. The following steps were then performed: (a) The soft tissue close to the bone was dissected and several small holes were drilled through the anterior cortex. to allow good penetration of embedding polymer. (b) The specimens were then fixed and defatted for 48 hr in absolute alcohol. (c) Impregnation with methyl methacrylate monomer was carried out under vacuum. (d) The monomer was polymerized under ultraviolet light and controlled temperature with benzoyl peroxide activator. (f) The plastic block surrounding each patella was then machined to a shape corresponding to the intended direction of sectioning. (g) Sectioning was performed with a diamond wheel ROOitrn in thickness: the resulting slices had an average thickness of 220pm and were separated b! approx. I mm (the material lost in cutting). (h) The thickness ofeach slice W?s reduced to 80 pm bq a three-step procedure using metallographic polishing and grinding papers (silicon carbide lubricated with water) in successivel] finer grades. The papers were backed b> plate glass and the standard metallographic procedures and precautions were observed to preserve flatness and smoothness.
P. RAUX et ~1.
2
(i) Microradiographs were made on an apparatus constructed for this particular work; a G.E. XRD-5 Xray diffraction unit was adapted for the purpose. Unfiltered CuKr radiation was used, and the specimen was held by vacuum to Kodalith thick base film in a special holder. The resulting microradiographs were then enlarged by a factor of ten. Horizontal, sagittal (vertical and antero-posterior) and frontal (vertical and medial-to-lateral) sections were all taken, to allow a truly three dimensional study: each slice was precisely located with regard to the outer contours and total length of the sample.
2. Selection of areas to study The articular surface of the patella can be divided into three regions: (1) the very convex medial side. henceforth denoted by (M): (2) the slightly concave lateral side, denoted by(L); and (3) the crest separating the ttio areas, denoted by (C). In general the location of the articular contact(s). and the magnitude and distribution of the interarticular forces are not known. However we can assume that the variations in properties and structure of the subchondrial bone will be related to the force distribution and may even be informative in this connection. The selection of areas was made in two planes: First. the ‘inter horizontal’ plane as shown in Fig. l(a): three areas were located with reference to the three articular regions mentioned above, area 1 corresponding to the lateral, area 2 to the crest, and area 3 AtltWlW
to the medial, each area being located in relation to the reference line which was constant from one section to the next, in any specimen. Second, the ‘Interior sagittal’ plane which is shown in Fig. l(b). Again, three areas, proximal (level a in the figure), middle (level b) and distal (level c) were selected. Thus, nine areas were selected for intensive study, as shown in the frontal view in Fig. l(c). Horizontal and sagittal serial sections were taken (in alternate specimens) and correlated to provide a three-dimensional study of the same volume. The frontal plane was only used to control the data and no measurements were made on it. 3. Quantitatice
stereoloyy
Several parameters were studied: 1. Trabecular volurnefiactio~l (Vy.). In the plane cf observation the volume fraction is equal to the fractional length (~5:) of a test line which lies over the trabeculae (Rosiwal, 1898). in an isotropic system. It is also equal to the area fraction (A$ of the plane of observation (Delesse, 1848). Thus
(a)
%
q
I
Lateral
I
Crest
Medial
I Pmximl
Proxlmol
(bl
Distal (b)
k)
Fig. I. Area and volume code. (a) horizontal plane,(b) sagittal plane. (c) frontal (coronal) plane.
Fig. 2. Rose-of-the-number-of-intersections for examples of (a) one orientation axis. 100 per cent degree of orientation. (b) two orientation axes. both 100 per cent degree and (c) one axis. less than 100 per cent degree.
Trabrcular architecture of the human patella
However. these relations are not generally true in anisotropic systems, unless certain conditions are satisfied. _. ’ .41w~yc~ rrahrctkw rhickwss ( ). This was determined by test lines. and averaging. 3. herage disturxe between nuheculae. This was also done with test lines. and could have been related to the size and volume of the intertrabecular spaces; however the latter two parameters were not measured in this study. 4. &~wcJfiOJl. The study of oriented structures has been well-developed (see. e.g. Underwood, 1970). The technique generally used is that of the ‘rose’ of the number of intersections. that is a polar plot of the intersection frequency versus the angle of the test line. In Fig. 2 we present three examples: an ideal parallel set of interfaces. a rectangular grid. and a partially oriented set of interfaces. together with the corresponding roses. A test grid was designed to permit the simultaneous extraction of the above mentioned parameters; it is shown in Fig. 3. The grid size was scaled down or up to suit the specimen area. and the intercept frequency and line fraction < ,!.z> measured for each line. Twent! four observations were made for each selected area.
Fig. 4. Microradiograph
RESL!LTS I. A proposed
4.
SCUJJJI~JJ~ dt~V0Jl
JJlicrOScOp~’
As a non-quantitative control on the above observations. a limited amount of scanning electron microscopy was performed. The bone was defatted in alcohol. dried in air. and coated with gold by vacuum evaporation. The instrument used was a Cambridge Stereoscan Mark II.
Fig. 3. Stereology test grid.
of a typical mid-horizontal plane.
AND
DISCCSSIOh
rJlode/
Typical microradiographs are shown in Figs. 4-6. Consider region 3b (crest area, midcoronal) as shown in these figures: horizontal plane in Fig. 4 and sagittal in Fig. 5. The horizontal section suggests that the essential elements in the structure are oriented sheets of hard tissue. Such sheets must be interconnected. and Fig. 5 suggests that the interconnecting elements are
Fig. 5. Sagittal plane-crest
region
P. RAUX et al.
Fig. 6. Sagittal plane-medial region.
rod-shaped. Figure 7 is a sketch illustrating the model we propose for the structure we observe. Figures 8 and 9 show scanning electron micrographs which tend to confirm this model. As a working hypothesis, we suggest at this point that all the cancellous bone in the patella, including even the high-density regions, is some variation of the basic model.
In Fig. 4 (horizontal section) it is apparent that area 2 (as defined in Fig. 1)consists of highly oriented trabeculae. However these same areas viewed in Fig. 5 (sagittal section) show no apparent orientation. Orientational roses constructed for these areas confirm these observations: Fig. IO(a) corresponds to the horizontal
plane of area 2. and 10(b) to the sagittal plane. On the medial side, the converse is true: comparing Figs. 4 and 6, and the corresponding roses in Fig. 1I. the orientation is apparent only in the sagittal plane. These observations can be reconciled by referring to the structural model. which is idealized in Fig. 12: the sheets are almost vertical in area 2, and the sagittal section cuts mostly rods, giving an essentially randomly oriented impression, in two dimensions. of what is in fact a highly oriented three-dimensional structure. (It is important to note that high apparent trabecular densities in two-dimensional sections are not an accurate indicator of true densities. since the observation plane may intersect the sheets obliquely in a region of slowly changing orientation.) The structure in area 3 is really the same as that in area 2. but simply rotated 90”. A self-consistency test may be made for the above model. Referring to Fig. 12, the parameters w, t and s may be extracted stereologically (as described in Settion 3 of Procedure). and then used to construct an
(a)
‘d-‘_’
(b)
Fig. 7. Schematic
of generaltrabecular structure.
Fig. 10. Rose-of-the-number-of-intersections for (at area 1 horizontal plane and (b) area 2. sagittal plane. See text for discussion of dashed figure in (a).
Trabecular
architecture
of the human
pat&a
Fig. 12. ldeallzed
I
structure
model
(a)
The fact that we have an anisotropic structure throughout the patella presents special problems. As discussed before. the equality LL” = Af: = I’;” holds only for isotropic structures. unless true spherical averages are taken. For anisotropic structures. in general
Roses for (a) area 3. horizontal plane and (b) area 3. sagittal plane. See text for discussion of dashed figure in
Fig. 11.
(b).
ideal rose. In Figs. IO(a) and 1l(b) we have superimposed the calculated roses on our measurements. The roses were calculated with the assumption that the orientation would change significantly across the area sampled. As a partial compensation for this effect, separate calculations were made for each end of the rose. and the two results were joined at the symmetry axis. An interesting result of this procedure is the ‘spike’ or protrusion noted at 5-6 o’clock in the calculated curves, and the corresponding details in the measured curves. These details. which appear at first glance to be scatter or artifacts. are actually due to slowly changing trabecufar orientation across the plane of observation. In fact. all the areas examined gave stereological roses similar to those above. Even the ‘dense’ areas did so; Fig. 13 shows a rose from area 4. which is essentially subcortical. It is also probable that most of the discrepancy between calculated and experimental roses is due to the fact that the calculated model used two axes of l(K) per cent orientation (one for each half of the rose) while the actual structure is not 100 per cent oriented.
and only area fractions can be reliably obtained. However. the structural model (see Fig. 12) can be used to correlate area fraction to volume fraction. The correction factor for .X--Xand _~-r views is generally less than 25 per cent and experimentally useful since these areas are quite well defined. The experimentally measured volume fractions are compared with those calculated from the model in Fig. 14. From the discussion above. only certain areas yield reliable volume fraction data. This information is given in Fig. 15 as volume fraction versus location in the patella. The parameter most responsible for the trends in volume fraction is the separation between sheets (s): correlation s vs I’! is given in Fig. 16.
Fig. 13. Rose for area 4. horizontal
plane.
6
P. Raux et al.
v: / /
I
0
0.2
I 0.4
V :,
eapefimentul
I 0.6
I 0
1
I
0.3
0.6
s.
I
I
09
Ii?
cm
Fig. 14. Experimental vs actual volume fraction of bone.
Fig. 16. Volume fraction of bone vs distance between sheets (s). CONCLUSIONS
By averaging over the ten patellae. and matching the stereological results and the microradiographs we have arrived at the conclusions described below. 1. Zones of single orientation There are five regions which may be characterized by single orientation axes, as shown in Fig. 17. Areas 3a and c, the proximal and distal regions of
04
c
Loteml
I-Pmxunol
04
0.2
.,
0.4
Io-
o-2
I
2
3
Crest
Proximal
-\
a
the medial side, consist mainly of horizontal sheets running from the articular surface to the anterior cortex. The main sort of deviations from this pattern are seen in Fig. 6 (a sagittal section on the medial side): the upper sheets are slightly oblique downward and backward, and the reverse is true for the distal sheets. Thus the sheets remain approximately orthogonal to the artic&r surface; they do not appear to be influenced by the high curvature of the medial side. Although it is not the point of this work to speculate on the relationship of internal architecture to the forces on the patella, the above arrangement is probably optimal in this connection. In areas la, b and 2b, the top and middle portion of the lateral side and the mid-crest region, respectively. the sheets are vertical and run perpendicular to the artitular surface, and extend from the articular side to the cortex. Because the lateral articular surface is relatively flat. the speculation again arises, that this trabecular geometry is optimal for transmitting compressive
b
c
V4
DlStal
Medial t
‘:;e 2
3
Fig. 15. Volume fraction of bone vs location in the patella.
Dista I Fig. 17. Regions of single orientation axis (frontal view).
Trabecular architecture of the human patella
Proximal
7
region’ where no well-characterized geometric organization exists. The neutral region extends almost from the articular surface to the cortex. in all ten of the patellae studied. although it is surrounded b) highly oriented regions. 3. Suhchondral and s&cortical regions
Distal Fig. 18. General trabecular structure (frontal view).
to note that the predominantly sagittal orientatiqn of the structure is not immediately apparent. e.g. from the sagittal section in Fig. 6. However. the roses of the intersection frequencies give quantitative answers to such questions. forces. It is important
In these zones. the roses showed a shift of orientation through the area of observation. Area ?a (top of the crest) is made of two kinds of sheets. The more lateral run vertically, but as one moves medially they become oblique to connect the horizontal structure of area 3a to the vertical one of area 2b (Fig. 18). Throughout this region. all sheets retain the same antero posterior direction orthogonal to the articular surface. Area lc (distal part of the lateral side) is an oblique system of sheets. still running posterior to anterior but connecting the vertical sheets of area 1b to the main vertical line of sheets of the crest area. Both sagittal and horizontal sections of these oblique sheets will have, though, a high degree of orientation. In region 2c (distal area of the crest), the vertical sheets of area 2b and the horizontal sheets of areas 3c and lc all converge continuously. as sketched in Fig. 18. Finally there is region 3b. the middle portion of the medial side. The structure here is quite different. The medial portion of 3b is essentially a continuation of 3a and c. above and below. But the orientation disappears as the crest is approached. and in fact at one point (see Fig. 18) very few sheets are found but rather a ‘neutral
Although the thickness of the subchondral zone varies from one specimen to another. the organization is quite consistent: polygonal cells with the cell walls oriented perpendicular to the articular surface. As Figs. 4 and 5 show. the subcortical zone is well defined. The structure is that of Figs. 7 and 12.but with the sheets running vertical and frontal. orthogonal to the sheets in the other regions. In addition, the distance between sheets is very low, corresponding to high densit) and high volume fraction of hard tissue. The highest data points in Fig. 16 (1’: _ @6. 0.7) were taken from the subcortical region. From this geometry arises the speculation that the transmission of tensile forces from quadriceps to patellar tendon plays a central role in determining the structure of the subcortical zone. An important implication of Fig. 18 is that the controlling parameter in bone density is the distance between the sheets. and that the sheet thickness remains relatively constant. Acknowledgemrnrs-This work was supported by the U.S. Office of Naval Research. In addition. the authors also gratefully acknowledge the help of I. M. Puffer and G. T. Freed of M.1.T. and J. Stukas of Massachusetts General Hospital. REFERENCES Delesse, A. (1848) Pro&de mtichanique pour determiner la composition des roches. Ann. Mints 13, 379. Hall. M. C. (1966) The Architecture ofdone. pp. 197-200. C. C. Thomas, Sprin&ield. Rosiwal, A. (1898) Ueber geometrische Gesteinsanalysen
usw. Verhmdl. K. K. Geol. Reich. Wein 5-6, 143. Underwood, E. E. (1970) Quantitatioe Stmeology. Chap. 3. Addison-Wesley. Reading. Mass. NOMENCLATURE area fraction of bone. dimensionless line fraction of bone. dimensionless intercept frequent!. intercept&m volume fraction of bone. dimensionless distance between sheets. cm trabecular thickness, cm average trabecular thickness. cm distance between struts. cm.
ARCHITECTURE
OF THE HUMAN
PATELLA”
P. RAUXt. P. R. TOWNSEW:. R. MEGEL:. R. M. ROSE: and E. L. RADIN~\
Abstract--The internal architecture of the human patella was studied bk quantitative stereologul anal!sis ofmicroradiographs made from sagittal and horizontal sections. The predominant structural (trabecular) element was found to be oriented sheets of hard tissue connected laterall? b> rods of the ume material. The sheets change orientation in a correlated and systematic manner which appears to be in response to the biomechanicdl demands made on the patella. The predommnnt variable in the determination of densit! (and. presumably. other physical properties)was the intertrabecuiar spacing rather than trabecular thickness. It was found that the sheet-and-rod model could be used to calculate all of the structural parameters in a consistent manner.
INTRODUCTlOK This work is the first phase of an investigation of the structure and function of human patella. To follow are
measurements of the mechanical properties, the relation of the properties to the structure, and the application to the known biomechanics of the patella. The key to the problem is the cancellous bone which lies between the articular surface and the anterior cortex. This region constitutes most of the patella, and must meet all of the mechanical demands placed upon it. To characterize the internal architecture. we have used serial sections in three planes and quantitative stereological techniques. The present literature on internal architecture is rather sparse: the only publication. to the best of our knowledge. consists of sagittal. coronal and horizontal radiographs of sawed sections made by Hall ( 1966). Since the techniques used by Hall (cutting sections with a band saw and radiography of defatted material) are relatively unsophisticated and should not be’ expected to have the geometrical retention or resolution necessary to quantitative microscopic studies. further discussion of internal architecture will be postponed to the final sections of this paper.
* RZL.CIW~20 Mu>, 1974. t Department of Anatomy. Faculte Necker-Enfants Malades. Parls. France. : Department of Metallurgy and Materials Science. Massachusetts Institute of Technology, Cambridge. Massachusetts 02139. U.S.A. $ Department of Orthopaedic Surgery. Harvard Medical School. Boston. Massachusetts 02115. U.S.A.
ESPERIMEYTAL PROCEDI’RE I, Material
ard prrparatiorl
Ten grossly normal knee caps were obtained at autopsy from cadavers whose age range was 4C76 yr old with a mean of 59. There were 6 males. 4 females. 5 right and 5 left sides. In each case the cause of death was known to have no effect on skeletal joints. The following steps were then performed: (a) The soft tissue close to the bone was dissected and several small holes were drilled through the anterior cortex. to allow good penetration of embedding polymer. (b) The specimens were then fixed and defatted for 48 hr in absolute alcohol. (c) Impregnation with methyl methacrylate monomer was carried out under vacuum. (d) The monomer was polymerized under ultraviolet light and controlled temperature with benzoyl peroxide activator. (f) The plastic block surrounding each patella was then machined to a shape corresponding to the intended direction of sectioning. (g) Sectioning was performed with a diamond wheel ROOitrn in thickness: the resulting slices had an average thickness of 220pm and were separated b! approx. I mm (the material lost in cutting). (h) The thickness ofeach slice W?s reduced to 80 pm bq a three-step procedure using metallographic polishing and grinding papers (silicon carbide lubricated with water) in successivel] finer grades. The papers were backed b> plate glass and the standard metallographic procedures and precautions were observed to preserve flatness and smoothness.
P. RAUX et ~1.
2
(i) Microradiographs were made on an apparatus constructed for this particular work; a G.E. XRD-5 Xray diffraction unit was adapted for the purpose. Unfiltered CuKr radiation was used, and the specimen was held by vacuum to Kodalith thick base film in a special holder. The resulting microradiographs were then enlarged by a factor of ten. Horizontal, sagittal (vertical and antero-posterior) and frontal (vertical and medial-to-lateral) sections were all taken, to allow a truly three dimensional study: each slice was precisely located with regard to the outer contours and total length of the sample.
2. Selection of areas to study The articular surface of the patella can be divided into three regions: (1) the very convex medial side. henceforth denoted by (M): (2) the slightly concave lateral side, denoted by(L); and (3) the crest separating the ttio areas, denoted by (C). In general the location of the articular contact(s). and the magnitude and distribution of the interarticular forces are not known. However we can assume that the variations in properties and structure of the subchondrial bone will be related to the force distribution and may even be informative in this connection. The selection of areas was made in two planes: First. the ‘inter horizontal’ plane as shown in Fig. l(a): three areas were located with reference to the three articular regions mentioned above, area 1 corresponding to the lateral, area 2 to the crest, and area 3 AtltWlW
to the medial, each area being located in relation to the reference line which was constant from one section to the next, in any specimen. Second, the ‘Interior sagittal’ plane which is shown in Fig. l(b). Again, three areas, proximal (level a in the figure), middle (level b) and distal (level c) were selected. Thus, nine areas were selected for intensive study, as shown in the frontal view in Fig. l(c). Horizontal and sagittal serial sections were taken (in alternate specimens) and correlated to provide a three-dimensional study of the same volume. The frontal plane was only used to control the data and no measurements were made on it. 3. Quantitatice
stereoloyy
Several parameters were studied: 1. Trabecular volurnefiactio~l (Vy.). In the plane cf observation the volume fraction is equal to the fractional length (~5:) of a test line which lies over the trabeculae (Rosiwal, 1898). in an isotropic system. It is also equal to the area fraction (A$ of the plane of observation (Delesse, 1848). Thus
(a)
%
q
I
Lateral
I
Crest
Medial
I Pmximl
Proxlmol
(bl
Distal (b)
k)
Fig. I. Area and volume code. (a) horizontal plane,(b) sagittal plane. (c) frontal (coronal) plane.
Fig. 2. Rose-of-the-number-of-intersections for examples of (a) one orientation axis. 100 per cent degree of orientation. (b) two orientation axes. both 100 per cent degree and (c) one axis. less than 100 per cent degree.
Trabrcular architecture of the human patella
However. these relations are not generally true in anisotropic systems, unless certain conditions are satisfied. _. ’ .41w~yc~ rrahrctkw rhickwss ( ). This was determined by test lines. and averaging. 3. herage disturxe between nuheculae. This was also done with test lines. and could have been related to the size and volume of the intertrabecular spaces; however the latter two parameters were not measured in this study. 4. &~wcJfiOJl. The study of oriented structures has been well-developed (see. e.g. Underwood, 1970). The technique generally used is that of the ‘rose’ of the number of intersections. that is a polar plot of the intersection frequency versus the angle of the test line. In Fig. 2 we present three examples: an ideal parallel set of interfaces. a rectangular grid. and a partially oriented set of interfaces. together with the corresponding roses. A test grid was designed to permit the simultaneous extraction of the above mentioned parameters; it is shown in Fig. 3. The grid size was scaled down or up to suit the specimen area. and the intercept frequency and line fraction < ,!.z> measured for each line. Twent! four observations were made for each selected area.
Fig. 4. Microradiograph
RESL!LTS I. A proposed
4.
SCUJJJI~JJ~ dt~V0Jl
JJlicrOScOp~’
As a non-quantitative control on the above observations. a limited amount of scanning electron microscopy was performed. The bone was defatted in alcohol. dried in air. and coated with gold by vacuum evaporation. The instrument used was a Cambridge Stereoscan Mark II.
Fig. 3. Stereology test grid.
of a typical mid-horizontal plane.
AND
DISCCSSIOh
rJlode/
Typical microradiographs are shown in Figs. 4-6. Consider region 3b (crest area, midcoronal) as shown in these figures: horizontal plane in Fig. 4 and sagittal in Fig. 5. The horizontal section suggests that the essential elements in the structure are oriented sheets of hard tissue. Such sheets must be interconnected. and Fig. 5 suggests that the interconnecting elements are
Fig. 5. Sagittal plane-crest
region
P. RAUX et al.
Fig. 6. Sagittal plane-medial region.
rod-shaped. Figure 7 is a sketch illustrating the model we propose for the structure we observe. Figures 8 and 9 show scanning electron micrographs which tend to confirm this model. As a working hypothesis, we suggest at this point that all the cancellous bone in the patella, including even the high-density regions, is some variation of the basic model.
In Fig. 4 (horizontal section) it is apparent that area 2 (as defined in Fig. 1)consists of highly oriented trabeculae. However these same areas viewed in Fig. 5 (sagittal section) show no apparent orientation. Orientational roses constructed for these areas confirm these observations: Fig. IO(a) corresponds to the horizontal
plane of area 2. and 10(b) to the sagittal plane. On the medial side, the converse is true: comparing Figs. 4 and 6, and the corresponding roses in Fig. 1I. the orientation is apparent only in the sagittal plane. These observations can be reconciled by referring to the structural model. which is idealized in Fig. 12: the sheets are almost vertical in area 2, and the sagittal section cuts mostly rods, giving an essentially randomly oriented impression, in two dimensions. of what is in fact a highly oriented three-dimensional structure. (It is important to note that high apparent trabecular densities in two-dimensional sections are not an accurate indicator of true densities. since the observation plane may intersect the sheets obliquely in a region of slowly changing orientation.) The structure in area 3 is really the same as that in area 2. but simply rotated 90”. A self-consistency test may be made for the above model. Referring to Fig. 12, the parameters w, t and s may be extracted stereologically (as described in Settion 3 of Procedure). and then used to construct an
(a)
‘d-‘_’
(b)
Fig. 7. Schematic
of generaltrabecular structure.
Fig. 10. Rose-of-the-number-of-intersections for (at area 1 horizontal plane and (b) area 2. sagittal plane. See text for discussion of dashed figure in (a).
Trabecular
architecture
of the human
pat&a
Fig. 12. ldeallzed
I
structure
model
(a)
The fact that we have an anisotropic structure throughout the patella presents special problems. As discussed before. the equality LL” = Af: = I’;” holds only for isotropic structures. unless true spherical averages are taken. For anisotropic structures. in general
Roses for (a) area 3. horizontal plane and (b) area 3. sagittal plane. See text for discussion of dashed figure in
Fig. 11.
(b).
ideal rose. In Figs. IO(a) and 1l(b) we have superimposed the calculated roses on our measurements. The roses were calculated with the assumption that the orientation would change significantly across the area sampled. As a partial compensation for this effect, separate calculations were made for each end of the rose. and the two results were joined at the symmetry axis. An interesting result of this procedure is the ‘spike’ or protrusion noted at 5-6 o’clock in the calculated curves, and the corresponding details in the measured curves. These details. which appear at first glance to be scatter or artifacts. are actually due to slowly changing trabecufar orientation across the plane of observation. In fact. all the areas examined gave stereological roses similar to those above. Even the ‘dense’ areas did so; Fig. 13 shows a rose from area 4. which is essentially subcortical. It is also probable that most of the discrepancy between calculated and experimental roses is due to the fact that the calculated model used two axes of l(K) per cent orientation (one for each half of the rose) while the actual structure is not 100 per cent oriented.
and only area fractions can be reliably obtained. However. the structural model (see Fig. 12) can be used to correlate area fraction to volume fraction. The correction factor for .X--Xand _~-r views is generally less than 25 per cent and experimentally useful since these areas are quite well defined. The experimentally measured volume fractions are compared with those calculated from the model in Fig. 14. From the discussion above. only certain areas yield reliable volume fraction data. This information is given in Fig. 15 as volume fraction versus location in the patella. The parameter most responsible for the trends in volume fraction is the separation between sheets (s): correlation s vs I’! is given in Fig. 16.
Fig. 13. Rose for area 4. horizontal
plane.
6
P. Raux et al.
v: / /
I
0
0.2
I 0.4
V :,
eapefimentul
I 0.6
I 0
1
I
0.3
0.6
s.
I
I
09
Ii?
cm
Fig. 14. Experimental vs actual volume fraction of bone.
Fig. 16. Volume fraction of bone vs distance between sheets (s). CONCLUSIONS
By averaging over the ten patellae. and matching the stereological results and the microradiographs we have arrived at the conclusions described below. 1. Zones of single orientation There are five regions which may be characterized by single orientation axes, as shown in Fig. 17. Areas 3a and c, the proximal and distal regions of
04
c
Loteml
I-Pmxunol
04
0.2
.,
0.4
Io-
o-2
I
2
3
Crest
Proximal
-\
a
the medial side, consist mainly of horizontal sheets running from the articular surface to the anterior cortex. The main sort of deviations from this pattern are seen in Fig. 6 (a sagittal section on the medial side): the upper sheets are slightly oblique downward and backward, and the reverse is true for the distal sheets. Thus the sheets remain approximately orthogonal to the artic&r surface; they do not appear to be influenced by the high curvature of the medial side. Although it is not the point of this work to speculate on the relationship of internal architecture to the forces on the patella, the above arrangement is probably optimal in this connection. In areas la, b and 2b, the top and middle portion of the lateral side and the mid-crest region, respectively. the sheets are vertical and run perpendicular to the artitular surface, and extend from the articular side to the cortex. Because the lateral articular surface is relatively flat. the speculation again arises, that this trabecular geometry is optimal for transmitting compressive
b
c
V4
DlStal
Medial t
‘:;e 2
3
Fig. 15. Volume fraction of bone vs location in the patella.
Dista I Fig. 17. Regions of single orientation axis (frontal view).
Trabecular architecture of the human patella
Proximal
7
region’ where no well-characterized geometric organization exists. The neutral region extends almost from the articular surface to the cortex. in all ten of the patellae studied. although it is surrounded b) highly oriented regions. 3. Suhchondral and s&cortical regions
Distal Fig. 18. General trabecular structure (frontal view).
to note that the predominantly sagittal orientatiqn of the structure is not immediately apparent. e.g. from the sagittal section in Fig. 6. However. the roses of the intersection frequencies give quantitative answers to such questions. forces. It is important
In these zones. the roses showed a shift of orientation through the area of observation. Area ?a (top of the crest) is made of two kinds of sheets. The more lateral run vertically, but as one moves medially they become oblique to connect the horizontal structure of area 3a to the vertical one of area 2b (Fig. 18). Throughout this region. all sheets retain the same antero posterior direction orthogonal to the articular surface. Area lc (distal part of the lateral side) is an oblique system of sheets. still running posterior to anterior but connecting the vertical sheets of area 1b to the main vertical line of sheets of the crest area. Both sagittal and horizontal sections of these oblique sheets will have, though, a high degree of orientation. In region 2c (distal area of the crest), the vertical sheets of area 2b and the horizontal sheets of areas 3c and lc all converge continuously. as sketched in Fig. 18. Finally there is region 3b. the middle portion of the medial side. The structure here is quite different. The medial portion of 3b is essentially a continuation of 3a and c. above and below. But the orientation disappears as the crest is approached. and in fact at one point (see Fig. 18) very few sheets are found but rather a ‘neutral
Although the thickness of the subchondral zone varies from one specimen to another. the organization is quite consistent: polygonal cells with the cell walls oriented perpendicular to the articular surface. As Figs. 4 and 5 show. the subcortical zone is well defined. The structure is that of Figs. 7 and 12.but with the sheets running vertical and frontal. orthogonal to the sheets in the other regions. In addition, the distance between sheets is very low, corresponding to high densit) and high volume fraction of hard tissue. The highest data points in Fig. 16 (1’: _ @6. 0.7) were taken from the subcortical region. From this geometry arises the speculation that the transmission of tensile forces from quadriceps to patellar tendon plays a central role in determining the structure of the subcortical zone. An important implication of Fig. 18 is that the controlling parameter in bone density is the distance between the sheets. and that the sheet thickness remains relatively constant. Acknowledgemrnrs-This work was supported by the U.S. Office of Naval Research. In addition. the authors also gratefully acknowledge the help of I. M. Puffer and G. T. Freed of M.1.T. and J. Stukas of Massachusetts General Hospital. REFERENCES Delesse, A. (1848) Pro&de mtichanique pour determiner la composition des roches. Ann. Mints 13, 379. Hall. M. C. (1966) The Architecture ofdone. pp. 197-200. C. C. Thomas, Sprin&ield. Rosiwal, A. (1898) Ueber geometrische Gesteinsanalysen
usw. Verhmdl. K. K. Geol. Reich. Wein 5-6, 143. Underwood, E. E. (1970) Quantitatioe Stmeology. Chap. 3. Addison-Wesley. Reading. Mass. NOMENCLATURE area fraction of bone. dimensionless line fraction of bone. dimensionless intercept frequent!. intercept&m volume fraction of bone. dimensionless distance between sheets. cm trabecular thickness, cm average trabecular thickness. cm distance between struts. cm.
