Bedsores are a major problem for people who are physically handicapped and forced to stay lying down or in a reclining position permanently. The practice of dermatology shows that ulceration begins in the deeper tissues and spreads from
there outwards to the surface of the skin (Krutul 2004). At the same time, cracking of the skin and necrosis of adipose tissue is observed. The finite elements method is an excellent tool to simulate the phenomena in the scope of physical engineering, and with it, one can calculate and present anatomical processes that occur in the human body. Numerical modelling of the human body’s tissues or its individual organs consists in discretization, using any flat or spatial elements that are the basic unit of algorithm of the finite elements method. Individual elements are connected with each other in the nodes, forming a flat or spatial grid, where each unit has attributed mathematical formulas describing its stiffness and treatability, as well as specific biomechanical properties. In the final stage of constructing the numerical model, the conditions of support and load are assigned. Hence, various forms of strengths, movements, pressures and other factors, which are necessary to reproduce natural load conditions, are also assigned to the object.
The problem of modelling the phenomenon of bedsores using the finite elements method has been presented in the work of Todd and Thacker (1994). It discusses the effect of the distribution of stresses caused by vertical forces representing gravity loads. However, it is known that horizontal forces appear when the user moves or rotates on a bed or seat. The resultant of vertical and horizontal forces gives the actual use load of the human body in contact with the base. According to Akimoto et al. (2007), such a load is a major cause of the rapid development of bedsores in the deeper layers of tissue. These authors also demonstrated that the application of special pads can reduce the occurrence of horizontal forces and the value of pressures on the resting body.
In the work of Akimoto et al. (2007), results of numerical calculations were presented the effect of the stiffness of a thin cushion on the value of pressures on the human body in standard operational loads. As a comparison model, a system without a cushion was made. The first numerical model developed presented the human body as a cylinder of equal stiffness. Another model consisted of two types of material: soft tissue and hard tissue. Soft tissue corresponded to the layout of the skin, adipose tissue and muscle tissue. Hard tissue constituted the equivalent of a bone. The numerical model, to simplify calculations, contained only the bottom symmetrical half of the cylinder. In cross section, the cylinder consisted of two concentric circles, of which the outer one depicted the soft tissue and the inner one depicted the hard tissue. The cushion was modelled as a layer of elements adjacent to the outer peripheral of the cylinder. The outer diameter of the cylinder, representing the layer of soft tissue, was 200 mm, while the inner diameter of the cylinder was 100 mm. It was also assumed that there is a contact between the cushion and the cylinder.
The actual, biologically living tissue is a nonlinear, anisotropic and viscoelastic material. For calculations, however, the authors adopted that the linear, isotropic body independent of time will correspond to soft tissue. The value of Young’s module of soft tissue amounts to 15 kPa and Poisson’s ratio 0.49. For the cushion, the value of Young’s modulus was calculated using the T coefficient, which figure was defined as the quotient of Young’s modulus of cushion Ec to Young’s modulus of soft tissue of the user’s body Est,
T = -. (8.194)
During each calculation cycle, the value of Young’s modulus of cushion Ec was changed using the T coefficient equal to 1/1, 1/2, 1/4, 1/8 and 1/16. In clinical conditions, the patient usually does not take a permanent position but during treatments is moved or rotated. In order to represent this state of loads and movements, horizontal and vertical movements were added to the model, each with a value of 10 mm.
In the work of Akimoto et al. (2007), it was also assumed that the patient rests on a horizontal, hard bed, not intended for sleeping (Fig. 8.52). This bed has been reproduced as a horizontal line fixed across all nodes. It was also assumed that there will be contact between the bed and bottom edge of the cushion or bottom edge of the soft tissue layer. The coefficient of friction between the bodies has been established at level 1.
Two places have been specified, in which stress values have been marked reduced according to Misses: the contact border between the hard and soft tissue, and the middle of the layer of soft tissue. In the event of direct contact of the human body with a hard base, the stress value in contact with the hard and soft tissue amounted to 5.83 kPa, while inside the soft tissue it is 4.64 kPa. In systems in which the human body was supported by a flexible cushion, the stresses at the border of the hard and soft tissue and inside the soft tissue decreased along with the decreasing value of the linear flexibility modulus of the cushion.
Chow and Odell (1994) developed an axial symmetrical numerical model of the human buttock. The aim of their work was to determine the distribution of stresses in the soft tissues of the buttocks at various operational loads. The buttocks were modelled by a system consisting of a stiff core and a layer of soft tissue surrounding
Fig. 8.52 Dependencies of the stresses reduced according to Mises inside the soft tissue and on the border of contact of soft and hard tissues from the value of Young’s modulus of cushion (Akimoto et al. 2007)
it as a hemisphere with properties of a linear elastic and isotropic body. This model was also used by Honma and Takahashi (2001), however, using more precise calculation models. In this work, this same model has been improved by its conversion from an axial symmetrical system to an asymmetrical system, taking into consideration the calculations in axially asymmetrical loads. As a result of the studies carried out, it has been shown that the state of usable loads increases the value of stresses in soft tissues and contributes to the faster development of bedsores. It has also been demonstrated that the use of soft cushions as layers supporting the buttocks has a beneficial effect on reducing stresses, especially in the layers of soft tissue. The more flexible the base, the lower the value of stresses on the border of soft and hard tissues, as well as in the middle area of soft tissues.
Brosh and Arcan (2000) presented a methodology to develop a realistic numerical model, using the finite elements method, a mutual effect of the anthro – potechnic system human body-seat of the chair. The built model constitutes a corset of the chest and the lower part of the spine, surrounded by soft tissue. The properties of soft tissue were determined by the in situ method. The primary purpose of the work was to determine the behaviour of the soft tissues under load caused by a sitting position of the user. Energy deformations function:
W = (G/2)(h – 3), (8.195)
/1 the first variable factor of the deformations matrix, which has been described in the works of Chow and Odell (1994), Reddy et al. (1982) and Candadai and Reddi (1992)
The results of studies of numerical calculations were compared with the results of experimental measurements carried out in vivo in the system human-seat. Two approaches have been presented in the work to determine the shear modulus of soft tissues in a seated position of the user:
• the transformation of the modulus determined during contact to the modulus of figural deformations, and
• test of identification with treatability.
To determine the stresses between the body of the user and the horizontal rigid seat board, the method of displaying contact pressures was used (Contact Pressure Display) (Brosh and Arcan 1994, Arcan 1990). The centre of the load constituted a smooth, stiff sphere situated in the middle part of the soft tissue of the buttock. By loading the sphere, pressures of soft tissue on the seat were forced. The observed movements were measured using the LVDT system (Linear Variable Differential Transducer). By substituting subsequent values of loads and movements (P, S), a graph was obtained that showed the behaviour of soft tissue during compression. Hence, it was calculated Gi = 11.7 kPa and G2 = 33.8 kPa. Then Brosh and Arcan (2000) built the two-dimensional axially symmetrical numerical model of the human-seat system, made of the femur (E = 20 GPa, v = 0.3) and soft tissue, using the values of moduli Gt calculated above. The seat was defined as a flat board, with a thickness of 30 mm. For a hard seat, it was assumed E =10 GPa and v = 0.3, for a semi-rigid seat E = 20 MPa and v =0.2, while for a soft seat, E =3 MPa and v = 0.1. The calculations carried out gave convincing results that a change in the hardness of the seat from a hard to semi-stiff one and then to soft causes a reduction of contact stresses, respectively, by 54 % and 80 %.
Based on these studies, it has been demonstrated that soft tissues are a bimodular material. Tissues accepts low value of shear strains when the contact stresses are low. On this basis, one can look for new ways to an optimal design of anthropo – technic systems human-seat and to the ergonomic modelling of seats, by selecting better linings, cushions or materials reducing contact stresses between the user’s body and the seat.
A numerical analysis of pressures of the buttocks of a physically impaired person and sitting on a wheelchair was also presented by Linder-Ganz et al. (2005). In particular in these studies, the distribution of stresses was defined in the middle layers of soft tissue far from the surface of pressure. In the cited work, on the basis of MRJ studies (Nuclear Magnetic Resonance), a cross section of a woman’s hips was established (29 years old, weight 54 kg) in a seated position. Based on this data, a two-dimensional mesh model was build for numerical analysis using the finite elements method and silicon phantom buttocks were constructed. The phantom (Fig. 8.53) contained a model of bones, made of a rigid material of Young’s modulus 12 MPa, and the soft tissue surrounding the bone, which was modelled using silicone of Young’s modulus 1.6 MPa. In order to determine the
Fig. 8.53 Silicone buttock phantom (Linder-Ganz et al. 2005)
Fig. 8.54 Mesh model: a actual cross section through the buttocks of a woman made using MRJ, b numerical model that includes the gluteal muscles, smooth muscles, adipose tissue and bone (Linder-Ganz et al. 2005) internal pressure stresses, six ultra-thin pressure sensors were introduced to the model between IT (ischial tuberosities). Moreover, 14 sensors have been distributed on the seat surface in order to determine contact stresses. The silicone phantom was loaded with a weight from 50 to 90 kg. The measured stresses were compared with the results of numerical calculations.
The numerical model, necessary for calculations using the finite elements method, was developed on the basis of the analysis of the cross-sectional image of the buttocks, done using the MRJ method (Fig. 8.54). Individual materials in the numerical model were assigned the properties that a real silicone phantom had. Load, simulating the actual conditions of using an armchair for the disabled, was applied axially symmetrically, and also from the left and right side, bending the force vector by 15° to the left or right.
On the basis of the studies conducted, it was demonstrated that the value of stresses on the surface of the body is at the level of 0.4 to 63 kPa. A particularly high stress concentration is formed at the height of the ischiatic bone and amounts to 130 kPa. Inside the soft tissue—at contact of the ischiatic bone and soft tissue— compressive stress reaches a value of 160 to 200 kPa. The results of these studies enable to monitor in real time the actual pressure of stresses on the surface of the human body in a seated position. Furthermore, they enable more easily than before to plan exposure time of a paralysed person in a wheelchair.