A study of plantar stresses underneath metatarsal heads in the human foot 3

3.1 Instrumented soft tissue indentor 3.1.1 Measurement of soft tissue property under the metatarsal heads The plantar soft tissue in the pads underneath the metatarsal heads MTHs is an

CHAPTER 3 EXPERIMENTAL TECHNIQUE

~Because a thing seems difficult for you, do not think it impossible for

anyone to accomplish~

Marcus Aurelius

3.1 Instrumented soft tissue indentor

3.1.1 Measurement of soft tissue property under the metatarsal heads

The plantar soft tissue in the pads underneath the metatarsal heads (MTHs) is an optimal load-bearing structure (Bojsen-Moller and Flagstad, 1976), particularly for cushioning the highest sub-MTH ground reaction forces (GRF) exerted in the terminal stance-phase of gait (Cavanagh, 1999) Identification of the mechanical response of the sub-MTH pad to external loading is essential for clinicians or users who wish to distinguish between normal and pathological tissue functions

Both in vivo and in vitro studies have observed stiffening (Gefen et al., 2001,

Klaesner et al., 2002, Pai and Ledoux, 2010), hardening (Piaggesi et al., 1999) or diminished energy dissipation (Hsu et al., 2007, Hsu et al., 2000) of the sub-MTH pad in neuropathic diabetic foot Many believe that such altered tissue properties that accompany diabetes may severely compromise its cushioning capacity, with the consequence of elevated peak plantar pressure at the sub-MTH region where ulcers are most common (Boulton et al., 1983)

Indentation tests offer a convenient way for direct in vivo investigation of the mechanical responses of the soft tissue, and commonly involves applying a known deformation (i.e., indentation) directly to the live subject’s tissue, e.g the amputee residual tissue covering long bones (Silver-Thorn, 1999, Vannah et al., 1999) and the heel pad (Rome and Webb, 2000), where the naturally-immobile skeleton acts as a rigid foundation However, the intrinsically-small MTH has great mobility in the plantar-dorsal direction, which often limits the maximum indenting-force to be directly applied at a desired loading rate, using general-

purpose indentors Previously, for sub-MTH pad indentation, large tissue deformation, similar to that during actual gait cannot always be achieved (Zheng

et al., 2000, Kwan et al., 2010) Moreover, poor instrument alignment is inherent

to hand-held devices (Kawchuk and Herzog, 1996, Zheng and Mak, 1999) and limited measurement reliability in trial-and-error procedures (Klaesner et al., 2001, Wang et al., 1999) often make interpretation of data difficult

Accurate mechanical characterization of the sub-MTH pad can be further complicated by metatarsophalangeal (MTP) joint configurations particular to structurally-specialized tissue frameworks Early cadaveric-dissection observations (Bojsen-Moller and Flagstad, 1976) have shown that the initially soft and pliable tissue pad can become increasingly “tightened” during MTP joint dorsiflexion Such tissue “tightening” may significantly restrict skin mobility against shear forces (Bojsen-Moller and Lamoreux, 1979) and increase the compressive stiffness of the sub-MTH pad (Garcia et al., 2008) However, this unique joint-angle-dependent tissue property has not yet been fully elucidated due to experimental technique limitations

In this study, a new instrument-driven, in vivo tissue tester, called the

sub-Metatarsal Pad Elasticity Acquisition Instrument (MPEAI), is devised The tissue tester enables collection of the localized mechanical response of the plantar soft tissue pad underneath an individual MTH, in relation to the MTP joint angle The intra-tester versus inter-tester variance of the tester was demonstrated when applied to the 2nd sub-MTH pad The characteristic force-displacement curves

were further utilized for extraction of the hyperelastic material constants to model the forefoot bulk soft tissue in the finite element model of the foot

3.1.2 Development of the tissue tester

The MPEAI consists of a special hinged foot-positioning apparatus integrated together with a portable motorized indentor This apparatus permits accommodation of the local sub-MTH pad and reproduction of MTP joint configurations generated by individuals during actual walking The integrated indentor can directly probe the mechanical response of the sub-MTH pad by inducing rate-controlled tissue deformation, in a way that is similar to that experienced in gait

3.1.2.1 Multiple DOF foot-positioning apparatus

A multiple degree-of-freedom (DOF) apparatus was devised for gait-related foot positioning and orientation This is achieved by using a kinematic linkage that consists of three linear translators and one hinge joint for connection to the base and forefoot plates (Fig 3.1.2.1) A cylindrical porthole is drilled into the rear-half

of the transparent acrylic (polymethyl methacrylate) forefoot plate The hole size was optimized (i.e 15 mm in diameter) in order to best encircle an individual MTH adjacent to the tissue pad The base of the porthole is internally threaded,

so that a portable indentor can be firmly mounted to it

Placement of a test subject’s foot on the device is shown in Fig 3.1.2.1, whereby the built-in hinge axis can be manipulated in bi-axial directions (i.e

antero-posterior and superio-inferior) for approximation of the MTP joint axis, which is assumed to pass through the medial aspect of the 1st MTH and the lateral aspect of the 5th MTH In this way, rotation of the base plate around the hinge joint would permit control of MTP joint dorsiflexion within a range of 0° ~ 90° This range of motion is sufficient to capture MTP joint configurations for simulation of a static stance-phase (Leardini et al., 2007) The joint angle Φ is measured by a digital inclinometer

Fig 3.1.2.1 Schematic diagram of the sub-Metatarsal Pad Elasticity Acquisition Instrument (MPEAI), showing details of probe tip, accommodation of sub-MTH pad and inside components of actuator to drive probe tip

3.1.2.2 Portable motorized indentor

A motorized indentor was developed; it contains a closed-housing linear actuator, comprising a 500-step per revolution stepper motor (MYCOM) and a 1.25 mm pitch tangential screw unit to drive a 5 mm diameter hemispherically-tipped probe

Fig 3.1.2.2 (A) Identified 2nd MTH pad (B) Photograph and (C) schematic diagram of test set-up, showing ‘trapped’ soft tissue pad and initial contact with probe tip

Fig 3.1.2.3 (A) Displacement-time profile of indentation cycle for probe tip

The indentor can be completely integrated into the positioning apparatus

by a snap-lock mechanism via the testing port through which the sub-MTH pad is fully exposed (Fig 3.1.2.2) Such a design ensures that the probe tip is consistently perpendicular to the tissue pad, regardless of testing conditions

corresponding to different MTP joint configurations The MPEAI can be mounted flush with the floor

A microchip-based controller (MNC-100 Indexer Unit) and driver are used

to prescribe the desired displacement profiles accurately As is shown in Fig 3.1.2.3, this facilitates smooth and continuous movement of the probe tip A miniature compression load cell (FUTEK), embedded between the actuator and the lower-end of the probe tip, records the magnitude of the local reaction force exerted on the tissue (Fig 3.1.2.1) Load cell outputs were fed into a signal-conditioning module and a data acquisition board (National Instruments, SCXI 1520/1314) To avoid tissue damage/pain during testing, a closed-loop control program for overload protection was written in LabVIEW (National Instruments) The indentation process automatically terminates when the indenting force magnitude exceeds 19 N This corresponds to a nominal stress of 435 kPa at indentor-soft tissue interface, approximating the peak plantar pressure that occurs at the sub-MTH region during normal walking (Hayafune et al., 1999) A schematic diagram of the entire MPEAI system is shown in Fig 3.1.2.1 Force and displacement data were collected at a sampling rate of 1,000 Hz

3.1.3 Assessing in-vivo tissue properties under MTHs

3.1.3.1 Repeatability test of the MPEAI

The repeatability test was conducted to determine the precision of the tissue tester- MPEAI when a single operator uses the device to perform a series of tests

to obtain the mechanical responses of the 2nd sub-MTH pad of two normal

subjects The location of the 2nd MTH of the right foot was first identified by palpating the underlying metatarsal tuberosity, and was marked by an ink ring, which defines the bounds of the plantar MTH region With the help of an assistant, the soft-tissue pad can be positioned and sited within the testing port, making it readily visible to a camera aimed at the side of the forefoot plate (Fig 3.1.2.1) After correction of joint axis misalignment, the foot was secured by Velcro straps (3M) and an appropriate distance with respect to the contralateral foot maintained to simulate a balanced stance-phase The indentor can be operated in manual mode by moving the tip axially at a speed of approximately 1 mm/s Such adjustments, coupled with visual guidance and force feedback, enabled initial contact between the indentor tip and the soft-tissue pad to be established easily and with confidence (Fig 3.1.2.2) Generally, subjects can sense a threshold indenting force of approximately at 0.2 N upon initial contact

Following the initial set-up, a sequence of pre-defined indentation cycles was used to induce large deformation to the local sub-MTH pad One cycle corresponds to complete loading and unloading, and exhibits a trapezoidal axial-displacement profile with a maximum probe depth δ (avg = 5.6 mm), a constant loading/unloading rate  (avg = 9.2 mm/s) and a holding time tr (avg = 85 ms) at the maximum deflection δmax (Fig 3.1.2.3) Selection of δ and  was based on a previous study that elicited detailed deformation characteristics of the 2nd sub-MTH pad during walking, via use of an in-floor ultrasound technique (Cavanagh, 1999) A volume reconstruction of the computer tomography scan images of the subjects’ right feet in non-weight-bearing conditions provided the initial tissue

thickness This facilitated determination of the local tissue indentation strain up to

an approximate value of 46% and a nominal strain rate of 0.76 /s Imposition of a short dwell-time tr at the tissue deformation δmax enables force relaxation characteristics to be observed within the same testing cycle (Fig 3.1.3.1.)

Similar indentation cycles on the 2nd sub-MTH pad were conducted, with the MTP joint configured at six different dorsiflexion angles – 0°, 10°, 20°, 30°, 40°, and 50° For each configuration, data was collected for three cycles after 3 cycles of pre-conditioning

Fig 3.1.3.1 Typical tissue reaction force patterns obtained for 2nd sub-MTH pad for similar indentation, but with MTP joint (MTPJ) at different dorsiflexion angles Note that the sub-MTH pad tissue response is dependent on MTP joint angle, i.e lower stiffness at lower joint dorsiflexion angles and increasing stiffness at higher joint angles

There was qualitative similarity in all sets of curves for given testing conditions, and this indicated that the experiments were well-controlled All the curves possess similar characteristic profiles, such as nonlinear loading/unloading phases and a substantial force relaxation component

Fig 3.1.3.2 Calculated initial stiffness (=initial tissue reaction force/ δ, δ1 mm)

Fig 3.1.3.3 Calculated end-point stiffness (= peak tissue reaction force/ δmax)

Fig 3.1.3.4 Force relaxation as percentages at δmax for 2nd Sub-MTH pad of two normal subjects, for increasing MTP joint angles

Reproducibility of experimental results for two normal subjects is as illustrated in Fig 3.1.3.2 ~ 4, standard deviation bars were shown Absolute measurement errors for the calculated initial stiffness (= peak tissue reaction force/ δ, for δ  1 mm), end-point stiffness (= peak tissue reaction force/ δmax), and force relaxation percentage, quantified in terms of standard deviation, were less than 0.084 N/mm, 0.133 N/mm, and 0.127% respectively across all testing configurations On average, the tissue initial stiffness correlated with data from literature, which relate to a 4.9 mm diameter tip and a cyclic indentation at 10 mm/s on lower limb soft tissue (Silver-Thorn, 1999) An average increase in end-point stiffness of the 2nd sub-MTH pad by 104.2% for a 50-degree MTP joint dorsiflexion generally agreed with that of a previous study (129% ±19.8), where indentation was applied at the plantar MTH region with the MTP joint extended to

its end-range (Garcia et al., 2008) Force relaxation of the in vivo tissue was

found to be significant (avg = 8.1%), even during a short holding-time

3.1.3.2 Force-displacement response of soft tissue under metatarsal heads

It was found that the mechanical responses of this load-bearing soft tissue (i.e., sub-MTH pad) depends not only on external loading conditions, such as the direction and rate of the loading, which generate responses governed by tissue anisotropy and viscoelasticity (Zheng and Mak, 1999, Klaesner et al., 2001), but also on the configuration of the joint articulation overlying the tissue (Garcia et al., 2008) Tests show that the proposed MPEAI technique is able to produce consistent results The force-displacement curve produced has the potential to

provide insights into the mechanical behavior of forefoot tissues under MTHs, and to be used for extraction of the hyperelastic material constants of this bulk soft tissue in the foot

3.1.4 Derivation of material constants for plantar soft tissue

3.1.4.1 Classical Hertz contact theory

In analyzing the force-displacement behavior obtained from indentation tests, it is common practice to refer to classical Hertz contact models, with its assumptions

of linear elasticity and infinitesimal strains, in order to obtain materials’ modulus values In hemi-spherical indentation, the Hertzian relationship between the applied indenting force (F) and the resulting indentation (δ) (Johnson, 1985) is:

 2

2321

1 3

Where E and  are Young’s modulus and Poisson’s ratio of the indented

material, respectively, and R is the radius of the rigid indenter The contact radius,

a, varies with displacement δ according to

a  R  3.2

The Hertz equation is valid when applies to hemi-spherical indentation provided that the following assumptions are satisfied:

 The strains are small and within the elastic limit,

 Each body can be considered an elastic half-space,

 The surfaces are continuous and non-conforming, and

 The surfaces are frictionless

However, for the present sub-MTH pad indentation, nonlinear and large tissue deformations (nominal strains up to 46%) were present Consequently, errors maybe incurred by directly applying the representation of Hertz equation beyond their validity range (i.e at the infinitesimal strain range)

It should be noted that, since the Hertz formalization is based on the theory of linear elasticity, it should be possible to define measures of stress and strain that satisfy a Hooke's law of elasticity The concept of an analogy between uni-axial compression and spherical indentation was first explored by (Tabor,

1948, Tabor, 1951) who proposed (what has now been widely accepted) definition of indentation stress (or mean pressure, ) and strain ():

20



 E 3.4

From the parallels between indentation and uni-axial compression, it stands to reason that non-Hooke, uni-axial stress–strain relations can be extended to non-Hertzian contact with some mathematical manipulations

3.1.4.2 Direct extraction of hyperelastic material constants

Let us list the Ogden strain energy functions for hyperelastic materials we derived in Chapter 2, and its corresponding uniaxial stress (σ)–stretch (λ) equations (1st-order):

1 , 2

1 3

terms of force (F) and contact radius (a, in eq 3.2) In most indentation tests,

however, the contact radius is not a measurable quantity Instead, the variation of

indentation depth or displacement (δ) with increasing magnitude of the applied force is monitored directly, an expression such as Eq 3.2 relating a and δ is

therefore necessary and useful Assuming material incompressibility and that the

contact radius variability with indentation depth according to Eq 3.2, we can have

01

a a

/

3.8

Where force (F) contact radius (a) relation corresponding to the Ogden strain

energy function was expressed in terms of two hyperelastic material parameters:

μ and α, which can be determined directly through nonlinear least square (NLS) curve fitting procedure

Fig 3.1.4.1 Values of material constants (;α) obtained through nonlinear least squares

(NLS) minimization using the deduced contact equations for of the 1 st -order Ogden hyperelastic model in MATLAB The calculated root-mean-square-error (RMSE) was as small as 0.512 N with a R 2 value of 0.9821

To best represent the forefoot soft tissue material behavior for push-off finite element simulation, the force-displacement curve corresponding to metatarsophalangeal joint angle at 30° was chosen to deduce material constants

using MATLAB (Math Works, Natick, MA) This yielded μ = 3.75 ｘ10-2 MPa and

α = 5.5 The results of optimal curve fitting were presented in Fig 3.1.4.1

Table 3.1.4.3 The material properties used in the current finite element foot model in comparison with those existing models for heel pad

Models Tissues μ (MPa) α D

Spears (2007)

Fig 3.1.4.2 Comparison of the stress–strain curves for the current sub-MTH pad and those previously models: heel pad by Erdemir (2005), heel fat pad and skin model by Spears (2009)

The material properties of the sub-MTH soft tissue determined presently were in between those recently published results of the skin and fat tissue of human heel pad (Erdemir et al., 2006, Spears et al., 2007) This could be explained by the fact that the current foot soft tissue was modeled as a

homogeneous lumped tissue volume and that material difference between the skin and fat pad had been weighted (Fig 3.1.4.2.)

3.1.4.3 Use of material constants in plane-strain FEM

The accuracy of the derived material constants were further evaluated in a strain FE model The indentation was simulated as frictionless contact between a rigid hemi-sphere (R = 2.5 mm) and an elastic slab that representative of a sub-MTH geometry in an axi-symmetric model using ABAQUS

plane-Although no viscoelastic effects were assumed, this displacement rate was chosen to be comparable to that from the experiments The mesh size was graded to be more refined in the vicinity of the sphere and coarse at the model extremes The bottom and side of the slab were fixed in space, and both the rigid sphere and axis of symmetry for the slab were only permitted to move in the vertical direction Contact between the sphere and slab was assumed to be frictionless The Ogden material model with the determined constants (μ = 3.75

ｘ10-2 MPa and α = 5.5) was used From the simulations, the agreement between simulation results and indentation data was extremely good (Figure 3.3.4.3.), suggesting that the material constants determined from this experiment

is valid and accurate to model the forefoot plantar soft tissue during heel rise

Figure 3.3.4.3 Application of the calculated material constants in a plane-strain finite element model (A) The MTH geometry was simplified as a sphere with a diameter of r (B) The r values was determined through optimal surface fitting of the 3-D contour lines which defines the actually shape of the 2 nd MTH The sub-MTH soft tissue thickness t was defined as the shortest line distance between the MTH and the plantar surface (C) Compressive stress distributions in the sub-MTH tissue during indentation process (D) Simulation results correlate well with experimental observation

Altogether, an integrative MPEAI tissue tester was developed to fulfill the

requirements imposed for in vivo mechanical characterization of localized plantar

soft tissue pads underneath an individual MTH Tests on the 2nd Sub-MTH pad show that the proposed MPEAI technique is able to produce consistent and repeatable results A key advantage of the proposed device is the integration of a portable indentor with a special foot-positioning apparatus; this facilitates