Can Loaded Interface Characteristics Influence Strain ... - CiteSeerX

Computer Methods in Biomechanics and Biomedical Engineering, Vol. 6, No. 3, June 2003, pp. 171–180

Can Loaded Interface Characteristics Influence Strain Distributions in Muscle Adjacent to Bony Prominences? C.W.J. OOMENSa,*, O.F.J.T. BRESSERSa, E.M.H. BOSBOOMa, C.V.C. BOUTENa and D.L. BADERa,b a

Eindhoven University of Technology, P.O. Box 513 5600MB, Eindhoven, The Netherlands; bQueen Mary, University of London, UK

Pressure distributions at the interface between skin and supporting tissues are used in design of supporting surfaces like beds, wheel chairs, prostheses and in sales brochures to support commercial products. The reasoning behind this is, that equal pressure distributions in the absence of high pressure gradients is assumed to minimise the risk of developing pressure sores. Notwithstanding the difficulty in performing reproducible and accurate pressure measurements, the question arises if the interface pressure distribution is representative of the internal mechanical state of the soft tissues involved. The paper describes a study of the mechanical condition of a supported buttock contact, depending on cushion properties, relative properties of tissue layers and friction. Numerical, mechanical simulations of a buttock on a supporting cushion are described. The ischial tuberosity is modelled as a rigid body, whereas the overlying muscle, fat and skin layers are modelled as a non-linear Ogden material. Material parameters and thickness of the fat layer are varied. Coulomb friction between buttock and cushion is modelled with different values of the friction coefficient. Moreover, the thickness and properties of the cushion are varied. High shear strains are found in the muscle near the bony prominence and the fat layer near the symmetry line. The performed parameter variations lead to large differences in shear strain in the fat layer but relatively small variations in the skeletal muscle. Even with a soft cushion, leading to a high reduction of the interface pressure the deformation of the skeletal muscle near the bone is high enough to form a risk, which is a clear argument that interface pressures alone are not sufficient to evaluate supporting surfaces. Keywords: Pressure distributions; Interface; High shear strains; Pressure sores

INTRODUCTION Pressure sores—also known as pressure ulcers—can arise when a prolonged mechanical load is applied to soft biological tissues, for example when patients are bedridden or wheelchair bound for a prolonged period. In addition, in situations where prostheses or ortheses are used to support soft tissues, pressure sores may occur. The prevalence of pressure sores is high. Surveys in acute care hospitals report prevalences ranging from 8% in the United Kingdom [1] to 9.2% in the United States [2] and 10% in The Netherlands [3]. In the Netherlands, the prevalence in total intramural healthcare varies between 6 and 25% [4]. It is generally accepted that the primary cause of pressure sores is prolonged external mechanical loading on soft tissues. Therefore, much research has focused on

preventive measures that reduce and periodically relieve these loads. However, the onset and development of pressure sores is influenced by several risk factors, such as age, impaired mobility, incontinence, temperature and nutritional state. Despite the growing knowledge about the effects of risk factors, it is still difficult to identify at an early stage specific patients at risk of developing pressure sores. Therefore, adequate clinical guidelines for prevention are difficult to provide. During the last 40 years several authors [5–7] many studies have attempted to unravel the aetiology of pressure sores. What is clear, is, that there exists an inverse relationship between the magnitude and duration of compressive loading that soft tissue can resist, but a ubiquitous damage threshold cannot be defined. Moreover, muscle tissue seems to be more susceptible to the effects of compressive loading than skin [8,9]. There is also plausible

*Corresponding author. Tel.: þ 31-40-2472818. E-mail: [email protected] ISSN 1025-5842 print/ISSN 1476-8259 online q 2003 Taylor & Francis Ltd DOI: 10.1080/1025584031000121034

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evidence that the presence of shear forces can increase the susceptibility of soft tissues to damage [10,11]. Previous research has spawned three basic hypotheses, implicating mechanical loading as the initiator of soft tissue damage. The most adhered of these involves local ischaemia of the soft tissues, following occlusion or collapse of capillaries. Although many authors found that capillary perfusion decreases with the degree of mechanical loading, it is extremely difficult to provide threshold values below which capillary perfusion becomes critical. The second hypothesis is focused on the interstitium between cells and terminal capillaries and lymph vessels. Mechanical loading influences pressures, fluid flows, concentrations and transport of nutrients and waste products in the interstitial space. In this way the delicate metabolic equilibrium around cells is disturbed, which may eventually lead to tissue necrosis [12 – 14]. The other hypothesis is, that a prolonged deformation of cells inside a loaded tissue causes damage, even when the bio-chemical environment of the cell remains unaltered [15 – 17]. It is clear that for a breakthrough in the prevention and treatment of pressure sores it is necessary to obtain a better understanding of their aetiology. A more complete understanding of the relationship between load and tissue damage needs to be established. This will provide design criteria for optimal pressure relieving strategies and may lead to measures which can lead to the enhancement of both tissue resistance and repair. Biomechanical studies are critical in the chain of activities necessary to understand aetiology. Several authors [18 – 20] have previously emphasized the need to establish the associations between global external mechanical loads and the internal local mechanical condition of the tissue. How these local mechanical conditions are influenced by a given external mechanical load is determined by the geometry and the material properties of the tissues and underlying bones. The enormous attention related to the interface pressures between tissues and supporting surface and the search for safe interface thresholds demands a renewed interest in the mechanics of the problem. Interface pressure measurements per se may be useful, but represent only a very small solution of the overall problem. It is likely that different tissues (skin, fat and muscle) have a different susceptibility to damage under mechanical loads. Moreover, because of the complex geometries and the differences in the mechanical properties of the tissue layers the mechanical state of each tissue is very complicated. Finally, interface pressure only gives information about the normal stress at the interface between tissue and supporting surface, while shear stresses can also lead to damage. The objective of this paper is to study the mechanical condition of a supported buttock contact. The paper focuses on the mechanical state of soft tissues of a sitting person, using a numerical model. Of the few related studies Chow and Odell [18] made an axisymmetric finite element model of a human buttock and studied the stress–strain state under different loading conditions, with varying cushions. They found that the highest stresses consistently occurred in

the tissues near the bone. Linear material properties were used, which were the same for all soft tissues (skin, fat and muscle). The contact properties were modelled by applying a modified cosine pressure distribution at the interface. Their most important conclusion was “the distortion of tissues is often more severe at internal locations than on the surface of the buttocks”. A three-dimensional computer model of the human buttocks was derived by Todd and Thacker [21]. They used MRI-images of a supine male and female person of a transverse cross-section of the human pelvis and transformed that into a three-dimensional finite element model. The transformation from supine to a seated position was achieved by adjusting the material properties of the soft tissues. The same linear, isotropic model was used for all soft tissues. Because the authors did not have contact elements at their disposal, they used common nodes between elements representing buttocks and cushion. They come to a comparable conclusion as Chow and Odell [18]. Internal stresses are high, especially near the bone. Moreover, they found very little correlation between interface pressure and internal stress. Contact elements, allowing a more detailed analyses of the interface between buttock and cushion were used by Dabnichki et al. [20]. They used both friction and frictionfree conditions. Furthermore, they used a rubber-like constitutive law for the overall behaviour of the soft tissues. The same properties were used for skin, fat and muscle. Again they found maximum compressive stresses near the bone. High shear stresses were found adjacent to the bone, midway between bone and seat and at the interface when friction is modelled. Previous authors commonly employed the same material properties for the different soft tissue layers, although all accepted that different properties of the layers is important. Their reasoning for this is obvious, due to the limited availability of appropriate mechanical data. Indeed only one previous author [20] employed non-linear properties. The objective of the present paper is to study the effect of different layers with non-linear material properties on the stress – strain state of the tissues. It employed the method of parameter variation, which can provide a relative indication of the influence of material properties of different layers on the stress – strain state in the tissue. Different models are used for the three materials which constitute the soft tissue composite overlying the bony prominences. In addition, the effects of varying the mechanical properties and the thickness of the fat layer, the friction coefficient between the cushion and the buttock and the cushion properties were examined in relation to different conditions at the interface. MODEL DEFINITION Geometry and Boundary Conditions A numerical model was developed using the finite element code MARC (MARC Analysis Research Corporation).

STRAIN DISTRIBUTIONS IN MUSCLE

The geometry of a buttock, similar to previous models [18,20], incorporates the ischial tuberosity, which is considered to be a rigid material, covered by muscle, subcutaneous fat and a skin layer. The former study showed that a critical point for pressure sore development is at the ischial tuberosities and that axisymmetric analyses can very well be defended. Thus the chosen geometry is a hemisphere with a rigid core. It should be noted that thigh contact is not incorporated in the model. Figure 1 shows the model with mesh dimensions. The thickness of the tissue layers have been estimated from MRI-data [22]. The skin, fat and muscle layers and the cushion are modelled with 4-node, iso-parametric quadrilateral elements. For all elements a full integration scheme is used and a Hermann-formulation is applied [23] to prevent locking due to incompressibility of the material. The origin of the coordinate-system is chosen at the symmetry-line at the point where cushion and buttock make first contact (point O in Fig. 1). At z ¼ 115 all displacements in z-direction are constrained, whereas on the symmetry line all displacements in the radial direction are constrained. At the boundary

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between bone and muscle all displacements in z-and r-direction are suppressed. All nodes at line PQ are coupled with tyings to assure equivalent displacements of these nodes in z-direction. In this way the buttock is fixed in space and the cushion will be pressed against the buttock. The force is applied as a point load in the z-direction at point Q. A spring of very low stiffness at point P is used to prevent free body movements of the cushion when there is no contact. After contact between buttock and cushion, the influence of the spring on the total contact force of the configuration is negligible. A sliding contact with a Coulomb friction model is used between buttock and cushion. In the reference model the friction coefficient was chosen to be zero, implying frictionless sliding. Subsequent analyses examined finite levels of the friction coefficient. The percentage of body weight carried by the ischial tuberosities reported in literature varies considerably between 18 and 77% [18,24,25]. The present study assumes an average of 50% body weight, leading to a load of 200 N on one ischial tuberosity for a typical male person weighing 80 kg. The load is applied in 30 equal time increments.

FIGURE 1 Original mesh of the reference model, with a definition of the material layers. The dimensions are in mm.

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Material Models It is assumed that as pressure sores develop after prolonged loading, equilibrium data are sufficient. Thus for skin, muscle and fat an elastic Ogden model is employed. The model is based on the following strain energy function W: W¼

N X mn an l1 þ la2 n þ la3 n 2 3 ; an n¼1

Material

m (MPa)

a (2)

Muscle Skin Fat Cushion

0.003 0.008 0.01 0.016

30 10 5 10

ð1Þ

with li representing extension ratios in the principle strain directions, and mn and an material parameters. Only first order models are used, i.e. N ¼ 1: The model has to account for large deformations and rotations. That is why a frame indifferent material law was used. In the finite element code MARC this is achieved by relating the second-PiolaKirchhoff stress S to the Green Lagrange strain E. These stress and strain are invariant, because they are material quantities, attached to the reference configuration. The second-Piola – Kirchhoff stress S is related to the Cauchy stress s by: S ¼ detðFÞF 21 ·s·F 2T ;

ð2Þ

where F is the deformation tensor. The Green –Lagrange strain E is defined as: 1 E ¼ ðF T ·F 2 IÞ; ð3Þ 2 where I is the unit tensor. In MARC the following elastic implementation of the Ogden model is used: S¼

TABLE I Material parameters for biological tissues and cushion used in reference model. Constitutive model is Ogden elastic

›W ›E

ð4Þ

There is a paucity of material data for human tissues. Thus material parameters have been selected based on animal studies, assuming that the parameters for these tissues are at least within an order of magnitude of human tissues. For skeletal muscle the authors have used data from in-vivo experiments on the transverse properties of skeletal muscle of rats [26]. The properties for skin have been obtained from experiments on pig skin by Oomens et al. [27]. No reliable data for the properties of fat were available and, therefore, a parameter study was performed. For the reference model m ¼ 0:01 MPa and a ¼ 5 are

chosen. The selected material parameters for each soft tissue layer and the cushion properties in the reference model are given in Table I. Several parameter variations were performed with respect to the reference model. The selected combinations for the modulus m and the parameter a for the fat are provided in Table II. In addition, this table indicates the variations of thickness values for the fat and muscle layers. Both skin and total thickness of the soft tissue composite remained constant. In addition, Coulomb friction in the sliding contact interface between cushion and buttock was superimposed on the reference model up to a maximum value of 1. The cushion properties were selected based on a previous study [28]. In this paper several materials, which are commonly used in cushions for wheelchairs were characterized. In the present analysis three of these cushions were selected. Two single layer cushions (1 and 2), each of 38 mm thickness, representing high density and firm foam, respectively. Cushion 3 was composed of a 38 mm soft foam layer overlying a 38 mm firm foam layer. All cushion materials are modelled with an elastic Ogden model, with parameters indicated in Table III.

Data Analysis The form of mechanical damage and hence the definition of mechanical parameters, which is best related to tissue damage still remains uncertain. However, there is evidence from both human observations and experiments on cell model systems that cells are very sensitive to deformation but relatively resistant to high hydrostatic pressure [7]. The von Mises stress is related to the deformational energy stored in the material, and is a derived property from the constitutive equations.

TABLE II Variations of the material and geometric parameters m and a of the fat Name Reference Moduli 0.006 Moduli 0.014 Moduli 0.032 Exponent 10 Exponent 20 Exponent 30 Fat 6 Fat 14 Fat 21

m (MPa)

a (2)

Thickness of fat (mm)

Thickness of muscle (mm)

0.02 0.006 0.014 0.032 0.02 0.02 0.02 0.02 0.02 0.02

5 5 5 5 10 20 30 5 5 5

10 10 10 10 10 10 10 6 14 21

18 18 18 18 18 18 18 22 14 7

STRAIN DISTRIBUTIONS IN MUSCLE TABLE III Material parameters for the different cushion materials. The data are chosen in such a way that they fit the experiments from Ref. [28] Material Ogden 1/reference Ogden 2 Ogden 3

m (MPa)

a (2)

0.016 0.001 0.001

10 10 7

The maximum shear strain in the material is also a good measure of the deformation and has the advantage that it can be measured directly, i.e. by means of MRI, in the case of biological materials [29,30]. Thus areas have been examined with the highest shear strains, either represented by peak von Mises stress and/or maximum differences between the principal strains.

RESULTS In the reference model the tissue layer underneath the bony prominence is reduced in thickness by approximately 25% (Fig. 2a) These relatively large deformations have been observed in human tissues, using MRI studies [22].

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The model results for the normal stress between buttock and cushion (Fig. 2b) can be compared to measured data on interface pressures. It was found that the normal stress is highest near the line of symmetry, i.e. underneath the ischial tuberosity, reaching a value of 2 120 kPa. This magnitude is within the range of interface pressures commonly measured for people sitting on hard surfaces [25,31,32]. The stress reduces to zero at the point where buttock and cushion no longer make contact, i.e. at 46 mm along the arc length from origin O. It appears there are two linear zones. One zone from the arc length from 5 to 25 mm, the second zone from 25 to 46 mm. It is interesting to note how this external load, equivalent to the interface pressure distribution, is transferred to the tissues. From Fig. 2a it can be observed that the stress distribution inside the tissues are higher than the interface stress. With the geometry and material properties defined in the reference model, three local maxima of the von-Mises stress were found. At point A the von-Mises stress is 170 kPa. At points B and C the equivalent von-Mises stresses are 150 and 180 kPa, respectively. Hence for the reference model the highest stress is found in the muscle layer.

FIGURE 2 (a) Equivalent von Mises stress in the reference model. (b) Interface stresses along the buttock in the reference model. (c) Maximum shear along line ORST starting at O.

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FIGURE 3 Maximum shear strain along ORST starting at O for the reference model with variations in (a) fat moduli and (b) fat exponents.

Figure 2c shows the maximal shear strains as a function of the arc length along ORST. At point A the maximal shear strain has a peak value of 0.3 and at point C a smaller peak occurs which reaches a value of 0.15. The peak in the von Mises stress at point B does not result in a visible peak in the maximal shear strains. In the sequel focus is made on the maximum shear strains following the arc ORST (see Fig. 1). Figure 3a shows the maximal shear strain along the symmetry-line ORST for models with different moduli for fat. Variation of the modulus from 0.006 to 0.032 MPa results in a large change of the maximal shear strain in the fat layer, particularly between point O and R, where there is a 60% increase compared to the reference model. It can be seen that with a decrease in the modulus of the fat there is an associated increase in the maximal shear strain. By contrast, differences in moduli for the fat do not result in changes in maximum shear strain in the muscle near the bone, i.e. between S and T. This is an important observation also found in other parameter variations. Figure 3b shows the maximum shear strain along symmetry-line ORST for models with a changed exponent of fat. The lowest value of the exponent was the same as the reference model. Higher values of the exponent means that the initial stiffness of the fat stays the same as in the reference model, but the stiffness at a certain strain increases faster with higher exponents. It is clear that there are large changes in the maximum shear strain in the fat, i.e. between points O and R, whereas there is minimal associated change in the muscle near the bone. Figure 4 shows the maximal shear strain as a function of the arc length along ORST for the different geometries. There is a shift in the location of the peak value to a larger arc length for thicker layers of fat. The highest value of the maximal shear strain in the muscle is not related to the thickness of the fat layer. Figure 5a shows that the stresses are much lower when friction is added to the sliding interface, compared to the frictionless condition (Fig. 2a).

Figure 5a and b show that adding friction to the sliding contact between cushion and buttock results in lower maximum shear strains. Nonetheless, the peaks at point A and C still exist. It is important to see that a friction coefficient of 0.5 produces a similar result to a value 1. Indeed the shear strain for a friction coefficient of 0.1 lies closer to the result of a friction coefficient of 1 than to the frictionless condition. The differences are again observed in the fat layer, but not in the muscle. In addition, the presence of friction at the sliding contact reduces both the von Mises stress and the absolute normal stress (data not shown). The effects of varying the cushion properties are shown in Fig. 6a –c. It is evident that there is a significant decrease in the amplitude of maximum shear strains along the arc ORST (Fig. 6c) in the region between 5 and 20 mm from the starting point O. This is in the fat. In particular, the shear strain at point A decreases most compared to the reference model (Ogden 1). The maximal shear strains in case of the soft foam cushion (Ogden 3) are almost constant from O to R. The absolute normal stress, as presented in Fig. 6b, indicates areas where the cushion supports the buttock increases when the cushion is softer. This produces an associated reduction in the normal stresses at the interface to maximum values of between 40 and 60 kPa.

DISCUSSION The present paper presents a parameter study with a model of a cushion supported buttock. The layered geometry around the ischial tuberosity and the different material models for the skin, fat and muscle lead to a complicated stress – strain state within the tissues, with two areas consistently yielding the highest shear strains (Fig. 2a). One local maximum, point A, is found in the fat layer, just underneath the bone at the symmetry line of the model. The second maximum, point C, is found in the deeper


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FIGURE 4 Maximum shear strain along ORST starting at O for the reference model with variations in geometry.

muscle layer close to the bone. A remarkable result is, that parameter variations with properties of the fat have a considerable influence on the maximum shear strains in the fat, but not in the deeper muscle layer (Figs. 3 and 4). The same is true for changes in the cushion properties. The comparison between softer and harder cushions shows a large reduction in interface stress for the softer

cushion (Fig. 6b). This results in a lower shear strain in the fat, with only small changes in the deeper muscle layer. These results are consistent with the findings in earlier studies, where high stresses were consistently found adjacent to the bony prominence [18,20,21], however the very large influence of cushion properties on the fat-layer has not previously been reported.

FIGURE 5 (a) Equivalent von Mises stress [MPa] in model with friction cooefficient 1. (b) Maximum shear strain in model with different friction coefficients.

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FIGURE 6 (a) Deformed mesh with von Mises stress in the Ogden 3 model. (b) Absolute normal stress along buttock [MPa] starting at O for models with different cushion properties. (c) Maximum shear strain along ORST for models with different cushion properties.

There have been many reports in literature, which suggest that it is difficult to perform reproducible and accurate measurements of interface pressure [33]. The present simulation model questions their validity further, indicating that interface pressure alone do not reflect the internal stress – strain state existing in loaded soft biological materials. An inverse analysis, to determine an internal stress strain state from measured interface stresses is possible, but it requires a similar finite element model, known material properties and data of the internal geometry of the buttock area. This has been previously reported by other authors [20,21] and is again confirmed by this study. In the present model, material properties for muscle and skin were based on experimental data from different animal models. No reliable data were available for the fat layer, but it is clear that the stiffness must be very low [34] and the mechanical behaviour is closer to that of an incompressible fluid than to the behaviour of a solid. Although the model can be quite sensitive to changes in the different material parameters, the qualitative trends do not change much, even when the geometry is totally changed or friction is added to the sliding contact. However, this is an area which needs considerable further investigation to enable the accurate quantifiable collection of data on material behaviour. High strain peaks are consistently observed in the muscle near the bony prominences. So even although the model is not yet

validated sufficiently, we expect that the observations with respect to the peak strain in the muscle and the dramatic changes in the fat, resulting from changes in cushion properties, are valid. We also observed that large changes in the material properties of the fat did change the internal strain state dramatically, but not the interphase normal stress. Only when the cushion properties were varied the normal stress changed. One of the obvious improvements of the model must be the constitutive equation for the cushion. An incompressible Ogden model was used, while a compressible model would probably have been better. The Ogden model was chosen, because we were able to fit it fairly well on the cushion data by Ferguson-Pell et al. [28] and it led to stable solutions at high deformations. We encountered stability problems with the available compressible cushion models in the code. It can be expected that using a compressible model for the cushion will not change the conclusions on the strain peaks in the muscle near the bone very much. However, it will probably influence the observed strain distribution in the fat and the interphase normal stress. Another discussion issue relates to the actual static load applied to the model. The distribution of the load over the thighs and the buttocks depends on posture and individual body shape. Moreover, this distribution will change when people are sitting on soft or hard cushions and also


changes as a function of time. To study these effects a more complicated model study is necessary, using whole body models, and/or more experimental data on load distributions. Results can also change when more complex composite models are used for the cushion and by using models of compressible foam material. Although the highest shear strain values were located in the fat layers this does not mean that pressure sores will be initiated in the fat. Indeed there is some evidence that muscle is more sensitive than fat. To understand the aetiology of pressure sores it is extremely important to determine the mechanical properties of the different biological tissues in the composite and to find damage thresholds for skin, fat and muscle individually. How realistic is it to assume that mechanical models can play a role in the future, for the design of supporting surfaces? In our opinion, models can be used already. For the present paper MARC was used, which is a commercially available software code, although other codes with similar features to MARC are currently available. This means that any mechanical engineer well trained in non-linear continuum mechanics can perform such an analysis. The geometries of the buttock and the cushion were kept fairly simple for the present analysis, but it is not in principle a problem to make these more realistic to the clinical setting. The load distribution between buttock and thighs can be determined quite accurately with whole body models, which are also commercially available. The bottleneck still is to determine the material properties for skin, fat and muscle, but also in this area many interesting tools have been developed in the recent past. The development of numerical/experimental methods has been formed basis of a number of in-vivo techniques to determine material properties of biological tissues [35,36] and has been recently used to measure in-vivo transverse mechanical properties of skeletal muscle [26]. Validation of the models is possible using MRI and/or MRI-tagging techniques [29,30]. So the authors believe that time and effort needs to be invested on two fronts. On the one hand, fundamental research is required to establish damage threshold values for individual tissues and, on the other, numerical models need to be employed as design tools for supporting surfaces. The present study, with all its limitations, confirms that a more equal distribution of the interface pressure not automatically means that the internal deformation in the soft tissues is reduced enough to prevent pressure sores to occur.

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