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Mechanical behavior and quantitative morphology of the equine laminar junction.

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Mechanical Behavior and
Quantitative Morphology of the
Equine Laminar Junction
Department of Biomedical Sciences, University of Guelph, Guelph, Ontario, Canada
School of Engineering, University of Guelph, Guelph, Ontario, Canada
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;
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
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:
Received 12 January 2005; Accepted 13 January 2005
DOI 10.1002/ar.a.20173
Published online 3 March 2005 in Wiley InterScience
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;
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
Another apparent response to mechanical behavior is in
the reworking of the inner border of the wall and the
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.
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.
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
TABLE 1. Measurements made on nine hooves (H1–H9) from which the finite-element models were
constructed parametrically*
TL, mm
HL, mm
LWL, mm
MWL, mm
MBH, mm
LBH, mm
Mass of horse, kg
*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.
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
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
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
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
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.
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.
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).
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
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.
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
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
⫺0.58 ⫺0.46
⫺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
Principal stress ␴3
⫺0.52 ⫺0.46
⫺0.60 ⫺0.45 ⫺0.48
⫺0.78 ⫺0.92 ⫺0.78
⫺0.73 ⫺0.72
⫺0.52 ⫺0.62
MWA Proximal
Principal stress ␴1
Von Mises stress
⫺0.76 ⫺0.46
0.44 ⫺0.56
0.65 ⫺0.61
Proximal ⫺0.81
⫺0.80 ⫺0.44
⫺0.51 ⫺0.63
*Significant coefficients r (P ⬍ 0.05) are given; • nonsignificant ones.
⫺0.58 ⫺0.70
⫺0.74 ⫺0.88
⫺0.75 ⫺0.73
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
morphology set
FEA set
TA, °
TL, cm
HA, °
MWA, °
LWA, °
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
Vertical relative displacement, mm
Resultant relative displacement,
Tangential relative displacement,
Shear stress in radial-parallel
plane, MPa
Principal stress 1, MPa
Principal stress 3, MPa
Von Mises stress, MPa
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
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. There are also local correlations between external capsule measurements and those of laminar morphology. The results give a strong indication that
aspects of mechanical behavior (relative displacement and
stress) of the laminar junction in the equine forehoof influence modeling of the primary epidermal laminae.
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