Mechanical behavior and quantitative morphology of the equine laminar junction.код для вставкиСкачать
THE ANATOMICAL RECORD PART A 283A:366 –379 (2005) Mechanical Behavior and Quantitative Morphology of the Equine Laminar Junction JEFFREY J. THOMASON,1* HEATHER L. MCCLINCHEY,1 BABAK FARAMARZI,1 AND JAN C. JOFRIET2 1 Department of Biomedical Sciences, University of Guelph, Guelph, Ontario, Canada 2 School of Engineering, University of Guelph, Guelph, Ontario, Canada ABSTRACT The horse’s hoof is structurally modiﬁed for its mechanical functions, but studying the functional design of internal structures is hampered by the external keratinous capsule. Finite-element analysis offers one method for evaluating mechanical function of components within the capsule, such as the laminar junction. This is the epidermodermal connection that binds the hoof wall strongly to the distal phalanx. Primary epidermal laminae (PEL), projecting inward from the wall, vary in morphology and are remodeled despite being keratinous. The aim of this study is to investigate the suggestion that remodeling of PEL is inﬂuenced by mechanical stress. Circumferential and proximodistal stress distribution and relative displacement in the laminar junction are assessed by ﬁnite-element analysis (FEA) of nine hoof models. Spacing, orientation, and curvature of PEL are assessed from sections through 47 other hooves and compared with the stress and displacement data. Signiﬁcant correlations are found between laminar spacing and seven displacement and stress variables, supporting the link between stresses and remodeling. Differences in external hoof shape cause regional variation in stress magnitudes around the laminar junction. This ﬁnding is in accord with previous observations that laminar morphology is individually regionally variable. This work provides the ﬁrst concrete link between mechanical behavior and laminar morphology. © 2005 Wiley-Liss, Inc. Key words: ﬁnite-element analysis; quantitative morphology; horse; hoof; laminar junction; displacement; stress; biomechanics As a result of being coopted as part of the musculoskeletal system, the equine hoof shares two attributes with that system: numerous modiﬁcations for the mechanical functions the hoof performs, and the capacity to respond to variations in loading over time. Hoof anatomy, microstructure, and growth are well documented (Stump, 1967), and ground reaction forces (GRFs) during locomotion have been experimentally recorded to determine the hoof’s general mechanical function (Merkens et al., 1993). But the hoof’s keratinous capsule and the nature of its attachment to the dermis and skeleton impede detailed study in vivo of its functional design and of the nature and mechanisms of its biological response to variability in loading regimes. Thus, the deceptively simple smooth exterior guards its secrets better than any crenellated castle wall. Finite-element analyses (FEAs) are clearly applicable to this situation, especially given that there are good data on © 2005 WILEY-LISS, INC. the external shape and loading of the hoof, the properties of its materials and strains in the wall during locomotion. Most previous FEAs of the equine hoof have focused on the capsule (Newlyn et al., 1998; Hinterhofer et al., 2000, Grant sponsor: the Ontario Ministry of Agriculture and Food; Grant sponsor: the Ontario Horse Racing Industry Association; Grant sponsor: the Ontario Veterinary College. *Correspondence to: Jeff Thomason, Department of Biomedical Sciences, University of Guelph, Guelph, Ontario, N1G 2W1, Canada. Fax: 519-797-1450. E-mail: firstname.lastname@example.org Received 12 January 2005; Accepted 13 January 2005 DOI 10.1002/ar.a.20173 Published online 3 March 2005 in Wiley InterScience (www.interscience.wiley.com). EQUINE LAMINAR JUNCTION 367 Fig. 1. a: Schematic transparent diagram showing salient features of the left forehoof of a horse that are described in the text. The coronet is the proximal border of the wall at the hairline. The extent of the laminar junction is shown, but only a few or the 200 – 600 primary laminae. b: Features of the volar or distal surface of the capsule. B, ground-contact or bearing border of the wall; DP, distal phalanx; LJ, laminar junction. 2001; Thomason et al., 2002; McClinchey et al., 2003). In addition to testing the applicability of FEA to hooves, some of these studies have used its power to address questions of functional relevance, such as the effect of shoeing on stresses in the capsule material (Hinterhofer et al., 2000) and the effects of individual capsule shape measurements on principal strain magnitudes (McClinchey et al., 2003). Bowker et al. (2001) combined FEA with in vitro joint pressure measurements to study the effects of contact pressures on bone and cartilage structure at the distal interphalangeal joint. The subject of this study is the laminar junction, the dermoepidermal structure attaching the hoof wall to the distal phalanx (Fig. 1a; LJ). It is important in absorbing the shock of hoof impact with the ground and transmitting force between the skeleton and ground (Gustås et al., 2001). It is also important to the equine industry because of its susceptibility to a disease called laminitis, which has numerous causes and can have debilitating effects on the animal (Pollitt, 1998). It is of particular interest to us because there are strong indications that it remodels in response to time-dependent variation in loading (Thomason et al., 2001; Bowker, 2003a). Kasapi and Gosline, 1999). It take 9 –12 months for the wall to grow out (Pollitt, 1990). The volar surface of the hoof comprises the keratinous sole and the frog, which is the corniﬁed covering of an internal digital pad (Fig. 1b). These two structures grow from a deep germinative epidermis and wear off superﬁcially, as is usual for corniﬁed epidermal thickenings. Wall, sole, and frog are termed the hoof capsule. Projecting inward from the wall are laminae that interdigitate with corresponding laminae of the epidermis and dermis. They greatly expand the area of attachment of wall to living tissue and give the laminar junction its name (Figs. 1a and 2; LJ). At low magniﬁcation, primary epidermal and dermal laminae are visible (Fig 2; PEL and PDL, respectively). The sides of each are covered with up to 100 secondary laminae, visible only at higher magniﬁcation. This laminar arrangement presumably functions to lower mechanical stress on the cells adjacent to the interface of wall and epidermis. The laminar junction, with the remaining dermis, suspends the distal phalanx within the wall. Because of this arrangement, transfer of force between ground and skeleton is predominantly via the wall and laminar junction (not simply vertically from ground to sole to solar dermis to distal phalanx). The location of the laminar junction impedes direct in vivo study of its mechanical adaptations, and most studies have been performed ex vivo in the laboratory (Willemen et al., 1999), or indirectly, based on GRF measurements (Hood et al., 2001). The proportions of GRF passing via laminar junction vs. going through the sole are under debate (Hood et al., 2001), because they have not been directly evaluated in vivo. The hoof has other modiﬁcations than in the capsule and attachment of the wall to the distal phalanx via the laminar junction, but these two are the most relevant for present purposes. Functional Anatomy of Hoof Capsule and Laminar Junction The hoof wall is an expansion of the primitive nail and covers the dorsum and sides of the terminal segment of the digit. It provides more material than does a regular nail for weight bearing, traction, and protection of internal structures. Regions of the expanded wall are commonly called toe, quarters, and heels (Fig. 1) and this terminology will be used here. The wall grows, as is usual for nails, from a proximal germinative region and is formed of keratinocytes. As they are germinated, cells of the wall are arranged into tubules and intertubular material with offset orientations (as in plywood and insect cuticle) for strength and toughness (Bertram and Gosline, 1986; 368 THOMASON ET AL. Fig. 3. Pathways of interaction among external loads (and their extrinsic modiﬁers), mechanical behavior (and its intrinsic modiﬁers), and biological responses. Extrinsic and intrinsic modiﬁers cause mechanical behavior under external load within single footfalls. Over time, biological responses to cumulative mechanical behavior can cause changes in the intrinsic modiﬁers in a feedback mechanism. Reproduced with permission from Thomason et al. (2004). Biological Responses to Variations in Mechanical Function Fig. 2. Appearance of primary epidermal and primary dermal laminae (PDL) and its variation in three different regions of the same hoof: (a) toe, (b) quarter, and (c) heel. Sections are parallel to the coronet, and the three parts are oriented approximately as in one half of the hoof. Secondary laminae are not visible at this magniﬁcation. The laminar junction is strictly the area labeled, but loosely includes the remainder of the dermis as well. Arrowheads in b indicate bifurcating PEL. An important attribute shared by hoof and musculoskeleton is the ability to respond (in time frames of weeks to months) to variations in applied loading. This is analogous to the well-documented stress responses in bone (Martin et al., 1998; Carter and Beaupre, 2001). The concept is represented for the hoof schematically in Figure 3. External loads include the energy at the moment of impact of the hoof with the ground and the forces of weight bearing and locomotion applied throughout the footfall (or stance). At a full gallop or racing trot, there are 150 or more footfalls per minute. Several factors, such as gait and speed (which we term extrinsic modiﬁers), cause variability in external loading (Fig. 3). With every footfall, external loading induces mechanical behavior (e.g., energy absorption, deformation, stress, and strain) in the tissues and other structural materials of the hoof. Mechanical behavior is affected by what we term intrinsic modiﬁers. These include the shapes of the capsule and bones within the capsule, and the mechanical properties of all constituent tissues and materials. Even if loading remains constant, changes in the intrinsic modiﬁers can cause variation in aspects of the mechanical behavior during each footfall. As in the skeleton, living tissues of the hoof appear to be able to sense variation over time in some aspects of mechanical behavior (Bowker, 2003a, 2003b). Relevant living tissues to this study are the germinative epidermis of the hoof wall and the epidermis of the laminar junction [Bowker (2003b) describes others]. These epidermal tissues appear to show biological responses to variations in intensity of the mechanical behavior in individual strides integrated over time frames of weeks to months. The most obvious response is that growth rates of wall, sole, and frog appear to be altered by mechanical behavior and lead to changes in hoof shape with time. Hoof shape is an intrinsic modiﬁer and therefore inﬂuences mechanical behavior, presumably keeping the feedback loop of Figure 3 active until an equilibrium is reached. Whether this mechanism is adaptive or simply a response has yet to be determined. Another apparent response to mechanical behavior is in the reworking of the inner border of the wall and the EQUINE LAMINAR JUNCTION primary epidermal laminae (PEL) as they grow past the dermal part of the laminar junction. Reworking in this case includes both modeling (apposition of new material) and remodeling (Bowker, 2003a). Approximately 20% of the material of the wall is added to its inner surface as it migrates distally (Budras et al., 1989). The rate of addition is greatest proximally and decreases 20-fold as the epidermal laminae migrate distally past the tip of the distal phalanx. Remodeling appears to be mediated by the action of matrix metalloproteinases within the epidermal cells at the boundary of wall and dermis (Daradka and Pollitt, 2004). The effects of remodeling include increasing the number of PEL with age, from approximately 200 at birth to between 500 and 600 in adults. The increase seems to be primarily by bifurcation of existing primary epidermal laminae (Bowker, 2003a). The role of stress in modeling and remodeling of the PEL is unproven, but is supported by a growing body of circumstantial evidence. Bowker (2003a) suggested that mechanical stress induces bifurcation, and hence multiplication of PEL, based on a study of many hundreds of hooves. Bowker (2003a) also documented that the appearance of PEL on section varies circumferentially (Fig. 2). This morphological variation is consistent with hypotheses of regional loading variability (Douglas and Thomason, 2000; Thomason, et al., 2001) as follows. At the toe, the distal phalanx is thought to pull the laminae down and back, exerting tension on the laminar junction in radial and vertical directions. PEL at the toe are straight, closely spaced, and oriented parallel to the direction of radial pull, i.e., perpendicular to the wall (Fig. 2a). At the quarters, the wall ﬂares abaxially during stance phase, exerting radial tension on the laminae. The distal phalanx moves palmarly, adding horizontal shear. Laminae at the quarters and heels (Fig. 2b and c) are more widely spaced, curved, and are rarely perpendicular to the wall. Feedback Path From External Shape to Internal Anatomy If we accept that the morphology of the laminar junction does vary regionally with loading variation as described above, there is an additional layer of complexity caused by individual variation in hoof capsule shape. Hoof shape is known to have complex effects on principal strains acting in the plane of wall’s surface (Thomason et al., 2004). By inference, capsule shape should also affect the distribution of stress and strain magnitudes in the laminar junction and in turn affect laminar morphology. Preliminary evidence is available for this three-way interaction between mechanical behavior and the two intrinsic modiﬁers, in that there are patterns of correlation between measurements of external hoof shape and those of laminar morphology (Douglas and Thomason, 2000; Thomason et al., 2001). In these two studies, capsule shape was quantiﬁed by 20 external measurements, based on a list in Kane et al. (1998), and including toe angle (TA; measured between the wall and ground surfaces at the toe in lateral view). Laminar morphology was quantiﬁed on sections parallel to the coronet (Fig. 1a) by way of three measurements: laminar spacing (LS) between adjacent PEL, laminar orientation (LO) with respect to the wall’s surface, and internal angle (IA) of bending of each PEL. Twenty samples of 25 laminae were assessed, arranged circumferentially and proximodistally as in Figure 4. 369 Fig. 4. Patterns of correlation among measurements of external hoof shape and orientation of PEL at ﬁve circumferential and four proximodistal sampling sites of 25 laminae each. a: TA and LS. b: LHL and LO. Filled rectangles indicate sites with signiﬁcant correlation (P ⬍ 0.05); open rectangles indicate nonsigniﬁcance. Data from Thomason et al. (2001). Patterns of local correlation between pairs of internal and external measurements were found. Figure 4a shows the pattern for LS with TA. Open squares are blocks where there was no signiﬁcant correlation between this pair of internal and external variables (P ⬎ 0.05). The cluster of ﬁlled squares indicates blocks where the correlation was signiﬁcant (P ⬍ 0.05). Most pairwise combinations of external and internal variables showed no such clustering. Only about 10 pairs did, and the location of the clusters was quite variable. Figure 4b shows the pattern of correlation between LO and length of the lateral heel (LHL), which gives an arrangement clearly different from that in Figure 4a. The impression these results convey is that some external shape variables affect laminar morphology and, by implication, patterns of strain distribution, but only in conﬁned regions of the laminar junction. It is this apparently complex and subtle interaction between external hoof shape, the morphology of the laminar junction, and its mechanical behavior that is the focus of the present work. Aims and Objectives Our ﬁrst objective is to use FEA to determine mechanical behavior of the laminar junction. For this, we use nine ﬁnite-element (FE) models that include the capsule, laminar junction, and distal phalanx and that have been validated against external data. In this case, the external data are in vivo surface strains (from the hooves on which the models’ shapes were based), which have been compared with predictions of the models (Thomason et al., 2002). The second objective is to evaluate laminar spacing, laminar orientation, and curvature or internal angle for PEL at multiple sites on the laminar junction of a large 370 THOMASON ET AL. TABLE 1. Measurements made on nine hooves (H1–H9) from which the ﬁnite-element models were constructed parametrically* TA,° TL, mm HA,° HL, mm LWA,° LWL, mm MWA,° MWL, mm MBH, mm LBH, mm Mass of horse, kg H1 H2 H3 H4 H5 H6 H7 H8 H9 52.1 89.8 40.4 41.3 68.8 61.3 82.5 59.2 28.9 25.9 421.5 51.5 94.4 33.6 40.2 76.2 69.5 76 65.4 26.9 24.1 425.0 47.5 99.3 37.3 47 70.2 63.9 82.7 58.7 29.1 24.7 424.0 48.6 91.3 40.6 38.2 73 55.9 76 58.3 23.1 26 460.0 52.8 91 46.9 38.3 79.8 60 83.2 59.6 29.7 30.6 471.0 48.2 99.3 33.2 40.4 67.7 63.2 73.3 59.4 31.5 26.9 425.5 49.2 84.9 28.8 25.7 84.1 63.9 72.3 57.1 18.4 33.2 528.0 48 89.3 48.1 34.6 70.9 57.2 90 54.4 27.1 26.1 417.5 58.3 90.4 39 35.7 74.1 61.3 74.3 64.9 24.6 25.2 509.0 *Measurements are illustrated in Figure 5. TA, angle between capsule dorsum and ground surface in lateral view; TL, length from ground to hairline at dorsum, parallel to wall; HA, angle between palmar margin of capsule and ground surface in lateral view; LWA, MWA, lateral and medial angles between wall and ground surface in dorsal view; LWL, MWL, length from ground to hairline along lateral and medial walls of capsule in dorsal view; LBH, MBH, vertical height of lateral and medial heel bulbs (cartilaginous projections above heel region of wall). sample of hooves to assess regional variation of these measurements. The third objective is to investigate whether correlations exist between the measures of mechanical behaviors and those of laminar morphology. MATERIALS AND METHODS It is likely that the response mechanisms under investigation here are the same in fore and hind hooves, but the mechanics and shape differ between them so this study focuses on the forehoof. FEA of Mechanical Behavior of Laminar Junction Description of FE models. Nine models were generated from measurements made on real hooves (Table 1). For each hoof, XY coordinates were recorded of 11 points on the circumference of the bearing border. From these points, a further 11 at the coronet (proximal border) were projected using linear and angular measurements from the hooves (Fig. 5). These operations generated a shell of the same basic shape as the real hoof. Coordinate calculations were performed in a spreadsheet (QuattroPro 8; Corel, Ottawa, Canada). All other operations (preprocessing of the shape data, processing or performing the analysis, and postprocessing of the results) were done in COSMOS/M software (Structural Research and Analysis, Los Angeles, CA). A series of commands were linked into a macro in the FE modeling software, which thickened the shell to generate the wall in two layers, added the laminar junction, a sole and solar dermis, and ﬁlled the interior with a block to represent the distal phalanx (Fig. 6a). These commands were common to each version of the model so all had the same thickness of wall (10 mm at the toe, tapering to 9 mm at the heels), laminar junction (7 mm), and sole and solar dermis (5 mm each). Each model was discretized into 1,920 isoparametric cuboidal elements, with 20 nodes on each element (8 at the vertices and 12 at the midpoints of the edges). This type of element was chosen to provide adequate resolution of gradients of stress, strain, and displacement within tissues without needing large numbers of small elements. Fig. 5. Mode of construction of the shell of each FE model, starting with XY coordinates of 11 points on the bearing border (B). Lines are projected from these points, based on shape measurements on real hooves, to 11 give more points for the coronet (C). Abbreviations for measurements are deﬁned in Table 1. Linear elastic behavior was assumed for all materials, and elastic moduli were assigned to elements as follows: outer layer of wall, 1,004 MPa; inner layer, 523 MPa (Douglas et al., 1996); laminar junction and solar dermis, 20 MPa (Douglas et al., 1998); sole, 230 MPa (Hinterhofer et al., 1998); and distal phalanx, 10,000 MPa. Preliminary FE models showed the frog had little impact on stress distribution at midstance, so it was omitted. Poisson’s ratio was set at 0.3, and isotropy was assumed for all materials because the distinct structural anisotropy seen particularly in the capsule material is not strongly reﬂected in the elastic moduli (Douglas et al., 1998). Loading each model in two stages. To load each model, it was preferable to apply force to the distal phalanx while constraining displacement at the ground-contact border of the wall. Forces and moments acting on the EQUINE LAMINAR JUNCTION 371 Fig. 6. a: One complete ﬁnite-element model with component layers and structures labeled. Region F on the distal phalanx encloses all nodes to which forces were applied. b: The same model after processing showing global deformation (exaggerated). Locations of three of ﬁve proximal elements for which elements were calculated are indicated at the MH, MQ, and TO. distal phalanx have not been recorded so we ﬁrst reversed the situation by constraining several nodes on the proximal aspect of the distal phalanx (within region F in Fig. 6a) and applying a resultant force of 1.15 times the known body weight (in Newtons) of each animal to the groundcontact border. This force, which is equivalent to the ground reaction force recorded at midstance for a mediumpaced trot (Merkens et al., 1993), was applied as a uniform 372 THOMASON ET AL. pressure to every node of the ground-contact surface of the wall in each model. After performing this preliminary FEA, reaction forces were derived from the results for the constrained nodes on the proximal aspect of the distal phalanx. In the subsequent test analyses, equal and opposite forces were applied to the distal phalanx (in region F). The distal border was constrained by gap elements (Fig. 6a), which prevented downward motion of the border, but not upward or horizontal motion. Two nodes (one at the toe-quarter boundary on each side) were fully constrained. The FE software did not account for friction between hoof and ground. Validation of models. Validation was achieved by comparing principal strains calculated by the FEA for ﬁve surface locations on the wall with those recorded at equivalent locations in vivo for the hooves on which the models were based [reported in Thomason et al. (2002)]. Considering the assumptions in the FE modeling process, the correspondence was remarkable. From medial to lateral, the mean FE strains expressed as percentages of the mean in vivo strains for all nine animals were 90.5%, 95%, 166%, 91.8%, and 76.2%. The results showed some underrepresentation at the quarters (90.5% and 76.2%) and overestimation at the toe (166%), which will be addressed when interpreting the results of the present work. The correspondence was, however, sufﬁciently accurate for the models to be applied to analyses of the laminar junction with some degree of conﬁdence. Quantiﬁcation of mechanical behavior. Mechanical behavior of the laminar junction was demonstrated qualitatively by the deformation of the whole FE model and was quantiﬁed as relative displacements and stresses. Relative displacements were calculated for 15 pairs of points arrayed around the laminar junction. The 15 pairs were arrayed in ﬁve circumferential columns and three rows, similar to the arrangement of Figure 4, but with three rows, not four. Circumferential locations were named medial heel (MH), medial quarter (MQ), toe (TO; Fig. 6b), lateral quarter (LQ), and lateral heel (LH). The rows were named proximal, middle, and distal. The outer point of each pair was at the interface of wall and laminar junction, the inner point was at the bonelaminar junction interface, on a radial line. Relative displacement of points in a pair indicated the degree to which the laminar junction was stretched or compressed at each location. Components of displacement were calculated in X (lateromedial), Y (dorsopalmar), and Z (vertical, or proximodistal) directions relative to a global coordinate scheme (Fig. 7a and b). At the toe, component X was tangential (i.e., tending to shear the laminar junction lateromedially in a horizontal plane) and Y was radial (directed inwardly or outwardly). At the quarters and heels, the X component was radial, and the Y, tangential. (Results will be given as radial or tangential values.) Resultant relative displacements were also calculated. Stress values were calculated at the centroids of all elements, and those for the elements corresponding to the 15 nodes used for displacements were extracted from the complete set. Each node was at the vertex of two or four elements, so stresses in the relevant elements were averaged at each of the 15 locations. Fig. 7. a: Global coordinate system for relative displacements in proximal view. b: Lateral view of global system. c: Local coordinate system for all stresses in proximal view. d: Lateral view of local system. P, parallel to the dorsal wall of the distal phalanx; R, radial; T, tangential; V, vertical; X, Y, Z, global coordinate axes. Stress components were calculated with respect to coordinate systems local to each ﬁnite element (Fig. 7c and d), which correspond more closely to the hoof shape than the global coordinates used for displacements. (The software did not give displacements in local coordinates.) Parallel components (P; Fig. 7d) were directed obliquely down, parallel to the surface of the distal phalanx at the toe. Radial components (R; Fig. 7c and d) were orthogonal to P, i.e., outwardly directed with a vertical component (contrasting with the radial component of displacement, which was horizontal; Fig. 7b). Tangential components (T; Fig. 7c and d) were tangential to the surface of the distal phalanx and also had a vertical component. Shear stresses were calculated in the three mutually perpendicular planes speciﬁed by the coordinate axes. Parallel-radial shear stress (P-R) was in the plane of the primary epidermal laminae; parallel-tangential shear (P-T) was in the plane of the surface of the distal phalanx; and radial-tangential shear (R-T) was parallel to the plane of the coronet (Fig. 7c and d). Principal stresses, 1, 2, and 3, which are orthogonal stresses of maximum absolute magnitude, were also calculated. Finally, Von Mises stresses were calculated to give a measure of total stress in each element (Newlyn et al., 1998). Quantiﬁcation of PEL Morphology As in previous work (Douglas and Thomason, 2000; Thomason et al., 2001), the morphology of samples of PEL was quantiﬁed as LS, LO, and IA (a measure of curvature). The previous works had a small sample size (n ⫽ 5) in each of two comparison groups. For the present work, the sample was expanded to include 47 front hooves from 25 adult Thoroughbred horses of mixed gender. Hooves were obtained immediately following euthanasia (which was for reasons other than musculoskeletal pathology or laminitis) and were immediately frozen. EQUINE LAMINAR JUNCTION 373 Scaled digital images were taken (with an Olympus Camedia E10 camera) of each hoof in four views (dorsal, volar, lateral, and medial), following which four 1 cm slices parallel to the hairline were cut with a band saw. Five circumferential samples of 25 PEL each (called blocks) were identiﬁed on each slice (and aligned proximodistally with each other using ﬁduciary marks made before slicing). High-resolution digital macro images were taken of each sample block and the adjacent wall. On each image, three points were identiﬁed on the wall and three along the length of each of the 25 PEL in the sample using image analysis software (Optimas; Bioscan, Edmunds, WA). From the scaled XY coordinates of these points, LS, LO, and IA were calculated in a custom-written program in Gauss (Aptech, Maple Valley, WA) and were averaged for each of the twenty blocks. From the external digital images, 20 measurements were made describing hoof shape. Correlations are described elsewhere between the full set of external measurements and the internal measurements for each block (Faramarzi, 2003). For the purposes of the present work, a subset of the external measurements was extracted so the shapes of the hooves in the quantitative morphology group could be compared with those used to develop the FE models. The measurement subset included TA, toe length (TL), heel angle (HA), medial wall angle (MWA), and lateral wall angle (LWA; Table 1, Fig. 5). A subset of the internal data was also extracted, comprising data for the 15 blocks on the proximal three slices, because the locations of these blocks corresponded to the locations of the 15 points studied in the FEA analysis. Comparison of Mechanical Behavior and Laminar Morphology Two data sets were available: set 1, the FE set, which comprised external measurements for 9 hooves; radial tangential, vertical, and resultant relative displacements; radial, tangential, parallel, shear principal, and Von Mises stresses at 15 locations; and, set 2, the quantitative morphology set, which comprised external measurements for 47 hooves, with mean LS, LO, and IA values for 15 locations on the laminar junction comparable to those of set 1. The ﬁrst comparisons were within set 1: correlations between external measurements and displacements at the 15 node pairs and then external measurements with stresses in the 15 elements. The aim of these comparisons was to test whether displacements and stresses correlated with external measurements regionally, as laminar morphology has been shown to do (Fig. 4). The second comparison was between the external shape measurements of set 1 and set 2 hooves. This was simply to establish whether comparing other results for the two sets was reasonable. Of course, it would have been desirable to have displacement stress and laminar morphology data for the same set of hooves, but these were not available. The next best step was to make cautious comparisons between sets of closely similar mean shape. The ﬁnal comparisons were correlating the laminar measurements (LS, LO, and IA) for the 15 sample blocks with stresses and displacements calculated at corresponding sites for hooves in the FE set. The aim was to perform a preliminary test of correspondence between regional variations in the loading and quantitative morphology of the laminar junction. Fig. 8. Radial (a), tangential (b), vertical (c), and resultant (d) relative displacements (mm) by circumferential and proximodistal location on the laminar junction. Dashed lines indicate zero. Graphs within each part have the same scale for comparison of magnitudes. RESULTS Finite-Element Results Global deformation. Under forces representing midstance loading, each model deformed in a consistent manner (Fig. 6b). The distal phalanx was pressed vertically down and rotated downward at the toe. The wall at the toe was drawn palmarly and distally. At the quarters and heels, it ﬂared abaxially, as shown by the angulations of the gap elements in these regions. Because of the motion of the phalanx, proximal elements at the toe (Fig. 6b) were sheared in a parallel-radial plane (Fig. 7c and d), which is equivalent to a parasagittal plane at this location. Proximal elements at the quarters (MQ) and heels (MH) were subjected to components of shear in a radial-tangential plane, which was approximately horizontal at those locations. Relative displacements. Absolute values of relative displacement of the 15 pairs of nodes ranged from 0.001 to 0.353 mm radially, 0.001 to 0.555 mm tangentially, 0.036 to 0.557 mm vertically, and 0.037 to 0.629 mm as resultants. When plotted against sample location (Fig. 8), three patterns were visible when comparing circumferential rows. In some rows, the value at the toe was greatest and declined toward each heel in an inverted V-shape (e.g., proximal and middle rows of vertical and resultant data). 374 THOMASON ET AL. Correlations of shape and mechanical behavior for FE set. At some of the 15 locations, signiﬁcant corre- lations (P ⬍ 0.05) were found between measurements of external hoof shape and some of the stress data (Table 2). The locations varied depending on the pair of variables being correlated. Six pairs showed 7–9 out of a possible 15 signiﬁcant correlations: TA and 1, TA and 3, TL and P-R, TL and Von Mises stress, MWA and Von Mises stress, MWA and 1, and LWA and 1 (Table 2). As TA increased, 1 decreased and 3 increased in absolute value. As TL increased, shear stress P-R decreased, but Von Mises stress increased. MWA showed positive correlations with Von Mises stress at most locations, but a negative correlation at one. MWA and LWA showed both positive and negative correlations with 1, depending on location. Patterns of similar general appearance were evident in correlations of the same shape variables with relative displacement. Quantitative Morphology Fig. 9. Radial stress (a), tangential stress (b), shear stress in the radial-parallel plane (c), Von Mises stress by location on the laminar junction (d). Dashed lines indicate zero; dotted line in d shows effect of compensating for overemphasis at the toe seen in these FE models. In other rows, the values were arranged in a W-pattern (e.g., proximal and middle radial data). In the remainder, the pattern was asymmetrical, with one quarter showing the highest absolute value. Vertical relative motion made the greatest contribution to the resultant, with a positive value indicating that the inner point moved downward relative to the outer point. Stresses. Values of normal stress at the 15 locations around the laminar junction ranged from ⫺0.177 to 0.334 MPa tangentially, ⫺0.326 to 0.861 MPa radially, and ⫺0.222 to 0.286 MPa parallel to the surface of the distal phalanx (where negative values represent compression and positive ones tension). Shear stress P-R ranged from ⫺0.87 to 0.04 MPa, P-T from ⫺0.10 to 0.12 MPa, and R-T from ⫺0.26 to 0.23 MPa. Ranges for the principal stresses were 1, 0.01 to 1.65 MPa; 2, ⫺0.22 to 0.4 MPa, and 3, ⫺0.002 to ⫺1.19 MPa (with the same sign convention as for normal stresses). Von Mises stresses fell in the 0.054 – 1.480 MPa range. Plots of the normal and Von Mises stresses against location are shown in Figure 9, and the two larger principal stresses (1 and 3) and shear stress (P-R) in Figure 10. Predominant shapes of the curves of circumferential distribution of stress are V or U and inversions of these. The two principal stresses plotted show W- or inverted W-patterns (Fig. 10a and b). Laminar spacing in the 15 sampled blocks of 25 laminae each fell in the 0.036 – 0.056 mm range, with a mean of 0.046 (⫾ 0.0066) mm. Laminar orientation was in the 77–103° range, where 90° is perpendicular to a tangent to the wall and other values deviate to either side of the perpendicular. Mean laminar orientation was 89.7° ⫾ 9.39°. Internal angle ranged from ⫺3.5° to 11.9°, where 0° represents a straight lamina, and other angles represent curvature to either side. Mean IA was 5.2° ⫾ 4.65°. When plotted against location, laminar spacing was least at the toe in all three proximal-to-distal slices and increased through the quarters to the heels in a V-shaped pattern (Fig. 11a). Laminar orientation was closest to 90° at the toe, departing from that abaxially in patterns that approximate to inverted W-shapes, particularly distally (Fig. 11b). Internal angles were closest to 0° at the toe, departing from that abaxially in V-shaped or inverted W-shaped patterns (Fig. 11c). Comparing FE and Morphological Data External measurements. The values of ﬁve variables that indicated the shape of the hoof capsule are given in Table 3 for the 9 hooves in the FE set and 47 in the quantitative morphology set. None were signiﬁcantly different between the two groups (P ⬎ 0.05). Correlations. Signiﬁcant correlations were found between laminar spacing and the following measures of mechanical behavior (Table 4): vertical, circular, and resultant relative displacement of nodes on opposite sides of the laminar junction; shear stress P-R; principal stresses 1 and 3; and Von Mises stress. There were no signiﬁcant correlations when laminar orientation or internal angle was paired with any of the stress or relative displacement measurements. DISCUSSION The purpose of this work was to provide a preliminary test of the hypothesis that regionally variable mechanical behavior in the laminar junction induces corresponding variations in morphology of the primary epidermal laminae via as yet unspeciﬁed biological responses. Before evaluating whether the results support the hypothesis, some discussion of conﬁdence in them is necessary. EQUINE LAMINAR JUNCTION 375 Fig. 10. Values of three of the four stress variables from the FE data set that correlated signiﬁcantly with laminar spacing from the quantitative morphology set. Principal stress 1 (a), principal stress 3 (b), shear stress P-R (c) in the parallel-radial plane plotted by circumferential and proximodistal location. The fourth such variable is Von Mises stress (shown in Fig. 9d). Dashed lines are at zero; dotted lines show effect of compensating for overemphasis at the toe. Conﬁdence in Results are implicated, and elucidate the role of external capsule shape in confounding the relationship of structure to mechanical behavior. The two areas that need to be addressed under this heading are the validity of the FE modeling and the comparisons of FE data with quantitative morphology assessed on different sets of hooves. For the modeling, we have previously shown that calculated surface strains are consistently higher at the toe than comparable in vivo results by a factor of 1.66 on average, and lower at other locations by factors of 0.76 – 0.95 (Thomason et al., 2002). The effects of dividing by these factors are shown for the stresses that showed signiﬁcant correlations with laminar spacing: Von Mises stress (Fig. 9d; dotted lines), principal stresses 1 and 3, and shear stress P-R (Fig. 10; dotted lines). This division changes the values of the signiﬁcant correlation coefﬁcients (Table 4) but not the fact that they are signiﬁcant (P ⬍ 0.05). The effects of such compensations will be addressed below, but they are sufﬁciently minor that they do not impair conﬁdence in the present results. For comparing FE and quantitative morphology data, there are a priori and posthoc arguments in support. A priori, the mean external shape measurements common to the two sets are not signiﬁcantly different (Table 3). Given the ranges of these variables in the horse population at large, the correspondence of mean hoof shape between the two groups is exceedingly close. The posthoc argument is that the shapes of the relative displacement and stress graphs (Figs. 9 and 10) show too much concurrence with those of laminar morphology (Fig. 11) to be entirely random. Inﬂuence of Mechanical Behavior on Laminar Junction Morphology The present data give a clear indication that morphology of the primary epidermal laminae is affected by local mechanical behavior, suggest which aspects of behavior Evidence that mechanical behavior affects laminar morphology. The strongest indicator of a causal effect of mechanical behavior on laminar morphology is in the number of signiﬁcant correlations between LS and various stresses and displacements (Table 4). Most of these variables are ones that would be expected to show a correlation. Vertical relative displacement reﬂects the primary direction of loading, as does R-P, which is in the plane of the PEL. Principal stresses 1 and 3 are the larger two of three principal stresses, and Von Mises stress reﬂects the resultant of all the stress components. Tangential relative displacement is unexpected (radial would have been expected) but is outweighed by the presence of the other correlations. The signs of the correlations also match expectation: the greater the level of displacement or stress, the smaller laminar spacing. In other words, laminar number and density increase with stress. A visual conﬁrmation of the correlations discussed above is in the correspondence between the graphs of mechanical behavior (Figs. 8 –10) and those of laminar quantitative morphology (Fig. 11). The V- or inverted Vshapes of the proximal two graphs for Von Mises stress (Fig. 9d) and the principal and shear stresses in Figure 10 are strongly reﬂected in the two proximal graphs of laminar spacing (Fig. 11a). Remodeling of the primary and secondary laminae occurs toward the proximal border of the laminar junction (Daradka and Pollitt, 2004). Nature of feedback loop. The speciﬁc feedback loop we are examining is the one whereby change in external capsule shape modiﬁes mechanical behavior, which in turn modiﬁes internal structure, particularly of the lami- TABLE 2. Correlations according to location among selected measurements of capsule shape of the nine hooves analyzed by FEA and principal stresses 1 and 3, shear stress in the radial-parallel plane, and Von Mises stresses* Shear stress P-R TA TL HA Proximal TO LQ LH MH MQ • • • • • • • ⫺0.58 ⫺0.58 ⫺0.46 • Distal • • ⫺0.57 • ⫺0.54 • • • • ⫺0.47 • • • TO • LH • • ⫺0.79 • ⫺0.65 ⫺0.70 ⫺0.71 ⫺0.54 ⫺0.45 • ⫺0.92 ⫺0.50 ⫺0.46 • ⫺0.86 ⫺0.96 ⫺0.67 • ⫺0.51 ⫺0.80 • • • • MH Principal stress 3 LQ • MQ TO LQ LH • • • • • MH ⫺0.61 MQ TO LQ LH • 0.48 • • • 0.44 0.53 0.63 • • • ⫺0.52 ⫺0.46 • • 0.55 • • • • 0.55 • • Middle • 0.79 0.66 0.78 • • ⫺0.60 ⫺0.45 ⫺0.48 0.51 • • • • • • 0.53 • • • Distal • 0.71 0.84 0.84 • • ⫺0.78 ⫺0.92 ⫺0.78 • • • • 0.51 • • 0.66 0.76 0.89 • Proximal • • • ⫺0.73 ⫺0.72 0.50 • 0.50 • • • • • • • • • ⫺0.52 ⫺0.62 • 0.45 • • • • 0.46 • Proximal Middle • Distal • MWA Proximal LWA MQ Middle Principal stress 1 Von Mises stress MH • ⫺0.46 • • ⫺0.56 • ⫺0.55 • • 0.65 • • 0.52 • ⫺0.59 • 0.62 • • • ⫺0.76 ⫺0.46 • • 0.46 0.87 0.72 • 0.44 ⫺0.56 • • 0.50 • • 0.45 0.74 • • 0.48 • 0.61 0.53 0.54 • 0.57 • • • ⫺0.50 • • • 0.59 • • • • ⫺0.49 • • 0.65 ⫺0.61 • • • • Middle • • • • Distal • • • • • • • • • • • • • • • • • • • • • 0.78 • 0.52 • • 0.46 • • Proximal ⫺0.81 Middle ⫺0.80 ⫺0.44 Distal ⫺0.69 • ⫺0.51 ⫺0.63 • • ⫺0.54 ⫺0.55 • ⫺0.53 *Signiﬁcant coefﬁcients r (P ⬍ 0.05) are given; • nonsigniﬁcant ones. ⫺0.69 ⫺0.61 • ⫺0.67 ⫺0.46 • • • • • • • ⫺0.58 ⫺0.70 • • • • • • 0.51 • 0.69 • • • ⫺0.80 ⫺0.68 • • ⫺0.74 ⫺0.88 ⫺0.65 • • • ⫺0.58 ⫺0.75 ⫺0.73 EQUINE LAMINAR JUNCTION 377 Fig. 11. Laminar spacing (a), laminar orientation (b), and internal angle (c) for primary epidermal laminae by circumferential and proximodistal location. Dashed lines are at same value in each column for reference. TABLE 3. Comparison of means and standard deviations of shape measurements of the nine hooves in the FEA set and the 47 in the quantitative morphology set Quantitative morphology set FEA set Measurement TA, ° TL, cm HA, ° MWA, ° LWA, ° Mean SD Mean SD 50.7 9.2 38.7 78.9 73.9 3.25 0.45 5.95 5.60 5.08 50.2 9.8 37.6 75.6 72.9 4.25 0.93 8.28 5.45 5.78 TABLE 4. Correlation coefﬁcients, r, with probability values, for the relative displacements and stresses from the FE set, which correlated with laminar spacing from the quantitative morphology set of hooves Variable Vertical relative displacement, mm Resultant relative displacement, mm Tangential relative displacement, mm Shear stress in radial-parallel plane, MPa Principal stress 1, MPa Principal stress 3, MPa Von Mises stress, MPa r P ⫺0.6666 ⫺0.7633 0.0033 0.0005 0.5291 0.0213 0.7508 0.0006 ⫺0.6536 0.6224 ⫺0.8015 0.0041 0.0066 0.0002 nar junction. Data from the present work help characterize that loop. Previous work has shown direct correlations between external shape and laminar structure (as in Fig. 4), but the distribution of clusters was difﬁcult to interpret (Tho- mason et al., 2001). The clusters implied that change in each external shape variable had an effect on a speciﬁc region of the laminar junction. From the present work, similar patterns of correlations exist between shape variables and stresses by location around the laminar junction (Table 2). Put these pieces of information together and an interesting scenario emerges. All hooves have some common features of laminar structure because they all deform under locomotory load in much the same way: the toe moves down and back, the quarters ﬂare (Fig. 6b). This mechanism causes regional differences in surface strains (Thomason, et al., 2004) and, from the present data, in stress and deformation of the laminar junction. Individual variation in external shape measurements among hooves superimposes individual variation in stress and deformation on the common pattern among hooves. When comparing external measurements with local stresses, some pairwise combinations produce signiﬁcant numbers of correlations (from 7 to 9 out of 15). Patterns are evident in the clustering (Table 2). Toe angle and toe length are on the midline axis of the hoof. Where seven to nine correlations appear between these two measurements and stress, the cluster is either centrally weighted (e.g., TL with P-R or Von Mises stress) or symmetrically distributed (e.g., TA with 1 or 3). Medial and lateral wall angles are abaxial. Clusters involving them are abaxially situated. These patterns demonstrate regional variability in stresses that appear to correlate with laminar morphology. Connecting the dots, regional variation in mechanical behavior stimulates similarly local variability in laminar morphology. To conﬁrm this suggestion, it would be necessary to model accurately a number of hooves for which quantitative morphological data were available on the primary epidermal laminae (or indeed on the nature of the secondary laminae, which are also thought to be responsive to stress). The speciﬁc models used in this work are likely not sufﬁciently accurate for that purpose, because they do not 378 THOMASON ET AL. model surface strains on individual hooves with close accuracy (Thomason et al., 2002). For that reason, we have not compared patterns of shape-stress clusters for the FE data with patterns of shape-laminar morphology clusters from the other data set. Future reﬁnements to hoof FE models should improve their accuracy and resolution, at which time it should be possible to test whether stress and structure correlate by region. Stress and laminar orientation and curvature. It was clear even prior to the present study that deformation of the laminar junction at the quarters and heels included greater horizontal shear than at the toe. Departure of laminar orientation from being perpendicular to the wall (as at the toe) and increased degrees of curvature were qualitatively reconciled with this perceived difference in mechanical behavior. At the distal margin of the distal phalanx, there are rapid deviations in spacing, orientation, and curvature, which were rationalized as being the effects of loss of physical support as the laminae migrate off the end of the bone (Douglas et al., 2000). Based on these prior inferences, the lack of signiﬁcant correlation between any aspect of mechanical behavior and laminar orientation and internal angle is unexpected. Despite this lack, there is correspondence among the graphs of mechanical behavior and of orientation and curvature, as was described for stress and spacing above. Tangential relative displacement in the proximal two rows (Fig. 8b) corresponds in distribution to both laminar orientation and internal angle proximally (Fig. 11b and c). The two largest principal stresses (Fig. 10a and b) show an inverse relationship distally to orientation and internal angle (which improves after the approximate compensation). These results support the earlier inference that abaxial laminar morphology responds to horizontal shear. Reﬁned FE models may produce statistically signiﬁcant correlations, as in the case of laminar spacing. Future directions. This work has provided concrete support for part of the feedback loop in Figure 3, between external shape and internal structure via stress patterns and the inferred response to them. It raises a number of questions, all of which require further study. What is the stimulus for change growth rate and remodeling? Based on a large body of work on the effect of mechanical stress on osteocytes and chondrocytes (Carter and Beaupre, 2001), it is likely that strains acting on epidermal keratinocytes due to hydrostatic pressure and shear stresses will be the initial stimulus. Stressing keratinocytes in vitro might be a useful avenue of study to examine this suggestion. Does the feedback loop reach equilibrium? The idea of an adaptive feedback loop is that change stimulates a response, which reverses the change or reduces its effects until equilibrium is reached. There is some indication that the regional structural differences in the laminar junction are reﬂected in its mechanical properties (Douglas et al., 1998). It is not known whether change in properties with structure tend toward equilibrium in stress levels. Are responses similar in other tissues of the hoof? The laminar junction is not the only part of the hoof showing responses to loading variation (Bowker, 2003b), and other tissues (such as cartilages in the heels and a digital pad deep to the frog) would beneﬁt from analyses similar to the present work. Are the biological responses adaptive? This is a question of central importance to understanding the feedback mechanism. It is naturally assumed that biological responses of the kind described here are beneﬁcial, but Bowker (2003b) documents cases where pathological changes occur in the hoof as an apparent response to excessive stress magnitudes. Perhaps, as in bone, the feedback is adaptive below a stress threshold, above which the response is detrimental. Research effort on the hoof is gathering pace, and the combination of anatomical (Bowker, 2003a,b), cellular (Daradka and Pollit, 2004), and biomechanical works, as here, may ultimately answer these questions and lead to a better understanding of the relationship of mechanics and morphology in the equine hoof. Stress and relative displacement are regionally variable across the area of the laminar junction. Quantitative morphology of the PEL is also regionally variable. Parameters of external capsule shape affect the regional variability in mechanical behavior. 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