Predictive prosthetic socket design: part 1-population-based evaluation of transtibial prosthetic sockets by FEA-driven surrogate modelling

Abstract

It has been proposed that finite element analysis can complement clinical decision making for the appropriate design and manufacture of prosthetic sockets for amputees. However, clinical translation has not been achieved, in part due to lengthy solver times and the complexity involved in model development. In this study, a parametric model was created, informed by variation in (i) population-driven residuum shape morphology, (ii) soft tissue compliance and (iii) prosthetic socket design. A Kriging surrogate model was fitted to the response of the analyses across the design space enabling prediction for new residual limb morphologies and socket designs. It was predicted that morphological variability and prosthetic socket design had a substantial effect on socket-limb interfacial pressure and shear conditions as well as sub-dermal soft tissue strains. These relationships were investigated with a higher resolution of anatomical, surgical and design variability than previously reported, with a reduction in computational expense of six orders of magnitude. This enabled real-time predictions (1.6 ms) with error vs the analytical solutions of < 4 kPa in pressure at residuum tip, and < 3% in soft tissue strain. As such, this framework represents a substantial step towards implementation of finite element analysis in the prosthetics clinic.

Keywords: Amputation; Finite element analysis; Principal component analysis; Statistical shape modelling.

Fig. 1

Flowchart of the developed workflow. a Segmentation of the MRI scan and creation of the FE mesh, b SSM from PCA of 30 surface scans, c parametric model of TSB socket design, showing the three design variables used to control the press fit at the proximal, mid and distal regions, d Latin hypercube sampling plan of the seven input variables to the parametric model, e application of model boundary conditions including the socket donning and loading, f solution of the FE models as training data, highlighting the regions of interest across the limb, g creation of the surrogate model based on the FE simulations. Dots denote the training data, and the surface shows the fitted function

Fig. 2

Results of the SSM. a Effect of varying the weights of PCs 1 and 2 by ± 1 σ with respect to the mean shape in the coronal plane, with the medial and lateral aspects labelled M & L, and the sagittal plane, with anterior and posterior aspects labelled A & P. b Effect of varying the baseline mesh from the MRI scan with the first two PCs, while fixing the remaining PCs

Fig. 3

Procedure used for morphing the baseline FE mesh (a), through modifying the bone length (b), then morphing the external shape of the limb to match the SSM (c) and finally morphing the external liner (d). The result of morphing the FE mesh to morphological parameters of the model informed by residuum length, v₁, residuum profile, v₂ and tibia length, v₃. Soft tissue is displayed as red, bone as grey and the liner as blue. The mesh has been visualised using a planar cut that goes through the elements

Fig. 4

Regression analysis of the surrogate models with different numbers of training data points. In each plot, the x-axis gives 75 observed data points from the simulations and the y-axis gives the predictions from the surrogate model for the corresponding observed data points

Fig. 5

Interface pressure, shear and soft tissue strain at key ROIs of the model for fixed values of tissue modulus and tibia length ($v_4=45\text{kPa},v_5=+7.5\%)$, and a uniform + 1% press fit socket ($v_5=v_6=v_7=+1.0$). The x-axis for each plot corresponds to residuum length, $v_1$, and the y-axis to residuum profile, $v_2$

Fig. 6

Distal soft tissue strain for different values of tibia length, $v_3$, and soft tissue modulus,$v_4$, for a + 1% press fit socket ($v_5=v_6=v_7=+1.0$). The x-axis for each plot corresponds to residuum length, $v_1$, and the y-axis to residuum profile, $v_2$

Fig. 7

Effects of prosthetic socket design on the biomechanical response of the limb in each of the ROI. The x-axis of each represents the proximal press fit, $v_5$ in %, and the y-axis the distal press fit, $v_7$ in %. The mid press fit is the average of the proximal and distal press fit, $v_6=0.5\left(v_5+v_7\right)$

Fig. 8

Interface pressure profiles for the four cases from the population with four different socket designs. Each press fit socket is designed so $v_5=v_6=v_7$. Four magnitudes of press fit corresponding to − 1, 1, 3 and 5% were selected. A ${45}^{\circ }$ anterior-lateral view is presented, to visualise the pressure at the tibial tuberosity and fibula head