Determination of muscle strength and function in plesiosaur limbs: finite element structural analyses of Cryptoclidus eurymerus humerus and femur

Osteology of the appendicular skeleton of plesiosaurs

The scapula and coracoid of the pectoral girdle, and the pubis and ischium of the pelvic girdle of plesiosaurs, consist of large flat bony plates lying ventrally. All except the scapula meet the element on the other side in a medial symphysis at the midline of the body in a slightly v-shaped configuration. In some plesiosaurs, the scapulae also meet in a medial symphysis. The coracoid and pubis are greatly expanded. The dorsal extension of the scapula and the dorsally directed ilium are greatly reduced (Andrews, 1910). Gastralia lie between the pectoral and pelvic girdles and stiffen the trunk region (Sues, 1987; Taylor, 1989). Humeri and femora of some plesiosaurs such as Cryptoclidus eurymerus, a Middle Jurassic cryptoclidid known from many specimens from the lower Oxford Clay Formation of England (Andrews, 1910), have a rounded proximal end and an oval midshaft cross-section. The epicondyles are expanded and hammer-shaped. The mounted skeleton of Cryptoclidus eurymerus in the Goldfuß Museum, University of Bonn (IGPB R 324) shows these features well. The humeral and femoral heads of plesiosaurs were probably covered by a thick and vascularized cartilaginous cap (Krahl, 2021), as has been reported for Dermochelys coriacea (Rhodin, Ogden & Conlogue, 1981; Snover & Rhodin, 2008).

The distal end of the humerus of Cryptoclidus is greater than that of the femur and rather atypical for most plesiosaurs (see, e.g., Großmann, 2006; Sachs, Hornung & Kear, 2016). Radius/ulna and tibia/fibula are greatly shortened and have a discoid appearance (Andrews, 1910). Metacarpal V and metatarsal V are integrated proximally into the rows of carpals and tarsals (Robinson, 1975). Fore- and hindflippers exhibit hyperphalangy (Andrews, 1910).

Flipper muscle reconstructions

Plesiosaur muscles have been previously reconstructed by several researchers, including Watson (1924), Tarlo (1958), Robinson (1975), Lingham-Soliar (2000), Carpenter et al. (2010), Araújo & Correia (2015), and Krahl & Witzel (2021). Carpenter et al. (2010), Araújo & Correia (2015), and Krahl & Witzel (2021) relied on the extant phylogenetic bracket (EPB), a method developed in the 1990s to make reliable inferences about the soft tissue anatomy of fossils (Bryant & Russel, 1992; Wittmer, 1995). Older studies (Watson, 1924; Tarlo, 1958; Robinson, 1975; Lingham-Soliar, 2000) did not use EPB and did not clearly indicate which living taxa they relied on for their muscle reconstructions. Muscles originating at the pectoral girdle and attaching to (or spanning) the humerus were reconstructed by Watson (1924), Tarlo (1958), Robinson (1975), Lingham-Soliar (2000), Carpenter et al. (2010), Araújo & Correia (2015), and by Krahl & Witzel (2021). Locomotory muscles originating from the pelvic girdle, traversing the femur, and attaching to the femur were partially reconstructed by Robinson (1975), Lingham-Soliar (2000), and Carpenter et al. (2010), and completely reconstructed by Krahl & Witzel (2021). Muscles originating distally from the humerus and femur were partially reconstructed by Robinson (1975) and completely by Krahl & Witzel (2021). Robinson (1975) appears to have reconstructed the ventral side of the foreflipper and the dorsal side of the hindflipper, although this is not clearly stated (Robinson, 1975; Krahl & Witzel, 2021). The superficial conclusion would be that the dorsal and ventral fore- and hindflipper sides might look the same in plesiosaurs, which is not supported by the EPB because the dorsal and ventral fore and hind limb musculature of living Sauropsida are not congruent (Walker, 1973; Meers, 2003; Russell & Bauer, 2008; Suzuki et al., 2011). The distal fore- and hindflipper musculature of plesiosaurs reconstructed by Robinson (1975) looks very similar to the foreflipper musculature of cetaceans in its extreme reduction (Cooper et al., 2007). This whale-like condition seems unlikely for plesiosaurs because the foreflippers of whales are merely control surfaces and not lift-producing propulsory organs (Fish, 2002; Woodward, Winn & Fish, 2006), whereas the main propulsive organ of whales is a large muscular swimming tail with a fluke (Fish, 1996; Woodward, Winn & Fish, 2006). In contrast, plesiosaurs swam actively with their fore- and hindflippers (Krahl & Witzel, 2021). Krahl & Witzel (2021) were the first to reconstruct the entire locomotor musculature of the fore- and hindflippers of a plesiosaur. They reconstructed a complex arrangement of muscles for plesiosaur fore- and hindflippers that would allow the plesiosaur to twist its two pairs of flippers along the flipper length axis and perhaps even actively control the flipper profile, as suggested by hydrodynamic calculations of plesiosaurs by Witzel, Krahl & Sander (2015) and Witzel (2020).

Hypotheses on the locomotion of plesiosaurs

The locomotion style of plesiosaurs has been the subject of an ongoing debate for over a century (Williston, 1914; Watson, 1924; Tarlo, 1958; Robinson, 1975, 1977; Feldkamp, 1987; Lingham-Soliar, 2000; Carpenter et al., 2010; Araújo et al., 2015; Araújo & Correia, 2015; Liu et al., 2015; Krahl & Witzel, 2021). It has been suggested that plesiosaurs rowed like ducks or otters (Williston, 1914; Watson, 1924; Tarlo, 1958; Araújo et al., 2015; Araújo & Correia, 2015), fly underwater like sea turtles and penguins (Robinson, 1975, 1977; Lingham-Soliar, 2000; Carpenter et al., 2010; Liu et al., 2015; Muscutt et al., 2017; Krahl & Witzel, 2021), or use rowing-flight like sea lions (Feldkamp, 1987; Liu et al., 2015). The main difference between the different modes of locomotion stems from the underlying hydrodynamics: rowing uses water resistance to push the body forward, whereas underwater flight generates lift and thrust from oncoming water currents moving around a cambered flipper profile (e.g., Baudinette & Gill, 1985; Fish, 1996; Walker & Westneat, 2000). Sea lion rowing-flight relies on both hydrodynamic mechanisms, drag and lift, at different stages of the limb cycle (Feldkamp, 1987). It has also been proposed that the anterior pair of flippers uses a different mode of locomotion than the posterior pair of flippers (Tarlo, 1958; Lingham-Soliar, 2000; Liu et al., 2015).

A flipper used in rowing is usually moved in an anteroposterior direction, with little dorsoventral movement (Pace, Blob & Westneat, 2001; Rivera, Rivera & Blob, 2011; Rivera, Rivera & Blob, 2013). The anteroposterior extension and dorsoventral reduction of the bony elements of the pectoral and pelvic girdles of plesiosaurs, and the accompanying reduction or hypertrophy of the locomotor musculature, have been interpreted as favoring the protraction and retraction of the pectoral flipper, i.e., a rowing motion (Watson, 1924; Tarlo, 1958; Godfrey, 1984).

In contrast, the pectoral flipper is flapped mainly dorsoventrally during underwater flight, with a minor anteroposterior component. The downstroke of the flippers of Cheloniidae and Spheniscidae is characterized by strong depression and slight retraction of the flipper. The upstroke is accomplished by elevation and protraction of the humerus. The flipper tip describes an oblique “O” in the anterodorsal-posteroventral direction (Clark & Bemis, 1979; Davenport, Munks & Oxford, 1984; Rivera, Wyneken & Blob, 2011; Rivera, Rivera & Blob, 2013). As Robinson (1975) noted, the hydrofoil-shaped flippers of plesiosaurs, tapering toward the tip and superficially comparable to those of penguins and sea turtles, suggest that they were used for underwater flight rather than rowing. In addition, the shoulder and hip joints of plesiosaurs restrict movement in the anteroposterior direction more than in the dorsoventral direction (Krahl, 2021).

In rowing-flight, the downstroke is lift-generating and similar to the downstroke of underwater fliers. At the point of maximum ventral flipper excursion, the flipper suddenly functions like a paddle and pushes against the water as it is retracted and elevated. During the recovery stroke, the flipper is protracted and elevated with little to no contribution to propulsion (Feldkamp, 1987). Godfrey (1984) noted that in recent underwater fliers, the shoulder girdles are characterized by a strong bony support that extends in a dorsoventral direction, which is not the case in plesiosaurs. Therefore, he concluded that sea lions and plesiosaurs share more similarities than recent “true” underwater fliers (Godfrey, 1984).

In addition to locomotion style, there is still debate about how the four flippers moved in relation to each other, i.e., fore- and hindflippers synchronous, asynchronous, or out of phase. This is the so-called “four-wing problem”, which is about how plesiosaurs avoided placing their hindflippers in the vortices shed by their foreflippers, which would result in a significant decrease in hindflipper performance (Frey & Riess, 1982; Tarsitano & Riess, 1982; Lingham-Soliar, 2000; Carpenter et al., 2010; Muscutt et al., 2017). Experiments in a water tank showed that plesiosaur underwater flight was most efficient when the fore- and hindflippers were slightly out of phase, i.e., the foreflipper was slightly in front of the hindflipper (Muscutt et al., 2017).

Basics of muscle physiology

During a limb cycle, muscles can follow either a shortening-stretch cycle or a stretch-shortening cycle. In the first case, the muscle is shortened while its force output increases. Then, the muscle is stretched and the force output decreases. In the latter, the muscle is initially stretched while its force output increases. As the muscle contracts, its force output decreases (Rassier, MacIntosh & Herzog, 1999). The force production of the muscle depends on the architecture of the muscle. Muscle architecture includes the length of the muscle and tendon (if any), lines of action, muscle mass, specific density of the muscle, intrinsic muscle force, fascial length, and pennation angle (Alexander & Vernon, 1975; Gans, 1982; Sacks & Roy, 1982; Powell et al., 1984; Narici, Landoni & Minetti, 1992; Anapol & Barry, 1996; Kummer, 2005; Azizi, Brainerd & Roberts, 2008). Parallel-fibered muscles have, on average, longer fascicles, greater volume, and can contract faster (which depends on the composition of the fiber types) than pennate muscles. However, more muscle fibers may be juxtaposed in a pennate muscle than in a parallel-fibered muscle of the same size. Therefore, a pennate muscle can exert a greater force than a parallel-fibered muscle of the same size, even though the pennate muscle has shorter fibers. This is because maximum muscle force depends not only on fiber length, but also on its physiological cross-sectional area (PCSA), i.e., the sum of fiber cross-sections (Gans, 1982; Burkholder et al., 1994; Allen et al., 2010; Huq, Wall & Taylor, 2015).

The muscle length of a parallel-fibered, fast-contracting muscle also varies considerably and comes at the expense of a high metabolic cost and relatively low force production. In contrast, highly pennate muscles exert relatively high forces at a much lower metabolic cost, but contract much more slowly and have poor control of fiber contraction (Biewener & Roberts, 2000).

Pennate muscles can generate relatively high forces while their muscle lengths behave almost isometrically, e.g., in turkey (musculus (m.) gastrocnemius) (Roberts et al., 1997) or wallaby (m. gastrocnemius, m. plantaris) (Biewener, Konieczynski & Baudinette, 1998). In contrast, the pennate m. pectoralis muscle, which has a very high output, shows a very large muscle length change of 30–40% in Columba livia (Biewener, Corning & Tobalske, 1998; Biewener & Roberts, 2000) or about 30% in Anas platyrhynchos (Williamson, Dial & Biewener, 2001). In general, the change in muscle length of striated vertebrate muscles can be up to +/– 25% (contraction and extension relative to resting length (= 0%)) before their ability to generate force decreases significantly (Biewener & Roberts, 2000).

Finite element structural analysis

As measurements with strain gauges show, the long bones of Tetrapoda are functionally loaded by torsion, compression, and bending in an intermittent fashion. Most often they are loaded by bending in alternate directions or mainly by compression and subordinately by tension. High torsional loads act on the long bones of terrestrial tetrapods (Biewener & Dial, 1995; Carrano, 1998; Blob & Biewener, 1999; Main & Biewener, 2004, 2007; Butcher et al., 2008; Butcher & Blob, 2008; Sheffield et al., 2011; Young & Blob, 2015; Young et al., 2017).

To represent such changing loading conditions, a series of load cases can be analyzed using finite element structural analysis (FESA; Witzel & Preuschoft, 2005) and then be superimposed on each other (Carter, Orr & Fyhrie, 1989). Reducing the bending moment (Klenner et al., 2015; Lutz et al., 2016; Milne, 2016; McCabe et al., 2017; Lipphaus & Witzel, 2018) can result in lightweight biological structures (Klenner et al., 2015). While structures under bending are subjected to compression on one side and tension on the opposite side, homogeneous compression with low tensile stresses indicates low bending. A further concept relevant for our analysis is bending-minimized lightweight design (Witzel et al., 2011; Bartz, Uttich & Bender, 2019; Gößling et al., 2014). The importance of bending-minimized lightweight design is that it reduces the energy required for locomotion. The principle of bending-minimized lightweight design is that the shape of the bone is guided by the functional superposition of all mechanical loads experienced by a given bone during its ontogeny (Wolff, 1893; Carter, Orr & Fyhrie, 1989; Witzel & Preuschoft, 2005). A homogeneous compressive stress distribution optimally utilizes the material: Bartz et al. (2018) conducted a study on a beam with a fixed support loaded with a single force at the end of the beam and showed a significant weight reduction when topology optimization and tension cables are combined to achieve homogeneous compressive stresses. We apply this principle in our FESA of the plesiosaur humerus and femur.

FESA is used in various disciplines that include engineering and biomechanics (Rayfield, 2007). FESA enables the analysis of mechanical stresses and strains in engineering and biological structures in 2-D or 3-D (Rayfield, 2007; Witzel et al., 2011) and can contribute to our understanding of the function of bony elements (Witzel et al., 2011). Compressive loads are applied to bone via tension chords. Tension chords are either muscles and tendons (active tension chords) or ligaments (passive tension chords), and they act in pairs of agonists and antagonists (Witzel & Preuschoft, 2005; Sverdlova & Witzel, 2010; Curtis et al., 2011; Witzel et al., 2011; Klenner et al., 2015; Felsenthal & Zelzer, 2017, Krahl et al., 2019). A movement is driven by the agonist while the antagonist opposes it to perform a controlled movement (Sverdlova & Witzel, 2010). When the same movement is reversed, the agonist becomes the antagonist and vice versa. Thus, agonists and antagonists constantly load a bony structure by compressive stress, although the agonist exerts a proportionally higher force than the antagonist. In the past, FESA has been successfully used in functional morphology to predict tension chords in living animals, such as a collagenous and elastic tissue extending longitudinally below the septum nasi and associated with the m. pterygoideus anterior in crocodylians, which was later confirmed in dissections (Klenner et al., 2015).

The objective of this study was to test muscle reconstructions of plesiosaurs using FESA. Muscle reconstructions obtained with the EPB, i.e., based on comparative anatomical studies, and mechanically imposed demands on muscles inform each other. We investigated how muscle physiological details, such as muscle length changes, can contribute to muscle reconstructions of fossils and whether FESA of the plesiosaur humerus and femur can provide information about plesiosaur locomotion. The results complement previous hydrodynamic and morphological studies suggesting that plesiosaurs must have used flipper twisting for efficient underwater flight (Witzel, Krahl & Sander, 2015; Witzel, 2020; Krahl, 2021), which is a common phenomenon in aquatic vertebrates (e.g., Walker & Westneat, 2000; Walker & Westneat, 2002) and confirm the myological mechanism of flipper twisting reconstructed by Krahl & Witzel (2021).

Analog model of the lines of action of the flipper muscles of Cryptoclidus

LOA represent the direct connection in a straight line between the origin and attachment of a muscle (Krahl et al., 2019). However, it should be noted that this is a simplification made for FE/multibody dynamics modeling of often more complex muscle pathways that may, for example, wrap around bone during part of a movement cycle (Krahl et al., 2019; Snively et al., 2013). LOA were obtained experimentally in an analog model (Fig. 1) using resin casts of the pectoral (Figs. 2–4) and pelvic girdles and limbs (Figs. 5–7) of the mounted skeleton of Cryptoclidus eurymerus (IGPB R 324) exhibited at the Goldfuß Museum, Section of Paleontology, Institute of Geosciences, University of Bonn (IGPB), on which the muscle reconstructions of Krahl & Witzel (2021) are based.

To build the analog model, the casts of the pectoral and pelvic girdles were mounted on a wooden frame built from slats mostly 2.5 by 5 cm in cross section and fixed with screws. Slats were also used to model the vertebral column. The vertebral column needed to be part of the model because it serves as the origin of some locomotor muscles. The anatomical positioning of the bone casts and the vertebral column was based on the mount. The missing cartilage cover in the shoulder and hip joints was replaced with thick styrofoam pads. The goal was to achieve congruency between the oval glenoid and acetabulum and the rounder humeral and femoral head. This required a styrofoam thickness of up to about ten millimeters. This assumption is based on the observation of specialized vascularized cartilage in Dermochelys coriacea and its associated osteological correlates (a highly grooved and pierced articular surface of the humeral head) (Rhodin, Ogden & Conlogue, 1981; Snover & Rhodin, 2008) and the presence of comparable osteological correlates in Cryptoclidus eurymerus humeri and femora, as noted by Krahl (2021). Non-elastic white nylon cords were used to physically model the muscle lines of action, hereafter termed muscle cords. The fore- and hindflippers were hung into the frame and attached to the pectoral and pelvic girdle in the respective joints with help of the muscle cords. Screw eye pins were screwed into the cast at the muscle origin and insertion points, and the muscle cords were tied to these. When further mechanical support was necessary, the flippers were fixed in the selected flipper positions by additional nylon cords (Fig. 1).

The insertions of all fore- and hindflipper locomotor muscles spanning either the glenoid or acetabulum (12 on the foreflipper, 14 on the hindflipper) were taken from Krahl & Witzel (2021) (Figs. 2, 3, 5, 6). Each muscle cord was threaded through the holes of three electrical terminal strips in sequence, later to be used in determining muscle length changes (Table 1). Hooks were then attached to both ends of the cords, which were then hooked into the screw eyes representing the muscle attachments (Fig. 1). If a muscle attachment area is small, the screw eye pin was screwed in approximately in the middle. In contrast, muscles with large attachment areas were divided into multiple subsections to better capture the different fiber attachment angles and directions and to avoid stress singularities that create artificially high stress and strain peaks at force transmission points (Kim, Sankar & Kumar, 2018). Accordingly, the total muscle force of a muscle was also subdivided, and portions of the total muscle force were assigned to the subsections. In general, the most anterior and posterior points in the body midline were chosen for screw eye pin placement (e.g., m. subcoracoscapularis, m. coracobrachialis brevis, m. pectoralis). In the case of the m. latissimus dorsi, for example, a position between the most cranial and the most caudal origin was chosen. This was done to represent the parts that are best supported by the EPB (cranial and middle parts), but also to cover the less well supported part (caudal part) (Krahl & Witzel, 2021).

These muscle subsections do not necessarily represent actual partitions of the reconstructed muscles, although some muscles were likely compartmentalized, e.g., m. pectoralis, m. latissimus dorsi, m. puboischiofemoralis internus, and m. puboischiofemoralis externus. Muscles with two or more heads (i.e., m. deltoideus scapularis, m. deltoideus clavicularis, m. coracobrachialis brevis, m. coracobrachialis longus, m. triceps brachii, m. caudofemoralis brevis (ilium and vertebral column), m. flexor tibialis internus, m. flexor tibialis externus, m. puboischiofemoralis internus, and m. puboischiofemoralis externus) were implemented as two (or more) cords. The resulting vectors of the different subsections of these muscles, which have a large area of origin, were included in the FE models. Agonistic and antagonistic muscles attaching to, originating from, or spanning the humerus (Table 2) and femur (Table 3) were inferred from the mount. Images for documentation were taken from cranial/anterior (Figs. 4A–4F), caudal/posterior (Figs. 7A–7F), ventral (Figs. 2A and 5A), and dorsal (Figs. 3A and 6A). Figures 2, 3, 5, and 6 show some muscles that are not relatively close to the humerus, femur, or pectoral flipper. This is probably not an anatomically correct muscle course. Muscles are normally held closer to the body, such as by ligament slings. We did not add loop-like structures to measure muscle length changes in the analog model because it proved impractical. The implementation of the muscles in the FESAs were based on sketches in which we assumed force vectors for each muscle were closer, on average, to adjacent bone elements. These muscles may have been held close by annular pulleys. Terminology for the limb motion cycle follows Rivera, Wyneken & Blob (2011) and Krahl & Witzel (2021), who use humeral and femoral depression, elevation, protraction, and retraction, which reflect well the requirements for underwater flight.

Determination of changes in flipper muscle length

Total muscle length changes were measured on the analog model to determine if the experimental data could be used to reconstruct plesiosaur muscles. Three positions in the inferred beat cycle of the foreflipper and hindflipper were selected for determining the total muscle length change of muscles originating at the pectoral and pelvic girdles or vertebrae and inserting or spanning the humerus and femur. These flipper positions are the maximum dorsal excursion of the fore- and hindflipper during upstroke (~+50° from horizontal) (Figs. 4A, 4B, 7A and 7B), the maximum ventral excursion of the fore- and hindflipper during downstroke (~−50°) (Figs. 4E, 4F, 7E and 7F), and the neutral position (0°) (Figs. 4C, 4D, 7C and 7D). Based on glenoid and acetabular alignment, the tip of the foreflipper points slightly anteriorly, and the tip of the hindflipper points slightly posteriorly. Protraction and retraction were not considered because they contribute little to the flipper beat cycle inferred from osteology. The degrees of maximum elevation and depression of the flipper were based on the determination of flipper motion by Carpenter et al. (2010) and Liu et al. (2015) for several plesiosaur species. However, we note that the inferences on degree of excursion above and below the horizontal are highly dependent on how much cartilage presumably covered the humerus and femur, as well as the glenoid and acetabulum, as noted by Liu et al. (2015), and on plesiosaur species (which differ in the size of the dorsal tuberosity/trochanter).

We chose not to refer to the neutral flipper position as the resting position of the flipper because it is probably impossible to determine the resting position of the flipper for an extinct species. Furthermore, in the muscle physiology literature, the term “resting length” usually refers to individual sarcomeres (Rassier, MacIntosh & Herzog, 1999) or fascicles of a muscle (Biewener & Roberts, 2000). Furthermore, not knowing the exact flipper muscle resting length affects the exact value of muscle stretching and contraction, but not the final result of the total length change of a muscle, which was calculated in this study (see below). This is because the absolute values of muscle stretching and contraction are indeed measured with respect to the neutral position, but the total change in length of the muscle is the difference between the maximum muscle stretching and contraction.

All three positions of the fore- and hindflippers were fixed in sequence with black nylon cords suspending the flippers from the wooden frame. For each of the three positions, the length of each muscle was fixed using the terminal strips by tightening the small screws in the terminal strips on the muscle cords. Then, each muscle cord was removed from the model by unhooking it from the screw eye pins, and all three muscle lengths, i.e., maximum deflection on downstroke, neutral position, and maximum deflection on upstroke, were measured in cm using a tape measure as the distance between the respective terminal strips. The changes in length between the maximum deflection on the downstroke and the neutral position and between the maximum deflection on the upstroke and the neutral position were recalculated as percentages, with the resting length set to 100%. Then, muscle stretching, muscle contraction, and the difference between the two, the total change in muscle length, were calculated in % (Table 1). Bar graphs for total muscle length change in % were created using Microsoft Excel (Figs. 8A and 8B). Some muscle length changes were given as 0 cm because the actual length changes could not be measured because they were smaller than the width of the terminal strips. In one case, i.e., the m. deltoideus scapularis, the total length change of the muscle was found to be unphysiological when attached to the lateral on the scapula blade (see below). Hence, a different area of origin (at the ventrolateral part of the scapula) was tested, which yielded physiologically plausible results, which were then measured for all three positions.

FESA and computational determination of muscle strength

FESA requires a 3D model of the bones to be investigated. Hence, the right humerus and left femur were removed from the mounted skeleton IGPB R 324 and scanned with the micro-CT scanner at IGPB. The scanner is an industrial high-resolution computed tomography scanner (model Phoenix v|tome|x s 240, manufactured by General Electric Phoenix X-ray, Wunstorf, Germany). The scans were processed using the dedicated datos|x software and the VGStudio MAX (Volume Graphics) program to obtain image stacks in the z-direction for the humerus and femur.

The two image stacks were loaded into Simpleware ScanIP 5.1 (Krahl et al., 2019) for further processing which consisted of segmentation and generating the 3D models. For each image in the stack, the bone surface was selected and segmented using grayscale intervals, and a 3D surface model was created and saved in .stl file format (Data S1 and Data S2). We did not model the internal inhomogeneities in the bone, i.e., cortical vs. spongy, because this would have precluded implementation of torsion in the FESA. The reason is that the much stiffer cortex would take up all the stress peaks.

The 3D model was then imported into ANSYS 16.0 (ANSYS Inc., Canonsberg, PA, USA) as the .stl file. The dimensions of the humerus and femur from IGPB R 324 were used to scale the respective volumetric model to the original size. Subsequently, the proximal articular cartilage or articular surface between the glenoid and acetabulum was modeled as a volume. Bonded contacts between the artificial cartilage structures were implemented in the analysis. The models were constrained by fixed boundaries on the upper surface of the cartilage volume. Similar to other established finite element models (Gil, Marcé-Nogué & Sánchez, 2015; Sellés de Lucas et al., 2018), the material was assumed to be linear-elastic and isotropic to reduce computational time. The FE models were meshed with 10-node tetrahedral elements (SOLID92). The humerus model consisted of 92665 elements, and the femur model consists of 75,784 elements. In the humerus, the cartilaginous joint structure is formed by 19,927 elements and in the femur by 15,472 elements. In both FE models, the bone was modeled with a Young’s modulus of 12,000 MPa (Currey, 1987) and the cartilage with a Young’s modulus of 5 MPa (Carter & Beaupré, 2001) and a Poisson’s ratio of 0.3 for both materials.

Next, the LOA and muscle insertions had to be implemented in the FE model. We did this by taking photographs of the analog model in anterior, posterior, dorsal and ventral views and in these traced the LOA and their angles of attachment on the humerus (Fig. 9A) and femur (Fig. 10E). We then implemented these angles of attachment in the FE models as vectors from two views of the respective angle of attachment (Figs. 9B and 10B). Two- or more-headed muscle bellies were implemented in the FE model in the form of the resultant vector. The two-joint muscles of the foreflipper are the m. triceps brachii and the m. biceps brachii, whereas the two-joint muscles of the hindflipper are m. ambiens, m. pubotibialis, m. flexor tibialis externus, m. flexor tibialis internus, m. iliotibialis, m. iliofibularis, and m. puboischiotibialis. Since it is not possible to represent curved vectors in ANSYS 16.0., the muscle wraps were modeled by dividing their lines of action into several smaller straight vectors.

Force transmission to the distal articular surfaces of the humerus and femur due to muscle activity was initially applied in one point. This resulted in artificially high, localized stress peaks. Therefore, the force application was divided into several application points distributed over the distal articular surfaces to perform a more realistic simulation of load application over one surface.

The stress distribution was calculated for both bones (Figs. 9 and 10C–10N). The forces of each humerus and femur muscle optimized using the ANSYS subproblem approximation method. Briefly, in this method, the first and third principal stresses were analyzed for 12 different nodes that were uniformly distributed over the outer bone surface and served as state variables. In addition, the deformation of the model was evaluated. The initial estimated starting points for the muscle force calculations were based on the general force level differences and correlations reported by Krahl et al. (2019) for a sea turtle. Optimization criteria were as follows: Minimization of displacement at a static time step, first principal stresses between 0 and 0.5 MPa, third principal stresses between −10 and −0.1 MPa. For each model and load case, 40 iterations were performed. The stress diagrams were then visually inspected, and some final adjustments were made manually. In this way, the muscle forces were iteratively approximated (Tables 3 and 4) (Witzel & Preuschoft, 2005; Sverdlova & Witzel, 2010). For the final analysis, the principal stresses were saved, and the 1st and 3rd principal stresses were plotted. In addition, the shear stress was calculated according to Carter & Beaupré (2001).

Load case generation for FESA

Two load cases, downstroke and upstroke, were selected for calculation to reflect the constantly changing load on the humerus and femur during the flipper beat cycle (Figs. 9C–9J and 10C–10J). The two load cases were later superimposed (Figs. 9K–9N and 10K–10N) to obtain a model functionally loaded by compression only. This is because the biological response of bone to mechanical stimuli is time-dependent. To calculate the long-term functional mechanical load, a physiological superposition of all stresses is performed: For each finite element, the highest principal stresses occurring in both load cases are summarized (Witzel & Preuschoft, 2005).

For both load cases, a position was chosen in which the humerus was held horizontally at the level of the glenoid and pointed laterally and slightly forward, as in the analog model. Similarly, the femur was positioned horizontally at the level of the acetabulum with the flipper tip pointing mainly laterally, but also angled slightly posteriorly. On the downstroke, the humerus and femur were also rotated anteriorly downward around their long axis by approximately 19° (Witzel, Krahl & Sander, 2015; Witzel, 2020) to model a position where the flippers would have generated lift. During the upstroke, the humerus and femur were rotated posteriorly around their long axes and downward by approximately 19°. We justify these angles of rotation as follows (Witzel, Krahl & Sander, 2015; Witzel, 2020): Assuming a flight speed of 2 m/s and a flipper stroke speed of 4 m/s at the distal flipper tips (based on Robinson (1975)), a rotation angle of about 19° is necessary to minimize angle-dependent drag and optimize lift generation (and thus underwater flight).

For the implementation of load cases, it is crucial to identify and consider which muscles act as agonists and antagonists (Witzel & Preuschoft, 2005). The shoulder and hip joint may allow a small amount of play for rotation and protraction/retraction and a large amount of play for elevation and depression of the flippers, which is stabilized by the interaction of agonists and antagonists.

To identify agonists and antagonists, opposing muscle functions (Tables 2 and 3) are taken from Krahl & Witzel (2021). The downstroke is driven primarily by the humeral and femoral depressors, but also by retractors and those muscles that allow slight downward rotation of the flipper leading edges. The flexor muscles of the humerus and femur are active during the downstroke, flexing the digits and contributing to the twisting of the fore- and hindflipper along the flipper lengths. The upstroke is largely driven by the humeral and femoral elevators. Protraction of the humerus and femur and upward rotation of the leading edge of the flipper also contribute to the upstroke. The extensor muscles originating from the distal humerus and femur assist in twisting the flipper and extending the digits during the upstroke (Krahl, 2021).

Tests of plesiosaur flipper muscle reconstructions

Reconstructed agonists and antagonists in the limbs of plesiosaurs

Hindlimb agonists and antagonists and their function

The elevators of the hindflipper are m. puboischiofemoralis internus, m. iliotibialis, m. iliofemoralis, m. iliofibularis, m. caudofemoralis brevis, m. caudofemoralis longus, m. flexor tibialis externus (iliac portion), and m. flexor tibialis internus (portion originating from the vertebral column). M. puboischiofemoralis externus, m. adductor femoris, m. ischiotrochantericus, m. puboischiotibialis, m. flexor tibialis externus (ischial portion) and m. flexor tibialis internus (ischial portion) act as femoral depressors. Protractors are the m. puboischiofemoralis externus (pubic portion), m. puboischiofemoralis internus (pubic portion and vertebral column portion), m. ambiens, and m. pubotibialis. The retractors of the hindflipper are m. puboischiofemoralis externus (ischial portion), m. puboischiofemoralis internus (ischial and iliac portions), m. adductor femoris, m. ischiotrochantericus, m. iliofemoralis, m. iliotibialis, m. caudofemoralis brevis, m. caudofemoralis longus, m. flexor tibialis externus, and m. flexor tibialis internus. The downward rotation of the flipper leading edge during the downstroke is controlled by the agonists m. puboischiofemoralis internus (pubic portion), m. puboischiofemoralis externus (ischial portion), m. caudofemoralis brevis, m. caudofemoralis longus, m. ambiens (when the femur is elevated), m. ischiotrochantericus, m. iliofibularis (as long as the fibula is below the origin of these muscles), m. puboischiotibialis, m. pubotibialis (when the femur is elevated), m. flexor tibialis internus and m. flexor tibialis externus. The agonists are opposed by the antagonistically acting m. iliotibialis, m. ambiens (when the femur is depressed), m. pubotibialis (when the femur is depressed), m. iliofemoralis, m. puboischiofemoralis internus (ischial and iliac portion) and m. puboischiofemoralis externus (large pubic portion) (Table 3).

In addition, the muscles can be assigned to the following subgroups: The m. puboischiofemoralis internus, which originates from the dorsal pubis and vertebral column, is opposed by muscles originating from the ventral ischium (m. puboischiofemoralis externus (ischial portion), m. adductor femoris, and the ischial portions of m. flexor tibialis internus and m. flexor tibialis externus). The pubic portion of m. puboischiofemoralis externus, m. ambiens and m. pubotibialis, which originate from the ventral region of the pubic bone, have muscles originating from the ilium and posterior vertebral column as antagonists (m. flexor tibialis internus and m. flexor tibialis externus, m. iliofibularis, m. iliotibialis, m. iliofemoralis, m. puboischiofemoralis internus (ischial portion)). Musculus ambiens and m. pubotibialis have m. iliofibularis as antagonist. M. femorotibialis and m. extensor digitorum longus mostly originate dorsal to the femur. M. gastrocnemius externus, m. gastrocnemius internus and m. flexor digitorum longus arise ventrally from the femur. M. gastrocnemius externus and m. gastrocnemius internus as well as m. flexor digitorum longus (flexion of the toes) appear to be opposite to m. extensor digitorum longus (extension of the toes) and m. femorotibialis (Table 3).

Muscle forces and length changes

Femur muscles

The compressive stress distribution and muscle forces were calculated for the down- and upstroke load cases of the femur FE model. In the initial femur FESA runs, we were unable to apply compressive stresses to the dorsal trochanter and distal epiphyses of the femur because the muscles would simply pull away from their origin. Thus, only localized tensile stresses were observed in the FESAs. We then introduced muscle wrappings as in the humerus, with the m. iliofemoralis and m. puboischiofemoralis internus wrapped around the dorsal trochanter and the extensors and flexors wrapped around the distally greatly expanded epicondyles of the femur. This resulted in these structures being loaded by compressive stress.

Color coding of compressive stress distribution in the plesiosaur femur (Figs. 10C, 10D, 10G, 10H, 10K and 10L) is the same as for the humerus (see above). Low compressive stress correlates mainly with the medullary region in the mid to distal femur and the distal extensions of the femur. Moderate compressive stresses occur mainly in regions where cortical bone is present, especially on the outer femoral shaft. High compressive stress values correspond mostly to regions of the femoral head and part of the cortical bone of the proximal shaft (Figs. 10C, 10D, 10G, 10H, 10K and 10L). As in the FESA of the humerus, the localized compressive stress peaks on the distal articular surface of the plesiosaur femur were due to the selective application of the counterforce at several points scattered across the articular surface (see above) (Figs. 10C, 10G and 10K). The shear stresses were 2.56 MPa (SD 2.21 MPa).

The muscle forces of the many two-joint muscles (m. pubotibialis, m. puboischiotibialis, m. flexor tibialis externus, m. flexor tibialis internus, m. ambiens, m. iliotibialis, m. iliofibularis) in the hindflipper cannot be determined, because they influence the femur only indirectly by contributing to the counterforce. On the downstroke, the m. puboischiofemoralis externus generates the highest muscle force (7,878 N). On the upstroke, the m. puboischiofemoralis internus generates up to 7,611 N. The forces of the extensor and flexor muscles are much lower in the femur than in the humerus. The gastrocnemius muscle, a flexor muscle, develops a total force of up to 1,176 N (Table 5).

Changes in length of the limb muscles

Muscles originating dorsally from the glenoid and acetabulum extend on the downstroke and contract on the upstroke. Muscles originating ventrally from the glenoid and acetabulum contract when the humerus and femur are depressed on the downstroke and lengthen on the upstroke when the humerus and femur are elevated.

The total muscle length changes of the foreflipper vary from 0% to 70.87%. Three muscles (or parts of them) (m. deltoideus clavicularis, m. triceps brachii (anterior and posterior part)) show no length change, i.e. the length changes were not measurable with the technique used here, i.e. they are smaller than 1.7 cm (width of the terminal strips). The m. coracobrachialis brevis (posterior part) shows very small muscle shortening (3.88%). Otherwise, the changes in total muscle length cover the entire physiological spectrum, from about 9% in the posterior part of the m. subcoracoscapularis to 37% in the anterior part of the m. latissimus dorsi. The only muscle that stands out is the m. deltoideus scapularis with a total length change of over 70%. This is clearly not physiological. Therefore, a screw eye pin was screwed into a different hypothetical region of origin of the m. deltoideus scapularis. This different origin was located at the ventral to ventrolateral scapula anterior to the glenoid. The total muscle length change was again measured in all three flipper positions and was now within the measurement error of the analog model and well within physiological limits (Table 1).

Total muscle length changes for the hindflipper range from 0% to 35.8%. We detected no length changes for the m. caudofemoralis brevis (ilium portion) and the m. pubotibialis. In addition, the m. caudofemoralis brevis, which originates from the vertebral column, shows little change in total muscle length (5.2%), while the muscle with the greatest change (35.82%) in total length is the part of the m. puboischiofemoralis internus that originates from the vertebral column (Table 1).

Considering the agonistic and antagonistic muscles, the total length changes of m. pectoralis and m. latissimus dorsi, the two muscles that mainly drive the downstroke and upstroke of the foreflipper, are quite similar: the anterior part of m. latissimus dorsi (36.96%) and the posterior part of m. pectoralis (35.65%), and the posterior part of m. latissimus dorsi (21.92%) and the anterior part of m. pectoralis (18.75%). We expected that the overall changes in muscle lengths of agonists and antagonists would be similar because of their opposite functions. Instead, we found that the muscles exhibiting comparable total length changes were more likely to be determined by their geometric arrangement relative to the glenoid or acetabulum. That is, a muscle originating from the posteroventral ischium (e.g., m. puboischiofemoralis externus (23.55%)), for example, exhibited similar shortening to a muscle originating from the anterodorsal pubis (m. puboischiofemoralis internus (21.04%)).

Myology

The muscle reconstructions on which this study is based were obtained by evaluating comparative anatomical data (i.e., using the EPB) (Krahl & Witzel, 2021). These biologically derived muscle reconstructions are examined to determine whether they also meet the mechanical criteria to which muscles are subjected. In most cases, we find that the reconstructed muscles also meet the mechanical criteria. However, some fore- and hindflipper muscle reconstructions (m. biceps brachii, m. deltoideus scapularis, m. gastrocnemius internus) were modified for mechanical reasons to obtain a more homogeneous compressive stress distribution in the FESA of the humerus and femur. We found mechanical evidence to support some reconstructions of Krahl & Witzel (2021) that were rather weakly supported by the EPB (i.e., coracoid portion of the m. subcoracoscapularis, m. coracobrachialis brevis, m. coracobrachialis longus, m. ambiens, m. iliofemoralis, m. puboischiofemoralis internus and externus).

One muscle, the m. scapulohumeralis anterior, was added here to the reconstructions of Krahl & Witzel (2021), as it may aid in rotation of the humerus. We reconstruct the area of origin of the m. scapulohumeralis anterior on the anterior scapular blade. Compared to the reconstruction of Araújo & Correia (2015), this muscle is located less ventrally and more laterally in our reconstruction. Robinson (1975) and Watson (1924) reconstructed its attachment surface on the medial and ventral regions of the scapula, which is not fully supported by the EPB (Jenkins & Goslow, 1983; Russell & Bauer, 2008). In contrast, Carpenter et al. (2010) reconstructed a large area of origin of the m. scapulohumeralis anterior on the lateral aspect of the scapula. Instead, we reconstructed a large m. deltoideus scapularis in approximately the same area, which is better supported by the EPB (Walker, 1973; Meers, 2003; Russell & Bauer, 2008; Suzuki & Hayashi, 2010). The results presented here disagree with Tarlo (1958) in that the origin of the m. scapulohumeralis anterior is on the anteroventral part of the scapula, as this is not supported by the living Sauropsida (Walker, 1973; Meers, 2003; Russell & Bauer, 2008; Suzuki & Hayashi, 2010). The muscle reconstructions by Lingham-Soliar (2000) are merely schematic. It is impossible to determine the exact muscle attachments from his drawings. However, judging from their geometric arrangement, his muscle reconstructions are similar to our results.

M. scapulohumeralis anterior occurs exclusively in lepidosaurs and not in turtles or crocodylians (Walker, 1973; Meers, 2003; Russell & Bauer, 2008; Suzuki & Hayashi, 2010). In lepidosaurs, it inserts posterodorsally into the humerus; therefore, according to the EPB, this pattern was transferred to the plesiosaur in this study. None of the previous authors who reconstructed this muscle reconstructed its insertion at this location. They placed it either anterodorsally on the humerus (Watson, 1924; Tarlo, 1958; Robinson, 1975) or on the dorsal surface of the humerus (Lingham-Soliar, 2000; Carpenter et al., 2010).

We reconstructed m. scapulohumeralis anterior in agreement with Tarlo (1958) and Watson (1924) as possibly subordinately elevating and rotating the humerus (Watson, 1924; Tarlo, 1958). Watson (1924) and Tarlo (1958) disagree on how the extension and rotation occurred, whereas Watson (1924) suggested that the muscle rotated the humerus anteriorly upward, Tarlo (1958) concluded the opposite. Thus, Tarlo (1958), Robinson (1975) and the present study agree on the direction of humeral rotation. However, Robinson (1975) additionally reconstructed the m. scapulohumeralis anterior as a depressor, which is contrary to the results of this study. The possible minor elevation function has not been described by any previous author.

Physiology of the muscles

Muscle forces

Musculature of the humerus

On average, the forces of the muscles involved in the downstroke, i.e., by the humeral and femoral depressors and retractors, appear to be higher than those of the muscles involved in the upstroke (Tables 4 and 5). This could mean that in plesiosaurs the downstroke of the fore- and hindflippers was stronger than the upstroke. Similarly, the downstroke of the foreflipper is more powerful than the upstroke in Cheloniidae (Davenport, Munks & Oxford, 1984; Krahl et al., 2019). However, this difference in efficiency is not found in all underwater fliers, as it does not occur in penguins, where the downstroke of the wing is as efficient as the upstroke (Clark & Bemis, 1979).

As reconstructed here, the m. scapulohumeralis anterior and posterior appear to be exclusively humeral rotators, as they operate with considerably high muscle forces during the downward stroke (Table 4). In this way, their lifting function is low. This is surprising because both muscles tend to be small in living lepidosaurs (Jenkins & Goslow, 1983; Russell & Bauer, 2008). Either this means that their areas of origin and attachment were enlarged in plesiosaurs, or the muscle forces of m. scapulohumeralis anterior and posterior would need to be tested with further FESA runs. These would show whether a similar homogeneous compressive stress distribution can be obtained by redistributing a large portion of the force to muscles with similar function and LOA, e.g., m. latissimus dorsi, m. subcoracoscapularis, etc. The LOA of m. scapulohumeralis anterior and m. scapulohumeralis posterior, which would wrap around the dorsal tuberosity in an unusual manner from posterior to anterior, seem to support the hypothesized redistribution of force to another muscle as described above.

A surprising result is that the m. pectoralis is the muscle that also develops the highest muscle force during the elevation of the foreflipper (Table 4). Overall, it should be assumed that humeral elevators and protractors should be capable of providing higher power than depressors and retractors, otherwise foreflipper elevation and protraction becomes impossible. In addition, the pectoral girdle is suspended by muscles and tendons from the vertebral column, thorax, and gastralia (e.g., (Avery & Tanner, 1964; Walker, 1973). A swinging pectoral and pelvic girdle may contribute significantly to locomotion in living Otariinae, Testudines, and Crocodylia (Walker, 1971a; Baier & Gatesy, 2013; Mayerl, Brainerd & Blob, 2016; Schmidt, Mehlhorn & Fischer, 2016). For a long time, the importance of the contribution of pectoral and pelvic girdle swinging to locomotion in Tetrapoda has been neglected and underestimated, and it certainly requires further research. In extinct marine reptiles, a swinging pectoral and pelvic girdle has never been considered, as far as the authors are aware. An actively swinging pectoral and pelvic girdle could contribute to the range of motion of the plesiosaurs’ fore- and hindflippers and the total force with which the flippers were moved. Especially in the shoulder region of plesiosaurs, where there is no bony or cartilaginous connection to the trunk (unlike to the pelvic region), strong shoulder muscles and ligaments connecting the pectoral girdle to the vertebral column, ribs, and gastralia would be necessary.

Acting on the region of the dorsal the foreflipper, the m. extensor carpi ulnaris develops rather low muscle forces (1,000 N) compared to the m. extensor digitorum communis (6,000 N). M. flexor carpi radialis and m. flexor digitorum longus are topologically arranged similarly to m. extensor carpi ulnaris and m. extensor digitorum communis, but on the ventral side of the foreflipper. In contrast, the m. flexor carpi radialis and m. flexor digitorum longus develop much lower muscle forces (both 1,500 N) (Table 4). However, extensor and flexor forces were calculated based only on their contribution to physiological loading of the femur epicondyles. Extending the model to include the rest of the flipper bones could help define them more precisely.

Musculature of the femur

When comparing the muscle forces of the extensor and flexor muscles of the plesiosaur foreflipper and hindflipper, it is noticeable that those acting on the femur (Table 5) are generally lower than those acting on the humerus (Table 4). This is because there are many more two-joint muscles and fewer, as well as less independently working, extensor and flexor muscles in the plesiosaur hindflipper than in the foreflipper. The two-joint muscles also aid in femur protraction/retraction, elevation/depression, and knee flexion in present-day Sauropsida (Snyder, 1954; Walker, 1973; Otero, Gallina & Herrera, 2010; Anzai et al., 2014). Because the plesiosaur knee was immobile, these muscles were interpreted by Krahl & Witzel (2021) as part of the flipper longitudinal axis twisting mechanism in addition to their functions as depressors/elevators and protractors/retractors. Therefore, it is possible that the numerous two-joint muscles of the plesiosaur hindflipper partially supported functions that were taken over by the much more differentiated extensor and flexor muscles of the front flipper (Krahl & Witzel, 2021). The forces of the two-joint muscles could not be determined in this study, as they only indirectly influence the FESA by increasing the counterforce imposed by the tibia and fibula. Therefore, it is expected that the single extensor and the two flexors of the hindflipper would have lower overall muscle forces than the numerous extensors and flexors of the front flipper. Finally, the femur and humerus differ morphologically in their distal region in Cryptoclidus (as opposed to many other plesiosaurs), and it is possible that the hindflipper contributes less to propulsion than the foreflipper, as suggested by Lingham-Soliar (2000) and Liu et al. (2015) for plesiosaurs in general.

Comparison with the cheloniid humerus

There are some similarities in the muscle forces of certain muscles in Cryptoclidus eurymerus and in Cheloniidae: The m. pectoralis develops the highest force of all muscles that attach proximally to the humerus (Krahl et al., 2019). In addition, of the major humeral elevators, the m. subcoracoscapularis produces higher forces than the m. latissimus dorsi in both taxa (Krahl et al., 2019). M. coracobrachialis brevis develops less force in sea turtles (Krahl et al., 2019) than in the plesiosaur. In contrast, the m. coracobrachialis longus develops higher forces in sea turtles (Krahl et al., 2019) than in the plesiosaur. While m. deltoideus scapularis and m. deltoideus clavicularis contribute to propulsion in very different ways in Cheloniidae (Krahl et al., 2019), they act with broadly similar forces in the plesiosaur.

Another difference between the forces of the upper arm muscles of cheloniids (Krahl et al., 2019) and plesiosaurs is that the forces vary by an order of magnitude in the former, whereas they do not necessarily differ greatly in the plesiosaur. These results support a hydrodynamic study of Cryptoclidus eurymerus showing that pectoral flipper twisting is critical for underwater flight in plesiosaurs (Witzel, Krahl & Sander, 2015; Witzel, 2020). Moreover, these results confirm the myological mechanism of flipper twisting proposed by Krahl & Witzel (2021). In general, the higher muscle forces in the plesiosaur could be due to scaling effects, i.e., the generally larger relative body size of plesiosaurs compared to sea turtles.

The muscle bellies generating these enormous muscle forces (up to 9,600 N) in the shoulder girdle were large and occupied a lot of space. Therefore, it is problematic that the extensor and flexor muscles were inferred to generate similarly large forces because their potential areas of origin are much smaller than those of the glenoid-spanning muscles. There may be several solutions to this paradox. For example, the m. flexor digitorum longus in Sauropsida has a second head originating from the carpus (Walker, 1973; Meers, 2003; Russell & Bauer, 2008), so it may have been able to develop a much greater force than just through the humeral muscle belly. In addition, these muscles may have a complex architecture that saves space compared to the muscles of the pectoral girdle. Long tendon structures may have been a mechanism for conserving energy during locomotion (Roberts et al., 1997; Biewener & Roberts, 2000).

Another possibility, how large muscle forces in distal muscles may have been attained, can be observed in dolphins. Dolphins have a relatively well ossified flipper skeleton, although essentially no individual muscles are recognizable. They have only layers of parallel, fibrous connective tissue covering the flipper bones (see Cooper et al., 2007, Fig. 4, p. 1128). Conversely, this means that the hydrodynamic forces plus the “muscle” force that these connective tissue layers can exert are, in sum, sufficient to cause ossification of the flipper bones. Similar aponeurotic stratification, perhaps also directed in the main directions of flipper twisting, could account for a significant portion of the muscle forces calculated with FESA. In addition, the connective tissue covering the broad space of the non-functional elbow joint, carpus, and wrist could passively store energy to compensate for some of the calculated forces.