Fig 1.
Musculoskeletal model of the ankle and foot.
Plantar intrinsic muscle is not visible, because it shares the same path as the plantar fascia. Visualised via OpenSim [38,39].
Fig 2.
Deformation of a standing foot under vertical compression.
Full lines indicate experimental data (digitised from (a) Ker et al. [2], (b) Yawar et al. [19], (c) Welte et al. [18]), and circles represent simulations. (a) Repeated loading of a cadaver foot after sequentially removing different soft tissue. The table gives an overview of structures that are present in each condition. Elongation was computed as the difference in length between calcaneus origin (defined as the most inferior, lateral point on the posterior surface of the calcaneus [73]) and MTP joint centre during the virtual experiment with respect to the resting condition, i.e. the unloaded intact foot. (b) Vertical force-displacement curves for different toe dorsiflexion (DF) positions. Displacement was calculated as the vertical position of the ankle joint centre, relative to its position when no external load is applied to the foot with toes at 0° DF. (c) Vertical loading of a standing foot of an in vivo subject, with toes passively dorsiflexed 30° and -30°. Including baseline muscle activation influenced the force-displacement curves and changed the effect of the toe position.
Fig 3.
Predictive simulation results with the presented model compared to experimental data and state-of-the-art simulation.
Vertical lines indicate stance-to-swing transition. (a) Kinematics. (b) Kinetics. (c) Joint powers. (d) Muscle activation. Experimental data was obtained from one subject and therefore the grey band represents stride-to-stride variability. Kinematics, kinetics, and powers of all joints can be found in section 11 in S1 Text.
Fig 4.
Deformation power and work by soft tissue distal to ankle-foot segments.
(a) Power distal to segments. (b) Positive, negative, and net work. Experiment-based data, digitised from Takahashi et al. [70], is plotted from reference.
Fig 5.
Effect of Achilles tendon stiffness.
A stiff Achilles tendon results in less ankle dorsiflexion and push-off power, and a different soleus activation pattern. Experimental data was obtained from one subject and therefore the grey band represents stride-to-stride variability.
Fig 6.
Effect of foot arch stiffness.
We reduced foot arch stiffness, or the ability to stiffen the arch, by removing the plantar intrinsic foot muscle, by reducing plantar fascia stiffness, or by reducing foot arch height. All changes resulted in alterations in (a) kinematics and (b) reductions in peak ankle power. (c) Simulated activation of the plantar intrinsic foot muscle. (d) Fibre length of the plantar intrinsic foot muscle, normalised by optimal fibre length. (e) Comparison of nominal and reduced foot arch height, visualised via OpenSim [38,39]. Experimental data was obtained from one subject and therefore the grey band represents stride-to-stride variability.
Fig 7.
Effect of removing the plantar intrinsic muscle on joint moments.
(a) Total joint moment. Experimental data was obtained from one subject and therefore the grey band represents stride-to-stride variability. (b) Joint moment by different muscle groups and plantar fascia. Extrinsic muscles crossing MTP are flexor digitorum and hallucis longus and extensor digitorum and hallucis longus. Extrinsic muscles crossing MTJ (midtarsal joint) additionally include tibialis anterior and posterior, and peroneus (brevis, longus, and tertius). Joint moments by individual muscles are shown in Fig AK in S1 Text.
Fig 8.
Joint powers of midtarsal joint, MTP joint, and summed power of both joints.
(a) Plantar fascia and plantar intrinsic muscle account for most power around these joints. (b) Plantar intrinsic muscle power has a lower magnitude and later onset than plantar fascia power.