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Published in final edited form as: Clin Biomech (Bristol). 2021 May 29;87:105403. doi: 10.1016/j.clinbiomech.2021.105403

Simple model of arch support: relevance to Charcot Neuroarthropathy.

BL Davis a, SM Tiell b, GR McMillan c, LP Goss c, JW Crafton c
PMCID: PMC8316300  NIHMSID: NIHMS1712582  PMID: 34091194

Abstract

Background

Charcot neuropathy is a common complication resulting from poorly controlled diabetes and peripheral neuropathy leading to the collapse, and ultimately the breakdown, of the midfoot. Mechanically, it is likely that a compromised arch support in this, or any other patient group that experiences foot flattening, would be associated with slippage at the distal and proximal interface regions of the plantar surface of the foot and the adjacent support surface. This slippage, although difficult to quantify with standard motion capture systems used in a gait laboratory, could potentially be assessed with systems for monitoring interface shear stresses. However, before investing in such systems, a correlation between arch flattening and interface shear stresses needs to be verified.

Methods

For this purpose, a sagittal plane model of a foot was developed using a multi-body dynamics package (MSC Adams). This model mimicked a subject swaying back and forth, and was constructed to show the dependence of interface stresses on altered arch support.

Findings

The model’s predictions matched typical FootSTEPS data: lengthening of the arch of 1–2mm, sway oscillations of 0.22–0.33 seconds and frictional force differences (calcaneus relative to forefoot) of 60N. Of clinical relevance, when the stiffness of the plantar spring (representing aponeurosis and intrinsic muscles) was reduced by 10%, the frictional force difference increased by about 6.5%.

Interpretation

The clinical implications of this study are that, while arch lengthening of less than 2mm might be difficult to measure reliably in a gait lab, using shear sensors under the forefoot and hindfoot should allow arch support to be assessed in a repeatable manner.

Keywords: Charcot Neuropathy, Arch Support, Computational Model, Diabetes, Foot

1. Introduction

There are a variety of foot conditions that are associated with arch flattening, including pes plano valgus (in pediatric and adult patients), posterior tibialis insufficiency (Ling and Lui, 2017), rheumatoid arthritis (Turner et al., 2006) and diabetic patients with dense neuropathy. In each case, the mechanics of arch support during the progression of a foot becoming flattened have not been addressed in the literature. These shortcomings are what led to the need to develop a theoretical model that shows the association between arch support and stresses at the foot-ground interface. The overall purpose of this research was to develop a biomechanical model to investigate the relationships between (i) arch support, (ii) relative displacements between the heel and metatarsal region, and (iii) interface stresses. From a clinical perspective, if a marker related to arch collapse (such as skin shear stresses) can be monitored during upright stance, it could potentially be used as a tool for predicting imminent collapse.

Diabetic neuropathic feet are associated with both bony and soft tissue breakdown, with previous research (Cheuy et al, 2013, Cheuy et al., 2016) focusing on metatarsophalangeal joint deformities and markers of diabetic disease (including neuropathy, advanced glycation end products and muscle deterioration). Charcot’s Neuroarthropathy (CN) is a serious complication affecting the entire foot that was first associated with neuropathy by Dr. Jean Marie Charcot in 1863. It is a diabetic complication associated with the collapse, and ultimately breakdown, of the midfoot. If left untreated, Charcot patients are at risk of developing ulcers, severe deformity, infection, osteomyelitis, and undergoing an amputation.

CN occurs in approximately 0.08% of the general diabetic population, however the prevalence increases to 13% in high-risk diabetic patients (Botek et al., 2010; Frykberg et al., 2008) and even 35% in patients with polyneuropathy in industrialized countries (Rosskopf et al, 2019). The midfoot collapse in Charcot patients commonly occurs in the tarsometatarsal and midtarsal joints (longitudinal and transverse arches), thus creating a “rocker bottom” deformity (Lamm et al., 2012; Varma, 2013). The flattening of the midfoot causes the forefoot to dorsiflex and adduct, placing increased compressive and shear forces on the skin beneath bony prominences (Strotman et al., 2016). This loading scenario has been associated with an increase in skin temperature (Yavuz et al, 2015). In these cases, the patient is at risk at developing ulcers at these high-stress regions. Quantifying risk level however is challenging because mechanical loading state, frictional forces at the skin surface, and internal tissue distortions and stresses are interrelated and depend on each other through complex mathematical relationships (Gefen 2017). Gefen also describes how temperature may exacerbate tissue breakdown by decreasing the tolerance of cells that are exposed to mechanical deformation.

There exist a number of theories as to the causes of tissue changes in diabetic patients, including kidney function (Bittel et al, 2021) and mitochondrial dysfunction (Sivitz and Yorek, 2010). In terms of the mechanics underlying Charcot foot collapse, theories range from bone stress (Chantelau et al. 2006) to altered foot loading (Davis, Crow, Berki & Ciltea, 2017) to proinflammatory cytokines (Jeffcoate, Game and Cavanagh, 2005). For reasons that are not well understood, the acute destructive Charcot process often ends abruptly, to be followed by bony coalescence. Typically, the patient is left with a non-functional, deformed foot that has no propulsive value. Moreover, due to bony prominences on the bottom of the foot, there is a high risk of ulceration. Whatever the root cause, a retrospective study has shown that 16% of patients with a neuropathic ulcer show evidence of Charcot changes (Cavanagh et al. 1994).

Currently, physicians typically offer only immobilization and palliative treatment while witnessing the destruction of bones, joints, and ligaments that support the arch of the foot. In terms of treating CN patients, Chantelau (2005) described the “perils of procrastination” and showed the benefits of early versus delayed detection. At the onset of acute diabetic Charcot foot problems, therapeutic intervention may be delayed because plain X-rays may not show fractures. This is clinically significant because immediate off-loading of incipient Charcot foot appears to minimize fractures and incapacitating deformities. This line of reasoning underpins the rationale for the current study. Our underlying hypothesis is that mechanical support of an arch (through muscular or soft tissue support) is compromised in CN patients and this is manifested by altered shear stresses at the foot-ground interface.

2. Methods

A computational model of the foot was developed using MSC Adams software (freely downloadable version) to provide insight to (i) the degree to which fore-aft forces under the forefoot change as a function of time and (ii) the dependence of fore-aft forces on internal arch support. While the human foot is comprised of various intricate structures, the current computational model was simplified, consisting of an upright body connected via a hinge joint to a triangular foot structure (Figure 1) that permits splaying of the longitudinal arch. The simplification removes the influence of complex bony geometrical and allows the focus to be on the mechanics of the arch and the foot-ground interface.

Figure 1.

Figure 1.

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Initial foot model developed with MSC Adams software. An upright subject is represented on the left, with a close-up of the foot shown on the right.

The mass of the upright body and the triangular foot structure are modifiable depending on the subject. The rearfoot was anchored to the supporting surface while the forefoot was allowed to slide in the antero-posterior direction. Movement of the metatarsal head (MTH) in the medio-lateral direction was restricted, due to the study focusing on the longitudinal arch. The anterior and posterior calf muscles were modeled as springs whose stiffness values were 100,000 N/m and 130,000 N/m respectively (Davis & Grabiner, 1996). Support afforded by the aponeurosis and plantar musculature was modeled as a spring whose stiffness was 100,000 N/m (similar to subject #1 in Gefen, 2003). The degree to which the foot arch changed its height was dependent on ankle spring forces, friction at the interface with the ground, and the stiffness of the plantar spring element. An oscillating motion was imposed on the body to replicate sway in the sagittal plane by implementing a step function of 50 N horizontal force acting anteriorly at the subject’s center of mass. This function replicates the effect of a subject being “pushed” from the posterior side and the magnitude was sufficient to initiate oscillations in the sagittal plane. To verify the model’s prediction, representative data were collected for a human subject swaying in the sagittal plane as in the model.

A typical adult male has a center of gravity 55% of the subject’s stature (in this case, 1m above the floor surface, Davis & Grabiner, 1996). As this model simulated the effect under one foot, the upright body was set to half the subject’s body mass with the assumption that the mass was equally distributed over each foot (Table 1). The configuration of the model was similar to that reported by Gefen (2003). The assumed coefficient of friction of 0.54 is based on the literature (Sanders et al., 1998, Dai et al., 2006). A simulation was also conducted with a coefficient of friction of 0.51 (Zhang and Mak, 1999) showing a decrease of 5%. Additionally, simulations were conducted with alterations to the calf muscle spring inputs by decreasing the stiffness by 10% (with a coefficient of friction of 0.54) as literature shows significant effects caused by Achilles tendon lengthening (Hastings et al., 2000, Holthusen and Kolodziej, 2009).

Table 1.

Key Quantities in the Computational Model used for Subject Comparison

Variable Assumed Value Justification
Upright Body Mass 42.5 kg ½ Equivalent mass of subject
Height of Center of Gravity 1 m 55% of the height of subject
Metatarsal Bone Mass 1214 kg/m3 Based on mass ratio of typical adult male
Links from Ankle to Metatarsal and Calcaneus 1214 kg/m3 Based on mass ratio of typical adult male
Anterior Calf Muscle 100,000 N/m Based on results found in Davis & Grabiner, 1996
Posterior Calf Muscle 130,000 N/m Based on results found in Davis & Grabiner, 1996
Plantar soft tissue support 100,000 N/m Gefen (2003)
Metatarsal Bone Friction
Mu Static 0.6 Typical values for interface friction coefficients
Mu Dynamic 0.54
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The primary variable of interest in this study is the antero-posterior frictional force measured beneath the metatarsal heads (and relative to the heel region). To assess the role of plantar aponeurosis in supporting the arch, a simulation of 18 full cycles (representing 16.6 seconds) with a 10% change in plantar spring stiffness was performed. Additional simulations were also conducted to assess the effects of increasing plantar aponeurosis stiffness from 100 kN/m to 200 kN/m (to match the cadaveric data for the aponeurosis reported by Kitaoka et al. 1994)

To verify the model’s prediction, representative data were collected for a human subject swaying in the sagittal plane as in the model. For validation purposes, plantar shear data were collected using ISSI’s FootSTEPS system, model FS3F-1, (Goss et. al, 2019) on an adult male (85 kg, 182 cm height) swaying in response to an impulsive force.

3. Results

The primary variable of interest in this study is the antero-posterior frictional force measured beneath the metatarsal heads (and relative to the heel region). This variable is analogous to the “S_flatten” force (Davis et al., 2017) that relates to plantar surface shear stresses during arch flattening. During simulation of a subject swaying back and forth in the sagittal plane, the frictional force showed a repetitive waveform (Figure 2). For an impulsive applied force of 50N, the force difference between each peak of an “M-shaped” pattern and “baseline” was approximately 60N. This magnitude represents the difference in interface shear between the heel and metatarsal head regions. From peak to peak, the sway lasted 0.28 seconds.

Fig 2.

Fig 2.

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Computational model simulating a 85 kg adult male swaying in the sagittal plane for 1.7 seconds.

While not a primary variable of interest, the model also predicted lengthening of the distance from the ankle to the metatarsal head (i.e., as the arch flattened). From the first to second oscillation, the displacement was 1.12 mm. This compares favorably with a value of 2.17 mm reported for translation of the first ray relative to the ankle as measured fluoroscopically (Martin et al. 2012). In the case where the coefficient of friction is changed to 0.51 (a decrease of 5%), the displacement was 1.10 mm.

When comparing the model to representative data from the human subject, there was close agreement of the timing S_flatten peaks forces (Figure 3). From peak to peak, the sway lasted between 0.22 and 0.33 seconds. The root mean square error (RMSE) when comparing S_flatten values (Davis et al, 2017) for the model and experiment, ranged from 9.41N to 14.07N.

Fig 3.

Fig 3.

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Computational model compared to patient trial data (two representative trials). Note that differences between model and trial data are comparable to the differences from one trial to another.

In terms of simulating the effect of compromised arch support (i.e., when the plantar aponeurosis stiffness was modified to a stiffness of 90,000 N/m) there was a change of between 6 and 7% in the frictional force prediction. This was dependent whether first versus second or subsequent sway cycles were assessed. If the plantar spring stiffness was increased to a value of 200kN/m then the displacement of the 1st MTH relative to the hindfoot decreased from 1.7mm to 0.43mm, and the shear force difference (MTH relative to hindfoot) decreased from 60N to 35N.

4. Discussion

A simple spring-based model of the foot that can be implemented on freely-downloadable software (students version, MSC ADAMS), allows researchers to probe the effects of compromised soft tissue support, interface friction and foot geometry. One output from the model that may have clinical implications relates to the difference in shear forces between the 1st MTH and the calcaneus. There are a variety of foot conditions that are associated with arch flattening, including pes plano valgus (in pediatric and adult patients), posterior tibialis insufficiency (Ling and Lui, 2017), rheumatoid arthritis (Turner et al., 2006), and diabetic patients who experience substantial changes in both structure and function of the foot (D’Ambrogi, 2005).

There have been numerous foot models reported in the literature. These include studies examining the functional role of the plantar fascia (Gefen 2003) in stabilizing a foot’s arch (but excluding the influence of interface shear forces), cadaveric models for analyzing the function of the plantar aponeurosis throughout the stance phase of the gait (Erdemir et al., 2004), generalized three-dimensional six-segment models of the foot to examine the effects of shoe design (Morlock and Nigg, 1991), and finite element models to examine stress distributions in bones and soft tissues (Filardi, 2018). Collectively, these have either required considerable computational resources to implement, or they have omitted the effects of frictional forces at the foot-ground interface.

In patients with diabetes, atrophy and reduced volume of intrinsic muscles, reduced strength of the lower limb and intrinsic foot muscles (Hastings et al., 2015), changes in calcaneal adipose tissue (Kao, Davis and Hardy, 1999), altered mechanics of tendons and ligaments (Morag and Cavanagh,1999, Ramirez and Raskin, 1998), are examples of complications that have been reported in clinical observations and experimental studies. Plantar soft tissue stiffening due to progressive, non-enzymatic glycosylation processes (e.g., Gefen, 2003b), and intrinsic muscle weakness (Kumar et al., 2015) further exacerbate foot mechanics in diabetic patients. Interestingly, these two factors - stiffening of the aponeurosis and weakening of intrinsic muscles - counteract each other in terms of arch support. This is particularly relevant to those patients who are at risk for arch collapse. For those patients experiencing deleterious effects of Charcot neuropathy, the structure of the arch is at risk, and an absence or delay of treatment will cause deterioration of bones, joints, and ligaments and may lead to immobilization (Chantelau, 2005), skin breakdown and even amputation.

The task under consideration in this study involves a person maintaining his or her upper body and legs in an upright orientation with movement occurring only at the ankle and subtalar joints (Davis & Grabiner, 1996). This task was selected because, (i) compared with walking, it requires less effort for a diabetic patient with peripheral neuropathy and/or impaired balance, and (ii) it allows the focus to be on arch support during stance, rather than during swing and stance phases of gait. Movements involving the hip or knee joints were not included in this simplified structure but could be added if needed. Using a spring for each muscle group allowed for simple alterations during simulation. In particular, this model permitted the relationship between arch support and interface shear forces to be assessed. Altering the plantar spring stiffness provided insight into arch support issues that may be experienced by a CN patient who has compromised muscular or plantar soft tissues.

The computational model successfully replicated the patient trial (Figure 3). The key aspect of these trends is that they can be assessed with sensor systems that are sensitive to shear. Traditional gait labs rely on marker-based systems for estimating bone orientations and movements (Telfer et al, 2010). The model’s prediction of a 1.7mm displacement of the 1st MTH relative to the calcaneus would be challenging to quantify in a gait lab; (i) noise of at least 1mm can be expected in marker position (Cereatti, Della Croce and Cappozzo, 2006), and (ii) soft tissue motion artefacts would further compromise any estimate of the distance between the 1st MTH and the calcaneus.

When the plantar spring stiffness was decreased, the antero-posterior shear difference increased in magnitude, reflecting a larger force tending to increase the splay of the foot. This is in agreement with findings of a compromised arch in neuropathic diabetic patients (Davis, Crow, Berki & Ciltea, 2017). The fact that a 10% decrease in spring tension caused an increase of about 6.5% in the magnitude of shear (forefoot relative to hindfoot), is explained by the fact that the model had friction at the foot-ground interface. If the static and dynamic coefficients of friction (set at 0.6 and 0.54 respectively) had been increased, they alone would have restricted the degree of arch flattening. This is potentially another aspect of the model that could have clinical implications – a person at risk for Charcot foot collapse who stands on a slippery surface, is much more likely to flatten their arch beyond physiological limits. To the authors’ knowledge, no study has examined the correspondence between the longitudinal arch flattening in Charcot patients and the nature of frictional properties of the support surface (including sock material). Further research is needed to track this in patients at risk for Charcot foot collapse (or in fact, foot flattening in any population).

Limitations of the model relate to the simplicity of its components, in particular, modeling the foot in the sagittal plane as opposed to a 3D representation. The calf and tibialis anterior muscles are modeled as linear springs, and the combined effects of plantar aponeurosis and intrinsic muscles are combined into a single element representing “soft tissue” support. Furthermore, the perturbation was caused by a simple 50N force lasting 0.01 seconds. The task itself is restricted to upright stance. Any extension to a gait movement would require considerable modifications to the model. In terms of applying this model to various patient cohorts, diabetic neuropathic patients and others with pathologies of the medial arch need to be assessed and, for each group, the response to varying amounts of fore-aft sway need to be quantified.

Despite these limitations, this model suggests that shear force differences as seen under the calcaneus and forefoot regions depend on arch support. Shear data collected on a representative subject showed RMSE differences when comparing the S_flatten magnitudes to those predicted with the model (RMSE values ranged from 9 to 14 N). The predications of MTH displacement relative to the calcaneus are what would be expected during weightbearing, and the pattern of shear forces under the MTH replicate those collected on an actual shear/pressure platform. In addition, the effects of compromised soft tissue support can be clearly seen in the splaying of the arch. The clinical implications of this modelling approach are (i) it suggests a very simple test of at-risk patients could be performed by collecting data during upright stance, (ii) it highlights variables that are relevant – most notably, the magnitude of the difference in shear between 1st MTH and calcaneus, and (iii) the study addresses the concern of Kumar et al. (2015), “neuropathic changes that are clinically undetectable may develop in parallel with changes in plantar tissues”. Certainly, this study suggests that monitoring foot-ground shear forces during upright stance may provide insights into incipient foot collapse that is not discernable with conventional marker-based gait systems.

5. Conclusions

This study highlighted the foot mechanics supporting stresses at the foot-ground interface. The significance of this is that if key factors (such as splaying of the arch or shear forces in hindfoot and forefoot regions) can be identified early, immediate off-loading of an incipient Charcot foot will minimize fractures and incapacitating deformities. The rationale for this study is in agreement with the recommendation that foot structure and function be monitored over time to assess deterioration of the medial column of the foot (Hastings et al., 2015). This research is a first step towards identifying markers that are indicative of foot flattening.

The computational model verified that when the plantar soft tissue support is compromised, the magnitude of the forces between the 1st MTH and calcaneus increases, reflecting a larger force tending to flatten the foot arch. These predictions may be useful for assessing the onset of acute diabetic Charcot foot problems before such symptoms are manifested clinically. The clear advantage of assessing shear forces at the foot-ground interface is that changes in foot support are apparent long before the arch shows manifest structural changes.

Fig 4.

Fig 4.

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Predicted metatarsal displacements as a function of arch stiffness. Foot flattening is initially difficult to observe, due to the small displacement of the forefoot relative to the hindfoot. As arch support deteriorates (as quantified by arch stiffness), the relative displacement increases in a slightly non-linear manner.

Highlights.

  • Model demonstrating the dependence of interface stresses on altered arch support.

  • Verified relationship between compromised arch support and plantar shear under foot.

  • Useful model for assessing the onset of acute diabetic Charcot foot problems.

  • Potential clinical applications for shear sensors

Funding:

This work was supported by the National Institutes of Health 1R41DK125238-01

Conflict of Interest Statement

All five authors have no financial nor personal relationships with other people or organizations that could inappropriately influence our work.

The research was performed at Cleveland State University through funding from the NIH.

Footnotes

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