J Appl Physiol 96: 2034–2049, 2004.
First published February 6, 2004; 10.1152/japplphysiol.00888.2003.
Mechanical compression-induced pressure sores in rat hindlimb:
muscle stiffness, histology, and computational models
E. Linder-Ganz and A. Gefen
Department of Biomedical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
Submitted 20 August 2003; accepted in final form 30 January 2004
PRESSURE SORES (PS) are soft tissue injuries associated with
ischemia, impaired metabolic activity, excessive tissue deformation, and insufficient lymph drainage caused by prolonged
and intensive mechanical loads (3, 8, 31, 39). PS range in
severity from irritation of superficial tissues to deep muscle
necrosis (1, 52).
Paralyzed and geriatric patients are especially vulnerable to
PS because of their limited ability to detect pain and to relieve
excessive pressures by changing postures. Despite considerable efforts to minimize the prevalence of PS, figures remain
unacceptably high, being 10–25% among patients hospitalized
in modern Western hospitals (2, 9, 43, 59) and 50–80% among
patients with spinal cord injury (30). Direct treatment costs in
the United States are approximated to exceed 1.2 billion US
dollars annually (1, 30).
The head, shoulders, elbows, pelvis, and heels are the sites
that are most susceptible to PS, not only because they make the
focal contact regions with the supporting surface during sitting,
lying, or recumbency, but also because they contain rigid bony
prominences that, from a mechanical engineering perspective,
tend to concentrate loads and stresses. The majority of wounds
appear on the lower part of the body (57), mostly around the
sacrum in the pelvis (30–36%) and heels (25–30%) (12, 19,
38, 59).
Prolonged compression of vascularized soft tissues is traditionally considered the most important mechanical cause for
onset of PS, although shear stresses, tissue deformation, temperature, and humidity are also likely to play a role in the
etiology of injury (2, 7, 16, 34). Most investigators agree that
the underlying mechanism of PS injury is inhibition or obstruction of the nutrient supply and/or waste clearance pathways in
affected tissues (31, 33).
When the body is in a static posture, tissue layers are
compressed and deformed between the supporting surface and
the bony prominences. Prolonged excessive compression was
shown to cause necrosis of skin, as well as of subcutaneous
tissues and striated muscle (34), but muscular tissue appears to
be the most sensitive one. Studies in a pig model of PS
revealed that compression injury threshold of muscle tissue
was substantially lower than that of skin (18), in agreement
with human patient studies identifying the primary site of
injury in deep muscles under bony prominences (48). Deep
muscular PS injuries are typically severe, and they are difficult
and costly to treat. Such injuries may progress toward the
tissue surface (4).
Exposure of striated muscle tissue to intensive and prolonged compression may pathologically alter its microstructure. Rat muscles exposed to compression of 250 kPa for ⬎2 h
showed loss of muscle fiber cross-striation and infiltration of
inflammatory cells, both indicating widespread necrotic cell
death (5). Tong and Fung (54) stated that material composition
and structure determine the mechanical properties of a tissue,
e.g., stiffness. Thus the tissue stiffness is expected to change
when composition and structure pathologically change. Specifically, necrosis or partial necrosis in muscular tissue is likely
to affect tissue stiffness.
Changes in the mechanical (constitutive) properties of injured muscle tissue may, in turn, affect the distribution of
mechanical stresses and strains around the site of injury,
thereby potentially exposing additional uninjured regions of
muscle tissue to intensified stresses. The study of internal
mechanical stresses and strains requires numerical or physical
Address for reprint requests and other correspondence: A. Gefen, Dept. of
Biomedical Engineering, Faculty of Engineering, Tel Aviv Univ., Tel Aviv
69978, Israel (E-mail: [email protected]).
The costs of publication of this article were defrayed in part by the payment
of page charges. The article must therefore be hereby marked “advertisement”
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
decubitus ulcers; soft tissue injury; muscle mechanical properties;
animal model; finite element analysis
2034
8750-7587/04 $5.00 Copyright © 2004 the American Physiological Society
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Linder-Ganz, E., and A. Gefen. Mechanical compression-induced pressure sores in rat hindlimb: muscle stiffness, histology, and
computational models. J Appl Physiol 96: 2034–2049, 2004. First
published February 6, 2004; 10.1152/japplphysiol.00888.2003.—
Pressure sores affecting muscles are severe injuries associated with
ischemia, impaired metabolic activity, excessive tissue deformation,
and insufficient lymph drainage caused by prolonged and intensive
mechanical loads. We hypothesize that mechanical properties of
muscle tissue change as a result of exposure to prolonged and
intensive loads. Such changes may affect the distribution of stresses in
soft tissues under bony prominences and potentially expose additional
uninjured regions of muscle tissue to intensified stresses. In this study,
we characterized changes in tangent elastic moduli and strain energy
densities of rat gracilis muscles exposed to pressure in vivo (11.5, 35,
or 70 kPa for 2, 4, or 6 h) and incorporated the abnormal properties
that were measured in finite element models of the head, shoulders,
pelvis, and heels of a recumbent patient. Using in vitro uniaxial
tension testing, we found that tangent elastic moduli of muscles
exposed to 35 and 70 kPa were 1.6-fold those of controls (P ⬍ 0.05,
for strains ⱕ5%) and strain energy densities were 1.4-fold those of
controls (P ⬍ 0.05, for strains ⱖ5%). Histological (phosphotungstic
acid hematoxylin) evaluation showed that this stiffening accompanied
extensive necrotic damage. Incorporating these effects into the finite
element models, we were able to show that the increased muscle
stiffness in widening regions results in elevated tissue stresses that
exacerbate the potential for tissue necrosis. Interfacial pressures could
not predict deep muscle (e.g., longissimus or gluteus) stresses and
injuring conditions. We conclude that information on internal muscle
stresses is required to establish new criteria for pressure sore prevention.
MECHANICAL COMPRESSION-INDUCED PRESSURE SORES
METHODS
Experimental protocol. The following protocol was approved by
the Institutional Animal Care and Use Committee (IACUC) of Tel
Aviv University and was carried out in compliance with institutional
guidelines for care and use of animal models (IACUC approval no.
M-02-41). Mechanical properties of gracilis muscles of adult SpragueDawley male rats (n ⫽ 33, age 3–4 mo, weight 280 ⫾ 20 g) were
measured in vitro, shortly after exposure of the limb containing the
gracilis muscles to compression in vivo.
Before compressing the limb, rats assigned for this purpose were
anesthetized with ketamine (90 mg/kg) and xylazine (10 mg/kg)
injected intraperitoneally, and one-third of this dose was used for
maintenance of the level of anesthesia during experiments. Depth of
anesthesia was verified by lack of pinch response. Hair of the
compressed limb was carefully shaved and care was taken not to
damage the skin during shaving. Anesthetized rats were placed on a
specially designed apparatus containing a spring-derived rigid plastic
indenter (diameter 20 mm) that applied precalibrated constant pressure on the gracilis of the intact right hindlimb in vivo (Fig. 1A). The
gracilis muscle was selected because a relatively large surface of it
could be subjected to pressure with this apparatus and because it is
located superficially, which made it possible to harvest it by cutting
both tendons without damaging muscular tissue at the time of dissection. Groups of three to four animals were exposed to pressure
magnitudes of 11.5, 35, and 70 kPa (86, 262, and 525 mmHg) for 2,
4, and 6 h (Table 1). These pressure values were determined to cover
the range between the rat (and human) diastolic blood pressure and the
near-maximal internal compression stress values in the longissimus
muscles of the human pelvis during recumbency as predicted in our
FE simulations, reported later on. It should be noted that focal internal
compression stresses in human muscles (30–100 kPa) that occur in
relatively small regions (5–100 mm2) were reproduced over a substantially larger surface in the rat muscle (315 mm2) to allow maniJ Appl Physiol • VOL
festation of their effect on mechanical properties by using standard
uniaxial tension testing.
After limbs were compressed, animals were euthanized with an
overdose of KCl that was injected intracardially. Control rats were
euthanized without prior intervention. The gracilis muscles were
harvested from the uninjured (control) and injured limbs (Fig. 1B). All
muscles were kept in saline tubes at 3°C until mechanical testing and
were tested within no more than 18 ⫾ 2 min from the time of
dissection. The testing procedure lasted ⬃10 min per muscle.
Length, volume, and weight of each muscle were recorded with use
of a digital caliper (resolution 0.1 mm), a measuring tube (resolution
0.5 ml), and a digital scale (resolution 0.01 g), respectively. Muscles
were then mounted within an Instron 5544 uniaxial tension system
with their tendons firmly fixed between customized jigs that were
covered with sandpaper to prevent slipping (Fig. 1, C and D). Tension
was applied to the muscles within a transparent aquarium (Fig. 1D)
filled with saline at the rat’s body temperature (33°C). A load cell with
capacity of 2 kN and resolution of 0.01 N was used for measuring the
tensile forces applied to the gracilis muscles. Load-deformation
curves were obtained for the injured and uninjured (control) muscles
at an extension rate of 1 mm/min. Deformation was visually monitored and recorded with both digital and analog video systems for
postexperiment slow motion analysis, in which it was verified that
muscles did not slip off the grippers. Plots of Lagrange stress (force
divided by the original mean cross-sectional area) vs. true strain
(calculated from transient distance between jigs) were derived from
the load-deformation curves. The original mean cross-sectional area
of muscles was obtained by dividing the volume of the muscle by its
unloaded length.
Tangent moduli of elasticity and strain energy densities (SED)
were calculated from every stress-strain curve at strain levels of 2.5,
5, and 7.5%, by differentiating polynomial functions of the fourthorder that were fitted to the experimental data (R2 ⫽ 0.99) and by
calculating the area under the curves at each strain level, respectively.
The range of tissue strains, 2.5–7.5%, conformed our FE simulations
of the strain distribution in the longissimus and gluteus muscles of the
pelvis during recumbency, as reported in the following sections.
Statistical analysis of measured mechanical properties. Tangent
elastic moduli and SED of control (uninjured) and injured gracilis
muscles were first evaluated via a two-way ANOVA (Systat v10.2).
At each strain level, the ANOVA tested the dependence of tangent
elastic moduli and SED (in separate analyses) on the factors of
pressure magnitude and duration of exposure. A P value ⬍0.05 was
considered statistically significant. None of the ANOVA tests showed
dependence of properties on the exposure time (2, 4, or 6 h), but
pressure was a significant factor. Post hoc Tukey-Kramer tests across
pressure magnitudes were then used to perform pairwise multiple
comparisons between properties obtained from muscles exposed to
pressures of 0 (control), 11.5, 35, and 70 kPa. Criteria for exclusion of
samples from the statistical analysis included apparent damage caused
by surgical tools during dissection, tearing of muscle tissue in the
immediate vicinity of the grippers, and slipping of tendons from the
grippers that was observed in the video analyses.
Histological evaluation of muscles. Cubic samples (face length
⬃10 mm) from gracilis muscles of the eight rats assigned for histological evaluation (Table 1) were harvested distally and proximally
from the site of compression and fixed in formalin. For noncontrol
animals, samples were extracted immediately after delivery of compression. Slicing of the tissue was carried out perpendicularly to the
direction of load, at thickness of 5 ␮m (diameter of muscle fibers is
⬃30 ␮m), and all slices were saved. Sections were mounted on
objective slides and stained with hematoxylin and eosin, toluidine
blue, and phosphotungstic acid hematoxylin (PTAH) to explore the
viability of cells and integrity of cross-striation immediately after
delivering the selected pressure doses.
FE modeling for stress analysis of muscles. Four three-dimensional
(3D) FE models of transverse slices through body parts that are most
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modeling. Focusing on the internal stress state in the buttocks
of seated wheelchair users, both finite element (FE) models
(41, 53) and instrumented phantom studies (46) concluded that
compression and shear stresses in deep soft tissues underlying
the bony prominences of the ischial tuberosities were higher
than respective contact stresses and could not be predicted by
contact pressure measurements. This initial result is important
in directing research efforts to the study of deep internal tissue
stresses rather than to characterization of interfacial body
support stresses, in the context of PS biomechanics. However,
these models were limited by assumptions of simple geometry,
linear-elastic material behavior of tissues and idealized musculoskeletal loading. Moreover, none of these models could
consider the time course of injury, constituted by interdependent effects of local changes in the microstructure and material
properties of muscle tissue.
We hypothesize that mechanical properties of striated muscle tissue change in vivo as a result of exposure to prolonged
and intensive loads. Such changes may affect the distribution
of mechanical stresses in soft tissues under bony prominences
and potentially expose additional uninjured regions of muscle
tissue to intensified stresses.
The goals of this study were, therefore, 1) to determine
changes in mechanical properties of muscles exposed to prolonged intensive compression in vivo as related to histological
tissue damage in a rat model and 2) apply the abnormal
mechanical properties of injured muscles to computational
models of the human body parts vulnerable to PS, to characterize consequent changes in the state of tissue stresses.
2035
2036
MECHANICAL COMPRESSION-INDUCED PRESSURE SORES
vulnerable to PS, i.e., the pelvis, shoulders, heels, and head, were
developed (Fig. 2). In the simulations, we considered a recumbent patient
(weight 60 kg) lying still in a hospital bed on an elastic mattress with
thickness of 15 cm, elastic modulus of 150 kPa, Poisson’s ratio of 0.11,
and static friction coefficient ␮s ⫽ 0.4 (60). In the neutral position of the
bed, the backrest was inclined 45° to the horizon.
For each anatomic site, a corresponding transverse cryosectional
image from the “Visible Human” male digital database was trans-
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Fig. 1. Experimental procedure: hindlimb of a rat model of
pressure sore being compressed (A), the harvested gracilis
muscle postcomperssion (B), apparatus for uniaxial tension
testing (C), and magnification showing the testing aquarium (D).
J Appl Physiol • VOL
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MECHANICAL COMPRESSION-INDUCED PRESSURE SORES
Table 1. Animal group size (total 6 controls and 35
injured rats)
2h
11.5 kPa
35 kPa
70 kPa
3
3
3(UT)
4h
6h
3
3(UT)
2(HS)
3(UT)
2(HS)
4
2(HS)
3
4
UT, uniaxial tension; HS, histological evaluation. Size of control group was
6 animals, from which 8 muscles were harvested: 6 control muscles were used
for uniaxial tension tests, and 2 control muscles were used for histology.
2037
ferred to a solid modeling software package (SolidWorks 2001).
Contours of hard and soft tissues were then detected on each image
and segmented to form the cross-sectional geometry (Fig. 2A). Next,
each cross section was transformed to a 3D solid model of a slice
through the body by projecting it 2 cm along the transverse direction
(Fig. 2B). Finally, the solid 3D slices were transferred to a FE solver
(NASTRAN 2001) for stress-strain analyses under a musculoskeletal
loading system that is typical to recumbency (Fig. 3). For each model,
loading included axial skeletal loads (F1 and F2), internal skeletal
bending moments (M1 and M2), and friction between the body and the
mattress (Figs. 3 and 4, Table 2). The pelvis model included abdominal pressure of 2 kPa (17). The specific weights of all tissues (Table
J Appl Physiol • VOL
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Fig. 2. Computational modeling of the vulnerable sites of the human body: reconstruction of the geometry from the “Visible Human” male database demonstrated by segmentation of musculoskeletal structures of
the shoulders (A) and complete 3-dimensional (3D) solid models (B).
2038
MECHANICAL COMPRESSION-INDUCED PRESSURE SORES
3) were also considered in the stress-strain analyses. The process of
calculation of the loading systems for each model is described in
detail in the APPENDIX. The models were meshed using hexahedron
eight-node elements (Fig. 3).
Skin, muscle, and fat tissues, which underwent larger deformations
during recumbency, were assumed to be homogenous, isotropic, and
nonlinear-elastic materials, and their properties were fitted to experimental data. For skin, we followed Trelstad and Silver (55) and fitted
a second-order polynomial relation to their measurements, where ␭ is
the stretch ratio (deformed to initial specimen length) required to
produce a stress ␴ in the tissue (Eq. 1). Using the same approach, we
followed Gefen et al. (25) for fat and fitted a third-order polynomial
to their data (Eq. 2), and we used our experimental results from rats
for the constitutive equation of striated muscle (Eq. 3)
2
␴ skin共kPa兲 ⫽ 2,650␭skin
⫺ 4,870␭skin ⫹ 2,227
(1)
3
2
␴ fat共kPa兲 ⫽ 2,300␭fat
⫺ 7,470␭fat
⫹ 8,160␭fat ⫺ 2,990
(2)
3
2
␴ muscle共kPa兲 ⫽ 3,707␭muscle
⫺ 12,117␭muscle
⫹ 13,261␭muscle ⫺ 4,850
(3)
All other tissues in the models, which undergo smaller deformations, were assumed to behave as linear-elastic materials with elastic
moduli and Poisson’s ratios as specified in Table 3. For each model,
we considered the friction between the contact surface and the body
(␮s ⫽ 0.4). Nodes at the bottom surface of the mattress were fixed for
horizontal and vertical translations. The FE models were applied to
predict internal stresses and strains in the uninjured body parts and,
subsequently, to predict the stress flow in the injured muscle tissues.
J Appl Physiol • VOL
To simulate the empirical data, we increased the tangent moduli of
muscle tissue exposed to critical stresses of 40 kPa or over by 60%,
locally for the muscle elements subjected to these stresses. The tissue
injury threshold of 40 kPa was set on the basis of our animal studies
and on FE analysis of the animal experiments, as described in the next
sections.
Using a modeling approach similar to the one used to reconstruct
the human anatomy, we also developed a FE model of the limb of a
rat to determine internal compression stresses within the gracilis
muscle for the 11.5, 35, and 70 kPa interfacial pressures applied to the
skin of the limb during the experiments (Fig. 5). As for the human FE
models, specific weights of all tissues were considered in the stressstrain analysis (Table 3). The rat limb model was similarly meshed with
hexahedron eight-node elements, and the rigid plate was assumed to be a
fixed foundation. Skin, muscle, and bone tissues were assumed to have
the same mechanical properties as in the human FE models (Eqs. 1 and
3, Table 3). The elastic modulus and Poisson’s ratio of the indenter tip
were taken as those of standard plastic, 13 GPa and 0.3, respectively (51).
The material properties for the rigid plate at the base were of stainless
steel (elastic modulus 200 GPa, Poisson’s ratio 0.3; Ref. 14).
Model predictions of contact stress between the body and mattress
under the head, shoulders, pelvis, and heels were validated using sets
of flexible (thickness 0.13 mm) contact pressure sensors (Flexiforce,
Tekscan, range 0–4.4 N, accuracy ⫾5%). The sensors were placed on
a specially designed test bench of a hospital bed covered by a mattress
with the same mechanical properties as the one simulated in the
human FE models. Fourteen healthy subjects volunteered for the
measurements of interfacial body-mattress pressures during recum-
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Fig. 3. Numerical method of solution: loading and finite element meshing of the pelvis (A, B), shoulder (C, D), head (E, F), and
heel (G, H) models. F1 and F2, skeletal forces acting on model; M1 and M2, skeletal moments acting on model; ␮, static coefficient
of friction between body and mattress.
MECHANICAL COMPRESSION-INDUCED PRESSURE SORES
2039
bency (7 women and 7 men, age 29 ⫾ 7, weight 71 ⫾ 16 kg, height
174 ⫾ 9 cm). Prior written consent was obtained from all volunteers
before the interfacial body-mattress pressure measurements. Using
unpaired t-tests, we verified that peak contact pressures predicted by
our set of FE models were statistically indistinguishable from peak
pressures generated by the group of recumbent subjects (Table 4).
A sensitivity analysis was run to assess the influence of selected
important model parameters on the predictions of stresses and strains
in deep tissues during recumbency. The parameters that were altered
were the body weight, backrest inclination, fat stiffness, skin stiffness,
and muscle stiffness. We altered the values of these parameters, one
at a time, and examined the effects on the maximal von Mises stress,
maximal principal compression stress, and maximal compression
strain in muscle tissue of each model. Alteration of the body weight
and backrest inclination affected the values of forces and moments
J Appl Physiol • VOL
applied to the surfaces of each model (APPENDIX, Fig. 4) and thereby
also affected the distributions of internal stresses and strains. Alteration of skin, fat, and muscle stiffness, which also influence the
pattern of internal stresses and strains, was carried out by changing the
stresses required to produce a given strain level of the tissue by ⫾20%
(for skin and fat) or ⫾25% (for muscle). We used our present standard
deviation of tissue stiffness for muscles and adapted variations reported in the literature for skin (47) and fat (25).
The mechanical properties of the supporting mattress may also
influence the interfacial and internal stress distributions. To determine
whether stiffness of the mattress affects the stress flow within deep
muscles, we modified the elastic modulus of the mattress (Em) across
a logarithmic scale (i.e., from 0.1Em to 10Em and 100Em, where Em ⫽
150 kPa) and calculated internal maximal principal stresses, contact
pressure, and contact shear for the pelvis model, in each case.
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Fig. 4. Free body diagrams used to calculate
skeletal forces, moments, and body-mattress
friction forces acting on the pelvis (A, B),
shoulder (C, D), head (E, F), and heel (G, H)
segment models. The loading systems (representing recumbency) were calculated for
each model to define the conditions for succeeding finite element stress-strain analysis.
The derivation of all loading systems is provided in the APPENDIX.
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MECHANICAL COMPRESSION-INDUCED PRESSURE SORES
Table 2. Loading systems for finite element modeling of the
sites vulnerable to pressure sores in the human body
(corresponding to Figures 3, 4 and the APPENDIX)
Skeletal force F1, N
Skeletal force F2, N
Skeletal moment M1, N䡠m
Skeletal moment M2, N䡠m
Static friction force f, N
Pelvis
Shoulders
Head
Heels
144
116
0.1
74
24
21
48
36
1.4
15
8
11
33
0.3
1.5
8
4
0.8
33
3.8
RESULTS
Table 3. Mechanical properties of tissues for finite
element modeling
Tissue
Density, g/cm3
Elastic Modulus
1.9 [20]
0.8 [56]
1.056 [50]
1.056 [50]
1.056 [50]
1.1 [44]
18 GPa
5 GPa
0.5 MPa
47 KPa
0.133 MPa
10 MPa
[20]
[28]
[58]
[53]
[23]
[42]
0.3
0.3
0.5
0.5
0.4
0.4
[28]
[28]
[53]
[53]
[23]
[42]
Tissues considered as non-linear-elastic
Skin
Fat
Muscle
1.056 [50]
1.2 [37]
1.056 [50]
695 kPa (Eq. 1)
80 kPa (Eq. 2)
75 kPa (Eq. 3)
strains of 2.5 and 5%. Moreover, SED values were greater for
muscles exposed to 35–70 kPa by 40% in average, for strains
of 5 and 7.5% (P ⱕ 0.03). Because a stiffer material requires
more energy to deform to a given strain level compared with a
more compliant material, this further indicates the abnormally
increased stiffness of the injured muscles.
Histology of muscle tissue under compression. Staining with
PTAH was shown to provide the most sensitive visualization of
histomorphological changes that were induced by our experimental protocol. From all staining methods that were used in
Poisson’s Ratio
Tissues considered as linear-elastic
Cortical bone
Trabecular bone
Colon
Ileum
Blood vessels
Cartilage
Fig. 5. Finite element model of the rat limb: transverse cross-sectional anatomy of the limb segment that was compressed (A), the 3D solid computer
model (B), and the 3D mesh for finite element analysis (C).
0.4 [24]
0.5 [53]
0.5 [53]
Numbers in brackets are references.
J Appl Physiol • VOL
Table 4. Peak contact pressures: experimental results vs.
model predictions
Peak Pressure
Pelvis
Shoulders
Heels
Head
Test-bench measurements
(n ⫽ 14), kPa
Model predictions, kPa
12 ⫾ 9
10 (NS)
4⫾2
3 (NS)
13 ⫾ 8
15 (NS)
5⫾3
5 (NS)
*Subject group included 7 women and 7 men with the following body
characteristics: age, 29 ⫾ 7 yr; weight, 71 ⫾ 16 kg; height, 174 ⫾ 9 cm. A
t-test was run for each anatomic site to verify that model predictions reflect the
normal contact pressure pattern. Significance was set at the 5% level; NS, not
significant.
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Mechanical properties of muscle tissue. Using our rat model
of PS, we found that muscle tissue generally increase its
stiffness as a result of injury caused by exposure to a critical
dose of prolonged pressure (Fig. 6). A two-way ANOVA for
pressure and time revealed that both tangent elastic moduli and
strain energy densities depended on the extent of applied
pressure. However, tangent elastic moduli and SED did not
depend on the time duration of exposure. Specifically, using
Tukey-Kramer pairwise comparisons, we found that tangent
moduli of muscles exposed to compression of 35 or 70 kPa for
2 h or more were significantly greater than those of normal,
uninjured muscles at strains of 2.5 and 5% (P ⬍ 0.05), but not
at a strain of 7.5% (Fig. 6A). Strain energy densities of muscles
exposed to compression of 35 kPa for 2 h or more were
significantly greater than those of normal, uninjured muscles at
strains of 5 and 7.5% (P ⬍ 0.05) but not at the smallest (2.5%)
strains (Fig. 6B). Tukey-Kramer pairwise comparisons revealed that tangent elastic moduli and SED of muscles exposed
to pressure of 11.5 kPa were statistically indistinguishable
from uninjured muscles (controls) across all strain levels.
Similarly, tangent elastic moduli and SED of muscles exposed
to 35 kPa were indistinguishable from those of muscles exposed to 70 kPa across all three strains. According to the later
result, we pooled property data of animals exposed to 35 and
70 kPa at each strain level (Fig. 6). We then performed an
additional one-way ANOVA, for pressure level only, which
indicated, consistent with our previous analyses, that muscles
exposed to 35–70 kPa for ⬎2 h were significantly stiffer (P ⬍
0.03) than noninjured muscles. The stiffness (in terms of the
tangent elastic modulus) of the muscles exposed to 35–70 kPa
was greater by 60% in average compared with controls, for
MECHANICAL COMPRESSION-INDUCED PRESSURE SORES
2041
Fig. 6. Mechanical property data for the normal and injured gracilis of the rat:
tangent elastic moduli (Et; A) and strain energy densities (SED; B). Cont,
control (uninjured muscles). Data for experimental groups exposed to 35 and
70 kPa were pooled after Tukey-Kramer tests showed that the mechanical
properties obtained from these groups were statistically indistinguishable.
*Statistically significant differences (P ⬍ 0.05) between properties from
different groups.
this study, PTAH was the only one which demonstrated pathological changes for specimens harvested immediately after
compression was delivered. The stained slides from animals
exposed to interfacial compression of 35 and 70 kPa showed
extensive necrotic death of muscle cells that was evident by
loss of cross-striation (Fig. 7). Some transitional regions of
necrobiosis (partially viable tissue) could also be identified in
the group exposed to 70 kPa (Fig. 7). Contrarily to the
specimens from muscles exposed to 35–70 kPa, PTAH-stained
slides from animals exposed to 11.5 kPa for 6 h were indistinguishable from slides of normal uninjured muscles (controls). Specifically, no evidence of loss of cross-striation or
necrosis of muscle tissue was apparent in slides from animals
exposed to 11.5 kPa. We conclude that the abnormal 1.6-fold
increase in muscle tissue stiffness observed in our uniaxial
tension experiments for muscles exposed to pressures of 35 and
70 kPa is accompanied by widespread necrotic damage.
J Appl Physiol • VOL
Fig. 7. Representative phosphotungstic acid hematoxylin (PTAH) staining of
control rat muscle tissue (A) and rat muscle tissue injured by exposure to 70
kPa for 2 h (B). Within the frame shown, ⬃30% of the muscular tissue was
identified as necrotic (unstained, e.g., region A) and the other ⬃70% was
viable tissue (stained blue, e.g., regions B). Magnification was set as ⫻300.
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Computational stress analysis. According to our rat limb FE
model (Fig. 8), the external pressures that were applied on the
rat limbs, 11.5, 35, and 70 kPa, induced internal compression
stresses of 13, 40, and 80 kPa, respectively. We found abnormal stiffening in muscles that underwent internal compression
of 40 kPa or over for 2 h but not in muscles that underwent
internal compression of 13 kPa for 6 h. Thus the injury
threshold for striated muscle tissue under compression is between 13 kPa delivered for 6 h and 40 kPa delivered for 2 h.
Because FE analysis of the injury process in humans requires
a definite single value for this threshold, we adopted a conservative assumption (in terms of the rate of diffusion of the
injury) and used the greater injury threshold limit, i.e., 40 kPa
delivered for 2 h.
In general, peak stresses in deep muscles under the bony
prominences of the human pelvis and shoulders were shown to
be greater (up to 35-fold for the shoulders model) than respective peak contact stresses (Fig. 9). Maximal von Mises stresses
in the normal, uninjured musculature of the pelvis during
recumbency were 290 and 150 kPa in the longissimus and
gluteus muscles, respectively (Fig. 9A), and were substantially
greater than peak contact pressure between the skin and the
2042
MECHANICAL COMPRESSION-INDUCED PRESSURE SORES
supporting surface (11 kPa). Both the longissimus and gluteus
peak stresses are to exceed the injury threshold obtained for
striated muscle in the rat if applied for 2 h or more. Similarly,
maximal von Mises stresses in the shoulders during recumbency were 222, 840, and 872 kPa in the infraspinatus, supraspinatus, and subscapularis muscles, respectively (Fig. 9B),
exceeding the peak contact pressure (25 kPa) by at least an
order of magnitude. The occipitofrontalis muscle in the head
model, however, was shown to bear maximal von Mises stress
of 21 kPa (Fig. 9D), which is in the same range as the 14 kPa
peak contact pressure between the skin of the scalp and the
mattress. The only case in which interfacial pressures were
greater than internal stresses was for the heel model. Interfacial
stresses between the skin around the posterior aspect of the
calcaneus and the mattress (50–75 kPa) were three- to fivefold
higher with respect to internal stresses in fat tissue around the
Achilles tendon (10–25 kPa) (Fig. 9C).
J Appl Physiol • VOL
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Fig. 8. Stress analysis of the rat limb under constant-pressure loading: internal
compression stresses within the gracilis for external pressures of 11.5 (A), 35
(B), and 70 kPa (C).
Maximal strain magnitudes in deep muscles of the pelvis,
shoulders, head, and heels were between 0.2 and 8% (Fig.
10A). This range of peak strains justifies our selection to
experimentally test material properties of the gracilis muscle of
the rat at strain levels of 2.5, 5, and 7.5%.
The internal stress distributions in soft tissues are evolving
with time during recumbency because of the abnormal stiffening of damaged muscular tissue that was subjected to compression stress of 40 kPa or over for 2 h or more. If certain regions
of muscular tissue are damaged (by lack of nutrients and/or
excessive cell deformation and/or deficient waste clearance),
and, thereby, the local stiffness is increased, the global stress
flow in the tissue is also expected to change. Accordingly, the
FE simulations predicted that 2 h after a patient was put in a
recumbent position, regions in the longissimus (pelvis) that
were exposed to compression stresses of 30 kPa or over expand
in area by 30% (Fig. 10B). Similarly, regions in the longissimus exposed to lower stresses of 8 and 10 kPa expand in area
by 13 and 50%, respectively (Fig. 10B). Thus the PS injury is
diffused to the regions more recently exposed to stresses that
may exceed the critical injury threshold.
Table 5 details the sensitivity of our predictions of stresses
and strains in the human musculature to variations in values of
the model parameters. Skin stiffness, fat stiffness, and muscle
stiffness all had a minor effect (⬍6.6%) on peak muscle
stresses in the pelvis, shoulders, and head models. Peak von
Mises stress in the posterior subcutaneous tissue of the heel
model, however, varied by 15% for the ⫾20% extent of change
in fat and skin stiffness. The maximal compressive strains in
the longissimus muscle (pelvis) and occipitofrontalis muscle
(head) were sensitive to variations in the muscle stiffness and
increased by 14 and 35%, respectively, when the overall
stiffness of muscle tissue was increased by 25%. Stiffness of
the fat tissue also had substantial influence on maximal muscle
strains. The maximal strain in the longissimus muscle was
amplified by 33% when the fat stiffness increased by 40%. The
parameters that had the most dominant effect on stress and
strain predictions were the body weight and the backrest
inclination, and both affected mostly the results from the pelvis
model. Additional 40 kg of body weight increased the maximal
von Mises stress, maximal compression stress, and maximal
compression strain in the longissimus muscles of the pelvis by
87, 89, and 67%, respectively. A backrest angle (␤) of 60° (Fig.
4) produced ⬃1.6-fold higher peak stresses and ⬃1.35-fold
higher peak strains in the deep musculature of the pelvis
compared with a 45° inclination. For example, maximal von
Mises stress, maximal compression stress, and maximal compression strain in the longissimus increased by 68, 56.8, and
35.4%, respectively, for ␤ ⫽ 60°. Consistently, lower backrest
inclination of ␤ ⫽ 30° decreased the maximal von Mises stress,
maximal compression stress, and maximal compression strain
in the longissimus by 117, 43.5, and 29.3%, respectively. We
conclude that internal stresses and strains in deep muscles are
sensitive to the posture of the body and can be relieved if the
posture is adequately changed.
We repeated the stress analyses of the pelvis for a more
compliant (0.1Em) and for stiffer (10Em, 100Em) mattresses.
Internal maximal principal stresses in the longissimus muscles
increased from 117 to 132 kPa when the stiffness of the
mattress was reduced from 100Em to 0.1Em. Unlike peak
internal stresses, the contact pressure and shear were strongly
MECHANICAL COMPRESSION-INDUCED PRESSURE SORES
2043
affected by the rigidity of the mattress (Fig. 11). For example,
the peak contact pressure for the softest (0.1Em) mattress
(predicted to be 8.5 kPa) increased by a factor of 1.6 when the
mattress was stiffened to 100Em (Fig. 11). This indicates that
interfacial pressures are a poor, inefficient indicator for deep
muscle stresses. Attempts to predict the risk for PS that affect
deep muscles on the basis of interfacial pressures are therefore
naive.
DISCUSSION
In this study, we employed animal and computer models to
demonstrate that deep muscle tissue that undergoes prolonged
compression may significantly increase its stiffness during
injury. The injured, stiffer tissue bears elevated stresses and
projects these stresses to adjacent tissue that was not yet
injured, thereby exposing it to the potentially damaging critical
pressure dose (the threshold used in this study is internal
compression of 40 kPa delivered for 2 h). This may drive a
positive-feedback mechanism in muscle PS in which the elevated stresses in widening regions around the bone-muscle
interface (Fig. 10) increase the potential for muscle tissue
necrosis.
Specifically, our experimental results demonstrated a statistically significant increase in the tissue’s elastic moduli (average rise of 60%) as well as a significant increase in SED
(average rise of 40%) as a result of prolonged compression
J Appl Physiol • VOL
(Fig. 6). We demonstrated, by means of PTAH histology, that
these changes in constitutive properties are associated with
extensive cell death and tissue necrosis. This finding of abnormally stiff mechanical properties that accompany cell death
agrees with previous in vitro studies, which reported of stiffer
properties of excised soft tissues postmortem, including cartilage (1.5-fold stiffening, Ref. 21), plantar fascia (1.2-fold
stiffening, Ref. 26), and brain (1.2-fold stiffening, Ref. 45).
The mechanism causing the stiffening of muscle tissue can be
an increase in the swelling pressure of the tissue, which may
follow destruction of cell membranes during necrotic cell death
due to ischemia (29). Additional damage other than ischemia
could have been produced by lack of tissue drainage (39) and
excessive tissue deformation (8), but our histology and mechanical testing protocols could not isolate the contribution of
each damage cause to cell death and abnormality of mechanical
properties. However, we expect the same phenomenon of
muscle tissue stiffening in vivo, in humans, during PS onset
when muscles become partially necrotic under prolonged bone
compression.
Kovanen et al. (35) measured tangent elastic moduli of 47 to
104 kPa for soleus and rectus femoris muscles of rat that were
tested under tension in strains lower than 7.5%. Bosboom et al.
(6) measured instantaneous shear modulus of 15.6 ⫾ 5.4 kPa
for tibialis anterior rat muscles. Utilizing the relation G ⫽
(E/2)/(1 ⫹ ␷), where G is the shear modulus, E is the elastic
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Fig. 9. Distribution of von Mises stresses in the pelvis (A), shoulders (B), heel (C), and head (D), with a region of interest magnified
on each stress diagram to show maximal internal stresses.
2044
MECHANICAL COMPRESSION-INDUCED PRESSURE SORES
modulus, and ␷ ⫽ 0.5 is Poisson’s ratio for an incompressible
material, it is shown that their tangent elastic moduli under
large strains (⬎5%) are in the range of 30–63 kPa. Thus both
Kovanen et al. and Bosboom et al. reported properties for
normal rat limb muscles that overlap our measurements of
normal properties of the gracilis muscle: 46–73 kPa (mean ⫾
SD for 7.5% strain, Fig. 6).
Our observation of stiffening of muscle tissue in some of the
experimental groups requires that the potential effect of crossbridging of muscle fibers in a rigor state will be discussed. A
rigor state is the elevated stiffness of skeletal muscles that
usually appears within 4 h after death (32) and maximizes 12
to 48 h from death (36). Muscle specimens in the present study
were tested within no more than 30 min after the rats were
killed. If some mild rigor mortis did occur within this timeframe, it should have led to elevated stiffness in control
muscles, but our experimental results for controls overlap
results from previous studies in which mechanical properties of
fresh uninjured normal rat muscles were measured, as indiJ Appl Physiol • VOL
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Fig. 10. A: principal compression strains in the normal longissimus muscles.
Strain levels in the longissimus of a recumbent subject are predicted to range
between 0.5 and 6%. B: principal compressive stresses in the uninjured and
injured longissimus muscles. Internal stresses in the longissimus evolve owing
to abnormal stiffening of injured muscle tissue so that regions subjected to
compression of 8 (A), 10 (B), and 30 kPa (C) expand in area by 13, 50, and
30%, respectively.
cated above (6, 35). Moreover, in the present study, injured
muscles were significantly stiffer than uninjured ones (controls), indicating that the effect of injury on stiffness overweighs the effect of rigor mortis if such existed.
Because of the finite number of animals that could be tested,
we selected three specific limb-pressure levels (11.5, 35, and
70 kPa) and, with the aid of our FE rat-limb model, found that
both histological and mechanical abnormalities appeared with
exposure to internal compression of 40 kPa for 2 h. Delivery of
13 kPa of internal compression did not cause an apparent
mechanical or histological effect even for the maximal exposure time of 6 h. We conclude that the actual stress threshold
for compression injury is between 13 kPa (internal) delivered
for 6 h and 40 kPa (internal) delivered for 2 h. Both conditions
involve delivery of about the same pressure dose: ⬃80 kPa䡠h.
Kosiak (34) delivered external pressures to rat hamstring
muscles for periods of 1 to 4 h and quantified corresponding
internal pressures using a needle connected to an interstitial
fluid pressure (IFP) transducer. Muscles subjected to pressure
of 4.6 kPa for up to 4 h and those subjected to 25.3 kPa for up
to 1 h appeared normal. Contrarily, muscles exposed to pressure of 10 kPa for 2 h were damaged. Puncture of the tissue
with the IFP needle could, however, cause some of the observed damage or increase the tissue’s sensitivity to pressure.
Salcido et al. (49) reported macroscopic lesions in the panniculus carnosus muscle of rats that were associated with cutaneous ulceration after exposure to external pressure of 20 kPa for
6 h. In the most recent study, Bosboom et al. (5) used
hematoxylin and eosin staining and IFP measurements to
evaluate the pressure tolerance of the tibialis anterior tissue in
a rat model of PS. They found that application of either 10 or
70 kPa for 2 or 6 h induced loss of cross-striation when
combined with IFP measurements. When IFP measurements
were excluded from their protocol, histological damage did not
appear. Damage did appear when the pressure level was
increased to 250 kPa and was more pronounced when IFP
measurements were again incorporated for this pressure level.
They suspected that insertion of the IFP needle affected the
occurrence of damage and that it reduced the injury thresholds
of muscle in their study, as well as in the study of Kosiak. Our
results for the injury threshold agree with those of Salcido et
al., who avoided an IFP needle. The use of a FE model of the
animal experiment provided the level of internal tissue stresses
in the present study (Fig. 8) and allowed avoidance of invasive
IFP measurements.
The human FE models demonstrated that deep muscles
under bony prominences of the pelvis and shoulders bear
substantially higher internal stresses compared with bodysupport interfacial pressures (Fig. 9). We found that peak
stresses (principal compression) in the longissimus muscles
(Fig. 9A) increased by 13% (from 117 to 132 kPa) when the
stiffness of the mattress was reduced over three orders of
magnitude. It is important to emphasize that even though the
stiffness of the mattress was decreased across such a broad
range (0.1Em–100Em), principal compression stresses in the
longissimus increased and remained highly above the 40 kPa
stress threshold for PS. Contact pressures and contact shear
between the pelvis and mattress, however, substantially decreased, from peaks of 13.8 and 2.4 kPa to 8.2 and 1.4 kPa,
respectively. This indicates that no simple relations exist between the internal and interfacial stresses for the body-support
2045
MECHANICAL COMPRESSION-INDUCED PRESSURE SORES
Table 5. Sensitivity analysis of parameters
Effects
Maximal principal compression
stress, kPa
Maximal Von Mises stress, kPa
Parameter
Reference
Backrest angle
Body weight
Skin stiffness
47
Fat stiffness
25
Muscle stiffness
Present experiments
Maximal compression strain, %
Variation
Pelvis
Shoulders
Head
Heels
Pelvis
Shoulders
Head
Heels
Pelvis
Shoulders
Head
Heels
60°
30°
100 kg
50 kg
⫹20%
⫺20%
⫹20%
⫺20%
⫹25%
⫺25%
636
192
606
323
374
382
378
380
388
364
844
844
844
844
844
843
827
869
837
843
21.2
20.7
20.9
20.9
20.9
20.9
20.9
21
21
20.8
82.3
81.7
82
82
87.8
75.6
79.1
91.2
82
82
196
70.6
201
106
124
126
125
125
126
123
226
226
226
226
226
226
223
232
223
228
27
26
26.4
26.5
26.6
26.3
26.5
26.4
26.3
26.7
59.4
58.4
58.9
58.9
58.4
59.4
59.8
58.1
58.9
58.9
7.57
3.95
8.26
4.93
5.53
5.65
3.29
4.39
5.26
6.01
1.3
1.3
1.3
1.3
1.28
1.33
1.28
1.42
1.18
1.62
7.12
5.96
6.49
6.54
6.35
6.75
6.24
6.84
5.7
7.69
20.9
20.8
20.8
20.8
20.4
21.6
20.3
22.9
20.8
20.8
Values indicate stresses and strains in the following deep tissues: longissimus (pelvis), supraspinatus (shoulders), occipitofrontalis (head), and subcutaneous
tissue between the Achilles tendon and skin (heel).
Fig. 11. Influence of mattress stiffness on contact pressure (A) and contact
shear distributions (B) between the pelvis and the mattress during recumbency.
The elastic modulus of the mattress (Em) equals 150 kPa.
J Appl Physiol • VOL
the basis of the present simulations and published literature
(11, 27, 53), we conclude that contact pressure measurements
are insufficient for design of patient management procedures
and characterization of mattresses for preventing PS. Alternatively, an insight into the internal stress state under the bony
prominences is necessary.
With respect to internal stresses in recumbent humans, we
showed that when the backrest angle is decreased, from 45 to
30°, the effect on reducing internal muscle stresses under the
pelvis is much more profound and consistent than that caused
by decreasing the mattress stiffness (Table 5). When the
backrest slope was decreased by 15°, maximal internal stresses
in the longissimus, von Mises (377 kPa) and principal compression (125 kPa), decreased by 117% (to 192 kPa) and 43%
(to 71 kPa), respectively (Table 5). We conclude that some
relief of internal compression in the deep musculature of the
pelvis can be achieved through a decrease of the backrest
inclination, but internal compression would still be higher than
the 40 kPa injury threshold for PS.
Limitations of the present study include measurement of
mechanical properties of a complete muscle whereas damage
may be localized at certain regions within the muscle, and the
assumption that soft tissues in the FE models are homogenous
and nonlinear elastic rather than viscoelastic. The mechanical
testing of gracilis muscles in this study involved application of
tension to the complete muscles including tendon insertions
and perimysium. The perimysium, which is primarily connective tissue (collagen, with an elastic modulus of ⬃1 GPa), has
a great resistance to tension and thus it is likely that it
contributed substantially to the tangent moduli of elasticity.
Despite this, our measurements of mechanical properties were
sensitive to abnormalities caused by prolonged compression
and revealed statistically significant stiffening of muscular
tissue postcompression with a sufficient statistical power for
experimental groups of four to five animals. Muscle tissue was
considered in the FE models as a composite comprised of the
perimysium, endomysium, and muscle fibers, and stress-strain
predictions therefore describe an apparent behavior that cannot
be used to isolate deformation of individual muscle fibers,
although overstretching of individual fibers may be important
in the onset of PS injury (8). The assumption that tissues are
elastic and not viscoelastic may have caused some overestima-
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contact problem. Previous computational models of the diabetic foot (27) and buttocks (11) also showed that internal
stresses are higher than interfacial pressures and that no simple
relation between contact pressure and tissue stress can be
established (53). The above findings are important in view of
the efforts put in predicting risks for PS on the basis of
interfacial pressures. For example, interfacial pressures are
used to decide about timing for changing postures and for
selection of materials for hospital mattresses (10, 15, 22). On
2046
MECHANICAL COMPRESSION-INDUCED PRESSURE SORES
ening into a computational stress analysis of the pelvis during
recumbency, we were able to demonstrate a positive-feedback
mechanism: the increased muscle stiffness in widening regions
results in elevated tissue stresses and thereby exacerbate the
potential for tissue necrosis.
APPENDIX
Glossary
p
s
hd
hs
Fi
f
Mi
W
N
␮
Pelvis model
Shoulders model
Head model
Heel model
Skeletal forces acting on a model (i ⫽ 1,2)
Friction between the body and the mattress
Skeletal moments acting on a model (i ⫽ 1,2)
Total weight of the tissues contained in a model
Reaction force between the body and the mattress
Static coefficient of friction between the body and mattress
(taken as 0.4 for all simulations)
Horizontal and vertical components of the moment arm of a
force acting on a model
Angle between the spinal column force vector and the
horizon
Angle between the backrest of a hospital bed and the horizon
x, y
␣
␤
Here we describe the derivation of loading systems for each of the
human FE models with respect to the free body diagrams of the pelvis,
shoulders, head, and heels during recumbency (Fig. 4). For each of
these anatomical sites, the equations formulated below are used to
obtain the skeletal forces (F1, F2), moments (M1, M2), and bodysupport friction forces (f) that are listed in Table 2. The geometrical
dimensions and weights of body parts that were used to solve these
equations are specified in Tables 6 and 7, respectively.
Because skeletal forces and moments that act on one slice model
(pelvis, shoulders, heel, or head) generally affect the solution of forces
and moments for other models, the coefficient of friction between the
skin and mattress (0.4) was adjusted for each model, over a range of
15%, to assure that the values obtained for all forces and moments
Table 6. Geometrical dimensions used to solve the loading systems for finite element modeling of the sites vulnerable
to pressure sores in the human body
Model
Pelvis
Shoulders
Head
Heel
Symbol
Description
Value
␣
␤
xp1
yp1
xp2
yp2
xs1
xs
ys1
xs2
ys2
xhd
1
xhd
yhd
1
xhd
2
yhd
2
xhs
1
yhs
1
xhs
2
xhs
yhs
2
yhs
Angle of the spinal force vector in the sagittal plane
Backrest inclination
Distance between the pelvis slice and the FBD center of mass
Distance between the spinal force vector and the mattress
Distance between the pelvis slice and the FBD center of mass
Distance between the spinal force vector and the mattress
Distance between the shoulders slice and spinal force vector
Distance between the shoulders slice and the FBD center of mass
Distance between the spinal force vector and the backrest
Distance between the shoulders slice and the FBD center of mass
Distance between the backrest and the FBD center of mass
Distance between the spinal force vector and the head slice
Distance between the head slice and the FBD center of mass
Distance between the spinal force vector and the backrest
Distance between the head slice and the FBD center of mass
Distance between the spinal force vector and the backrest
Distance between the heel slice and the FBD center of mass
Distance between Fhs
1 vector and the mattress
Distance between the heel slice and the pelvis slice
Distance between the heel slice and the FBD center of mass
Distance between Fhs
2 vector and the mattress
Distance between Fhs
2 vector and the spinal force vector
13°
45°
0.3 m
0.07 m
0.8 m
0.06 m
0.6 m
0.2 m
0.06 m
0.08 m
0.05 m
0.55 m
0.2 m
0.06 m
0.04 m
0.05 m
0.035 m
0.1 m
0.2 m
0.85 m
0.06 m
0.025 m
The above data represent a normal adult man and are adopted from Clauser et al. (13) and Morse and Kjeldsen (40). FBD, free body diagram.
J Appl Physiol • VOL
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tion of stresses, because stress relaxation in the long term was
not considered. However, the assumption of nonlinear elasticity of soft tissues allowed assignment of considerable computational efforts for obtaining accurate anatomical representations of the pelvis, shoulders, heels, and head, because the
computational complexity of the material models was compromised.
In closure, integration of animal and FE models provides a
powerful tool for studying PS onset and progression. It also has
the potential of being an aid in design of seats and beds with
protective supporting surfaces as well as in designing new
patient management procedures.
Conclusions. Using an integrated approach of animal and
computer model studies of the biomechanics of PS, we found
the following. 1) Maximal internal principal compression and
von Mises stresses at deep muscles around the bony prominences of the pelvis and shoulders exceed the interfacial
contact stresses by at least an order of magnitude. Specifically
for the pelvis region, we found no correlation between external
pressures and internal muscle stresses. Surprisingly, a more
compliant mattress was shown to increase deep muscle stresses
instead of relieving them. A lower (30°) backrest angle could
decrease these deep muscle stresses, but only to a limited
extent. 2) Tangent elastic moduli and SED of rat gracilis
muscles injured by exposure of 2–6 h to external pressure of
35–70 kPa, which is transformed to internal muscle compression of 40–80 kPa, were 60 and 40% higher in average (P ⬍
0.04), respectively, than those of uninjured muscles. Abnormal
properties were accompanied by widespread necrotic cell
death. 3) On the basis of these findings, we conclude that
mechanical properties of striated muscle can be used as an
indicator for a compression injury. 4) Taken together, our
histological and mechanical testing results indicate that the
injury threshold for onset of PS in skeletal muscles is between
internal compression of 13 kPa delivered for 6 h and 40 kPa
delivered for 2 h. 5) Incorporating the effect of muscle stiff-
2047
MECHANICAL COMPRESSION-INDUCED PRESSURE SORES
Table 7. Weights of body segments used to solve the loading
systems for finite element modeling of the sites vulnerable
to pressure sores in the human body
Model
Pelvis
Shoulders
Head
Heel
Symbol
p
1
p
2
p
W
W
W
Ws1
Ws2
Ws
Whd
1
Whd
2
Whd
Whs
1
Whs
2
Whs
Body Segments
Total Weight, N
Lower pelvis and legs
Upper pelvis, trunk, arms, and head
Pelvis slice
Lower shoulders, trunk, and arms
Upper shoulders and head
Shoulders slice
Lower head, trunk, and arms
Upper head
Head slice
Feet
Legs, thighs, and pelvis
Heel slice
276
311
20
282
107
60
306
24
6
16.8
260
2
and calculate the static friction force between the upper body (Fig. 4B)
and mattress f p2
f 2p ⫽ N2p␮
To calculate the friction force under the pelvis slice, fp, we now
analyze this slice as a free body diagram. Using the above results for
Fp1 and Fp2 (Eqs. 1.5 and 2.5) and a force balance on the pelvis slice,
we obtain that
f p ⫽ F1p cos ␣ ⫺ F2p
兺 F ⫽ 0: F cos ␣ ⫹ f
p
1
x
p
1
p
1
y
兺M
0
p
1
p
1
p
1
p
1
⫽ 0: M1p ⫹ f 1py 1p ⫹ W1px1p ⫺ N1px1p ⫽ 0
p
1
p
1
y
s
1
s
1
F 1p ⫽
(1.5)
p
1
N 1s ⫽
F1s cos ␤ ⫺ F1p cos ␣
␮ cos ␤ ⫺ sin ␤
F 1s ⫽ F 1p共␮ cos ␣ sin ␤ ⫹ sin ␣ sin ␤ ⫹ cos ␣ cos ␤
⫺ ␮ cos ␤ sin ␣兲 ⫹ W1s共␮ cos ␤ ⫺ sin ␤兲
M 1s ⫽ M1p ⫹ N1sxs ⫺ F1px1s cos共90 ⫺ ␤ ⫹ ␣兲
⫺ W1sxs cos ␤ ⫺ N1s␮y1s
(1.7)
兺M
0
x
p
2
y
p
2
p
2
p
2
s
2
兺M
0
s
2
s
2
s
2
s
2
⫽ 0: ⫺M2s ⫹ N2sx2s ⫺ W2sx2s cos ␤ ⫹ f 2sy2s ⫽ 0
(4.1)
(4.2)
(4.3)
We solve for Ns2, Fs2, Ms2
N 2s ⫽ W2s cos ␤
(4.4)
F ⫽ W 共sin ␤ ⫺ ␮ cos ␤兲
(4.5)
(4.6)
s
2
s
2
p
2
(2.1)
M ⫽ W y ␮ cos ␤
p
2
(2.2)
and calculate the static friction force between the head-neck-shoulder
part (Fig. 4D) and mattress f s2
(2.3)
f 2s ⫽ N2s␮
⫽ 0: ⫺M2p ⫺ W2px2p cos ␤ ⫹ f 2py 2p ⫹ N2px2p ⫽ 0
We solve for Np2, Fp2, Mp2
N 2p ⫽ F2p sin ␤ ⫹ W2p cos ␤
(2.4)
W sin ␤ ⫺ W ␮ cos ␤
F 2p ⫽
␮ sin ␤ ⫹ cos ␤
(2.5)
M 2p ⫽ 共N2p ⫺ W2p cos ␤兲x2p ⫹ N2p␮y2p
(2.6)
p
2
(3.6)
(3.7)
兺 F ⫽ 0: F ⫹ f ⫺ W sin ␤ ⫽ 0
兺 F ⫽ 0: N ⫺ W cos ␤ ⫽ 0
Similarly, from static equilibrium of forces and moments on the
free body diagram of the upper body part located above the slice that
was selected for the pelvis model (Fig. 4B)
兺 F ⫽ 0: f ⫹ F cos ␤ ⫺ W sin ␤ ⫽ 0
兺 F ⫽ 0: N ⫺ W cos ␤ ⫺ F sin ␤ ⫽ 0
(3.5)
where F and M in Eqs. 3.1–3.6 are calculated from Eqs. 1.5 and 1.6,
respectively.
We continue with static equilibrium of the free body diagram of the
head, neck, and segment of the shoulders located above the shoulders
slice model (Fig. 4D)
y
f ⫽N ␮
(3.4)
p
1
(1.6)
p
1
(3.3)
We solve for N , F , M
and calculate the static friction force between the lower body (Fig. 4A)
and mattress f p1
p
1
p
1
s
1
x
p
1
s s
1
f 1s ⫽ N1s␮
W1p ␮
cos ␣ ⫺ ␮ sin ␣
p
1
s s
1
(3.2)
(1.3)
(1.4)
p
1
s
1
s
1
and calculate the static friction force between the trunk part that is
under the shoulders slice (Fig. 4C) and mattress f s1
F cos ␣
␮
M ⫽ x 共N ⫺ W 兲 ⫺ N ␮y
p
1
s s
1 1
s
1
(3.1)
(1.2)
We solve for N , F , M
p
1
s
1
p
1
N 1p ⫽
s
1
(1.1)
p
1
p
1
cos ␤ ⫺ N1s sin ␤ ⫺ F1s cos ␤ ⫽ 0
p
2
J Appl Physiol • VOL
s
2
s s
2 2
(4.7)
We obtain the friction force under the shoulders slice fs from
balance of forces on this slice
f s ⫽ F1s ⫺ F2s ⫹ Ws sin ␤
(4.8)
Head model. Similarly, we start with static equilibrium for the free
body diagram of the head and trunk segments below the selected slice
(Fig. 4E)
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maintain static equilibrium across all models simultaneously. The
corrected coefficients of friction that simultaneously satisfy the static
equilibrium equations across all models were obtained through a
trial-and-error analysis and were found to be 0.455, 0.36, 0.35, and
0.466 for the pelvis, shoulders, head, and heel models, respectively.
Pelvis model. From static equilibrium of forces and moments on the
free body diagram of the lower body part located below the slice that
was selected for the pelvis model (Fig. 4A)
s
1
兺 F ⫽ 0: F sin ␣ ⫹ f sin ␤ ⫺ W ⫹ N cos ␤ ⫺ F sin ␤ ⫽ 0
兺 M ⫽ 0: M ⫹ f y ⫹ W x cos ␤ ⫺ N x ⫺ M
0
x
(2.8)
Shoulders model. The method of derivation is similar to the one
used to obtain the loading system for the pelvis model. We start with
static equilibrium for the free body diagram of the trunk, considering
only the trunk segment below the slice used to model the shoulders
(Fig. 4C)
The above data represent a normal adult male and are adopted from Clauser
et al. (13) and Morse and Kjeldsen (40). The positions of the weight vectors are
shown in Fig. 4 and the method of calculation is provided in the APPENDIX.
兺 F ⫽ 0: f ⫺ F cos ␣ ⫽ 0
兺 F ⫽ 0: N ⫺ W ⫺ F sin ␣ ⫽ 0
(2.7)
2048
MECHANICAL COMPRESSION-INDUCED PRESSURE SORES
兺 F ⫽ 0: F cos ␣ ⫹ f
兺 F ⫽ 0: F sin ␣ ⫹ f
x
p
1
hd
1
cos ␤ ⫺ N1hd sin ␤ ⫺ F1hd cos ␤ ⫽ 0
y
p
1
hd
1
sin ␤
⫺ W ⫹ N cos ␤ ⫺ F sin ␤ ⫽ 0
hd
1
兺M
0
hd
1
hd
1
⫽ 0: M ⫹ f y ⫹ W x cos ␤ ⫺ N x ⫺ M
hd
1
hd hd
1 1
hd hd
1
hd hd
1
p
1
⫹ F1px1hd cos共90 ⫺ ␤ ⫹ ␣兲 ⫽ 0
(5.1)
and calculate the static friction force between the foot (Fig. 4G) and
mattress fhs
1
f 1hs ⫽ N1hs␮
(5.2)
(5.3)
We continue with equilibrium of the free body diagram of the legs,
to account for forces and moments acting above the slice of the heel
model (Fig. 4H)
兺 F ⫽ 0: F
兺 F ⫽ 0: N
x
hd
hd
We solve for Nhd
1 , F1 , M1
F1hd cos ␤ ⫺ F1p cos ␣
N ⫽
␮ cos ␤ ⫺ sin ␤
y
hd
1
(5.4)
F 1hd ⫽ F1p共⫹␮ cos ␣ sin ␤ ⫹ sin ␣ sin ␤ ⫹ cos ␣ cos ␤
⫺ ␮ cos ␤ sin ␣兲 ⫹ W1hd共␮ cos ␤ ⫺ sin ␤兲
M 1hd ⫽ M1p ⫹ N1hdxhd ⫺ F1px1hd cos共90 ⫺ ␤ ⫹ ␣兲
⫺ W1hdxhd cos ␤ ⫺ N1hd␮y1hd
hd
2
hd
2
y
兺M
0
hd
2
hd
2
⫽ 0: ⫺M2hd ⫹ N2hdx2hd ⫺ W2hdx2hd cos ␤ ⫹ f2hdy2hd ⫽ 0
(8.2)
(8.3)
N 2hs ⫽ W2hs ⫹ F1p sin ␣
p
1
(8.4)
hs
2
(8.5)
M ⫽ N x ⫺ W x ⫹ N ␮y ⫹ M ⫹ F 共y cos ␣ ⫺ x sin ␣兲
(8.6)
hs
2
hs hs
2
hs hs
2
hs
2
hs
2
p
1
p
1
hs
hs
2
and calculate the static friction force between the legs (Fig. 4H) and
mattress fhs
2
f 2hs ⫽ N2hs␮
p
1
(8.7)
p
1
(6.2)
where F and M in Eqs. 8.1–8.6 are calculated from Eqs. 1.5 and 1.6,
respectively.
Using balance of forces on the heel slice, it is now possible to
obtain the static friction force between the heel slice and mattress, f hs
(6.3)
f hs ⫽ F1hs ⫺ F2hs
(6.1)
(8.8)
ACKNOWLEDGMENTS
N ⫽ W cos ␤
(6.4)
F 2hd ⫽ W2hd共sin ␤ ⫺ ␮ cos ␤兲
(6.5)
M ⫽ W y ␮ cos ␤
(6.6)
hd
2
hd
2
hd
2
hd hd
2 2
We now calculate the static friction force between the head part
that is above the slice (Fig. 4F) and mattress f hd
2
f 2hd ⫽ N2hd␮
(6.7)
The friction force under the head slice, fhd, can now be calculated
hd
by using the results for Fhd
1 and F2 and a balance of forces on the head
model slice
f hd ⫽ F1hd ⫺ F2hd ⫹ Whd sin ␤
(6.8)
Heel model. Again, we start with static equilibrium for the free
body diagram of the body segments lower than the heel slice model
(i.e., the foot, Fig. 4G)
兺 F ⫽ 0: f
兺 F ⫽ 0: N
x
y
0
⫺ W2hs ⫺ F1p sin ␣ ⫽ 0
F ⫽ F 共cos ␣ ⫺ ␮ sin ␣兲 ⫺ W ␮
hd
hd
and solve for Nhd
2 , F2 , M2
兺M
hs
2
⫹ M1p ⫹ F1pyhs cos ␣ ⫺ F1px2hs sin ␣ ⫽ 0
hs
2
(5.7)
hd
2
(8.1)
⫽ 0: ⫺M2hs ⫹ N2hsxhs ⫺ W2hsxhs ⫹ f 2hsy2hs
(5.6)
where F and M in Eqs. 5.1–5.6 are calculated from Eqs. 1.5 and 1.6,
respectively.
We perform a second free body diagram analysis for the section of
the head above the slice (Fig. 4F)
x
⫹ f 2hs ⫺ F1p cos ␣ ⫽ 0
hs
hs
We solve for Nhs
2 , F2 , M2
p
1
兺 F ⫽ 0: F ⫹ f ⫺ W sin ␤ ⫽ 0
兺 F ⫽ 0: N ⫺ W cos ␤ ⫽ 0
0
hs
2
hs
1
⫺ F1hs ⫽ 0
(7.1)
hs
1
⫺ W1hs ⫽ 0
(7.2)
⫽ 0: M1hs ⫹ f 1hsy1hs ⫹ W1hsx1hs ⫺ N1hsx1hs ⫽ 0
(7.3)
hs
hs
we solve for Nhs
1 , F1 , M1
N 1hs ⫽ W1hs
(7.4)
F ⫽W ␮
hs
1
hs
1
(7.5)
M ⫽ ⫺W ␮y
hs
1
hs
1
hs
1
(7.6)
J Appl Physiol • VOL
We appreciate the help of Drs. M. Scheinowitz and D. Castel from the
Neufeld Cardiac Research Institute of Sheba Medical Center in handling of
animals and conducting the dissections. Dr. S. Engelberg from the Laboratory
for Vascular Biology, Sheba Medical Center is thanked for conducting and
interpreting the histological analyses. Dr. S. Margulies from the Department of
Bioengineering at the University of Pennsylvania is thanked for valuable
critique, which allowed improvement of the study.
GRANTS
Funding was provided by the Slezak Super Center for Cardiac Research and
Biomedical Engineering and by the Internal Research Fund of Tel-Aviv
University.
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