The present study is the first to classify PIFMs based on their morphological parameters such as PCSA and FL, which represent the potentials for maximal force generation and shortening velocity, respectively. The main findings obtained here indicate that individual PIFMs are assigned to each of the four clusters by k-means clustering, based on the similarity in morphological profiles reflecting contractile properties, except for ABDH, which was equivalently subdivided into two clusters (Table 2 and Fig. 3).

Cluster 1 was characterized by a large PCSA and short FL (Table 2) and the primary components of this cluster were the following three muscles: ABDH, ADDH-OH, and FHB. The three muscles involved in cluster 1 cross the first metatarsophalangeal (MTP) joint and attach either just below (FHB), medially (ABDH), or laterally (ADDH-OH) to the proximal phalanx via the ligamentous or tendonous extension. Thus, these muscles are involved in motions of this joint: FHB flexes the first MTP joint, whereas ABDH and ADDH-OH mainly cause the abduction/adduction and partly assist with the flexion of the first MTP joint. Considering this morphological characteristic, it seems that these three muscles possess high force generation potentials at the great toe and may play an important role in walking or running. More specifically, during the push-off phase of walking or running, the forefoot is the only part contacting the ground, and the trajectory of the center of pressure typically passes from the medial forefoot toward the hallux [25, 26]. The magnitude of the plantarflexion (or simply flexion) moment at the first MTP joint is the greatest among all other MTP joints [27]. Based on this, the three primary muscles in this cluster (i.e., ABDH, ADDH-OH, and FHB) may act as major force generators of the great toe during walking or running because of their potential to generate a high moment around the first MTP joint and anchor this joint in a stable position.

Cluster 2 had a moderate PCSA and FL (Table 2), indicating a well-balanced potential for force generation and shortening velocity. The number of ABDM and FDB data samples assigned to this cluster was significantly higher than that for the other clusters, while ABDH had a comparable number of data samples in clusters 1 and 2 (Table 2). Thus, the function of this cluster should be discussed based on the three primary constituents, i.e., ABDH, ABDM, and FDB, which are positioned underneath the LAs in the first/superficial layer. ABDH runs along the medial LA and abducts the first MTP joint, whereas ABDM is located underneath the lateral LA and causes abduction at the fifth MTP joint. The FDB is located between these arches immediately above the plantar aponeurosis and flexes the second to fifth interphalangeal and MTP joints. Accordingly, these three muscles appear to be arranged like a framework stabilising the arched structure of human feet [28], and contribute to achieving a wide and stable base of support by spreading the great and little toes and grabbing the ground with the lesser toes. For example, the impaired activation of ABDH, caused by a tibial nerve block, decreases the medial LA height [29]. Conversely, the increased activation of ABDH and FDB (as well as QP) induced by intermuscular electrical stimulation inhibits the joint motion within the foot toward the pronated posture, resulting in resistance to the collapse of the LAs [30]. Furthermore, the activities of ABDH, ABDM, and FDB positively contributes to the vestibular control of postural balance in the upright posture [31, 32]. Taken together, the muscles consisting of cluster 2, i.e., ABDH, ABDM, and FDB, may primarily act as 1) stabilizers for the arched structure of the human foot, and 2) regulators for maintaining a stable posture with their well-balanced potentials of force generation and shortening velocity.

The muscles involved in cluster 3 were characterized by a small PCSA and long FL (Table 2), indicating a high potential for shortening velocity. Interestingly, among the clusters confirmed in the present study, this cluster consisted only of a single muscle, QP (Table 2). Among the PIFMs, QP is a unique muscle that does not directly attach to the toes. Alternatively, this muscle inserts into the flexor digitorum longus tendon, an extrinsic foot muscle which causes lesser toe flexion [33]. Furthermore, a study involving 116 legs of 62 specimens reported that, in most cases, the tendon of the flexor hallucis longus slips into the great toe and branches into the tendons of the flexor digitorum longus where QP is attached [34]. This implies that QP causes flexion at the lesser toes and flexion at the great toe [34]. Moreover, an electromyographic study suggested that the preceding or simultaneous activity of QP relative to the extrinsic toe flexors (flexor digitorum longus and flexor hallucis longus) during walking enhances the efficient torque generation at the toes [35]. Considering these aspects, it is assumed that cluster 3 (QP) may contribute to regulating force generation at the toes by extrinsic toe flexors by quickly controlling the direction of muscle tension produced by extrinsic toe flexors.

Cluster 4 was characterized by an extremely small PCSA and moderate FL, reflecting a very low force generation potential. Of the 27 data samples in this cluster, 26 were from ADDH-TH (Table 2), indicating that the function of this cluster depends on that of ADDH-TH. The PCSA of ADDH-TH measured in healthy young males in the present study was approximately 5–12 times smaller than that measured in non-hominid primates in a previous study [36]. This implies that the functional requirement for ADDH-TH in non-hominid primates is high because of their well-developed ability to grasp branches at the hallux during arboreal locomotion [37], whereas it is lost in humans during adaptation to terrestrial locomotion. Thus, this cluster’s extremely small PCSA or force generation potential may be involved in the transition of humans from an arboreal to a terrestrial lifestyle. However, a recent study showed that ADDH-TH, which lies along the anterior transverse arch in the distal forefoot, plays a role in bipedal locomotion in humans [3]. Their results suggested that the activation of ADDH-TH increased during the initial contact and push-off phases, indicating that this muscle contributes to stabilising the forefoot and the hallux during the propulsion [3]. Considering these results, it is likely that cluster 4, which primarily consists of ADDH-TH, may act as a forefoot stabilizer for human locomotion but with an extremely small force generation potential.

The present study had some limitations. First, the PCSA and FL were estimated in accordance with the procedure described by Fukunaga et al. [13], who used the combined data obtained from living subjects and cadavers. A recent study determined the FL and pennation angle of the gastrocnemius in vivo by using diffusion MRI [38]. Applying the new approach for determining FL and pennation angle in vivo may enable the precise estimation of the contractile properties of each individual. Second, we had no data on the moment arms of the PIFMs, which is a factor in discussing muscle function during living activities. From the findings of a cadaveric study with older samples, the average moment arms of several PIFMs causing the first MTP joint movement ranged from 4.5 mm (ADDH-TH) to 8.2 mm (FHB medial head) [39]. If the moment arms, in addition to the abovementioned variables used to calculate PCSA (i.e., pennation angle and FL), could be obtained from living subjects, the PIFMs’ function would be determined in more detail. Third, this study aimed to estimate the function of PIFMs from their PCSA and FL. However, even though these morphological profiles may indicate force output potentials, the magnitude and temporal patterns of the muscle recruitment may also significantly affect PIFMs’ function. This point will need to be paid attention to if the current findings are to be applied to clinical settings.

Finally, the participants of this study were healthy young adult males only. The reason for this was to collect a dataset from a homogeneous sample to avoid potential confounding influences of sex and/or age on muscle morphology. More specifically, k-means clustering analysis used in this study is an unsupervised algorithm that assigns each data sample to specific clusters with the nearest mean (cluster centroid) [18]. Thus, if the individual samples in the dataset have a vast variety of muscle morphological profiles, k-means clustering analysis may fail to function for addressing the purpose of this study, which was to examine how individual PIFMs can be classified based on their morphological parameters. Currently, it is unknown whether morphological profiles of the PIFMs are affected by sex and/or age, but sex differences have been found to exist in other muscles such as those in the lower/upper extremities [20,21,22] and around the pelvis [40]. Thus, more studies are needed to further examine sex differences in morphological profiles of the PIFMs and the applicability of the current results to other populations, such as females.