A study of plantar stresses underneath metatarsal heads in the human foot 5

5.1 Conclusion This study explored a sophisticated computational model of human foot using musculoskeletal FE modeling, to investigate forefoot plantar stresses underneath MTHs.. A 3-D h

CHAPTER 5 CONCLUSIONS

~ There is a wisdom of the head, and a wisdom of the heart~

Charles Dickens

5.1 Conclusion

This study explored a sophisticated computational model of human foot using musculoskeletal FE modeling, to investigate forefoot plantar stresses underneath MTHs A 3-D human foot FE model with detailed anatomy was constructed to study the foot mechanism of muscular control, internal joint movements, and plantar stress distributions in three-dimensions Mechanical responses of the foot’s soft tissue were specifically collected by using an instrumented tissue tester and the material hyperelasticity were determined for the plantar soft tissue under the MTHs Experimental validation was conducted by a novel gait platform system that is capable of measuring the vertical and shear force components acting at local MTHs during walking It was found that, with accurately quantified tissue property, muscular loading characteristics, and foot’s geometric positioning, a realistic stress response during foot-ground interactions can be reproduced

The unique joint-angle-dependent tissue responses obtained from underneath an individual MTH provide more accurate and realistic mechanical characterization of the plantar soft tissue property in the forefoot The force-displacement curve and force relaxation behavior produced, pertinent to the foot geometry and loading regime applied to the foot model, has the potential to provide insights into the mechanical behavior of forefoot tissues An important feature of this tissue tester is that the tester alone is generally applicable for exploration of (joint-angle-dependent) tissue property as an indicator of disease states and risks, such as ulcer formation at the MTH region in neuropathic

diabetic feet These data collected was used in this study for extraction of the hyperelastic material constants of the sub-MTH soft tissue By transforming the uni-axial stress (σ)–stretch (λ) equations of the Ogden model into contact equations, the material constants can be directly extracted The material properties of the sub-MTH tissue determined presently were in between those published results of the skin and fat tissue of human heel pad This could be explained by the fact that only single a homogeneous lumped tissue volume was used to model such tissue, and that material difference between the skin and fat pad had been weighted And the use of such patient-specific lumped tissue property input for the 3-D foot FE model appears to produce reasonable accurate plantar contact stresses

The dynamic in vivo plantar forces obtained underneath MTHs during gait

allows regional interfacial contact stresses to be calculated between the foot and its support surface The peak sub-MTH shear stresses were quantified The shear readings correlate well with existing data in the literature The three-dimensional contact stresses predicted at sub-MTH areas of forefoot by the model that interacts with a highly deformable foam pad is in agreement the present measurements as well as previous observations in terms of its magnitude and distributions following heel rise Based on the simulation results, it was found that plantar shear stresses varied its distribution throughout the domain A model with specific frictional interactions, based on actual calculated local shear traction ratio, can reproduce the pattern of regional shear distribution

at plantar surface

The model sensitivity study predicted the adaptive changes of the foot mechanism, in terms of internal joint configurations and plantar loads distributions, due to reduced muscle effectiveness in G-S complex The simulation results correspond well with clinical observations in diabetic patients following tendo-Achilles lengthening procedures Pressure reductions at individual MTHs could be site-specific and possibly dependent on foot structures, such as intrinsic alignment of the metatarsals These highlighted the clinical relevance of the model in analyzing the foot mechanism

Inclusion of a metatarsal support into the foam pad for enhanced forefoot (i.e sub-MTH areas) plantar stress relief requires more technical efforts Plantar pressure distributions were very sensitive to the metatarsal support’s placement

as well as its material selection Based on the simulation results, an additional soft metatarsal support placed at 12 mm proximal to the 2nd MTH helped to reduce local peak pressure compared to using soft foam pad alone However, placing a stiffer metatarsal support just underneath the 2nd MTH could cause local increase in peak pressure at forefoot plantar surface The current FE model provides an efficient computational tool to investigate the efficacy of certain design variables used in therapeutic footwear, and also, the model has potential for three-dimensional contact stress analysis at foot-shoe interface

5.2 Original Contributions

The results of this present study may have significant impact on both understanding the three-dimensional plantar stresses tensor, and providing a

useful tool for effective evaluation of existing or the development of new

‘Off-loading’ techniques at the foot-support interface for sub-MTH stress relief

This thesis examines both plantar pressure and shear stress distributions at

plantar surface of the foot experimentally and analytically In terms of

experimental work, an instrumented indentation device was developed to

quantify material characteristics of the sub-MTH soft tissue Also, an integrated

gait platform system, incorporating a customized sensor array and high-speed

photogrammetry, was designed, fabricated, and calibrated to measure the

dynamic interfacial stresses underneath individual metatarsal heads during gait

This provided valuable data for verification of such a sophisticated

musculoskeletal foot FE model A series of parametric modeling analysis was

conducted to highlight potential implications of specific muscle force variations on

forefoot stress redistribution The validated model was further demonstrated as a

basic tool for possible applications in studying the influence of therapeutic

interventions using metatarsal support on plantar forefoot stress redistributions

5.3 Future directions

 The analysis was performed in the model with a homogeneous mass of

plantar soft-tissue underneath MTHs The tissue stress values were only

extracted from the soft-tissue boundary, i.e contact stress distributions at

the plantar surface A more adequate integration of the “true” internal

structures of the plantar soft-tissue, such as the one recently presented in

the 54th Orthopaedic Research Society (ORS) by Cavanagh et al., (2009),

with layered sections of skin, plantar fat pad, and muscle, might help in the future to clarify for example internal tissue trauma among different levels more precisely

 During walking, the time-dependent properties of the soft tissue may affect the stress response of the foot for various phases during gait Advanced material models that include hyperelasticity and viscoelasticity may be used

in the future dedicated to improving the current model Such models could potentially be calibrated separately using the current instrumented indentation device, or other possible techniques that address both tissue elastic as well as time-dependent behaviors

 The current model only considered the flexor muscle forces for Tibialis posterior, Flexor hallucis longus, Flexor digitorum longus, Peroneus brevis, and Peroneus longus, other than the Achilles tendon For stance phase gait simulation (i.e heel strike to toe off), modeling of the extensors was necessary Future simulation studies should consider using both flexors and extensors when applying muscular loads

Fig 5.3.1.1 FE mesh of a musculoskeletal foot model with flexors and extensors for stance phase gait simulation

 The model was validated against the novel gait platform system at specific level However, the system is subjected to limitations such as the relatively small sensor array size, which requires targeted walking in order

patient-to take specific measurements at each MTHs Future studies may consider expanding the number of sensors used in the gait platform that should allow large scale experimental investigations to be performed The schematic diagram of such ‘next generation’ force platform system is in Fig 5.3.1.2

Fig 5.3.1.2 A future gait platform system with a larger sensor array can be

installed in a typical gait lab for large-scale experiments

 Application of the current model in design of therapeutic footwear is only preliminary Analysis of other design factors such as custom-molded insole, arch profiles, wedged shoe soles and variable-stiffness shoe soles may also equally applicable

Sensors

Mounting Plate

Customized force plate

Pit cover

Heel Strike Push-off

Walkway

Appendix A: Finite element analysis (FEA)

Finite element analysis is a numerical based method; the basic idea is that rather than obtaining an exact algebraic solution of the governing partial differential equations throughout the domain of interest, one instead numerically solves a system of simultaneous equations that arise from enforcing those governing equations for an array of discrete simplified sub-domains (known as elements) Within these individual elements, specific interpolation basis functions (usually polynomials) are assumed, from which continuous internal variables (e.g., strains) are piecewise approximated on the basis of corresponding parameters (e.g., displacements, in the case of strain) evaluated at a discrete number of characteristic local points (known as nodes)

Although the theory of FEA is rather complicated, below is a code written

in MATLAB to solve the 2-D Helmholtz equation using the Galerkin finite element method The basic concept of FEA as numerical approximation techniques was demonstrated The following MATLAB code is provided:

1 “Main.m” contains code to generate meshes at different resolutions and

to generate the boundary conditions described above along with some necessary initializations (including Gaussian quadrature points and weights) The mesh resolution can be changed through the “elemsPerSide” variable

2 “psi.m” contains code to evaluate bilinear Lagrange basis functions and their derivatives, and should not need modification

3 “dxiIdxJ.m” is designed to calculate the transformation Jacobian and the term gu(i,j) =(dxi_i/dx_k)*(dxi_j/dx_k)

%======================================================

% Program to solve 2D Helmholtz equation using Galerkin

% numNodes = total number of global nodes

% nodePos = each row is (x,y), row number is the node number

% numElems = total number of global elements

% elemNode = each row gives the four nodes for each element

% in order, the row number is the element number

% BCs = boundary conditions (type,value).

% Type 1 = essential (displacement)

% Type 2 = natural (gradient)

numNodes = nodesPerSide * nodesPerSide;

numElems = elemsPerSide * elemsPerSide;

% This initialization is for the Stiffness matrix and

% pi, dpibydxi1 and dpibydxi2.

% This is the matrix that contains the function PSI value for each of the

% Set up the numerical integration points 'gaussPos'

% and weights 'gaussWei' (2x2)

% THIS IS TO CALCULATE PI(N) , DPIBYDXI1 AND DPIBYDXI2.

% These matrices are 4x4 in nature These matrices contains the values for

% the 4 basis points at the four Gaussian points.

for j = 1:numerator

for h = 1:numGaussPoints

der = 0;

num = j;

%*** Q Write code here to make the

%*** element stiffness matrix, ES

% Initialise element stiffness (ES)

% Loop over elements

for elem = 1:numElems

value1 = psi(q,1,xi1,xi2);

value2 = psi(q,2,xi1,xi2);

result(1,1) = result(1,1) + ( value1*dx(q) );

result(1,2) = result(1,2) + ( value2*dx(q) );

result(2,1) = result(2,1) + ( value1*dy(q) );

result(2,2) = result(2,2) + ( value2*dy(q) );

%*** Q Write code here to assemble this ES

%*** into the global stiffness matrix, GM

GM(a,a) = GM(a,a) + ES(1,1);

GM(a,b) = GM(a,b) + ES(1,2);

GM(a,c) = GM(a,c) + ES(1,3);

GM(a,d) = GM(a,d) + ES(1,4);

GM(b,a) = GM(b,a) + ES(2,1);

%*** Q Write code here to apply the boundary

%*** conditions to K You can use any method

%*** but may find overwriting the rows of K easiest.

%*** This method finds rows that has known boundary conditions and

%*** adjusts the values.

%*** This method removes the rows and columns passing the daigonal

%*** elements with known values

for n = numNodes:-1:1

if BCs(n,1) == 1

% This step is to calculate element in which given values of x & y are

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