J Appl Physiol 96: 2034-2049, 2004.
First published February 6, 2004; doi:10.1152/japplphysiol.00888.2003
8750-7587/04 $5.00
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
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ABSTRACT
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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 
5%) and strain energy densities were 1.4-fold those of controls (P < 0.05, for strains 
5%). 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.
decubitus ulcers; soft tissue injury; muscle mechanical properties; animal model; finite element analysis
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 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.
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METHODS
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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 Sprague-Dawley 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 manifestation of their effect on mechanical properties by using standard uniaxial tension testing.
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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).
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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 fourth-order 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 µm (diameter of muscle fibers is 30 µm), 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 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 µs = 0.4 (60). In the neutral position of the bed, the backrest was inclined 45° to the horizon.
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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).
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For each anatomic site, a corresponding transverse cryosectional image from the "Visible Human" male digital database was transferred 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 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).
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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; µ, static coefficient of friction between body and mattress.
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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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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)
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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)
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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 (µs = 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. 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 stress-strain 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).
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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).
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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 recumbency (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 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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RESULTS
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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 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 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.
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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.
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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 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.
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.
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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).
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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 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).
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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.
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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%.
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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.
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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 (
)of60° (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 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.
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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.
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DISCUSSION
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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 (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 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 cross-bridging 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 time-frame, 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 indicated 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 over-weighs 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·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 body-support 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 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 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 overestimation 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 stiffening 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.
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APPENDIX
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Glossary
- p
- Pelvis model
- s
- Shoulders model
- hd
- Head model
- hs
- Heel model
- Fi
- Skeletal forces acting on a model (i = 1,2)
- f
- Friction between the body and the mattress
- Mi
- Skeletal moments acting on a model (i = 1,2)
- W
- Total weight of the tissues contained in a model
- N
- Reaction force between the body and the mattress
- µ
- Static coefficient of friction between the body and mattress (taken as 0.4 for all simulations)
- x, y
- 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
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 body-support 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.
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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
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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
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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 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)
 | (1.1) |
 | (1.2) |
 | (1.3) |
We solve for 
, 
, 
 | (1.4) |
 | (1.5) |
 | (1.6) |
and calculate the static friction force between the lower body (Fig. 4A) and mattress
 | (1.7) |
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)
 | (2.1) |
 | (2.2) |
 | (2.3) |
We solve for 
, 
, 
 | (2.4) |
 | (2.5) |
 | (2.6) |
and calculate the static friction force between the upper body (Fig. 4B) and mattress 
 | (2.7) |
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 and (Eqs. 1.5 and 2.5) and a force balance on the pelvis slice, we obtain that
 | (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)
 | (3.1) |
 | (3.2) |
 | (3.3) |
We solve for 
, 
, 
 | (3.4) |
 | (3.5) |
 | (3.6) |
and calculate the static friction force between the trunk part that is under the shoulders slice (Fig. 4C) and mattress 
 | (3.7) |
where and in Eqs. 3.1, 3.2, 3.3, 3.4, 3.5, 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)
 | (4.1) |
 | (4.2) |
 | (4.3) |
We solve for 
, 
, 
 | (4.4) |
 | (4.5) |
 | (4.6) |
and calculate the static friction force between the head-neck-shoulder part (Fig. 4D) and mattress 
 | (4.7) |
We obtain the friction force under the shoulders slice fs from balance of forces on this slice
 | (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)
 | (5.1) |
 | (5.2) |
 | (5.3) |
We solve for 
, 
, 
 | (5.4) |
 | (5.5) |
 | (5.6) |
and calculate the static friction force between the lower body (Fig. 4E) and mattress 
 | (5.7) |
where and in Eqs. 5.1, 5.2, 5.3, 5.4, 5.5, 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)
 | (6.1) |
 | (6.2) |
 | (6.3) |
and solve for 
, 
, 
 | (6.4) |
 | (6.5) |
 | (6.6) |
We now calculate the static friction force between the head part that is above the slice (Fig. 4F) and mattress 
 | (6.7) |
The friction force under the head slice, fhd, can now be calculated by using the results for and and a balance of forces on the head model slice
 | (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)
 | (7.1) |
 | (7.2) |
 | (7.3) |
we solve for 
, 
, 
 | (7.4) |
 | (7.5) |
 | (7.6) |
and calculate the static friction force between the foot (Fig. 4G) and mattress 
 | (7.7) |
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)
 | (8.1) |
 | (8.2) |
 | (8.3) |
We solve for 
, 
, 
 | (8.4) |
 | (8.5) |
 | (8.6) |
and calculate the static friction force between the legs (Fig. 4H) and mattress 
 | (8.7) |
where and in Eqs. 8.1, 8.2, 8.3, 8.4, 8.5, 8.6 are calculated from Eqs. 1.5 and 
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