Finite element analysis

Finite element analysis (FEA) as an alternative to experimental measurement of socket interface pressures had become a practical possibility by the late 1980s. FEA modelling relies on the creation of a model of the prosthesis/residuum system from mathematical elements with estimated interactions and material properties: by applying external loads to the system, the distribution of forces at particular points of interest can be estimated. The socket is often modelled as a rigid boundary (in comparison to the more pliant soft tissues), liners modelled as boundary elements as linear springs and so on. By modifying the

application of external loads and the precise construction of the system model, many behaviours and conditions can be evaluated.

The earliest work in transtibial amputees was published in 1987 (Childress and Schnur 1987; Steege et al. 1987a; Steege et al. 1987b). 3D models of residual limbs were produced based on CT scans in three participants, and a parametric study of effective stiffness of the tissue and liner components was undertaken. Results were validated against a strain gauge diaphragm transducer; however detailed results were not presented at this stage.

Quesada and Skinner (1991) described a model of a below knee prosthesis capable of assessing normal and shear stresses on the residuum during a simulated heelstrike loading condition. The authors noted that clinically relevant changes in limb loading could be obtained by modifying the construction of the prosthesis materials.

Contemporaneous research (Silver-Thorn et al. 1992; Steege et al. 1992) used a modified model to measure different applications of medial-lateral force, flexion-extension moment and loading modification via prosthesis alignment. This information was used in a proposal for a socket design procedure utilising the results of these studies as part of a CAD-CAM system.

In 1993 (Sanders and Daly 1993b) a model was presented of a single transtibial amputee, with residuum geometry produced by magnetic resonance imaging. The residuum was then modelled with different properties with skin and fat, muscle and the Pelite liner, with results of socket stresses were measured with reference to a strain gauge pressure measurement device. The authors recognised that the model was still simplistic when compared to real prostheses; in particular that tissue was modelled as homogenous and

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isotropic. Slip at the interface was also not included. The result was that the model was not accurate in representing the effects of applied loads.

The difficulty of modelling the slip effects at the skin/liner/socket interface was recognised in a study of non-linear transtibial prosthesis modelling published by Zhang et al. (1995). The sensitivity of the model to the value of friction selected was highlighted.

In a 1998 review of early work in FEA (Zhang et al. 1998) highlighted the difficulties experienced in the modelling of these techniques: in particular the large, non-linear deformations experienced by tissue, boundary non-linear properties (including friction/slip effects) and material non-linearity – viscoelasticity, time dependent properties, anisotropy and over-time changes in composition and properties. The difficulties of appropriate loading were also reported; particularly the variability of load magnitude and direction.

In 2000 (Zachariah and Sanders 2000), a suggestion that gap models be replaced by automated contact models was made, thus avoiding the issues of defining an arbitrary correspondence between the hard and soft surfaces, and more effectively describing slip between these interfaces. The authors felt that the results of this study were more reflective of prosthetics experience in this situation.

Friction and slip were implemented in a publication by Zhang and Roberts (2000), and compared against a set of experimental measures. Although the results were deemed good in terms of magnitude and direction of normal and shear stresses, the estimates were on average 11% lower than the experimentally measured values. The model was tested with a ‘standing’ load only.

The elements of a dynamic model incorporating the automated contact model was

described by Jia et al. (2004). The socket was tested using results obtained from an inverse- dynamics model of the residual limb, including both variable external loads and the effects of inertia. It was found that inertial effects were significant during swing phase, up to 20.1% of the average load.

Liner stiffness was investigated by Lin et al. (2004) in a study of a single unilateral transtibial amputee. The authors concluded that sliding of the stump within the socket was a crucial

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parameter of FEA model design. A moderate sensitivity to liner stiffness modelling was reported, however the effect was not easily predictable.

By the mid-2000s, FEA models were being used in investigations of other aspects of transtibial socket care. In 2005 Lee et al. (2005) examined regional differences in pain threshold using a variety of indenters and positions across the residuum. Pain threshold was variable across the limb and between participants. The FEA model successfully measured that the peak stresses at the skin were close to the pain threshold of the volunteers in the study. Peery et al. (2006) attempted to model residual limb temperature using FEA, with a good overall correlation to experimental measures.

Papers by Portnoy et al. (2007, 2008, 2009, 2010) investigated the development of real- time FEA models to predict tissue stresses. The boundary conditions were set by measurements taken from force sensors placed in-between the socket and the residual limb, and then supplied to an FEA model based on a simplified limb geometry obtained by X-ray imaging and indenter studies of tissue stiffness. Such an approach ameliorates one of the key difficulties experienced in FEA studies: the time required procuring clinically relevant results from a test session. However the residual limb model was oversimplified compared to contemporary models – work that the authors aimed to rectify with a more detailed study of residual limb anatomy via MRI.

In particular, the 2010 report (Portnoy et al. 2010) developed a handheld instrument that evaluated tissue stresses during a range of activities including stair, slope and uneven terrain. Modelling the effect of the tibia compressing the tissue at the stump end was able to identify meaningful changes in tissue loading during more complex tasks.

The complexity of generating a reasonable computer model of the residual limb was illustrated by Sengeh et al. (2016). Their methodology included (as part of the process of investigation) imaging, patient specific models, in-vivo indentation of tissue and inverse finite element optimisation of the key tissue parameters. Although the force predictions were considered reasonable (~7% difference), the difficulties of producing a useable model were clear.

In summary, the FEA modelling approach is in some ways an attractive method of providing patient specific load estimates. It can be adjusted for stumps and sockets of any dimension,

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and can provide results for within tissue loading which is not easily achievable in other ways. However, the complexity of this approach requires detailed measurement of the residuum and socket systems and a considered approach to the application of loading and boundary conditions. The process is further hindered by the large degree of inter-subject variance in terms of limb constitution and the challenges of altered device prescription and practical use. Some issues have not yet been investigated in detail: these include the differences present between imaging and actual use (Papaioannou et al. 2010), and

alteration of the stump condition over time. These issues have restricted the routine clinical use of such techniques. A recent systematic review into FEA and lower limb assessment was published in 2017 (Dickinson et al. 2017)