A Theoretical Analysis of Damage Evolution in Skeletal Muscle Tissue With Reference to Pressure Ulcer Development

Contributed by the Bioengineering Division for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received by the Bioengineering Division April 14, 2003; revision received July 16, 2003. Associate Editor: C. Dong. Soft tissues are sensitive to prolonged compressive loading, eventually leading to tissue necrosis in the form of pressure ulcers 1. Pressure ulcers can occur in situations where people are subjected to sustained mechanical loads, such as when bedridden, sitting in a wheelchair or from wearing prostheses. Pressure ulcers severely affect the patient’s quality of life, since the ulcers are painful, difficult to heal and often prolong hospitalization periods. Despite considerable attempts to prevent pressure ulcers, prevalence figures remain unacceptably high. In a prevalence study involving more than 16,000 patients in the Netherlands, a mean prevalence of 23.1% in health care institutions was reported 6. Pressure ulcers are often classified in four different stages, ranging from discoloration of intact skin (Stage I) to full thickness skin loss involving tissue damage that extends to underlying bone involving both fat and muscle tissues (Stage IV). Although this classification is widely used in clinical practice, it does not necessarily relate to the origin of the ulcers. Depending on the nature of loading, pressure ulcers can either initiate superficially at the skin 1533, or initiate in deeper layers such as muscle tissue 14182028. The present study focuses on deep pressure ulcers that initiate in muscle tissue, since deeper ulcers are more harmful and show more extensive ulceration. In addition, muscle tissue is more susceptible to the development of pressure ulcers 223 and, hence, deep ulcers develop at a faster rate than superficial ulcers, making them particularly dangerous 214. Yet, these deep ulcers are difficult to prevent and identify, since they are rarely visible at the skin surface at the time of initiation. As such, the four stage classification scheme can be misleading, since it does not represent an ordinal scale. In literature, a number of theories have been proposed to explain the pathophysiology of pressure ulcers. These theories suggest that compression of a tissue can lead to localized ischaemia, impaired interstitial fluid flow and/or insufficient lymphatic drainage. Furthermore, relieving the tissue after sustained compression may lead to reperfusion injury. Recently, it was demonstrated that the deformation of cells due to external loading of the tissue can directly induce cell damage 8. The primary cause of deep pressure ulcers is the external load applied at the patient support interface, resulting in compression of the tissue between the skin surface and the bony prominences. However, the externally applied load is not indicative of the local mechanical conditions in underlying muscle tissue (for example expressed in terms of stresses and strains), and thus not directly related to tissue damage 122430. In particular, when a tissue is compressed against an irregularly shaped bony prominence, the local mechanical condition within the muscle tissue may well exceed the measured loading condition at the skin interface. Therefore, the local mechanical loading condition could prove a more reliable predictor for the onset of tissue damage in these deeper tissue layers. When considering the local mechanical tissue condition, it should be noticed that an averaged mechanical condition associated with a small volume within the tissue, is not representative of the mechanical condition experienced at the cellular level. This is due to the heterogeneity of the microstructure 101731. Since tissue damage initiates with local cellular damage 7112023, it is necessary to consider this microstructure. In addition, the microstructural behavior must be considered since it inevitably determines the macroscopic constitutive behavior of the tissue. For example, when cell damage occurs, the microstructure is likely to change, which will be reflected in the macroscopic behavior of the tissue. In this case, it is not possible to describe the macroscopic behavior with a conventional constitutive law 1021. Since local mechanical conditions are difficult to measure experimentally, theoretical and numerical models have been developed, which relate externally applied pressures to the local mechanical condition within a tissue. In a theoretical model based on dimensional analyses, Sacks 27 derived a relationship between tolerable external pressure and duration of pressure. The rationale behind this analysis was that there is a definable pressure that causes a pressure ulcer, which is a function of both tissue properties and the blood flow through the tissue. The model did not take into account the local geometry of, for example, a bony prominence, leading to load distributions in the tissues. Zhang and coworkers 33 performed a theoretical analysis on the stress distribution within the tissue after application of shear and normal forces at the skin. To allow calculation of an analytical solution, both skin and muscle tissue were assumed to behave as linear, isotropic elastic materials. This model demonstrated that the highest stress concentrations were found within deeper layers of the soft tissue. To analyze more complex geometries and material behavior, the use of computer models, in particular the finite-element (FE) approach, is indispensable. Chow and Odell 12 and Todd and Tacker 30 developed finite element models of the human buttocks. In the model of Todd and Tacker 30, seated positions were simulated, thereby manipulating boundary conditions of the model. The authors concluded that there is no clear correlation between interface pressure and the local mechanical conditions. Oomens and coworkers 24 created a FE model of a human subject sitting on a cushion, which incorporated three different tissue layers overlaying the human ischial tuberositas, muscle, fat and skin. These soft tissues were modeled as nonlinear viscoelastic materials. Despite the uncertainties in material properties, the high peak stresses were consistently found near the bone prominences and in the fat layer. Furthermore, models based on mixture theory have been proposed to examine the transient biomechanical response of a skin layer as a result of tissue fluid flow within the tissue 2233. The numerical models described in literature focus on determination of local mechanical conditions in skin and underlying tissues in terms of homogenized tissue stresses and strains 122225303233. However, from the previous discussion it is clear that a microstructural analysis is required to determine the mechanical conditions that a cell experiences. Moreover, knowledge of the local mechanical condition alone is not sufficient to predict tissue damage initiation and evolution. Also the loading history of the tissue is essential, since the time that a tissue is subjected to a sustained compression is a major determinant of tissue damage 26. A second aspect that, to date, has received relatively little attention, is the tissue tolerance against compression. Different tissues, such as skin, fat and muscle, may have a different tolerance level, which in turn may be patient dependent. The objective of the present study is to illustrate that prediction of pressure ulcer initiation on the basis of external load measurements is inadequate. By considering local load-time threshold curves, it is illustrated which variables quantitatively influence the threshold curves and, therefore, should be considered for the prediction of damage initiation. To this end, a numerical model was developed, which is based on a multilevel FE approach. This model can relate external loads applied to the skin, to the local mechanical conditions at the cell level. With this model, simulations were performed in which muscle tissue is compressed against a bony prominence. As a starting point, the model focuses on the role of cell deformations on cell damage. The model incorporates both the time aspect and a tissue tolerance level for damage in the form of a damage law that was derived from in vitro experiments 9. A parameter study was performed to illustrate the effect of the cell tolerance and cell stiffness on the macroscopic tissue damage evolution. In the following section, the multilevel finite-element (FE) approach 102129 is briefly reviewed. In the multilevel FE approach, a macroscopic FE model is created by discretizing the macroscopic tissue into a finite element mesh. The microstructure at a particular point of the macroscopic tissue is given by a representative volume element (RVE). Microstructural FE models, that represent the RVEs, are assigned to each integration point of the macroscopic elements. The coupling between macroscopical and microstructural FE models is based on two principles: local periodicity and stress/strain averaging. Local periodicity is a concept that is based on the assumption that the length scale of the microstructure is orders of magnitude smaller than the length scale of the macroscopic tissue. As a consequence, the deformation field in the vicinity of the microstructure will be approximately the same as the deformation field in neighboring microstructures 21. This implies that the microstructure can be thought of as surrounded by copies of itself. Stress and strain averaging means that macroscopic stresses and strains equal the averaged microstructural stresses and strains. On the basis of strain averaging and local periodicity, boundary conditions for the microstructural FE model can be derived from the macroscopic deformation field 10. Using these boundary conditions, the microstructural FE model is solved. After convergence of the microstructural FE models, these models supply the macroscopic stresses and effective stiffnesses, which are derived using a computational homogenization procedure. For computations involving a large macroscopic mesh, multiple load/time increments and complex RVEs, computational times can become unacceptably high. Fortunately, the multilevel approach is ideally suitable for parallel computing facilities, since each RVE calculation runs independently from other RVE calculations without data exchange between different RVEs. Only a limited amount of data transfer is required between the macroscopic FE simulation and the RVEs. Thus, running multiple RVE simulations parallel in time, would computational Therefore, the multilevel was into that can Furthermore, the FE was with which a of that data between different The present simulations were on a of The compression of muscle tissue against a bony was by using a macroscopic as in The model a muscle layer on a which is compressed against a bony prominence. The bone is assumed to be and, therefore, not modeled as a The macroscopic of strain each with integration To a geometry with of the different geometries by Chow and Odell 12 were with a bone of and a muscle thickness of The skin and fat layer were modeled as a layer with an of The muscle layer was compressed by a pressure applied at the skin surface in the in were at in were the interface of the muscle layer with the bony prominence, in both and were The microstructural FE models were assigned to the macroscopic integration of the associated with the muscle layer. This in microstructural FE For the microstructural model, a of the of muscle tissue was used were due to the present microstructural model is to the of the model. The microstructural finite element a of muscle in an material The same microstructural was assigned to the macroscopic integration of the muscle layer. cells and were modeled with elements. The material behavior of both cells and was modeled with a nonlinear constitutive law is the compression and the shear This constitutive law a relationship between the stress and the as with the deformation The different material properties of the cells and are reflected by different for the compression and shear The skin layer was described as a of the material behavior from the underlying as was for the muscle layer. For the microstructural FE models, material for the were from of and for and These were from on For the muscle the and were derived from measured by the stiffness of muscle using For the skin material were from with and of the damage law is based on the following 1. deformation is as the for cell damage. deformation is by computing the strain averaged a For the constitutive model the strain is given and the and of the To a the is by the stiffness of the This will be with The relationship between damage and deformation is based on in vitro experiments in which muscle tissue were compressed the of cells 9. The of these experiments are in which that a compressive strain of to a of cells when to a compression. Furthermore, at damage initiation in time and more did not show an in cell damage. The threshold for an that when the effect of deformation and time causes cell damage will be with is assumed that cells will not be at when cell deformations remain a level. is well that cells are of to However, when the cell deformations exceed the of the damage will The of the cell can be as a tolerance level, which will be with a parameter In the present model, no cell is incorporated in the damage For the present model does not microstructural by deformations and cell damage. The previous are in a damage law by a damage parameter for each cell in the microstructure. will with time when the cell deformation in terms of than the cell tolerance does not the damage parameter the threshold the cell will become in form this the present time and it can be that the damage initiation time for a cell is to For a given the between damage initiation time and is in for three different of should be that in lead to a of these To the amount of tissue the following is After convergence of a time the cell deformations in each microstructure are from the microstructural finite element The of averaged a are in to a of it is a particular cell to the in For each microstructure the cell damage is by the number of cells and this with the cell number in the microstructure. This microstructural cell damage is assigned to the associated macroscopic point to a tissue damage level. In this the tissue damage will be as the of microstructural cell from the underlying microstructure. the damage in a microstructural RVE compression was with the damage curves from the in vitro a of the macroscopic tissue damage is Furthermore, the influence of in the material properties of the microstructural and the damage law and will be in damage and the microstructural properties in patient related For example, the microstructural properties are related to the of a since is associated with a in material properties of the tissue. The and the tolerance level of the which for example, be related to the of a As such, and are associated with for pressure ulcer the behavior of which are at different positions in the macroscopic model, will be for different external In the a load was The damage in time is in This is when the microstructural material behavior is not time and when cell damage does not affect the behavior of the as was assumed in the present In other a full of each time is As a starting point, the and were for the damage Although no on the data was this implies that the microstructural time scale of damage in an RVE to the time scale as was found in the in vitro experiments can be that of these in and implies that in a shear the tolerable shear is approximately and that a shear strain of to cell damage after an pressure of was applied to the macroscopic mesh. The damage law was by considering a microstructure that was subjected to an compressive strain of and This was by directly boundary conditions to a microstructural FE model as in The of cells in this microstructure was for using time For each time the damage in the microstructure was by application of the damage that a compressive strain to a and in for a compressive damage was and the in damage was more Thus, damage was in form to that in the in vitro experiments In the macroscopic damage sustained compression of a muscle tissue layer is The represent the macroscopic and show the tissue damage for increments of damage initiates at the bony due to large macroscopic deformations in this as by the did not from this since the high peak deformations are limited to a small and damage was at two these damage extends the skin layer. As be the model that damage from deep within the muscle tissue where shear strains in the tissue are To illustrate the influence of microstructural material properties, a simulation in which the cells were to be than the were with of and for and that damage from the same macroscopic as to However, the cell stiffness in a effective macroscopic stiffness which in macroscopic tissue deformations and, hence, cell deformations in the microstructure. This in an of tissue damage and a faster damage parameter to an tolerance of the The effect of parameter is a a the deformation that can be without effect on the to an cell a for implies that in at a rate and that the cells within a microstructure more with To illustrate the effect of on macroscopic damage a simulation was in which was from to that has to a smaller as to 6. Furthermore, damage is and is after parameter will the since the damage initiation time is to parameter For example, by will show damage at the loading to the heterogeneity of the each cell will a different This implies that the deformation of cells will remain the cell tolerance other a are and will become in To study the effect of the microstructural heterogeneity on the damage in the four simulations were in which the macroscopic tissue was with and The of these simulations are in the of cells in four microstructures and which are at different in the macroscopic mesh. The of the represent the time and the the external pressure The represent the cells in the in the the tissue, positions the no damage. microstructure an external pressure of cells between approximately and the external pressure to a damage initiation and a in damage initiation time, as by the for the For example at a pressure of damage at and in damage of a which that at this load level, the cell deformation of cells the cell tolerance level is at a macroscopic that smaller deformations than microstructure Therefore, an external pressure of will lead to damage at Furthermore, an external pressure did not cause damage at is in a near the bony prominence. the microstructure in this experienced a large deformation which to a initiation of cell damage. at a pressure of cells were eventually in this particular microstructure. microstructure experienced an such that a pressure of of the is from these that for the and heterogeneity to a and distribution in the initiation of cell damage. This is particularly at small the external pressure to a damage initiation and a more damage The biomechanical cause of pressure ulcers has to the development of numerical models, a from external loads applied to the skin to the local mechanical condition within skin and underlying tissues. a relationship is since the local mechanical condition is more directly related to the onset of tissue damage than the externally applied In previous it was that the local mechanical condition is by the external load geometry and material properties of the tissue Furthermore, the boundary conditions in a model severely affect the and magnitude of the tissue The of the present simulations show that, in addition, in the tolerance of a tissue and the local microstructural properties have a on the time at which tissue damage was The of these for the of pressure ulcers may be by considering the in related to the damage threshold as by and 26. This an relationship between external load magnitude and time required for pressure ulcer development in in a local damage that is derived on the basis of a microstructural analysis in a particular macroscopic of the tissue. that the of a damage threshold on a number of it should be that each macroscopic point in the tissue threshold Thus, the and in the on the local mechanical condition within a tissue, as was demonstrated in 8. the of the tissue microstructure the mechanical condition that cells and thus the and of the the tolerance of the tissue, in the present model expressed in terms of a cell tolerance and threshold the and of the local threshold the microstructural heterogeneity a on the threshold the in the that cell damage in the microstructure. by the that tissue damage is at a of the microstructural heterogeneity may have a on tissue damage. In of these it is not that a considerable in external load threshold was found in in which the external pressure applied to the skin was related to tissue damage. in a where from the same and were the in the and of damage was large considering the externally applied load as determinant for tissue damage is inadequate. However, it is insufficient to relate the local mechanical condition to tissue since the tissue tolerance and microstructural properties an In the present a of the local microstructure of muscle tissue was used for This of cells in material However, the local cell deformations compression of the tissue on the local of the microstructure. the use of a more microstructural FE model, cells in little as in muscle tissue, would lead to different cell This influence of the local microstructural was in a previous which cell deformations for two different microstructural the microstructural used in the present study and a cell 10. This study that cell deformations in the microstructure were in with the cell deformations in a microstructure. Since the present model the onset of damage to cell damage initiation on the local microstructural For example, for a microstructural mesh, the of the in would become smaller and damage initiation would be or for small external load These stress the of not the material of the different microstructural the local When a particular cell in the microstructure is the material properties of that cell will This implies that the of the cell the which has for the mechanical condition experienced by neighboring cells in the microstructure. A simulation in which the shear of the cells was by a that the load on neighboring cells was due this in local microstructural properties not This in a of the cells in the since the of of the cells the cell Since the stiffness of the microstructure the macroscopic tissue deformations will be which in turn has for microstructures associated with other macroscopic In present the model does not take into account tissue damage was However, a small of cells in the microstructure to tissue since cell damage is a in the of a tissue. When the heterogeneity of the microstructure to a large in the of damage knowledge of the damage that to damage will become since it determines the of a damage within the of the as in 9. The present simulations did not to at a in tissue damage evolution. a number of were in this which of the was that cell deformation is the cause of cell damage. Although the present simulations were to a mechanical the are in with of These the that damage often initiates near bony and as the in time of damage initiation and of damage. Furthermore, of compressed muscle tissue has that cell damage in localized as by of and cells This may be to the in the local mechanical condition, experienced by as was demonstrated by the present model. and other an role in the onset of cell damage and to be performed to the of the possible causes in pressure ulcer by these the microstructural model may to be In this simulations with microstructural models, which are not in a full multilevel FE analyses, may be to study damage at the cellular level. of the present model will be more microstructural and macroscopic conditions of the macroscopic model to be and more microstructural properties to be In addition, microstructural models may be assigned to the skin the local microstructural of the skin. Different material properties and cell tolerance can be assigned to this layer to study the behavior of the muscle and skin layer. With to the damage no on material properties and damage law was should be noticed that the cells in the in vitro model to primary stage and have a different than 9. In addition, the of the in vitro model has different material properties which may affect the response of cells to deformation in with the This to be considered in the determination of for the damage Furthermore, the present damage law does not When is in the damage it would be to simulations in which the external load is after time, to study this can prevent tissue damage. determination of an for loading is for the of pressure ulcers. the of the present model, on patient related simulations are a from in vitro that were used as a basis for the present the development of of within deeper tissues, should of these numerical models within The model by the should lead to the application in more involving patient data on geometry and tissue numerical model simulations may be used to for from the present it can be concluded that it is not to relate external loads to local tissue damage and that a for a numerical model is to the local and the local tissue