Introduction

During running, the ankle joint transmits large forces and moments, and produces the greatest fraction of joint power for propulsion1. Although the ankle primarily rotates in the sagittal plane, its frontal plane kinematics and kinetics play equally important roles in governing ankle stability and preventing injury, most notably sprains from excess inversion or sometimes eversion. The ankle’s behavior during running has been shown to be influenced by the geometric and material properties of shoes, particularly the heel region, which can alter the nature of forces transmitted through the foot and ankle compared to barefoot running2. There is great diversity in the heel design of commercial running shoes: while minimal shoes have sole thicknesses of just a few millimeters with no heel-toe offset, some cushioned shoes have heels over 30 mm high and heel-toe offsets as high as 12 mm3. Here, we investigate how this wide variation in heel height in running shoes affects ankle stability and motion in the frontal and sagittal planes.

One of the major loads on the ankle joint is the torque in the frontal plane, which has contributions from the vertical and mediolateral components of the ground reaction force (\(F_z\) and \(F_x\) respectively in Fig. 1). These force components produce moments proportional to their respective moment arms about the ankle joint (\(r_x\) and \(r_z\) respectively in Fig. 1), both of which can be influenced by the size and shape of the shoe heel (Fig. 1b). In particular, during heel strike in single limb support when the center of pressure (COP) must lie inside the heel base, a high heel increases the vertical moment arm of the mediolateral GRF, and the width of the heel constrains the maximum mediolateral moment arm of the vertical GRF. In this simple model, the height and width of the heel, which could potentially be large in modern running shoes, may significantly influence the torque about the ankle joint as compared to barefoot running. This frontal plane torque is primarily a response to external gravitational loading and changes in body momentum, but may also play a role in the control of stability4. Shoe design features significantly interact with each other3,5, making it difficult to disentangle the effects of heel height from other sole characteristics like stiffness or cushioning6. Thus, few studies have considered the specific effects of variations in heel geometry and heel toe offset of running shoes on frontal plane ankle dynamics2,7.

Figure 1
figure 1

Frontal plane schematic of the foot. (a) In the frontal plane, the mediolateral moment arm of the vertical component of the ground reaction force \(F_z\) is \(r_x\), and the vertical moment arm of the mediolateral component \(F_x\) is \(r_z\). (b) The presence of a shoe increases \(r_z\) by the height of the shoe, and changes the possible mediolateral positions of the center of pressure, allowing for potentially larger \(r_x\).

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Heel height may also affect the sagittal plane torques and range of motion of the ankle through stance2,8,9,10. It is unclear if these effects on ankle dynamics are direct mechanical consequences of higher heels, or secondary outcomes of changes in stride length caused by changes in heel height11. When the foot collides with the ground during running, the pre-collision kinetic energy of the lower limb is partially converted into rotational kinetic energy of the foot to varying degrees depending on strike type12. The effects of variation in strike type on post-collision ankle dynamics are well understood via mechanical models and experimental measurements12,13,14, but what might be the effects of variation in shoe heel height? This is specifically useful to ask in rearfoot strike (RFS) running where the heel may be the only point of contact in early stance. In this context, for a given pre-collision foot and shank velocity, heel height can be reasonably expected to govern the pre- and post-collision angular momentums and the moments of inertia of the foot and shank system in the sagittal plane, about the point of collision under the heel. Assuming a rigid, plastic collision of the foot with the ground, the post-collision angular velocity of the ankle likely depends on heel height, but the extent and direction of this relationship require collision modeling and experimental measurement to be fully understood. We present here a simple collision model that extends the analyses in Lieberman et al.12.

Figure 2
figure 2

Schematic and free body diagrams of the collision model. (a) The shank has mass M, length L, moment of inertia \(\underline{{\textbf{I}}}_{M}\) and center of mass at point E; the foot has mass m, length l, moment of inertia \(\underline{{\textbf{I}}}_{m}\) and center of mass at point D. The shank and foot are connected by a frictionless hinge at point B which models the ankle joint. The heel extends by a length sl posterior to the ankle and has a massless vertical projection of height h. The centers of mass of the foot and shank segments are at points D and E respectively, and the ground contact occurs at point O. The direction of running is along the y axis in this view. (b) Free body diagram of the entire system showing the reaction force at the ground contact point O. Finite forces like gravity are ignored in the model and not shown here. (c) Free body diagram of the shank alone, showing the reaction force at the hinge B.

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The goal of the following calculation is to derive the dependence of ankle plantarflexion velocity on heel height, defined as the angular velocity of the foot with respect to the shank, just after collision with the ground. Figure 2 shows a schematic of the lower limb collision model which is adapted from Lieberman et al.12. Our analysis is restricted to the sagittal plane (yz), and the direction of running is along the positive y axis.

We assume that just before collision, the entire lower limb is moving with the velocity \({\textbf{v}}_{\textrm{D}}^- = {\textbf{v}}_{\textrm{E}}^- = v_y^- \hat{{\textbf{j}}} + v_z^- \hat{{\textbf{k}}}\), and with zero initial angular velocity \(\varvec{\Omega }_m^- = \varvec{\Omega }_M^- = 0\). The foot and shank system collides with the ground at point O, and the post collision angular velocities of the foot and shank segments are \(\varvec{\Omega }_m^+ = \omega _m^+\hat{{\textbf{i}}}\) and \(\varvec{\Omega }_M^+ = \omega _M^+ \hat{{\textbf{i}}}\). Here, \(\hat{{\textbf{i}}}\), \(\hat{{\textbf{j}}}\) and \(\hat{{\textbf{k}}}\) denote the usual unit vectors along the x, y and z axes respectively. Quantities just before the collision are labeled with superscript ‘−’ and those just after with superscript ‘\(+\)’. Subscripts m and M refer to the foot and shank segments respectively, and \(m+M\) refers to the two segments together.

Following Lieberman et al.12, we assume a rigid, plastic collision at point O, so that the collision is instantaneous, the configuration of the system does not change during the collision, and the point O comes to rest after the collision. At any time before, during or after collision, the angular momentums of the shank about the point B (\({\textbf{H}}_{M/\mathrm B}\)) and the whole system about the point O (\({\textbf{H}}_{{M+m}/\mathrm O}\)) are given by

$$\begin{aligned} \begin{aligned} {\textbf{H}}_{M/\mathrm B}&= M {\textbf{r}}_{\mathrm{E/B}} \times {\textbf{v}}_{\textrm{E}} + \underline{{\textbf{I}}}_M\varvec{\Omega }_M\\ {\textbf{H}}_{{M+m}/\mathrm O}&= m {\textbf{r}}_{\mathrm{D/O}} \times {\textbf{v}}_{\textrm{D}} + \underline{{\textbf{I}}}_m\varvec{\Omega }_m + M {\textbf{r}}_{\mathrm{E/O}}\times {\textbf{v}}_{\textrm{E}} + \underline{{\textbf{I}}}_M \varvec{\Omega }_M, \end{aligned} \end{aligned}$$
(1)

where \({\textbf{v}}_{\textrm{D}} = {\textbf{v}}_{\textrm{O}} + \varvec{\Omega }_m \times {\textbf{r}}_{\mathrm{D/O}}\) and \({\textbf{v}}_{\textrm{E}} = {\textbf{v}}_{\textrm{O}} + \varvec{\Omega }_m \times {\textbf{r}}_{\mathrm{B/O}} + \varvec{\Omega }_M \times {\textbf{r}}_{\mathrm{E/B}}\) are the velocities of the points D and E respectively, and \({\textbf{r}}_{\mathrm{E/B}}\), \({\textbf{r}}_{\mathrm{D/O}}\) and \({\textbf{r}}_{\mathrm{E/B}}\) are relative position vectors between respective labeled points (Fig. 2).

Since the collision is assumed to be instantaneous, the contact forces acting at points B and O are infinitely large. Finite forces such as gravity are negligible compared to the contact forces, and they contribute no torque-impulses in the collision. Thus, there are no torque-impulses about the points B and O, and we can write angular momentum balance for the shank segment about point B, and for the whole system about point O,

$$\begin{aligned} \begin{aligned} {\textbf{H}}_{M/\mathrm B}^+&= {\textbf{H}}_{M/\mathrm B}^- \\ {\textbf{H}}_{M+m/\mathrm O}^+&= {\textbf{H}}_{M+m/\mathrm O}^-, \end{aligned} \end{aligned}$$
(2)

where only the x-components the angular momentums are non-zero, resulting in two independent equations. Using equations (1) and (2) we solve for the two unknowns, \(\omega _m^+\) and \(\omega _M^+\) which are the post-collision foot and shank angular speeds respectively, and thus obtain the post collision ankle plantarflexion velocity \(\varvec{\Omega }_{\textrm{pf}}^+ = (\omega _m^+ - \omega _M^+)\hat{{\textbf{i}}}\) as a function of heel height h, which may be readily tested against experiments.

In this study, we experimentally measure the effects of increase in heel height (up to 26 mm) on the early stance ankle dynamics in RFS running. We evaluate the two biomechanical models outlined above, one in the frontal plane and the other in the sagittal plane. In the frontal plane, we test the hypothesis that an increase in heel height increases the ankle torque averaged over the first half of stance, due to an increase in the vertical moment arm of the mediolateral ground reaction force about the ankle (Fig. 1). We focus our analysis on the first half of stance when we expect heel height to have the most significant effect. In the sagittal plane, we experimentally measure the dependence of peak ankle plantarflexion velocity on heel height just after foot contact (around 1–3% of stance), and compare our experimental findings to the predictions of the collision model above (Fig. 2).

Methods

Participants

To estimate sample size, we first estimated the expected effect sizes based on data from a previous study on conventional running shoes10. Using group means and pooled standard deviations from the “barefoot” and “wedged” conditions as defined in Ref.10, we found Cohen’s \(d=1.2\) for frontal plane ankle torque, and \(d=1.3\) for ankle plantarflexion velocity. Then, we estimated the sample size necessary to achieve 80% statistical power with \(\alpha =0.05\) in a paired t-test. The estimated sample size was 7.8 and 6.5 for frontal torque and ankle plantarflexion velocity comparisons respectively.

We recruited \(N=8\) participants (6 males, 2 females; age \(29.5\pm 7.1\,\hbox {years}\), body mass \(82.9\pm 14.4\,\hbox {kg}\), leg length \(0.92\pm 0.06\,\hbox {m}\), mean±s.d.) with no recent history of lower limb injury. The study protocol was approved by the Committee on the Use of Human Subjects which serves as the Institutional Review Board at Harvard University. All research was performed in accordance with regulations established by the Committee, and the Declaration of Helsinki. Each participant provided written informed consent.

To determine the statistical limitations of our sample size, we additionally performed a sensitivity power analysis15 with the following parameters: \(k=4\) groups (for four experimental conditions described below), \(N=8\) participants per group (repeated), \(\alpha = 0.05\), and required statistical power of 80%. We found that the minimum effect size detectable using our sample at this power was \(\eta _p^2 = 0.34\). A main effect in an ANOVA was considered meaningful only when it was statistically significant (\(p<0.05\)) and had effect size \(\eta _p^2 \ge 0.34\) (see the Statistical Methods subsection for more details).

Experimental protocol

Subjects ran at a speed of Froude = 1 (Froude number is defined as \(v^2/gL\), where v is the belt speed, g is acceleration due to gravity, and L is leg length) on an instrumented treadmill (Bertec, Columbus, OH, USA). The average speed across participants was \(3.0\pm 0.1\,\hbox {m/s}\) (mean±s.d.). Subjects were asked to rearfoot strike, and strides with non rearfoot-strikes were removed from the analysis. Rearfoot strikes were judged by observing foot and ankle kinematics (sagittal plane foot-to-floor angle and ankle plantarflexion velocity) in the first 20% of stance. Each trial lasted 30 s. The trials were conducted in four conditions in a randomized order: barefoot, in zero-drop minimal shoes of 6 mm sole thickness (“low”), minimal shoes with an additional 6 mm heel (“medium”), minimal shoes with an additional 20 mm heel (“high”). All shoes were zero-drop minimal shoes (Merrell Rockford, Michigan, USA, model: Vapor Glove, US Men’s size 10, Fig. 3) modified by a professional cobbler (Felix Shoe Repair, Cambridge, MA, USA) who added custom designed heels (for more details see Addison and Lieberman16). The material used to construct heels had a Young’s modulus of 32 MPa. Subjects were encouraged to familiarize themselves on the ground in each shoe condition for as long as they needed (typically taking between 1-3 minutes). Subjects then walked on the treadmill at Froude 0.3 for one minute, then ran at Froude = 1 for another minute before data collection started.

Figure 3
figure 3

Photographs of the experimental shoe conditions. The low heel condition is a zero drop minimal shoe of 6 mm sole thickness with no additional heel attached; medium heel condition has an additional 6 mm heel for a total heel height of 12 mm, and the high heel condition has an additional 20 mm heel for a total heel height of 26 mm.

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All data were collected on the left limb of each participant. In the barefoot condition, three markers were placed on the calcaneus following the Leardini marker set17, and a fourth marker on the head of the second metatarsal. In the shod conditions, four markers were placed directly on the shoe approximately aligned with the markers used in the barefoot condition, following the guidelines for shoe mounted markers18. The rearfoot markers were used to define a foot segment. Additional markers were placed on the medial and lateral malleoli, the tibial tuberosity, and the medial and lateral femoral epicondyles. A four marker cluster was also placed on the shank.

Data collection and analyses

Kinematic data were collected using an 8-camera motion capture system at 200 Hz (Qualisys AB, Gothenburg, Sweden). Kinetic data were recorded at 2000 Hz. Kinematic and kinetic data were low-pass filtered using fourth and eighth order Butterworth filters respectively, with a common cutoff frequency of 25 Hz. Data were initially processed in Visual3D (C-Motion, Inc., Moyds, MD, USA). Further data processing and analyses were performed in MATLAB 9.11.0.1837725 (Natick, MA, USA) and Python 3.1. A total of 32 trials of duration 30 s each were analyzed for 8 subjects and 4 conditions per subject. For each trial, measured quantities were ensemble averaged over all stance phases in that trial. The number of analyzed stance phases varied among trials: on average per subject, there were 42 stances in the barefoot condition, 39 in the low heel condition, 40 in the medium heel condition and 40 in the high heel condition.

The laboratory and all joint coordinate axes are defined such that x is along the medio-lateral direction, y is along the antero-posterior direction, and z is along the superior-inferior direction. Each 30 s trial was segmented into intervals from touchdown to toe off (stance) using \(F_z = 20\,\hbox {N}\) as the threshold for foot contact detection, and the stance time was normalized to be between 0-100%. The mid-point of the two malleoli markers was defined as the ankle joint. The mean mediolateral moment arm of the vertical ground reaction force is defined as the difference between the x components of the center of pressure and the ankle joint position, averaged over the first 50% of stance. The mean frontal plane ankle torque is defined as the cross product of the vector from the center of pressure to the ankle, with the frontal plane ground reaction force vector and averaged over the first 50% of stance. The mean mediolateral and vertical ground reaction forces were the x and z components of the ground reaction force respectively, averaged over the first 50% of stance. The frontal plane orientation of the ground reaction force is defined as the inverse tangent of the ratio of the mediolateral and vertical ground reacion forces, averaged over the first 50% of stance. Ankle plantarflexion velocity in the sagittal plane is defined as the maximum x component of the ankle joint angular velocity expressed in the shank coordinate system in the first 20% of stance. The rotation of the foot segment is measured with respect to the lab frame following an intrinsic x–y–z Euler angle scheme, and normalized within each stance period to the foot segment at the moment of heel strike. The mean foot eversion angle is the angle of rotation about the y axis averaged over the first 50% of stance. Mediolateral ankle displacement is defined as x coordinate of the virtual ankle joint with respect to its position at heel strike, and is averaged over the first 50% of stance.

Collision model parameters

Shank length L is assumed to be half the mean leg length of the participants. We use \(l = L/1.53\), \(M=4.5\%\) and \(m=1.4\%\) of the mean participant body weight19. The heel to foot length ratio \(s=0.21\) based on published radiographic data20. The pre-collision foot velocity components were estimated to be \(v_y^- = 1.34\,\hbox {m/s}\) and \(v_z^- = -0.80\,\hbox {m/s}\) using the mean fore-aft and vertical velocity of the ankle joint at heel strike across all subjects and conditions (since the foot and shank are assumed to move with the same velocity just prior to collision).

Statistical methods

We performed a Type-III one-way analysis of variance (ANOVA) with Satterthwaite’s method to test the effect of heel condition on various measured quantities. First, we created linear mixed models with heel condition as the fixed factor (four levels: barefoot, low heel, medium heel, high heel), and subject as random factor, given by

$$\begin{aligned} Y_{ij} = (\beta _0 + S_{0j}) + \beta _i\ { condition}_i + \epsilon _{ij}, \end{aligned}$$
(3)

where \(i = 1\ldots 3\) is the heel condition index and \(j = 1\ldots 8\) is the subject index. Thus, the dependent variable Y has 32 values. The model estimates are the global intercept \(\beta _0\) corresponding to the barefoot condition (\(i=0\)), and the fixed effects coefficients \(\beta _i\) corresponding to the three shod conditions (\(i=1\ldots 3\)). The random intercepts \(S_{0j}\) quantify inter-subject variability and are assumed to be normally distributed with zero mean. The overall model residuals \(\epsilon _{ij}\) are also assumed to be normally distributed with zero mean. If the ANOVA was significant and effect size \(\eta _p^2 \ge 0.34\) we performed post-hoc pairwise comparisons with Bonferroni adjustments to the p-values. For sample size estimation, power analysis was performed using pwr.t.test function in R, for a paired comparison. For sensitivity power analysis, we used the pwr.f2.test function in R with the effect degrees of freedom \(u=3\), and error degrees of freedom \(v = 21\).

Statistical tests were performed in R 4.1.221, using the lme4 and multcomp packages22,23 for linear mixed models analysis; the effectsize package for for effect size calculation24; and pwr package for statistical power analysis based on Cohen25.

Results

There was a significant effect of heel height condition on the frontal plane ankle torque averaged over the first 50% of stance (\(F_{3,21}=30.9,p<0.001, \eta _p^2 = 0.82\), Fig. 4a). Post-hoc tests indicated a significant change in mean frontal plane ankle torque between heel conditions: a 25.4% decrease from barefoot to high heels (\(p<0.001\)); 13.55% decrease from low to medium heels (\(p<0.001\)); 32.6% decrease from low to high heels (\(p<0.001\)); and a 22% decrease from medium to high heels (\(p<0.001\)). There was a 10.6% increase in the torque from barefoot to low heel (\(p=0.035\)).

Figure 4
figure 4

Effects of heel height on ankle dynamics. Box plots of (a) the frontal plane ankle torque, averaged over the first 50% of stance; (b) the mediolateral moment arm of the vertical ground reaction force about the ankle, averaged over the first 50% of stance; (c) the peak ankle plantarflexion velocity just after foot contact. Each color and line denote one subject’s data.

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There was a significant effect of heel height condition on the mediolateral moment arm of the vertical ground reaction force about the ankle, averaged over the first 50% of stance (\(F_{3,21}=16.42, p<0.001, \eta _p^2 = 0.7\), Fig. 4b). Post-hoc tests indicated significant changes in the mean mediolateral moment arm between heel conditions: a 23.2% decrease from barefoot to high heels (\(p<0.001\)); 11.4% decrease from low to medium heels (\(p=0.03\)); 26.7% decrease from low to high heels (\(p<0.001\)); 17.3% decrease from medium to high heels (\(p<0.001\)).

There was a significant effect of heel height condition on the mean peak ankle plantarflexion velocity just after heel strike (\(F_{3,21}=39.5, p<0.001, \eta _p^2=0.85\) Fig. 4c). Post-hoc tests indicated significant changes in the mean peak ankle plantarflexion velocity between heel conditions: a 47.9%, 41.9% and 72.1% increase from barefoot to low, medium and high heel conditions respectively (\(p<0.001\) for all comparisons);16.3% increase from low to high heels (\(p=0.002\)); 21.3% increase from medium to high heels (\(p<0.001\)).

Figure 5
figure 5

Collision model predictions for ankle plantarflexion velocity. Scatter plot of measured ankle plantarflexion velocity against heel heights in different conditions (barefoot: 0 mm; low: 6 mm; medium: 12 mm; high: 26 mm), and normalized by the barefoot condition. Black squares show means for each heel height, whiskers show standard deviation, and gray dots show individual subjects’ data. The solid gray curve is a plot of the model predicted magnitude of the ankle plantarflexion velocity (\(\varvec{\Omega }_m^+ - \varvec{\Omega }_M^+\)) normalized by the barefoot condition.

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From the collision model, the post-collision ankle plantarflexion velocity is \(\varvec{\Omega }_{\textrm{pf}}^+ = \varvec{\Omega }_m^+ - \varvec{\Omega }_M^+\) where,

$$\begin{aligned} \begin{aligned} \varvec{\Omega }_m^+&= \dfrac{-3Mhv_y^- - 12hmv_y^- + 6lmv_z^- + 12Mlsv_z^-}{(3M+12m)h^2+(4l^2m+12Ml^2s^2)}\ \hat{{\textbf{i}}} \\ \varvec{\Omega }_M^+&= \dfrac{-3l(6Mls^2v_y^- + 6Mhsv_z^- + 3hmv_z^- + 2lmv_y^-)}{L\left[ (3M+12m)h^2+(4l^2m+12Ml^2s^2)\right] }\ \hat{{\textbf{i}}}. \end{aligned} \end{aligned}$$
(4)

Magnitude of the barefoot-normalized ankle plantarflexion velocity \(\varvec{\Omega }_{\textrm{pf}}\) is plotted in Fig. 5.

There was a significant step-to-step correlation in the mediolateral displacement of the ankle joint and the eversion angle of the foot, both measured with respect to the initial moment of foot contact and averaged over the first 50% of stance (\(r=0.93\pm 0.04\), mean±s.d across all analyzed stance phases, Fig. 6a). Averaged over all analyzed steps in each condition, the mean mediolateral moment arm of the vertical ground reaction force about the ankle was correlated positively with mean foot eversion (\(r=0.62\), \(p<0.001\), Fig. 6b).

There was a significant effect of heel height condition on the foot eversion angle, averaged over the first 50% of stance (\(F_{3,21}=11.22, p<0.001, \eta _p^2 = 0.62\), Fig. 6c). Post-hoc tests indicated significant changes in the mean foot eversion angle between heel conditions: a 59.2% increase from barefoot to low heels (\(p < 0.001\)); a 19.8% decrease from low to medium heels (\(p=0.03\)); a 33% decrease from low to high heels (\(p < 0.001\)).

There was no significant effect of heel height condition on the mediolateral GRF (\(F_{3,21}=1.2, p=0.33\)) or on the orientation of the GRF in the frontal plane (\(F_{3,21}=0.24, p=0.87\)). There was a significant effect of heel height condition on the vertical GRF (\(F_{3,21}=7.75, p=0.001, \eta _p^2 = 0.53\)). Post-hoc tests indicated significant changes in the vertical GRF between heel conditions: a 6.1% increase from barefoot to low heels (\(p = 0.001\)); a 6.7% decrease from low to high heels (\(p<0.001\)); a 4.3% decrease from medium to high heels (\(p = 0.04\)).

Figure 6
figure 6

Frontal plane posture of the foot. (a) Mediolateral ankle displacement from its position at heel strike, averaged over the first 50% of stance, plotted against the foot eversion angle across all subjects. Each dot corresponds to the average over the first 50% of each analyzed stance phase in each subject. (b) Mediolateral moment arm of the vertical ground reaction force about the ankle, plotted against foot eversion angle in each condition and subject, averaged over the first 50% of stance. The linear regression line is shown in gray. (c) Box plot of the foot eversion angle averaged over the first 50% of stance. Dots show individual subjects’ data. (Each color denotes the same subject in all three panels).

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Discussion

Over the last 50 years, there has been a general trend towards higher heels in many but not all running shoes, and today’s runners can now choose between heels that vary from just one or two millimeters to about 40 mm3,26. Here we tested how these variations affect the kinematics and kinetics of the ankle in the frontal and sagittal planes during running. In order to minimize the influence of shoe features such as bending stiffness and cushioning5, we used minimal running shoes that offered little to no support, equipped with rigid, custom-built heels. The custom heels in our study ranged in height from 6–26 mm, typical of commercial shoes, but were far more rigid than the heels in most running shoes. Our observations may be different if measured using conventional running shoes, since we must take into consideration the well-known effects of running surface and sole stiffness on foot biomechanics7,27. In this setting, we experimentally tested two specific predictions from simple models of the effect of heel height, one on frontal plane ankle torque in early stance (upto 50%) and the other on sagittal plane ankle plantarflexion velocity just after heel strike.

As predicted, the magnitude of the frontal plane torque changed significantly with increasing heel height, but not in accordance with a simple model based solely on the effects of changing vertical moment arms. Notably the torque in the frontal plane was higher in the minimal shoe condition with no heel relative to the barefoot condition, but with increasing heel height, torque declined (Fig. 4a). Overall, frontal plane torque in the highest heel condition (26 mm) was found to be about 25% lower than in the barefoot condition. This measured reduction in torque was accompanied with reduction in the mediolateral moment arm (\(r_x\)) of the vertical ground reaction force about the ankle (Fig. 4b), as runners tended to run with a center of pressure (COP) closer to the ankle joint in the mediolateral direction over the first half of stance. The reduction in ankle mediolateral torque was also accompanied by small but statistically significant changes in the mean vertical GRF which likely contributed to the observed differences in the frontal plane ankle torque. The mediolateral GRF and the frontal plane GRF orientation were not significantly different.

While this study was not designed to identify specific mechanisms underlying ankle control, we propose that modulation of foot posture in the frontal plane was the strongest influence on \(r_x\). Frontal plane foot posture has distinct but related effects on the mediolateral positions of the ankle and COP. In this study, across all participants and conditions, the COP was located lateral to the ankle joint (defined as the mid point of the two malleoli markers) averaged over the first half of stance (\(14\pm 4.5\,\hbox {mm}\), mean±s.d.). So, in order to reduce \(r_x\), which is the distance between the ankle joint and the COP, either the ankle has to be displaced laterally relative to the COP, or the COP displaced medially relative to the ankle. Once contact is made with the ground, the mediolateral position of the ankle joint is kinematically coupled to the posture of the foot in the frontal plane, assuming no slipping28. Consistent with this coupling, we observed high step-to-step correlation in the mediolateral displacement of the ankle joint and the eversion angle of the foot within each trial: the more everted (inverted) the foot, the more medially (laterally) displaced the ankle (Fig. 6a). Foot posture also affects the location of the COP under the foot by influencing the area of contact with the ground within which the COP must lie during the single support phase, although the COP also depends on the position and acceleration of the center of mass [29, p. 130]. Foot inversion/eversion is correlated with medio-lateral COP location under the foot in walking30, and to a small but significant extent in running31. The more inverted the foot, the more lateral the COP is likely to be under the foot, until it reaches the foot’s lateral boundary. The net effect of these lateral movements of the ankle and COP is that across all conditions and subjects, mean \(r_x\) is correlated positively with mean foot eversion (Fig. 6b). With increasing heel height, foot eversion angle significantly changed (Fig. 6c), in a trend similar to that observed in the moment arm and ankle torque (Fig. 4a,b). The effect of heel condition is still significant if instead of the mean eversion angle over the first half of stance we consider the eversion angle at 50% stance (\(F_{3,21} = 13.2, p<0.001, \eta _p^2 = 0.65\)) or peak eversion in the first half of stance (\(F_{3,21} = 12.3, p<0.001, \eta _p^2 = 0.64\)).

The ways in which runners adjust foot posture and the GRF moment arm in heels of different heights could be interpreted as a strategy by RFS runners to reduce frontal plane ankle torques. It is especially notable that compared to the barefoot condition, even minimal shoes with soles just 6 mm thick led to increased frontal plane ankle torques. Thus, while there is abundant evidence that foot dynamics in barefoot running are closer to running in minimal shoes as compared to conventional shoes5,32, our results highlight that there are still salient differences between running barefoot and in minimal shoes whose consequences may not be completely understood. Interestingly, minimal shoes slightly increased ankle torque relative to the barefoot condition, but as heels got higher this torque decreased (Fig. 4a). We did not investigate the specific proprioceptive feedback mechanisms that underlie runners’ adaptations to heel height, but these mechanisms presumably include both cutaneous33 and sensory organs in muscles34. While a minimal shoe almost certainly reduces proprioceptive feedback from cutaneous sensors35, perhaps the increased vertical moment arm associated with higher heels alters the contraction velocity and tension profiles of the foot invertor/evertor muscles, notably the posterior tibialis and peroneus longus. This hypothesized mechanism is analogous to how during walking, soleus tension increases and shortening velocity decreases with increasing moment arms of the ground reaction force in the sagittal plane due to a change in the gear ratio about the ankle36. Muscle length/velocity and tension are stimuli for muscle spindles and Golgi tendon organs respectively, which in turn modulate reflexive contraction and relaxation of muscle to control movement37,38. Both in vitro and in vivo studies show that variations in individual leg muscle tension can modulate center of pressure under the foot4,39, which has the potential to modulate the frontal plane torque. Further research is necessary in order to test this hypothesized mechanism underlying the foot posture strategies that we observe in this study.

Higher heels also have significant effects in the sagittal plane. In particular, using heel heights within the range of those typically found in running shoes, we found that higher heels were associated with faster ankle plantarflexion velocities in early stance, with the highest heel condition showing an almost 75% increase in peak plantarflexion velocity compared to barefoot. This effect is predicted reasonably well by a simple model of collision at heel strike extended from Lieberman et al.12 (Fig. 5). The pre-collision translational kinetic energy of the foot and shank is partially converted into rotational kinetic energy of the two segments post-collision as they rotate forwards in the sagittal plane. Our simple model sheds light on the magnitude of the post-collision segmental angular velocities, which depend on the pre-collision angular momentum and the moment of inertia of the segments (both defined about the point of collision). The higher the initial angular momentum, greater the final plantarflexion velocity. Conversely, the higher the segment moment of inertia, lower the plantarflexion velocity. Heel height affects both of these quantities: initial angular momentums of the two segments are linear in h and the segment moments of inertia are quadratic in h. Upon substitution of the experimentally measured model parameters (\(L,v_y^-,v_z^-\) and s), the expression for ankle plantarflexion velocity from Eq. (4) reduces to the form \((ah+b)/(ch^2+d)\) where \(a,b,c,d > 0\) are constants. Over the range of heel heights considered in our study, this function grows monotonically with h, and predicts about a two-fold increase in ankle plantarflexion velocity in the high heel condition relative to the barefoot condition. This is consistent with our experimental measurements when the model input parameters used are mean values across participants and conditions (see the Collision model parameters subsection for details), and the ankle plantarflexion velocities are averaged across participants (Fig. 5). Measurements reported in a previous study using conventional shoes10 also show an increase in ankle plantarflexion velocity with higher heels. However, as seen in Fig. 5, there are deviations from model predictions. This is likely because impulsive collision is one of many physical phenomena that together govern ankle plantarflexion velocity at foot strike and our simple model excludes several of these variables like muscle activity, variation in lower limb mass distribution, initial ankle plantarflexion angle etc. The biomechanical effects of high ankle plantarflexion velocities are not well studied but repetitive, fast plantarflexion of the foot during running may contribute to overuse injuries of the tibialis anterior muscle and tendon, including the relatively rare chronic exertional compartment syndrome in the lower leg40,41. Future studies are necessary to test this hypothesis, but we note that chronic exertional compartment syndrome of the anterior tibialis has been shown to be prevented or treated by switching from a rearfoot strike in conventional shoes which presumably involve rapid plantarflexion right after heel strike to a forefoot strike which may reduce this plantarflexing motion42.

Our findings have implications for future studies on shoe design and how runners adapt to higher heels. Currently, data do not exist to evaluate the extent to which runners adapt differently to higher heels in terms of controlling the center of pressure or the rate of plantarflexion, or if there is a critical heel height above which foot posture cannot mitigate high frontal plane torques. In people with tibialis anterior paresis, rapid ankle plantarflexion at heel strike (or “drop foot”) leads to spatiotemporal gait modifications43. It could be useful to evaluate if using minimal shoes or shoes with shorter than usual heels can reduce the initial ankle plantarflexion velocity and a return to pre-paretic gait. Finally, shoes that modulate foot posture, and therefore mediolateral center of pressure, might help runners manage ankle instability injuries.

This study has several limitations. We used heels made of a relatively rigid material compared to the materials used in conventional running shoes. The difference between the loaded and unloaded heights of a compliant shoe heel must be taken into account when evaluating its effects on foot biomechanics, specially since for a given material, higher heels are more compliant44. Further, the rigidity of the running surface and shoe sole material are known to affect some aspects of ankle dynamics in running7,27. Specifically, ankle plantarflexion speeds increase with increased midsole hardness27. Therefore, our measurement of increasing ankle plantarflexion speeds with heel height is possibly exaggerated due to the hard heels used in this study. Unlike any commercial shoe, the additional rigid material was present only under the heel region and not the mid- or forefoot (Fig. 3), which might have led to more midfoot flexion than if the material extended throughout the length of the shoe. Joint ranges of motion and joint velocities are also thought to change due to shoe and surface hardness as a strategy to minimize metabolic cost27, but these adaptations take place over several tens of minutes and thus are unlikely to have played a role in our study given the short time scale of our measurements (30 s). Heel widths in this study were approximately 60 mm, which is about 25–40% smaller than the width of some conventional shoe heels26. The width of the heel constrains the mediolateral range of motion of the COP. Since wider heels allow a greater mediolateral range of motion of the COP, runners’ strategies to control ankle torque might differ from what we observed. Finally, subjects did not run at self selected speeds, and since each trial duration was 30 s, any gait adaptations or effects of fatigue were not present.